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http://www.nag.com/numeric/MB/manual64_24_1/html/F07/f07cef.html
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Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int
Chapter Contents
Chapter Introduction
NAG Toolbox
# NAG Toolbox: nag_lapack_dgttrs (f07ce)
## Purpose
nag_lapack_dgttrs (f07ce) computes the solution to a real system of linear equations AX = B $AX=B$ or ATX = B ${A}^{\mathrm{T}}X=B$, where A $A$ is an n $n$ by n $n$ tridiagonal matrix and X $X$ and B $B$ are n $n$ by r $r$ matrices, using the LU $LU$ factorization returned by nag_lapack_dgttrf (f07cd).
## Syntax
[b, info] = f07ce(trans, dl, d, du, du2, ipiv, b, 'n', n, 'nrhs_p', nrhs_p)
[b, info] = nag_lapack_dgttrs(trans, dl, d, du, du2, ipiv, b, 'n', n, 'nrhs_p', nrhs_p)
## Description
nag_lapack_dgttrs (f07ce) should be preceded by a call to nag_lapack_dgttrf (f07cd), which uses Gaussian elimination with partial pivoting and row interchanges to factorize the matrix A $A$ as
A = PLU , $A=PLU ,$
where P $P$ is a permutation matrix, L $L$ is unit lower triangular with at most one nonzero subdiagonal element in each column, and U $U$ is an upper triangular band matrix, with two superdiagonals. nag_lapack_dgttrs (f07ce) then utilizes the factorization to solve the required equations.
## References
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia http://www.netlib.org/lapack/lug
## Parameters
### Compulsory Input Parameters
1: trans – string (length ≥ 1)
Specifies the equations to be solved as follows:
trans = 'N'${\mathbf{trans}}=\text{'N'}$
Solve AX = B$AX=B$ for X$X$.
trans = 'T'${\mathbf{trans}}=\text{'T'}$ or 'C'$\text{'C'}$
Solve ATX = B${A}^{\mathrm{T}}X=B$ for X$X$.
Constraint: trans = 'N'${\mathbf{trans}}=\text{'N'}$, 'T'$\text{'T'}$ or 'C'$\text{'C'}$.
2: dl( : $:$) – double array
Note: the dimension of the array dl must be at least max (1,n1)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
Must contain the (n1)$\left(n-1\right)$ multipliers that define the matrix L$L$ of the LU$LU$ factorization of A$A$.
3: d( : $:$) – double array
Note: the dimension of the array d must be at least max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
Must contain the n$n$ diagonal elements of the upper triangular matrix U$U$ from the LU$LU$ factorization of A$A$.
4: du( : $:$) – double array
Note: the dimension of the array du must be at least max (1,n1)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-1\right)$.
Must contain the (n1)$\left(n-1\right)$ elements of the first superdiagonal of U$U$.
5: du2( : $:$) – double array
Note: the dimension of the array du2 must be at least max (1,n2)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}-2\right)$.
Must contain the (n2)$\left(n-2\right)$ elements of the second superdiagonal of U$U$.
6: ipiv( : $:$) – int64int32nag_int array
Note: the dimension of the array ipiv must be at least max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
Must contain the n$n$ pivot indices that define the permutation matrix P$P$. At the i$i$th step, row i$i$ of the matrix was interchanged with row ipiv(i)${\mathbf{ipiv}}\left(i\right)$, and ipiv(i)${\mathbf{ipiv}}\left(i\right)$ must always be either i$i$ or (i + 1)$\left(i+1\right)$, ipiv(i) = i${\mathbf{ipiv}}\left(i\right)=i$ indicating that a row interchange was not performed.
7: b(ldb, : $:$) – double array
The first dimension of the array b must be at least max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$
The second dimension of the array must be at least max (1,nrhs)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nrhs}}\right)$
The n$n$ by r$r$ matrix of right-hand sides B$B$.
### Optional Input Parameters
1: n – int64int32nag_int scalar
Default: The first dimension of the array b The dimension of the arrays d, ipiv.
n$n$, the order of the matrix A$A$.
Constraint: n0${\mathbf{n}}\ge 0$.
2: nrhs_p – int64int32nag_int scalar
Default: The second dimension of the array b.
r$r$, the number of right-hand sides, i.e., the number of columns of the matrix B$B$.
Constraint: nrhs0${\mathbf{nrhs}}\ge 0$.
ldb
### Output Parameters
1: b(ldb, : $:$) – double array
The first dimension of the array b will be max (1,n)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$
The second dimension of the array will be max (1,nrhs)$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nrhs}}\right)$
ldbmax (1,n)$\mathit{ldb}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
The n$n$ by r$r$ solution matrix X$X$.
2: info – int64int32nag_int scalar
info = 0${\mathbf{info}}=0$ unless the function detects an error (see Section [Error Indicators and Warnings]).
## Error Indicators and Warnings
info = i${\mathbf{info}}=-i$
If info = i${\mathbf{info}}=-i$, parameter i$i$ had an illegal value on entry. The parameters are numbered as follows:
1: trans, 2: n, 3: nrhs_p, 4: dl, 5: d, 6: du, 7: du2, 8: ipiv, 9: b, 10: ldb, 11: info.
It is possible that info refers to a parameter that is omitted from the MATLAB interface. This usually indicates that an error in one of the other input parameters has caused an incorrect value to be inferred.
## Accuracy
The computed solution for a single right-hand side, $\stackrel{^}{x}$, satisfies an equation of the form
(A + E) x̂ = b , $(A+E) x^=b ,$
where
‖E‖1 = O(ε)‖A‖1 $‖E‖1 =O(ε)‖A‖1$
and ε $\epsilon$ is the machine precision. An approximate error bound for the computed solution is given by
(‖x̂ − x‖1)/(‖x‖1) ≤ κ(A) (‖E‖1)/(‖A‖1) , $‖ x^-x ‖1 ‖ x ‖1 ≤ κ(A) ‖E‖1 ‖A‖1 ,$
where κ(A) = A11 A1 $\kappa \left(A\right)={‖{A}^{-1}‖}_{1}{‖A‖}_{1}$, the condition number of A $A$ with respect to the solution of the linear equations. See Section 4.4 of Anderson et al. (1999) for further details.
Following the use of this function nag_lapack_dgtcon (f07cg) can be used to estimate the condition number of A $A$ and nag_lapack_dgtrfs (f07ch) can be used to obtain approximate error bounds.
The total number of floating point operations required to solve the equations AX = B $AX=B$ or ATX = B ${A}^{\mathrm{T}}X=B$ is proportional to nr $nr$.
The complex analogue of this function is nag_lapack_zgttrs (f07cs).
## Example
```function nag_lapack_dgttrs_example
trans = 'No transpose';
dl = [0.8823529411764706;
0.01960784313725495;
0.1400560224089636;
-0.01479925303454714];
d = [3.4;
3.6;
7;
-6;
-1.015373482726424];
du = [2.3;
-5;
-0.9;
7.1];
du2 = [-1;
1.9;
8];
ipiv = [int64(2);3;4;5;5];
b = [2.7, 6.6;
-0.5, 10.8;
2.6, -3.2;
0.6, -11.2;
2.7, 19.1];
[bOut, info] = nag_lapack_dgttrs(trans, dl, d, du, du2, ipiv, b)
```
```
bOut =
-4.0000 5.0000
7.0000 -4.0000
3.0000 -3.0000
-4.0000 -2.0000
-3.0000 1.0000
info =
0
```
```function f07ce_example
trans = 'No transpose';
dl = [0.8823529411764706;
0.01960784313725495;
0.1400560224089636;
-0.01479925303454714];
d = [3.4;
3.6;
7;
-6;
-1.015373482726424];
du = [2.3;
-5;
-0.9;
7.1];
du2 = [-1;
1.9;
8];
ipiv = [int64(2);3;4;5;5];
b = [2.7, 6.6;
-0.5, 10.8;
2.6, -3.2;
0.6, -11.2;
2.7, 19.1];
[bOut, info] = f07ce(trans, dl, d, du, du2, ipiv, b)
```
```
bOut =
-4.0000 5.0000
7.0000 -4.0000
3.0000 -3.0000
-4.0000 -2.0000
-3.0000 1.0000
info =
0
```
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https://www.physicsforums.com/threads/what-did-i-do-wrong-with-these-vectors.512427/
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# What did I do wrong with these vectors?
1. Jul 6, 2011
### Newphysicsguy
Find $\vec{a}+\vec{b}$ (Look at the picture)
The book shows the solutions as :
a. 4.1m Along the +x axis.
I however do not know where I went wrong in my calculations.
$\vec{a}+\vec{b}=\begin{bmatrix} a_x+b_x\\ a_y+b_y \end{bmatrix}=\begin{bmatrix} |\vec{a}|\cos(30)+|\vec{b}|\cos(45)\\ |\vec{a}|\sin(30)-|\vec{b}|\sin(45) \end{bmatrix}=\begin{bmatrix} \frac{3\sqrt{3}}{2}+\sqrt{2}\\ 1.5-\sqrt{2} \end{bmatrix}=\begin{bmatrix} 4.01\\ .085 \end{bmatrix}$
NOTE: If I posted this is the wrong location I am sorry. This is not homework, I am doing it on my own time.
EDIT: thank you for moving my post to the correct location.
#### Attached Files:
• ###### matrix_result.JPG
File size:
10.8 KB
Views:
77
Last edited: Jul 6, 2011
2. Jul 6, 2011
### Staff: Mentor
Check your calculation for $a_y$.
3. Jul 6, 2011
### Newphysicsguy
That was a typo, it should be 3sin(30) which comes to be 1.5 which I had in the 3rd step. Sorry for the typo. Unless I did it wrong anyways? Either way $a_y$ does not effect $a_x+b_x$ which is also off from what the book says.
4. Jul 6, 2011
### Staff: Mentor
You're right, your numbers in the next to last step are OK. I noticed it while you were writing your latest post. As far as I can tell, your answer is OK. Whoever wrote the answer you were given, didn't round it off correctly or consistently. To one decimal place, the components should be 4.0 and 0.1. To zero decimal places, they should be 4 and 0.
It's probably a typo for 4.01 instead of 4.1. Those things do happen. I've seen it lots of times.
5. Jul 6, 2011
### Newphysicsguy
Thank you. I am never sure if I am wrong or if the book is wrong. It's better to always assume I am wrong.
Similar Discussions: What did I do wrong with these vectors?
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|
https://www.physicsforums.com/threads/cycloid-motion-of-electron-in-perpendicular-e-and-b-field.614936/
|
# Homework Help: Cycloid motion of electron in perpendicular E and B field
1. Jun 18, 2012
### bobred
1. The problem statement, all variables and given/known data
An infinite metal plate occupies the xz-plane. The plate is kept at zero potential. Electrons are liberated from the plate at y = 0. The initial velocity of the electrons is negligible. A uniform magnetic field B is maintained parallel to the plate in the positive z-direction and a uniform electric field E is maintained perpendicular to the plate in the negative y-direction. The electric field is produced by a second infinite plate parallel to the first plate, maintained at a constant positive voltage $V_{0}$ with respect to the first plate. The separation of the plates is $d$. Show that the electron will miss the plate at $V_{0}$ if
$d>\sqrt{\frac{2mV_{0}}{eB^2}}$
2. Relevant equations
$v_{x}=\frac{E}{B}\left(1-\cos\left(\frac{qB}{m}t\right)\right)$
$v_{y}=\frac{E}{B}\sin\left(\frac{qB}{m}t\right)$
$v_{z}=0$
3. The attempt at a solution
I know this produces a cycloid travelling in the minus x direction. If $r$ is the radius of a rolling circle then $d>2r$ to miss. I think I should be using conservation of energy but dont know the form of the velocity. I am assuming the perpendicular velocity will be the sum of a transverse and rotational velocity?
2. Jun 18, 2012
### TSny
You might try integrating the expression for vy with respect to time to get an expression for y as a function of time. Choose the constant of integration to match the initial condition for y. Then examine the expression.
I don't see an easy way to use energy conservation.
3. Jun 18, 2012
### collinsmark
Oooh, nice problem.
You can use conservation of energy to solve this problem. Well, that and the work-energy theorem. Conservation of energy makes this problem a lot easier. Here are a few things that are noteworthy (you can call them hints if you like):
1) The magnetic forces always acts in a direction perpendicular to the electron's velocity. In other words, the magnetic force never causes the electron's speed to increase or decrease, it only changes the direction. Still in other words, the magnetic force does no work on the electron.
2) You're going to have to determine the maximum speed of the electron. But there are couple of tricks you can do to make it simpler, if you choose to use them. When the electron is at its maximum speed, which direction is going? What's the maximum value of [1-cos(x)]?
3) You'll need to determine a relationship between E and V0, but that should be pretty simple.
4. Jun 18, 2012
### TSny
Ah, nice. I now see that using conservation of energy is a good way to get the result.
My suggestion of integrating vy to get y as a function of time also gets the answer in short order. But I like the energy approach. Thanks.
5. Jun 19, 2012
### bobred
Hi, thanks for the replies.
Part of the question before asked for the expressions of $x(0)=0$ and $y(0)=0$ giving
$x=\frac{E}{B}t-\frac{Em}{qB^{2}}\sin\left(\frac{qB}{m}t\right)$
$y=\frac{Em}{qB^{2}}\left(1-\cos\left(\frac{qB}{m}t\right)\right)$
The expression $\left(1-\cos\left(\frac{qB}{m}t\right)\right)$ at maximum is 2 so $y$ has a max of
$y=\frac{2Em}{qB^{2}}$ and $E=V_{0}/d$ so
$y=\frac{2mV_{0}}{qdB^{2}}$
I keep going around in circles with this.
6. Jun 19, 2012
### TSny
You're essentially there Just interpret what you got. The electron will barely reach the plate if y-max equals what value? Put this value of y into your result and solve for d.
7. Jun 19, 2012
### collinsmark
I think you're on the right track.
What's the magnitude of the electron's charge q? (As in terms of e)?
The variable y is a measure of length (well, technically displacement in the y direction, but that's still a measure of length). What is the value of y when it is at its maximum? (I.e. what's the significance of ymax = d?)
[Edit: TSny beat me to the hint.]
Last edited: Jun 19, 2012
8. Jun 19, 2012
### bobred
Hi
Sorry, went back to the start and had a look at the Lorentz force equations and worked forward from there and using conservation of energy to get the result.
Thanks again.
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https://codereview.stackexchange.com/questions/178628/hackerearth-learning-graph
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# Hackerearth - Learning Graph
Problem:
Monk goes to graph city to learn about graphs, and meets an undirected graph having $N$ nodes, where each node has a value $i$ such that $1 \le i \le N$. Each node of the graph is very curious and wants to know something about the nodes which are directly connected to it.
For each node, if we sort the nodes directly connected to it, according to their values in descending order, what is the value of the node at the $k$ th position? The graph is 1-based.
Note: If two nodes have the same value, they are sorted according to their indices in ascending order.
My accepted solution:
import sys
from collections import defaultdict
node_value_dict = defaultdict(int)
connected_graph_component = defaultdict(list)
def connect_graph():
n, m, k = list(map(int, sys.stdin.readline().split()))
for i in range(1, len(node_values) + 1):
node_value_dict[i] = node_values[i - 1]
for m_i in range(m):
n1, n2 = list(map(int, input().split()))
connected_graph_component[n1].append(n2)
connected_graph_component[n2].append(n1)
for i in range(1, n + 1):
if i in connected_graph_component:
curr_co = connected_graph_component[i]
sort_list = sorted(curr_co, key=lambda value: node_value_dict[
value], reverse=True)
for i in range(len(sort_list) - 1):
if node_value_dict[sort_list[i]] == node_value_dict[sort_list[i + 1]] and sort_list[i] < sort_list[i + 1]:
sort_list[i], sort_list[
i + 1] = sort_list[i + 1], sort_list[i]
print(sort_list[k - 1])
else:
print(-1)
connect_graph()
With a runtime of 9.14092 sec.
How can I improve the code quality and further optimize runtime duration?
In case of equal values, I need to sort the nodes according to their indices in ascending order. Currently I'm doing it by looping over the sorted list and then comparing values again side by side maintaining two pointers.
Can you please suggest some elegant way of doing this.
As for runtime duration, there is not really much you can do, as the algorithm is already optimum.
However, code can be simplified a bit. Here are some tips:
• node_value_dict has same data as node_values -> not needed
• Use input() instead of sys.stdin.readline().split() so you can avoid an import
• Is there a need for connected_graph_component to be a dict? It should be fine as an array of arrays
• As for the sorting, note that you can make the key a pair instead of only 1 value and it will sort first by first value, and if equal it sorts according to second value.
• list(map(int, sys.stdin.readline().split())) is repeated multiple times, put it in a function
• Sometimes batching print calls in 1 call instead of printing for each value is faster
This is my version of the code after applying these tips:
def read_line_values():
return list(map(int, input().strip().split(' ')))
def connect_graph():
connected_graph_component = [[] for _ in range(n + 1)]
for m_i in range(m):
connected_graph_component[n1].append(n2)
connected_graph_component[n2].append(n1)
for i in range(1, n + 1):
neighbours = connected_graph_component[i]
if len(neighbours) < k:
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|
https://www.physicsforums.com/threads/need-help-solving-initial-value-differential-equation.253552/
|
# Need Help Solving Initial Value Differential Equation
1. Sep 3, 2008
### swooshfactory
1. The problem statement, all variables and given/known data
dy/dx + y*cos(x) = 3*cos(x) . Find the particular solution of the differential equation dy/dx + y*cos(x) = 3*cos(x) satisfying the initial condition y(0)=5.
y(x) = ________________________
2. Relevant equations
3. The attempt at a solution
I thought I had done it the right way, but my computer based homework system disagreed.
Heres my work:
p(t)=cos(x)
g(t)=3cos(x)
m: mu
m(t)=exp [int] cos(x)dx
m(t)= e^sin(x)
then,
e^sinx(y)= [int]3cosx(e^sinx)dx
[int]3cosx(e^sinx)dx= 3(e^sinx)+C
then to solve for y,
y= 3(e^sin(x)+C)/(e^sin(x))
using the intial value to solve for C, [[the initial value was y(0)=5]]
5=3(e+C)/e
5e=3e + C<<<right here is it C or 3c?>>
c=2e
and plugging it back into the y-equation, I get y=(3(e^sinx)+2e)/(e^sinx)
Where have I gone wrong? My homework system says this is wrong... Any help would be greatly appreciated. Thank you for looking.
2. Sep 3, 2008
### Dick
sin(0)=0 and e^(0)=1 not e.
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http://math.stackexchange.com/questions/208976/what-prime-number-generating-algorithms-are-used?answertab=votes
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# What prime number generating algorithms are used?
You sometimes hear bout these huge prime numbers (RSA prime number challenge comes to mind) and I was curious about what algorithms or formulas prime-number generators use in practice ? For example in cluster / cloud computing, parallel computing ...etc.
I imagine that everyone has their own "custom" optimized versions of more known prime number generational algorithms but what are the "base methods" used to do so.
Thank you very much in advance !
edit: I hope that I used the right [tags].
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Suppose we are interested in producing a prime near a very large number $M$. It is convenient to not bother testing for primality the multiples of small primes, like the even numbers! For the remaining numbers, test, one after the other, candidates using a "probable prime" test such as Miller-Rabin.
Miller-Rabin is very fast, and can be used to quickly rule out candidates.
If we are not too fussy, we can accept such a probable prime as prime. There is a possibility of being wrong, but if we make the probability of error less than say $10^{-100}$, effectively we have certainty.
Or else, after locating a number which is "almost certainly prime" via Miller-Rabin, one can use one of the relatively expensive primality tests to make sure.
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Thank you very much for both of your answers ! – Awake Zoldiek Oct 8 '12 at 0:40
As far as I know, the AKS primality test is the most effective known method to decide if a large number picked at random is prime or not.
If we pick a large number $N$, the probability it is prime is about $\frac{1}{\ln (N)}$. Thus, if you look for a prime number with $t$ digits, if you pick about $t \log(10)$ $t$-digit numbers at random, there is a pretty big chance one will be prime...The time involved is usually reasonable for a computer....
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AKS is seldom used in practice. When it comes down to it, algorithms that were present before it - especially the Miller-Rabin algorithm and its variants - are much faster, even if AKS is asymptotically better (or just deterministic). – Yoni Rozenshein Oct 7 '12 at 23:55
Neither of the algorithms mentioned in the two previous answers are used to find record large primes. Lucas-Lehmer has the advantage that it is as fast as Miller-Rabin, and deterministic (it guarantees primality/compositeness rather than being probabilistic). However it is severely limited in that it only works on numbers of the form $2^n-1$ (Mersenne numbers). All of the last dozen or so record primes have been Mersenne primes located by massive volunteer effort and verified by Lucas-Lehmer test.
As far as I know, RSA has no prime number challenge, but it does have factoring challenges (which require considerably different algorithms). Are you perhaps thinking of the EFF cooperative computing awards for finding large primes?
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yes, I kind of mistakenly took the RSA challenge for the EFF one. Sorry about that. – Awake Zoldiek Oct 8 '12 at 10:12
but shouldn't better to generate primes AT RANDOM ??¿ i mean if i were a 'hacker' i first would study all the prime generating algorithms to crack codes :D :D so perhaps a prime-generating algorithm is not quite safe. – Jose Garcia Oct 8 '12 at 10:45
@JoseGarcia My point is that the method for generating primes depends on your intent. It could be for cryptography, for amusement, for record-breaking, etc. And the standards for testing could vary in strictness (probabilistic vs provable primes). – Erick Wong Oct 8 '12 at 14:12
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http://www.reference.com/browse/ADM+formulation
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Definitions
The ADM Formalism developed by Arnowitt, Deser and Misner is a Hamiltonian formulation of general relativity.
The formalism supposes that spacetime is foliated into a family of spacelike surfaces $Sigma_t$, labeled by their time coordinate $t$, and with coordinates on each slice given by $x^i$. The dynamic variables of this theory are taken to be the metric of three dimensional spatial slices $gamma_\left\{ij\right\}\left(t,x^k\right)$ and their conjugate momenta $pi^\left\{ij\right\}\left(t,x^k\right)$. Using these variables it is possible to define a Hamiltonian, and thereby write the equations of motion for general relativity in the form of Hamilton's equations.
In addition to the twelve variables $gamma_\left\{ij\right\}$ and $pi^\left\{ij\right\}$, there are four Lagrange multipliers: the lapse function, $N$, and components of shift vector field, $N_i$. These describe how each of the "leaves" $Sigma_t$ of the foliation of spacetime are welded together. These variables are nondynamical, and their "equations of motion" are constraint equations that enforce invariance under time reparameterizations and coordinate changes on the spatial slices, respectively.
Using the ADM formulation, it is possible to attempt to construct a quantum theory of gravity, in the same way that one constructs the Schrödinger equation corresponding to a given Hamiltonian in quantum mechanics. That is, replace the canonical momenta $pi^\left\{ij\right\}\left(t,x^k\right)$ by functional differential operators
$pi^\left\{ij\right\}\left(t,x^k\right) to -i frac\left\{delta\right\}\left\{delta gamma_\left\{ij\right\}\left(t,x^k\right)\right\}$
This leads to the Wheeler-deWitt equation.
Search another word or see ADM formulationon Dictionary | Thesaurus |Spanish
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http://mathhelpforum.com/calculus/90121-del-operator-divergence-curl.html
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# Thread: del operator, divergence , and the curl
1. ## del operator, divergence , and the curl
In physics the del operator is fundamental.The basic laws of Electromagnetism are defined using it.I wanted to know the actual significance of the curl ( $\nabla \times$)and divergence.I also intended this post to be a starter for a discussion about mathematical fields,their difference and applications(in physics or other subjects).
2. One reason why $\nabla$ is so important is that it is invariant under rigid motions: rotating or translating the coordinate system does not change the form of $\nabla$. Roughly speaking, the "divergence", $\nabla\cdot \vec{v}$, measures how much a vector field "spreads out" (diverges) while the "curl", $\nabla\times\vec{v}$ measure its tendency to rotate- hence the names "divergence" and "curl".
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https://www.science.gov/topicpages/p/positron+annihilation+lifetime.html
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#### Sample records for positron annihilation lifetime
1. Position-resolved Positron Annihilation Lifetime Spectroscopy
Wagner, A.; Butterling, M.; Fiedler, F.; Fritz, F.; Kempe, M.; Cowan, T. E.
2013-06-01
A new method which allows for position-resolved positron lifetime spectroscopy studies in extended volume samples is presented. In addition to the existing technique of in-situ production of positrons inside large (cm3) bulk samples using high-energy photons up to 16 MeV from bremsstrahlung production, granular position-sensitive photon detectors have been employed. A beam of intense bremsstrahlung is provided by the superconducting electron linear accelerator ELBE (Electron Linear Accelerator with high Brilliance and low Emittance) which delivers electron bunches of less than 10 ps temporal width and an adjustable bunch separation of multiples of 38 ns, average beam currents of 1 mA, and energies up to 40 MeV. Since the generation of bremsstrahlung and the transport to the sample preserves the sharp timing of the electron beam, positrons generated inside the entire sample volume by pair production feature a sharp start time stamp for positron annihilation lifetime studies with high timing resolutions and high signal to background ratios due to the coincident detection of two annihilation photons. Two commercially available detectors from a high-resolution medial positron-emission tomography system are being employed with 169 individual Lu2SiO5:Ce scintillation crystals, each. In first experiments, a positron-lifetime gated image of a planar Si/SiO2 (pieces of 12.5 mm × 25 mm size) sample and a 3-D structured metal in Teflon target could be obtained proving the feasibility of a three dimensional lifetime-gated tomographic system.
2. First positron annihilation lifetime measurement of Pu
SciTech Connect
Colmenares, C.; Howell, R.H.; Ancheta, D.; Cowan, T.; Hanafee, J.; Sterne, P.
1996-11-21
We have made the first measurement of defects in an aged sample of {delta} phase, Ga stabilized Pu, using positron annihilation lifetime spectroscopy. This measurement validates the procedure necessary to perform measurements on this highly toxic material and obtain data representative of sample conditions. Comparison of the positron annihilation lifetime analysis of the data with calculated values suggests that He filled vacancies or vacancy clusters dominate the defect population. Such defects are the necessary precursor to void growth and swelling. The evolution of defects resulting from the radioactive decay of Pu during its life in the stockpile is one of the unknown quantities affecting our confidence in predictions of the limit on stockpile components. Radiation damage leads to changes in the size and strength of metals studied for reactor and accelerator use and similar effects may be expected in Pu. The evolution of radiation produced vacancies into larger void structures and accompanying macroscopic swelling may occur in Pu at some age. A detailed understanding of the defects in self irradiated Pu is required to predict the time scale of void swelling and related radiation effects. 1 fig.
3. Positron annihilation lifetime spectroscopy at a superconducting electron accelerator
Wagner, A.; Anwand, W.; Attallah, A. G.; Dornberg, G.; Elsayed, M.; Enke, D.; Hussein, A. E. M.; Krause-Rehberg, R.; Liedke, M. O.; Potzger, K.; Trinh, T. T.
2017-01-01
The Helmholtz-Zentrum Dresden-Rossendorf operates a superconducting linear accelerator for electrons with energies up to 35 MeV and average beam currents up to 1.6 mA. The electron beam is employed for production of several secondary beams including X-rays from bremsstrahlung production, neutrons, and positrons. The secondary positron beam after moderation feeds the Monoenergetic Positron Source (MePS) where positron annihilation lifetime (PALS) and positron annihilation Doppler-broadening experiments in materials science are performed in parallel. The adjustable repetition rate of the continuous-wave electron beams allows matching of the pulse separation to the positron lifetime in the sample under study. The energy of the positron beam can be set between 0.5 keV and 20 keV to perform depth resolved defect spectroscopy and porosity studies especially for thin films.
4. Study of Chemical Carcinogens by Positron Annihilation Lifetime Spectroscopy
Pivtsaev, A. A.; Razov, V. I.; Karasev, A. O.
2013-11-01
We have used positron annihilation lifetime spectroscopy to study the carcinogens C21H20BrN3, C4H7Cl2O4P, CCl4, CHCl3, AlF3, C8H12N4O, C6H4Cl2 and the non-carcinogens H2O, AlCl3, CH2Cl2, C2H6OS. We have established a correlation between the annihilation characteristics of the studied compounds and their degree of carcinogenicity.
PubMed
Rätzke, Klaus; Wiegemann, Maja; Shaikh, Muhammad Qasim; Harms, Stephan; Adelung, Rainer; Egger, Werner; Sperr, Peter
2010-07-01
Barnacles attach to a wide variety of surfaces underwater and show substrate-specific adhesion mechanisms. Investigating and understanding these mechanisms is a key for developing new technical adhesives. We expected open volume (porosity) at the sub-nanometre scale to occur in barnacle adhesive. With positron annihilation lifetime spectroscopy (PALS) it is possible to detect porosity at the nanometre scale by determining the lifetime of positrons. This method has not been applied to bioadhesives so far. We showed that PALS is a suitable technique for the investigation of the barnacle base and its adhesive with respect to open volume. The results were interpreted using a standard model adapted from polymers. We thereby estimated pore sizes of 0.5 nm.
6. Single-shot positron annihilation lifetime spectroscopy with LYSO scintillators
Alonso, A. M.; Cooper, B. S.; Deller, A.; Cassidy, D. B.
2016-08-01
We have evaluated the application of a lutetium yttrium oxyorthosilicate (LYSO) based detector to single-shot positron annihilation lifetime spectroscopy. We compare this detector directly with a similarly configured PbWO4 scintillator, which is the usual choice for such measurements. We find that the signal to noise ratio obtained using LYSO is around three times higher than that obtained using PbWO4 for measurements of Ps excited to longer-lived (Rydberg) levels, or when they are ionized soon after production. This is due to the much higher light output for LYSO (75% and 1% of NaI for LYSO and PbWO4 respectively). We conclude that LYSO is an ideal scintillator for single-shot measurements of positronium production and excitation performed using a low-intensity pulsed positron beam.
7. Positron annihilation lifetime spectroscopy of ZnO bulk samples
SciTech Connect
Zubiaga, A.; Plazaola, F.; Garcia, J. A.; Tuomisto, F.; Munoz-Sanjose, V.; Tena-Zaera, R.
2007-08-15
In order to gain a further insight into the knowledge of point defects of ZnO, positron annihilation lifetime spectroscopy was performed on bulk samples annealed under different atmospheres. The samples were characterized at temperatures ranging from 10 to 500 K. Due to difficulties in the conventional fitting of the lifetime spectra caused by the low intensity of the defect signals, we have used an alternative method as a solution to overcome these difficulties and resolve all the lifetime components present in the spectra. Two different vacancy-type defects are identified in the samples: Zn vacancy complexes (V{sub Zn}-X) and vacancy clusters consisting of up to five missing Zn-O pairs. In addition to the vacancies, we observe negative-ion-type defects, which are tentatively attributed to intrinsic defects in the Zn sublattice. The effect of the annealing on the observed defects is discussed. The concentrations of the V{sub Zn}-X complexes and negative-ion-type defects are in the 0.2-2 ppm range, while the cluster concentrations are 1-2 orders of magnitude lower.
Roberts, J.; Gaugliardo, P.; Farnan, I.; Zhang, M.; Vance, E. R.; Davis, J.; Karatchevtseva, I.; Knott, R. B.; Mudie, S.; Buckman, S. J.; Sullivan, J. P.
2016-04-01
Zircons are a well-known candidate waste form for actinides and their radiation damage behaviour has been widely studied by a range of techniques. In this study, well-characterised natural single crystal zircons have been studied using Positron Annihilation Lifetime Spectroscopy (PALS). In some, but not all, of the crystals that had incurred at least half of the alpha-event damage of ∼1019 α/g required to render them structurally amorphous, PALS spectra displayed long lifetimes corresponding to voids of ∼0.5 nm in diameter. The long lifetimes corresponded to expectations from published Small-Angle X-ray Scattering data on similar samples. However, the non-observation by PALS of such voids in some of the heavily damaged samples may reflect large size variations among the voids such that no singular size can be distinguished or. Characterisation of a range of samples was also performed using scanning electron microscopy, optical absorption spectroscopy, Raman scattering and X-ray scattering/diffraction, with the degree of alpha damage being inferred mainly from the Raman technique and X-ray diffraction. The observed void diameters and intensities of the long lifetime components were changed somewhat by annealing at 700 °C; annealing at 1200 °C removed the voids entirely. The voids themselves may derive from He gas bubbles or voids created by the inclusion of small quantities of organic and hydrous matter, notwithstanding the observation that no voidage was evidenced by PALS in two samples containing hydrous and organic matter.
9. [Positron annihilation lifetime spectrometry (PALS) and its pharmaceutical applications].
PubMed
Sebe, István; Szabó, Barnabás; Zelkó, Romána
2012-01-01
PALS is one of the most widely used "nuclear probe" techniques for the tracking of the structural characteristics of materials. The method is based on the matter-energy equivalence principle recognized by Einstein: the electrons and positrons as particle-antiparticle pairs disappear in mutual destruction of particles, they annihilate with high-energy gamma-radiation, thus "particle-energy transition" occurs. The properties of the resulting radiation exactly correspond to the relevant properties of the electron and positron preceding the annihilation. Since electrons occur in all types of materials, the phenomenon of positron annihilation can play in any environment; consequently the method can be used for the analysis of each type of materials (crystalline and amorphous, organic and inorganic, biotic and abiotic). The present paper provides an overview of the theoretical physical background, the practical realization and evaluation of methods, their limitations, and summarizes the pharmaceutical applications published in recent years.
10. Positron annihilation lifetime study of polyvinylpyrrolidone for nanoparticle-stabilizing pharmaceuticals.
PubMed
Shpotyuk, O; Bujňáková, Z; Baláž, P; Ingram, A; Shpotyuk, Y
2016-01-05
Positron annihilation lifetime spectroscopy was applied to characterize free-volume structure of polyvinylpyrrolidone used as nonionic stabilizer in the production of many nanocomposite pharmaceuticals. The polymer samples with an average molecular weight of 40,000 g mol(-1) were pelletized in a single-punch tableting machine under an applied pressure of 0.7 GPa. Strong mixing in channels of positron and positronium trapping were revealed in the polyvinylpyrrolidone pellets. The positron lifetime spectra accumulated under normal measuring statistics were analysed in terms of unconstrained three- and four-term decomposition, the latter being also realized under fixed 0.125 ns lifetime proper to para-positronium self-annihilation in a vacuum. It was shown that average positron lifetime extracted from each decomposition was primary defined by long-lived ortho-positronium component. The positron lifetime spectra treated within unconstrained three-term fitting were in obvious preference, giving third positron lifetime dominated by ortho-positronium pick-off annihilation in a polymer matrix. This fitting procedure was most meaningful, when analysing expected positron trapping sites in polyvinylpyrrolidone-stabilized nanocomposite pharmaceuticals.
11. Digitized detection of gamma-ray signals concentrated in narrow time windows for transient positron annihilation lifetime spectroscopy.
PubMed
Kinomura, A; Suzuki, R; Oshima, N; O'Rourke, B E; Nishijima, T; Ogawa, H
2014-12-01
A pulsed slow-positron beam generated by an electron linear accelerator was directly used for positron annihilation lifetime spectroscopy without any positron storage devices. A waveform digitizer was introduced to simultaneously capture multiple gamma-ray signals originating from positron annihilation events during a single accelerator pulse. The positron pulse was chopped and bunched with the chopper signals also sent to the waveform digitizer. Time differences between the annihilation gamma-ray and chopper peaks were calculated and accumulated as lifetime spectra in a computer. The developed technique indicated that positron annihilation lifetime spectroscopy can be performed in a 20 μs time window at a pulse repetition rate synchronous with the linear accelerator. Lifetime spectra of a Kapton sheet and a thermally grown SiO2 layer on Si were successfully measured. Synchronization of positron lifetime measurements with pulsed ion irradiation was demonstrated by this technique.
12. Digitized detection of gamma-ray signals concentrated in narrow time windows for transient positron annihilation lifetime spectroscopy
SciTech Connect
Kinomura, A. Suzuki, R.; Oshima, N.; O’Rourke, B. E.; Nishijima, T.; Ogawa, H.
2014-12-15
A pulsed slow-positron beam generated by an electron linear accelerator was directly used for positron annihilation lifetime spectroscopy without any positron storage devices. A waveform digitizer was introduced to simultaneously capture multiple gamma-ray signals originating from positron annihilation events during a single accelerator pulse. The positron pulse was chopped and bunched with the chopper signals also sent to the waveform digitizer. Time differences between the annihilation gamma-ray and chopper peaks were calculated and accumulated as lifetime spectra in a computer. The developed technique indicated that positron annihilation lifetime spectroscopy can be performed in a 20 μs time window at a pulse repetition rate synchronous with the linear accelerator. Lifetime spectra of a Kapton sheet and a thermally grown SiO{sub 2} layer on Si were successfully measured. Synchronization of positron lifetime measurements with pulsed ion irradiation was demonstrated by this technique.
13. Analysis of positron annihilation lifetime data by numerical laplace inversion with the program CONTIN
Gregory, Roger B.; Zhu, Yongkang
1990-05-01
The performance of the program CONTIN [Stephen W. Provencher, Comput. Phys. Commun. 27 (1982) 229], modified to solve Fredholm integral equations with convoluted kernels of the type that occur in the deconvolution and analysis of positron annihilation lifetime data, is investigated with computer-simulated test data. The method avoids direct determination of the instrument resolution function by employing the decay curve of a reference material with a well-known single lifetime. CONTIN employs a constrained, regularized least-squares analysis to calculate a continuous annihilation-rate probability density function (pdf) which is the most parsimonious solution that is consistent with the experimental data and prior knowledge. The performance of the algorithm for extracting positron annihilation lifetime information was evaluated by using several measures of the information content of the data described by Schrader and Usmar [in: Positron Annihilation Studies of Fluids, ed. S. Sharma (World Scientific, Singapore, 1988) p. 215]. The quality of the CONTIN reconstruction of the annihilation-rate pdf is strongly dependent on the information content of the data and is greatly improved as the total number of counts in the data set is increased. Nevertheless, the method provides excellent estimates of the intensities and mean lifetimes of peaks in the annihilation-rate pdf, even when the total counts in the data set are relatively low (10 5-10 6). The sensitivity of the algorithm to systematic errors in the data, including errors in the instrument resolution function, shifts in the positron of the zero-time channel of the sample and reference data and contamination of the reference decay by additional lifetime components was also evaluated. Errors in the FWHM of the instrument resolution function and shifts in the zero time channel as small as {1}/{10}to{1}/{5} of the channel width of the instrument generate additional spurious peaks in the annihilation-rate pdf and
14. Novel method for stratum corneum pore size determination using positron annihilation lifetime spectroscopy.
PubMed
Itoh, Yoshiaki; Shimazu, Akira; Sadzuka, Yasuyuki; Sonobe, Takashi; Itai, Shigeru
2008-06-24
Positron annihilation lifetime spectroscopy (PALS) is a powerful tool for the investigation of microstructure. Three main classes of materials, metals, semiconductors and polymers, have been studied by using this technique. But, relatively few investigations have been performed in the biological sciences. PALS provides important information on pore properties and free volume at the molecular level. Our PALS study showed that Yucatan miniature pig stratum corneum separated with heat and trypsin digestion had a longer positron annihilation lifetime than cyclodextrins. This indicates that the stratum corneum has larger pores and/or free volume than cyclodextrins, whose pores have a diameter of 0.5-0.8 nm and a torus height of 0.79 nm. Positron annihilation spectroscopy may be developed as a new technique for the detection of nano-pore properties and free volume in the biological sciences.
15. The study of synthetic food dyes by positron annihilation lifetime spectroscopy.
Pivtsaev, A. A.; Razov, V. I.
2015-06-01
By method of positron annihilation lifetime spectroscopy (PALS), substances are food dyes were studied: E-102 (Tartrazine), E-124 (Ponso 4R), E 132 (Indigo carmine), E-133 (Brilliant Blue), E-151 (Black Shiny). They are examined for the presence of carcinogenic properties. The difference between dyes having explicit carcinogenic properties and mutagenic properties (non-explicit carcinogens) is established.
16. Development and Optimization of a Positron Annihilation Lifetime Spectrometer to Measure Nanoscale Defects in Solids and Borane Cage Molecules in Aqueous Nitrate Solutions
DTIC Science & Technology
2008-03-01
DEVELOPMENT AND OPTIMIZATION OF A POSITRON ANNIHILATION LIFETIME SPECTROMETER TO MEASURE NANOSCALE DEFECTS IN SOLIDS AND BORANE CAGE MOLECULES...DEVELOPMENT AND OPTIMIZATION OF A POSITRON ANNIHILATION LIFETIME SPECTROMETER TO MEASURE NANOSCALE DEFECTS IN SOLIDS AND BORANE CAGE MOLECULES IN AQUEOUS...RELEASE; DISTRIBUTION UNLIMITED AFIT/GNE/ENP/08-M05 DEVELOPMENT AND OPTIMIZATION OF A POSITRON ANNIHILATION LIFETIME SPECTROMETER TO MEASURE NANOSCALE
17. Study of PRIMAVERA steel samples by positron annihilation spectroscopy technique II - Lifetime measurements
Krsjak, V.; Grafutin, V.; Ilyukhina, O.; Burcl, R.; Ballesteros, A.; Hähner, P.
2012-02-01
In the present article, a positron annihilation lifetime technique was used for the study of VVER-440/230 weld materials, manufactured in the frame of the international PRIMAVERA project on microstructural investigation of the irradiated WWER-440 reactor pressure vessel steel. The present results complement our previous report of positron angular correlation experiments and provide in-depth characterization of vacancy type defects behavior under irradiation and thermal treatment. The results give new insight into the previously published atom probe tomography and angular correlation of annihilation radiation studies. The measurements do not show any association of phosphorus or its segregation to the open volume defects investigated by positron annihilation spectroscopy. The embrittlement effects related to the phosphorus seem to be effectively annealed-out during 475 °C thermal treatment and the post annealing microstructure and mechanical properties of the material are consequently affected mostly by agglomerations of vacancy clusters coarsened during thermal treatment.
18. Positron annihilation lifetime evaluation of thermal cycling effects in atactic polystyrene
SciTech Connect
Kasbekar, A.D.; Jones, P.L.
1989-01-01
Positron annihilation lifetime spectroscopy (PALS) is an atomic-level probing technique that has been shown to be extremely sensitive to vacancy-type defects in a wide variety of solids. In amorphous and semicrystalline polymers this technique is uniquely sensitive to free-volume-based structural changes such as the glass transition. As such, PALS complements conventional macroscopic polymer characterization techniques. Positron annihilation lifetime spectroscopy (PALS) was used to investigate the thermal-cycling characteristics of two different-molecular-weight atactic polystyrene reins. Annealed compression-molded samples were thermally cycled over the temperature range 253 to 393 K with PAL spectra taken in 10 K increments upon both cooling and heating. The longest-lived component lifetime and intensity, indicative of orthopositronium pick-off, exhibit thermal dependencies that can be interpreted in a manner consistent with anticipated free-volume changes associated with structural transitions.
Onodera, K.; Oka, T.; Kino, Y.; Sekine, T.
2017-01-01
Degradation of electron beam irradiated high-density polyethylene was studied by positron annihilation lifetime spectroscopy (PALS), micro-FT-IR, and gel fraction measurements. The obtained results indicated that ortho-positronium intensity is influenced not only by the irradiation but also the post oxidation, which illustrates that PALS may be a promising tool to monitor/evaluate the degradation of polyethylene induced by irradiation and long-term storage.
20. Transitions and relaxations in gamma-irradiated polypropylene studied by positron annihilation lifetime spectroscopy
Djourelov, N.; Suzuki, T.; Shantarovich, V. P.; Dobreva, T.; Ito, Y.
2005-01-01
The changes in the relaxation and transition temperatures in PP due to gamma irradiation in a vacuum were measured by means of positron annihilation lifetime spectroscopy. It was shown that the gamma and beta relaxation temperatures, as well as the melting point follow the changes in the crystallinity with the irradiation dose. For the glass transition temperatures and premelting point, after irradiation dose of 88 kGy, an inverse of the changes was observed.
1. Vacancy profile in reverse osmosis membranes studied by positron annihilation lifetime measurements and molecular dynamics simulations
Shimazu, A.; Goto, H.; Shintani, T.; Hirose, M.; Suzuki, R.; Kobayashi, Y.
2013-06-01
The positron annihilation technique using a slow positron beam can be used for the study of the vacancy profiles in typical reverse osmosis (RO) membranes. In this study, the vacancy profile in the polyamide membrane that exhibits a high permselectivity between ions and water was studied using the positron annihilation technique and molecular dynamics simulations. Ortho-positronium (o-Ps) lifetimes in the surface region of the membranes were evaluated by using a slow positron beam. The diffusion behavior of Na+ and water in the polyamides was simulated by molecular dynamics (MD) methods using the TSUBAME2 supercomputer at the Tokyo Institute of Technology and discussed with the vacancy profile probed by the o-Ps. The results suggested that the large hydration size of Na+ compared to the vacancy size in the polyamides contributes to the increased diffusivity selectivity of water/Na+ that is related to the NaCl desalination performance of the membrane. Both the hydration size of the ions and the vacancy size appeared to be significant parameters to discuss the diffusivity selectivity of water/ions in typical polyamide membranes.
2. Free volumes studies in Thymoquinone and Carvone β-cyclodextrin nanoparticles by positron annihilation lifetime spectroscopy
Ferreira Marques, M. F.; Gordo, P. M.; Moreira da Silva, A.
2013-06-01
Positron annihilation lifetime spectroscopy is used to study free volume in β-cyclodextrin with the encapsulation of thymoquinone and S-carvone, in samples covering the guest to host fraction range from 1:0.1 to 1:1. The results clearly indicate the presence of long lifetime components related to Ps-formation. Although the behavior of the two guests is different, in both cases the results indicate the formation of 1:1 cyclodextrin inclusion compounds. Data show that the addition of carvone to β-cyclodextrin results in a decrease of the o-Ps lifetime corresponding to a reduction of the average radius of cavities from 2.41 Å to 2.29 Å, whereas the addition of thymoquine decreases the radius from 2.57 Å to 2.35 Å. In turn, the intensity varied from 20.55 to 19.20% and from 20.83 to 0.41%, respectively.
3. Thermal stability of nanocrystalline Cu studied by positron annihilation lifetime spectroscopy and X-ray diffraction
Zhou, Kai; Li, Hui; Pang, JinBiao; Wang, Zhu
2012-06-01
Thermal stability of nanocrystalline Cu prepared by compacting nanoparticles (mean grain size about 50 nm) under high pressure has been studied by means of positron annihilation lifetime spectroscopy and X-ray diffraction. A gradual increase of mean grain size in the sample is observed with an increase in ageing time at 180°C, indicating an increase of volume fraction of the ordered regions. Furthermore, during the ageing, the increase in average size of the vacancy clusters in grain boundaries is confirmed by the positron lifetime results. The recrystallization is observed at the temperature of about 180°C, and becomes significant above 650°C. Three annealing stages, which are at the intervals 180-400°C, 400-650°C and 650-900°C have been characterized by positron average lifetime. The average volume of the defects almost remains constant in the interval 400-650°C but becomes considerably smaller in the interval 650-900°C.
4. Preliminary studies on a variable energy positron annihilation lifetime spectroscopy system
Kwan, P. Y.; Cheung, C. K.; Beling, C. D.; Fung, S.
2006-02-01
There are many advantages in being able to perform positron annihilation lifetime spectroscopy (PALS) using a variable energy positron beam, the most obvious being the easy identification of different defect types at different depths. The difficulty in conducting variable energy (VE) PALS studies lies in the fact that a "start" signal is required to signal the entry of the positron into the target. Two methods have been used to overcome this problem, namely the bunching technique, which employs radio frequency (RF) cavities and choppers, and secondly the use of secondary electrons emitted from the target. The latter technique is in terms of experimental complexity much simpler, but has in the past suffered from poor time resolution (typically ˜500 ps). In this work, we present a series of computer simulations of a design based on the secondary electron emission from thin C-foils in transmission mode which shows that significant improvements in time resolution can be made with resolutions ˜200 ps being in principle possible.
5. Photon-induced positron annihilation lifetime spectroscopy using ultrashort laser-Compton-scattered gamma-ray pulses
SciTech Connect
Taira, Y.; Toyokawa, H.; Kuroda, R.; Yamamoto, N.; Adachi, M.; Tanaka, S.; Katoh, M.
2013-05-15
High-energy ultrashort gamma-ray pulses can be generated via laser Compton scattering with 90 Degree-Sign collisions at the UVSOR-II electron storage ring. As an applied study of ultrashort gamma-ray pulses, a new photon-induced positron annihilation lifetime spectroscopy approach has been developed. Ultrashort gamma-ray pulses with a maximum energy of 6.6 MeV and pulse width of 2.2 ps created positrons throughout bulk lead via pair production. Annihilation gamma rays were detected by a BaF{sub 2} scintillator mounted on a photomultiplier tube. A positron lifetime spectrum was obtained by measuring the time difference between the RF frequency of the electron storage ring and the detection time of the annihilation gamma rays. We calculated the response of the BaF{sub 2} scintillator and the time jitter caused by the variation in the total path length of the ultrashort gamma-ray pulses, annihilation gamma rays, and scintillation light using a Monte Carlo simulation code. The positron lifetime for bulk lead was successfully measured.
6. Photon-induced positron annihilation lifetime spectroscopy using ultrashort laser-Compton-scattered gamma-ray pulses.
PubMed
Taira, Y; Toyokawa, H; Kuroda, R; Yamamoto, N; Adachi, M; Tanaka, S; Katoh, M
2013-05-01
High-energy ultrashort gamma-ray pulses can be generated via laser Compton scattering with 90° collisions at the UVSOR-II electron storage ring. As an applied study of ultrashort gamma-ray pulses, a new photon-induced positron annihilation lifetime spectroscopy approach has been developed. Ultrashort gamma-ray pulses with a maximum energy of 6.6 MeV and pulse width of 2.2 ps created positrons throughout bulk lead via pair production. Annihilation gamma rays were detected by a BaF2 scintillator mounted on a photomultiplier tube. A positron lifetime spectrum was obtained by measuring the time difference between the RF frequency of the electron storage ring and the detection time of the annihilation gamma rays. We calculated the response of the BaF2 scintillator and the time jitter caused by the variation in the total path length of the ultrashort gamma-ray pulses, annihilation gamma rays, and scintillation light using a Monte Carlo simulation code. The positron lifetime for bulk lead was successfully measured.
7. Voids in mixed-cation silicate glasses: Studies by positron annihilation lifetime and Fourier transform infrared spectroscopies.
PubMed
Reben, M; Golis, E; Filipecki, J; Sitarz, M; Kotynia, K; Jeleń, P; Grelowska, I
2014-08-14
PALS in comparison with FTIR studies have been applied to investigate the structure of different oxide glasses. Three components of the positron lifetime τ (τ1 para- and τ3 ortho-positronium and τ2 intermediate lifetime component) and their intensities were obtained. The results of the calculation of mean values of positron lifetimes for the investigated glasses showed the existence of a long-living component on the positron annihilation lifetime spectra. From the Tao-Eldrup formula we can estimate the size of free volume. On the basis of the measurements we can conclude that the size and fraction of free volume reaches the biggest value for the fused silica glass. The degree of network polymerisation increases void size.
8. Clay particles - potential of positron annihilation lifetime spectroscopy (PALS) for studying interlayer spacing
Fong, N.; Guagliardo, P.; Williams, J.; Musumeci, A.; Martin, D.; Smith, S. V.
2011-01-01
Characterisation of clays is generally achieved by traditional methods, such as X-ray diffraction (XRD) and transmission electron microscopy (TEM). However, clays are often difficult to characterise due to lack of long-range order, thus these tools are not always reliable. Because interlayer spacing in clays can be adjusted to house molecules, there is growing interest to use these materials for drug delivery. Positron annihilation lifetime spectroscopy (PALS) was examined as an alternative tool to characterise a series of well-known clays. XRD of two layered double hydroxides; MgAl-LDH and MgGd-LDH, natural hectorite, fluoromica and laponite, and their PALS spectra were compared. XRD data was used to calculate the interlayer d- spacing in these materials and results show a decrease in interlayer spacing as the heavy metal ions are substituted for those of large ionic radii. Similar results were obtained for PALS data. This preliminary study suggests PALS has potential as a routine tool for characterising clay particles. Further work will examine the sensitivity and reliability of PALS to percent of metal doping and hydration in clay microstructure.
9. Supramolecular interactions between triphenylphosphine oxide and benzamide evaluated by positron annihilation lifetime spectroscopy
Oliveira, F. C.; Denadai, A. M. L.; Fulgêncio, F.; Oliveira, A. M.; Andrade, A. C. A.; Melo, A. C. A.; Yoshida, M. I.; Windmöller, D.; Magalhães, W. F.
2017-04-01
In the present work, intermolecular interactions between triphenylphosphine oxide (TPPO) and benzamide (BZM) has been studied in solid state by Positron Annihilation Lifetime Spectroscopy (PALS) and supported by several analytical techniques (in solid state and in solution) and by computational modeling (in gaseous phase). Isothermal Titration Calorimetry (ITC) in ethyl acetate solvent showed that complexation is a stepwise process, with 2:1 and 1:1 TPPO/BZM stoichiometries, both driven by entropy. HPLC analysis of isolated single crystal confirmed the existence of a 2:1 TPPO/BZM crystalline complex in solid state. The results of thermal analysis (TGA, DTA and DSC) and FTIR spectroscopy showed that the interactions in the complexes are relatively weaker than those found in pure precursors. Finally, PALS showed higher positronium formation probability (I3) at [TPPO0.62·BZM0.38] and [TPPO0.25·BZM0.75] molar fractions, corroborating the existence of two stoichiometries for the TPPO/BZM system and suggesting greater electronic availability of n- and π-electrons in heterosynton complexes, as resulting of interactions, bring forward new evidences of the participation of electronic excited states on the positronium formation mechanism.
10. Positron annihilation lifetime studies of changes in free volume on some biorelevant nitrogen heterocyclic compounds and their S-glycosylation.
PubMed
Mahmoud, K R; Khodair, A I; Shaban, S Y
2015-11-01
A series of N-heterocyclic compounds was investigated by positron annihilation lifetime spectroscopy as well as Doppler broadening of annihilation radiation (DBAR) at room temperature. The results showed that the formation probability and life time of ortho-positronium in this series are structure and electron-donation character dependent, and can give more information about the structure. The DBAR provides direct information about the change of core and valance electrons as well as the number of defect types present in these compounds.
11. Structural study of polymer hydrogel contact lenses by means of positron annihilation lifetime spectroscopy and UV-vis-NIR methods.
PubMed
Filipecki, J; Kocela, A; Korzekwa, P; Miedzinski, R; Filipecka, K; Golis, E; Korzekwa, W
2013-08-01
A study has been conducted in order to determine presence of free volume gaps in the structure of structure of polymer hydrogel contact lenses made in phosphoryl choline technology and of the degree of defect of its structure. The study was made by means of positron annihilation lifetime spectroscopy. As a result of the conducted measurements, curves were obtained, which described numbers of counts of the acts of annihilation in the time function. The conducted studies revealed existence of three components τ(1), τ(2) and τ(3). The τ(3) component is attributed to the pick-off annihilation of o-Ps orthopositronium trapping by free volume gaps and provides information about geometrical parameters of the volumes. At the same time, the UV-vis-NIR spectrometry examination was conducted on the same samples in the spectral range 200-1,000 nm.
12. Prediction of the stability of polymeric matrix tablets containing famotidine from the positron annihilation lifetime distributions of their physical mixtures.
PubMed
Szente, Virág; Süvegh, Károly; Marek, Tamás; Zelkó, Romána
2009-04-05
The aim of the present work was to elucidate the impact of the structural changes of polymeric excipients during the course of storage on the drug release stability of tablets containing different polymers. Matrix tablets were formulated with famotidine as a model drug, using polyvinylpyrrolidone and carbopol matrix. Dissolution tests were carried out before and after storing the tablets under stress conditions for different time intervals. Parameters characterizing the release kinetics of matrix tablets, just as difference and similarity factors, were calculated to compare the release profiles as a function of storage time. Positron annihilation lifetime measurements were carried out to track the structural changes of the physical mixtures containing polymers during the course of storage. The changes in the positron lifetime distribution curves of the famotidine-polymer mixtures were in good correlation with the significant changes of release parameters of tablets. Thus the method would be a valuable tool for the screening of possible destabilizing interactions in the preformulation phase.
13. A study of inter-crystallite spaces in some polycrystalline inorganic systems using positron annihilation lifetime spectroscopy
Shantarovich, V. P.; Suzuki, T.; Ito, Y.; Kondo, K.; Gustov, V. W.; Melikhov, I. V.; Berdonosov, S. S.; Ivanov, L. N.; Yu, R. S.
2007-02-01
Positron annihilation lifetime spectroscopy (PALS) was used for calculation of number density and effective sizes of free volume holes (inter-crystallite spaces) in polycrystal CaSO 4, CaCO 3 (vaterit) and Ca 10(PO 4) 6(OH) 2 (apatite). The effect of substitution of two-valence Ca(II) for three-valence Eu(III) on annihilation characteristics of apatite, studied together with the data on thermo-stimulated luminescence (TSL) and low-temperature sorption of gas (N 2), helped to elucidate mechanism of positronium atom (Ps) localization in the free volume holes and perform corresponding calculations. It came out that PALS is more sensitive to inter-crystallite sites (10 16 cm -3) in polycrystallites than to the free volume holes in polymer glasses (10 19 cm -3). This is due to higher mobility of the precursor of localized Ps in crystallites.
14. Positron annihilation lifetime measurement and X-ray analysis on 120 MeV Au+7 irradiated polycrystalline tungsten
Dube, Charu Lata; Kulriya, Pawan Kumar; Dutta, Dhanadeep; Pujari, Pradeep K.; Patil, Yashashri; Mehta, Mayur; Patel, Priyanka; Khirwadkar, Samir S.
2015-12-01
15. Characterization of γ-irradiated polymethyl methacrylate by means of mechanical properties and positron annihilation lifetime spectroscopy
Rubiolo, G. H.; Somoza, A.; Goyanes, S. N.; Consolati, G.; Marzocca, A. J.
1999-08-01
An experimental investigation was undertaken to assess the effect of γ irradiation on the structural'' state and the corresponding inelastic deformation behavior of polymethyl methacrylate (PMMA). Uniaxial and constant strain rate compression tests were conducted over a range of strain rates at room temperature on glassy polymer specimens of PMMA subjected to different γ-irradiation doses. Measurements of positron annihilation lifetime spectroscopy were performed on samples before the compression test in an attempt to correlate free volume content with yield stress. A kinetic law of plastic flow considering a local shear transformation in a small volume Ω is used to represent the observed mechanical behavior. The density and size of the clusters are found for the material subjected to different irradiation dose. Positron annihilation lifetime spectroscopy was also used to estimate the size and number density of free volume sites in the polymer specimens. The dependence of both magnitudes with the irradiation dose follows those of the plastic cluster of volume Ω. Both results provide experimental evidence that the density and the size of high free volume sites can be used as an internal state variable for characterizing the mechanical state of glassy polymers.
16. Utility of positron annihilation lifetime technique for the assessment of spectroscopic data of some charge-transfer complexes derived from N-(1-Naphthyl)ethylenediamine dihydrochloride.
PubMed
Refat, Moamen S; Adam, Abdel Majid A; Sharshar, T; Saad, Hosam A; Eldaroti, Hala H
2014-03-25
In this work, structural, thermal, morphological, pharmacological screening and positron annihilation lifetime measurements were performed on the interactions between a N-(1-Naphthyl)ethylenediamine dihydrochloride (NEDA·2HCl) donor and three types of acceptors to characterize these CT complexes. The three types of acceptors include π-acceptors (quinol and picric acid), σ-acceptors (iodine) and vacant orbital acceptors (tin(IV) tetrachloride and zinc chloride). The positron annihilation lifetime parameters were found to be dependent on the structure, electronic configuration, the power of acceptors and molecular weight of the CT complexes. The positron annihilation lifetime spectroscopy can be used as a probe for the formation of charge-transfer (CT) complexes.
17. Utility of positron annihilation lifetime technique for the assessment of spectroscopic data of some charge-transfer complexes derived from N-(1-Naphthyl)ethylenediamine dihydrochloride
Refat, Moamen S.; Adam, Abdel Majid A.; Sharshar, T.; Saad, Hosam A.; Eldaroti, Hala H.
2014-03-01
In this work, structural, thermal, morphological, pharmacological screening and positron annihilation lifetime measurements were performed on the interactions between a N-(1-Naphthyl)ethylenediamine dihydrochloride (NEDA·2HCl) donor and three types of acceptors to characterize these CT complexes. The three types of acceptors include π-acceptors (quinol and picric acid), σ-acceptors (iodine) and vacant orbital acceptors (tin(IV) tetrachloride and zinc chloride). The positron annihilation lifetime parameters were found to be dependent on the structure, electronic configuration, the power of acceptors and molecular weight of the CT complexes. The positron annihilation lifetime spectroscopy can be used as a probe for the formation of charge-transfer (CT) complexes.
18. Characteristics of vinyl-ester and carbon fiber composite dry and wet probe by Positron Annihilation Lifetime Spectroscopy
2015-03-01
Carbon fiber composites of vinylester resins, Derakane 8084 and 510A, were studied dry and after water exposure. In this study, positron annihilation lifetime spectroscopy (PALS) was used to investigate the free volume fraction and the size of the free volume voids within the polymer matrix. The relative free volume (fractions replae by of positron lifetime intensities) in VE8084 polymer and in VE510A (Space) polymer were 35.2% and 13.8%, respectively. The free volume lifetime and intensities were determined as a function of the polymer thickness and significant differences were observed in both polymers with versus without post-curing. The effects of water uptake in these materials were also determined by PALS. Water uptake showed a 2% change in intensity of the longer lifetime (1.85 ns) in VE8084 polymer and in VE510A about 1.8%. The longer lifetime intensities in the wet composites were 17.1% in the 8084 polymer and its carbon fiber composite and 7.1% in the 510A polymer and its carbon fiber composite. For composite with 8084 polymer saturated (0.33% water gain) with seawater at 40 or 60 °C, no change in the longer lifetime intensity was observed which indicates no water entered the free volume voids (indicates replace by and) some differences between composite and neat polymer. For 510A resin the third lifetime intensity dropped from 7.1% to 3.9% indicating 48% of the free volume filled with water in the composite only after saturation with seawater with respect to dry one.
19. Positron annihilation processes update
NASA Technical Reports Server (NTRS)
Guessoum, Nidhal; Skibo, Jeffrey G.; Ramaty, Reuven
1997-01-01
The present knowledge concerning the positron annihilation processes is reviewed, with emphasis on the data of the cross sections of the various processes of interest in astrophysical applications. Recent results are presented including results on reaction rates and line widths, the validity of which is verified.
20. The assessment of pore connectivity in hierarchical zeolites using positron annihilation lifetime spectroscopy: instrumental and morphological aspects.
PubMed
Zubiaga, Asier; Warringham, Robbie; Boltz, Marilyne; Cooke, David; Crivelli, Paolo; Gidley, David; Pérez-Ramírez, Javier; Mitchell, Sharon
2016-04-07
Recent studies demonstrated the power of positron annihilation lifetime spectroscopy (PALS) to characterise the connectivity and corresponding effectiveness of hierarchical pore networks in zeolites. This was based on the fractional escape of ortho-positronium (Ps), formed within the micropore framework, to vacuum. To further develop this technique, here we assess the impact of the positron implantation energy and of the zeolite crystal size and the particle morphology. Conventional measurements using fast positrons and beam measurements applying moderated positrons both readily distinguish purely microporous ZSM-5 zeolites comprised of single crystals or crystal aggregates. Unlike beam measurements, however, conventional measurements fail to discriminate model hierarchical zeolites with open or constricted mesopore architectures. Several steps are taken to rationalise these observations. The dominant contribution of Ps diffusion to the PALS response is confirmed by capping the external surface of the zeolite crystals with tetraethylorthosilicate, which greatly enhances the sensitivity to the micropore network. A one-dimensional model is constructed to predict the out-diffusion of Ps from a zeolite crystal, which is validated experimentally by comparing coffin-shaped single crystals of varying size. Calculation of the trends expected on the application of fast or moderated positrons indicates that the distinctions in the initial distribution of Ps at the crystal level cannot explain the limited sensitivity of the former to the mesopore architecture. Instead, we propose that the greater penetration of fast positrons within the sample increases the probability of Ps re-entry from intercrystalline voids into mesopores connected with the external surface of zeolite crystals, thereby reducing their fractional escape.
1. Confined water in controlled pore glass CPG-10-120 studied by positron annihilation lifetime spectroscopy and differential scanning calorimetry
Šauša, O.; Mat'ko, I.; Illeková, E.; Macová, E.; Berek, D.
2015-06-01
The solidification and melting of water confined in the controlled pore glass (CPG) with average pore size 12.6 nm has been studied by differential scanning calorimetry (DSC) and positron annihilation lifetime spectroscopy (PALS). The fully-filled sample of CPG by water as well as the samples of CPG with different content of water were used. The measurements show the presence of amorphous and crystalline phases of water in this type and size of pores, freezing point depression of a confined liquid and presence of certain transitions at lower temperatures, which could be detected only for cooling regime. The localization of confined water in the partially filled pores of CPG at room temperature was studied.
2. Hydrolytic Degradation of Poly(L-Lactide-co-Glycolide) Studied by Positron Annihilation Lifetime Spectroscopy and Other Techniques
Pamuła, E.; Dryzek, E.; Dobrzyński, P.
2006-11-01
Changes of the poly(L-lactide-co-glycolide) structure as a function of degradation time in phosphate-buffered saline for 7 weeks were investigated by gel permeation chromatography, differential scanning calorimetry, nuclear magnetic resonance (1H NMR), and positron annihilation lifetime spectroscopy. Surface properties as wettability by sessile drop and topography by atomic force microscopy were also characterized. Chain-scission of polyester bonds in hydrolysis reaction causes a quite uniform decrease in molecular weight, and finally results in an increase in semicrystallinity. Molecular composition of the copolymer and water contact angle do not change considerably during degradation time. Atomic force microscopy studies suggest that the copolymer degrades by "in bulk" mechanism. The average size of the molecular-level free volume holes declines considerably after one week of degradation and remains constant till the sixth week of degradation. The free volume fraction decreases as a function of degradation time.
3. Effect of water on glass transition in starch/sucrose matrices investigated through positron annihilation lifetime spectroscopy: a new approach.
PubMed
Sharma, Sandeep Kumar; Zaydouri, Abdelhadi; Roudaut, Gaëlle; Duplâtre, Gilles
2011-11-21
Glass transition is studied through positron annihilation lifetime spectroscopy (PALS) in maize starch matrices containing 10 (batch STS10) and 20 (STS20) w/w% sucrose, as a function of temperature (T) and water content (c(w)). To circumvent important losses of water upon heating while recording the PALS spectra, a new method is developed: instead of a series of measurements of τ(3), the triplet positronium lifetime, at different T, the latter is kept constant and the series relates to c(w), which is left to decrease at a constant rate. Similarly to the changes in τ(3) with T, the τ(3)vs. c(w) plots obtained show a smooth linear increase until a break, denoting the occurrence of glass transition, followed by a sharper increase. The gradients appear to be independent of T. The variation of the glass transition temperature, T(g), with c(w) shows a broad sigmoid with a large linear central part; as expected from the plasticising effect of sucrose, the plot for STS20 lies some 10 K below that for STS10. Results from differential scanning calorimetry for STS20 yield T(g) values some 15 K higher than from PALS. On the basis of the general shape of the τ(3)vs. T variations, a general equation is set for τ(3)(T, c(w)), leading one to expect a similar shape for τ(3)vs. c(w), as experimentally observed.
4. Ion induced modification in free volume in PN-6 and PES polymers by positron annihilation lifetime studies
2007-03-01
The irradiation of polymeric materials with swift heavy ions (SHI) results in a change of their free volume properties which have strong correlation with their macroscopic properties. Positron annihilation lifetime spectroscopy (PALS) has been developed into a powerful characterization tool for the study of free volume and free volume fraction in polymers. Polyamide nylon-6 (PN-6) and polyethersulphone (PES) films of thickness of 250 μm were irradiated with C5+ ions of energy 70 MeV from 15 UD Pelletron accelerator at Inter University Accelerator Centre (IUAC), New Delhi, India. PN-6 films were irradiated to the fluences of 1011, 1012 and 1013 ions/cm2 whereas PES films were irradiated to the fluences of 9.3 × 1011, 9.3 × 1012 and 1.2 × 1013 ions/cm2. Characterization of the effect of ion irradiation on free volume has been done by PALS. The average free volume and fractional free volume obtained from long lived component, attributed to ortho-positronium (o-Ps) lifetime, are found to decrease with the fluence in both the cases. With increasing fluence, scissioned segments cross-link randomly, resulting in a decrease of average free volume due to overlapping of tracks.
5. Free volume evolution in 50 MeV Li3+ ion-irradiated polymers studied by positron annihilation lifetime spectroscopy
Singh, Paramjit; Kumar, Rajesh; Prasad, Rajendra
2013-02-01
6. Dependence of alpha particle track diameter on the free volume holes size using positron annihilation lifetime technique
El-Gamal, S.; Abdalla, Ayman M.; Abdel-Hady, E. E.
2015-09-01
The alpha particle track diameter dependence of the free volume holes size (Vf) in DAM-ADC and CR-39 nuclear track detectors was investigated using positron annihilation lifetime technique. The effect of temperature on the alpha particle track diameter and free volume were also investigated in the T-range (RT-130 °C). The obtained results revealed that the values of ortho-positronium lifetime τ3 and Vf increases while I3 slightly increases as T increases for the two detectors. The values of τ3, Vf and I3 are higher in CR-39 than DAM-ADC. The interpretation of obtained results is based on the fact that increasing T leads to significant enhancement of thermal expansion of the polymer matrix and consequently Vf increases. The track diameter increases as T increases. This can be explained by the fact that the increase in T increases the crystal size and Vf in the polymer. A relationship between Vf and the alpha particle track diameter was obtained. Moreover results of detector irradiation, along with free volume evaluation are addressed and thoroughly discussed.
7. Method of processing positron lifetime spectra
SciTech Connect
Valuev, N.P.; Klimov, A.B.; Zhikharev, A.N.
1985-05-01
This paper describes a method for the processing of spectra of positron annihilation which permits a much more relaible determination of the lifetime during numerical processing of spectra by computer.
8. Positron Annihilation in Insulating Materials
SciTech Connect
Asoka-Kumar, P; Sterne, PA
2002-10-18
We describe positron results from a wide range of insulating materials. We have completed positron experiments on a range of zeolite-y samples, KDP crystals, alkali halides and laser damaged SiO{sub 2}. Present theoretical understanding of positron behavior in insulators is incomplete and our combined theoretical and experimental approach is aimed at developing a predictive understanding of positrons and positronium annihilation characteristics in insulators. Results from alkali halides and alkaline-earth halides show that positrons annihilate with only the halide ions, with no apparent contribution from the alkali or alkaline-earth cations. This contradicts the results of our existing theory for metals, which predicts roughly equal annihilation contributions from cation and anion. We also present result obtained using Munich positron microprobe on laser damaged SiO{sub 2} samples.
9. Detection of atomic scale changes in the free volume void size of three-dimensional colorectal cancer cell culture using positron annihilation lifetime spectroscopy.
PubMed
Axpe, Eneko; Lopez-Euba, Tamara; Castellanos-Rubio, Ainara; Merida, David; Garcia, Jose Angel; Plaza-Izurieta, Leticia; Fernandez-Jimenez, Nora; Plazaola, Fernando; Bilbao, Jose Ramon
2014-01-01
Positron annihilation lifetime spectroscopy (PALS) provides a direct measurement of the free volume void sizes in polymers and biological systems. This free volume is critical in explaining and understanding physical and mechanical properties of polymers. Moreover, PALS has been recently proposed as a potential tool in detecting cancer at early stages, probing the differences in the subnanometer scale free volume voids between cancerous/healthy skin samples of the same patient. Despite several investigations on free volume in complex cancerous tissues, no positron annihilation studies of living cancer cell cultures have been reported. We demonstrate that PALS can be applied to the study in human living 3D cell cultures. The technique is also capable to detect atomic scale changes in the size of the free volume voids due to the biological responses to TGF-β. PALS may be developed to characterize the effect of different culture conditions in the free volume voids of cells grown in vitro.
10. Free volume anomalies in mixed-cation glasses revealed by positron annihilation lifetime spectroscopy (PALS).
PubMed
Ingram, Malcolm D; Pas, Steven J; Cramer, Cornelia; Gao, Yong; Hill, Anita J
2005-04-21
PALS experiments reveal a minimum in ortho-positronium (o-Ps) lifetimes and a maximum in the corresponding intensities that emerge when mixed-cation (Li/Na) borate glasses are heated from ambient temperatures up to 473 K. These free volume 'anomalies' appear to be a true manifestation of the mixed alkali effect (MAE). They are consistent with a mechanism of ion transport involving cooperation between hops of unlike cations, resulting in increased disturbance of the glass network. The result lends support to the dynamic structure model.
11. Cholesterol-Ceramide Interactions in Phospholipid and Sphingolipid Bilayers As Observed by Positron Annihilation Lifetime Spectroscopy and Molecular Dynamics Simulations.
PubMed
García-Arribas, Aritz B; Axpe, Eneko; Mujika, Jon Iñaki; Mérida, David; Busto, Jon V; Sot, Jesús; Alonso, Alicia; Lopez, Xabier; García, Jose Ángel; Ugalde, Jesus M; Plazaola, Fernando; Goñi, Félix M
2016-05-31
Free volume voids in lipid bilayers can be measured by positron annihilation lifetime spectroscopy (PALS). This technique has been applied, together with differential scanning calorimetry and molecular dynamics (MD) simulations, to study the effects of cholesterol (Chol) and ceramide (Cer) on free volume voids in sphingomyelin (SM) or dipalmitoylphosphatidylcholine (DPPC) bilayers. Binary lipid samples with Chol were studied (DPPC:Chol 60:40, SM:Chol 60:40 mol ratio), and no phase transition was detected in the 20-60 °C range, in agreement with calorimetric data. Chol-driven liquid-ordered phase showed an intermediate free volume void size as compared to gel and fluid phases. For SM and SM:Cer (85:15 mol:mol) model membranes measured in the 20-60 °C range the gel-to-fluid phase transition could be observed with a related increase in free volume, which was more pronounced for the SM:Cer sample. MD simulations suggest a hitherto unsuspected lipid tilting in SM:Cer bilayers but not in pure SM. Ternary samples of DPPC:Cer:Chol (54:23:23) and SM:Cer:Chol (54:23:23) were measured, and a clear pattern of free volume increase was observed in the 20-60 °C because of the gel-to-fluid transition. Interestingly, MD simulations showed a tendency of Cer to change its distribution along the membrane to make room for Chol in ternary mixtures. The results suggest that the gel phase formed in these ternary mixtures is stabilized by Chol-Cer interactions.
12. Photon correlations in positron annihilation
SciTech Connect
Gauthier, Isabelle; Hawton, Margaret
2010-06-15
The two-photon positron annihilation density matrix is found to separate into a diagonal center-of-energy factor implying maximally entangled momenta, and a relative factor describing decay. For unknown positron injection time, the distribution of the difference in photon arrival times is a double exponential at the para-Ps decay rate, consistent with experiment [V. D. Irby, Meas. Sci. Technol. 15, 1799 (2004)].
13. Infrared, Raman, 1H NMR, thermal and positron annihilation lifetime studies of Pb(II), Sn(II), Sb(III), Bi(III)-barbital complexes
Refat, Moamen S.; Sharshar, T.
2012-05-01
Metal complexes of Pb(II), Sn(II), Sb(III) and Bi(III) with a barbital sodium were synthesized and characterized by several techniques, including elemental analysis (C, H and N), molar conductance measurements, infrared, Raman, 1H NMR, positron annihilation lifetime and thermogravimetric analysis. Reactions of barbital sodium (NaL) with salts of Pb(NO3)2, SnCl2ṡ2H2O, SbCl3 and BiCl3 affords four novel mononuclear complexes [Pb(HL)2], [Sn(L)(H2O)], [Sb(HL)(L)] and [Bi(HL)(L)]. In complexes of Pb(II), Sb(III) and Bi(III), the molar ratio of metal-to-ligand is 1:2. Both of Sb(III) and Bi(III) complexes have six coordination via two molecules of barbital (HL and L), one of them deprotonated NH. The Pb(II) complex has a central metal ion adopts tetradentate fashion which surrounded by two (HL) barbital moieties. The elemental analysis shows that Sn(II) complex is tetradentate 1:1 ratio, chelated through oxygen sbnd O of (ONa), deprotonated (sbnd NH) and one coordinated water molecule. The positron annihilation lifetime parameters were found to be dependent on the structure, electronic configuration and molecular weight of metal complexes.
14. Drug release profiles and microstructural characterization of cast and freeze dried vitamin B12 buccal films by positron annihilation lifetime spectroscopy.
PubMed
Szabó, Barnabás; Kállai, Nikolett; Tóth, Gergő; Hetényi, Gergely; Zelkó, Romána
2014-02-01
Solvent cast and freeze dried films, containing the water-soluble vitamin B12 as model drug were prepared from two polymers, sodium alginate (SA), and Carbopol 71G (CP). The proportion of the CP was changed in the films. The microstructural characterization of various samples was carried out by positron annihilation lifetime spectroscopy (PALS). The drug release kinetics of untreated and stored samples was evaluated by the conventionally applied semi-empirical power law. Correlation was found between the changes of the characteristic parameters of the drug release and the ortho-positronium (o-Ps) lifetime values of polymer samples. The results indicated that the increase of CP concentration, the freeze-drying process and the storage at 75% R.H. decreased the rate of drug release. The PALS method enabled the distinction between the micro- and macrostructural factors influencing the drug release profile of polymer films.
15. Positron annihilation studies of organic superconductivity
SciTech Connect
Yen, H.L.; Lou, Y.; Ali, E.H.
1994-09-01
The positron lifetimes of two organic superconductors, {kappa}-(ET){sub 2}Cu(NCS){sub 2} and {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br, are measured as a function of temperature across {Tc}. A drop of positron lifetime below {Tc} is observed. Positron-electron momentum densities are measured by using 2D-ACAR to search for the Fermi surface in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br. Positron density distributions and positron-electron overlaps are calculated by using the orthogonalized linear combination atomic orbital (OLCAO) method to interprete the temperature dependence due to the local charge transfer which is inferred to relate to the superconducting transition. 2D-ACAR results in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br are compared with theoretical band calculations based on a first-principles local density approximation. Importance of performing accurate band calculations for the interpretation of positron annihilation data is emphasized.
16. Applications of positron annihilation spectroscopy in materials research
NASA Technical Reports Server (NTRS)
Singh, Jag J.
1988-01-01
Positron Annihilation Spectroscopy (PAS) has emerged as a powerful technique for research in condensed matter. It has been used extensively in the study of metals, ionic crystals, glasses and polymers. The present review concentrates on applications of positron lifetime measurements for elucidation of the physicochemical structure of polymers.
17. Determination of the activation enthalpy for migration of dislocations in plastically deformed 8006 Al-alloy by positron annihilation lifetime technique
2016-06-01
The activation enthalpy for migration of dislocations of plastically deformed 8006 Al-alloy was investigated by positron annihilation lifetime technique. Plastic deformation using a hydraulic press produces mainly dislocations and may produce point defects. The type of defect was studied by isochronal annealing which determines the temperature range of recovery of each type. Only one type of defect (dislocations) was observed for the investigated sample and was found to be recovered within the range 455-700 K. Isothermal annealing by slow cooling was performed through this range and used in determination of the activation enthalpy of migration of dislocations which was found to be 0.26 ± 0.01 eV.
18. Effect of storage on microstructural changes of Carbopol polymers tracked by the combination of positron annihilation lifetime spectroscopy and FT-IR spectroscopy.
PubMed
Szabó, Barnabás; Süvegh, Károly; Zelkó, Romána
2011-09-15
Different types of Carbopols are frequently applied excipients of various dosage forms. Depending on the supramolecular structure, their water sorption behaviour could significantly differ. The purpose of the present study was to track the supramolecular changes of two types of Carbopol polymers (Carbopol 71G and Ultrez 10NF) alone and in their physical mixture with a water-soluble drug, vitamin B(12), as a function of storage time. The combination of FT-IR spectroscopy, positron annihilation lifetime spectroscopy (PALS) and Doppler-broadening spectroscopy was applied to follow the effect of water uptake on the structural changes. Our results indicate that water-induced interactions between polymeric chains can be sensitively detected. This enables the prediction of stability of dosage forms in the course of storage.
19. Dislocation Substructure in the Cold-Rolled Ni-20 Mass Pct Cr Alloy Analyzed by X-ray Diffraction, Positron Annihilation Lifetime, and Transmission Electron Microscopy
Yonemura, Mitsuharu; Inoue, Koji
2016-12-01
The systematic change in the dislocation density and characteristics that develop under cold rolling as a simulated deformation was studied in order to examine the fundamental behavior of dislocations in terms of the dislocation substructure formation. In particular, the dislocation density was quantified by X-ray line profile analysis (XLPA), which is effective for quantifying the dislocation density and character; positron annihilation lifetime (PAL), which is sensitive to vacancy-type lattice defects; the Bailey-Hirsch equation from the hardness (Hv); and transmission electron microscopy (TEM). The strain dependency of the dislocation density analyzed by XLPA, PAL, TEM, and Hv showed a similar tendency with an increase in the dislocation. In particular, the dislocation density by XLPA had good agreement with the results of TEM at low strain levels and with PAL at high strain levels. As a result, a combination of these techniques successfully showed the behavior of the dislocation substructure.
20. Positron annihilation in the interstellar medium
NASA Technical Reports Server (NTRS)
Guessoum, Nidhal; Ramaty, Reuven; Lingenfelter, Richard E.
1991-01-01
Positronium formation and annihilation are studied in a model for the interstellar medium consisting of cold cloud cores, warm partially ionized cloud envelopes, and hot intercloud gas. The gamma-ray spectra resulting from positron annihilation in these components of the interstellar medium are calculated. The spectra from the individual components are then combined, using two limiting assumptions for the propagation of the positrons, namely, that the positrons propagate freely throughout the interstellar medium, and that the positrons are excluded from the cold cloud cores. In the first case, the bulk of the positrons annihilate in the cloud cores and the annihilation line exhibits broad wings resulting from the annihilation of positronium formed by charge exchange in flight. In the second case, the positrons annihilate mainly in the warm envelopes, and the line wings are suppressed.
1. Application of positron annihilation lifetime spectroscopy (PALS) to study the nanostructure in amphiphile self-assembly materials: phytantriol cubosomes and hexosomes.
PubMed
Dong, Aurelia W; Fong, Celesta; Waddington, Lynne J; Hill, Anita J; Boyd, Ben J; Drummond, Calum J
2015-01-21
Self-assembled amphiphile nanostructures of colloidal dimensions such as cubosomes and hexosomes are of interest as delivery vectors in pharmaceutical and nanomedicine applications. Translation would be assisted through a better of understanding of the effects of drug loading on the internal nanostructure, and the relationship between this nanostructure and drug release profile. Positron annihilation lifetime spectroscopy (PALS) is sensitive to local microviscosity and is used as an in situ molecular probe to examine the Q2 (cubosome) → H2 (hexosome) → L2 phase transitions of the pharmaceutically relevant phytantriol-water system in the presence of a model hydrophobic drug, vitamin E acetate (VitEA). It is shown that the ortho-positronium lifetime (τ) is sensitive to molecular packing and mobility and this has been correlated with the rheological properties of individual lyotropic liquid crystalline mesophases. Characteristic PALS lifetimes for L2 (τ4∼ 4 ns) ∼ H2 (τ4∼ 4 ns) > Q(2 Pn3m) (τ4∼ 2.2 ns) are observed for the phytantriol-water system, with the addition of VitEA yielding a gradual increase in τ from τ∼ 2.2 ns for cubosomes to τ∼ 3.5 ns for hexosomes. The dynamic chain packing at higher temperatures and in the L2 and H2 phases is qualitatively less "viscous", consistent with rheological measurements. This information offers increased understanding of the relationship between internal nanostructure and species permeability.
2. Positron annihilation spectroscopy with magnetically analyzed beams
NASA Technical Reports Server (NTRS)
Singh, J. J.; Holt, W. H.; Mock, W., Jr.
1982-01-01
Lifetime measurements with magnetically analyzed positron beams were made in condensed media with uniform and non-uniform properties. As expected, the lifetime values with magnetically analyzed positron beams in uniform targets are similar to those obtained with conventional positron sources. The lifetime values with magnetically analyzed beams in targets which have non-uniform properties vary with positron energy and are different from the conventional positron source derived lifetime values in these targets.
3. Multimode vibrational couplings in resonant positron annihilation.
PubMed
d'A Sanchez, Sergio; Lima, Marco A P; Varella, Márcio T do N
2011-09-02
The mechanisms for multimode vibrational couplings in resonant positron annihilation are not well understood. We show that these resonances can arise from positron-induced distortions of the potential energy surface (target response to the positron field). Though these distortions can transfer energy into single- and multiquantum vibrations, they have so far been disregarded as a pathway to resonant annihilation. We also compare the existing annihilation theories and show that the currently accepted model can be cast as a special case of the Feshbach annihilation theory.
4. Packing and mobility of hydrocarbon chains in phospholipid lyotropic liquid crystalline lamellar phases and liposomes: characterisation by positron annihilation lifetime spectroscopy (PALS).
PubMed
Dong, Aurelia W; Fong, Celesta; Waddington, Lynne J; Hill, Anita J; Boyd, Ben J; Drummond, Calum J
2015-01-07
Lipid lamellar mesophases and their colloidal dispersions (liposomes) are increasingly being deployed in vivo as drug delivery vehicles, and also as models of biological membranes in fundamental biophysics studies. The permeability and diffusion of small molecules such as drugs is accommodated by a change in local curvature and molecular packing (mesophase behaviour) of the bilayer membrane molecules. Positron annihilation lifetime spectroscopy (PALS) is capable of providing in situ molecular level information on changes in free volume and void space arising from such changes in a non-perturbative manner. In this work PALS was used to systematically characterise the temperature-induced melting transitions (Tm) of saturated and unsaturated phospholipid-water systems while systematically varying lipid chain length, as both bulk lamellar mesophase and as aqueous colloidal dispersions (liposomes). A four-component fit of the data was used that provides separate PALS lifetimes for the aqueous (τ3) and organic domains (τ4). The oPs lifetime (τ4), for the lamellar phases of DSPC (C18:0), DPPC (C16:0), DMPC (C14:0) and DLPC (C12:0) was found to be independent of chain length, with characteristic lifetime value τ4 ∼ 3.4 ns. τ4 is consistently larger in the dispersed liposomes compared to the bulk mesophases, suggesting that the hydrocarbon chains are more mobile. The use of contemporary and consistent analytical approaches as described in this study is the key to future deployment of PALS to interrogate the in situ influence of drugs on membrane and cellular microenvironments.
5. Positron annihilation induced Auger electron emission
SciTech Connect
Weiss, A.; Jibaly, M.; Lei, Chun; Mehl, D.; Mayer, R.; Lynn, K.G.
1988-01-01
We report on measurements of Auger electron emission from Cu and Fe due to core hole excitations produced by the removal of core electrons by matter-antimatter annihilation. Estimates are developed of the probability of positrons annihilating with a 3p electron in these materials. Several important advantages of Positron annihilation induced Auger Electron Spectroscopy (PAES) for surface analysis are suggested. 10 refs., 2 figs.
6. Positron annihilation study on hafnium metals given various treatments
SciTech Connect
Min, Duck Ki; Kang, Myung Soo ); Yoon, Young Ku )
1993-08-01
The positron annihilation technique that enables measurements of positron lifetime, two-photon angular correlation and Doppler broadening due to annihilation radiation has been established for studies of the electronic configuration and defect properties in solids. In metals, positrons can be trapped at vacancies and their agglomerates as well as at dislocations, but not at interstitials. Because of these interactions, the positron annihilation method can be applied to studies of the behavior of dislocations during annealing of plastically deformed metals. Furthermore, it is possible by measurements of annihilation characteristics to identify defects such as vacancies, dislocations and vacancy-clusters, and to determine spatial dimensions of defects. In this work, positron annihilation measurements for annealed, cold worked, annealed and then quenched, and cold worked and then cathodically hydrogen charged hafnium specimens were made to obtain information on (a) positron annihilation characteristics of hafnium metal, (b) role of vacancy-type defects on hydrogen charging, (c) defects produced during hydrogen charging and (d) recovery of lattice defects in hafnium and effects of hydrogen on defects recovery upon annealing.
7. Positron annihilation spectroscopy on a beam of positrons the LEPTA facility
Ahmanova, E. V.; Eseev, M. K.; Kobets, A. G.; Meshkov, I. N.; Orlov, O. S.; Sidorin, A. A.; Siemek, K.; Horodek, P.
2016-12-01
The results and possibilities of the samples surfaces research by the Doppler method of positron annihilation spectroscopy (PAS) for a monochromatic beam of positrons at the LEPTA facility are presented in this paper. Method with high-resolution sensitivity to defects like vacancies and dislocations allows scanning of the surface and near-surface sample layers to a depth of several micrometers by the method of Doppler broadening of annihilation lines. The opportunities for the development of a PAS method based on the measurement of the positron lifetime in the sample irradiated by ordered flow of positrons from the injector of accelerator complex LEPTA at JINR are discussed.
8. Positron annihilation in superconducting 123 compounds
SciTech Connect
Peter, M.; Manuel, A.A.; Erb, A. . Dept. of Physics of Condensed Matter)
1998-12-20
After a brief review of the theory of angular correlation of positron annihilation radiation (ACAR), the authors illustrate experimental principles and give examples of successful determination of electron momentum density (EMD) and of positron lifetime in solids. The central question which the authors try to answer concerns the contribution of positron spectroscopy to the knowledge and understanding of the new high temperature superconducting oxides. They find that in these oxides also, partially filled bands exist and they can observe parts of their Fermi surface and measure lifetimes in accordance with band theoretical calculations. There are characteristic differences, however. The intensity of the anisotropy of the ACAR signal is below theoretical expectation and signals depend on sample preparation. Recent studies by the Geneva group have concerned dependence of the signals on impurities, on oxygen content and on the thermal history of preparation. Of particular interest are correlations between the variations of these signals and between the variations of structural and transport properties in these substances. Besides deliberate additions of impurities, the Geneva group also reports progress in the preparations of samples of highest purity (barium zirconate crucibles). The alloy series Pr[sub x]Y[sub 1[minus]x]Ba[sub 2]Cu[sub 3]O[sub 7[minus][delta
9. Method for photon activation positron annihilation analysis
DOEpatents
Akers, Douglas W.
2006-06-06
A non-destructive testing method comprises providing a specimen having at least one positron emitter therein; determining a threshold energy for activating the positron emitter; and determining whether a half-life of the positron emitter is less than a selected half-life. If the half-life of the positron emitter is greater than or equal to the selected half-life, then activating the positron emitter by bombarding the specimen with photons having energies greater than the threshold energy and detecting gamma rays produced by annihilation of positrons in the specimen. If the half-life of the positron emitter is less then the selected half-life, then alternately activating the positron emitter by bombarding the specimen with photons having energies greater then the threshold energy and detecting gamma rays produced by positron annihilation within the specimen.
10. Microstructure variation in fused silica irradiated by different fluence of UV laser pulses with positron annihilation lifetime and Raman scattering spectroscopy
Li, Chunhong; Zheng, Wanguo; Zhu, Qihua; Chen, Jun; Wang, B. Y.; Ju, Xin
2016-10-01
We present an original study on the non-destructive evaluation of the microstructure evolution of fused silica induced by pulsed UV laser irradiation at low fluence (less than 50% Fth). Positron annihilation spectroscopy discloses that the spatial size of the vacancy cluster is increased exponentially with the linearly elevated laser fluence. Particularly, the vacancy cluster size in bulk silica is significantly increased by 14.5% after irradiated by pulsed 355 nm laser at F = 14 J/cm2 (50% Fth), while the void size varies only ∼2%. UV laser-excited Raman results suggest that the bond length and average bond angle of Sisbnd Osbnd Si bridging bond are both slightly reduced. Results reveals that the rearrangement process of (Sisbnd O)n fold rings and breakage of the Sisbnd O bridging bond in bulk silica occurred during pulsed UV laser irradiation. The micro-structural changes were taken together to clarify the effect of sub-threshold laser fluence on material stability of silica glass. The obtained data provide important information for studying material stability and controlling the lifetime of fused silica optics for high power laser system.
11. Characterization of free volume during vulcanization of styrene butadiene rubber by means of positron annihilation lifetime spectroscopy and dynamic mechanical test.
PubMed
Marzocca, A J; Cerveny, S; Salgueiro, W; Somoza, A; Gonzalez, L
2002-02-01
An experimental investigation was performed to study the effect on the free volume of the advance of the cross-linking reaction in a copolymer of styrene butadiene rubber by sulfur vulcanization. The dynamic modulus and loss tangent were evaluated over samples cured for different times at 433 K by dynamic mechanical tests over a range of frequencies between 5 and 80 Hz at temperatures between 200 and 300 K. Using the William-Landel-Ferry relationship, master curves were obtained at a reference temperature of 298 K and the coefficients c(0)(1) and c(0)(2) were evaluated. From these parameters the dependence of the free volume on the cure time is obtained. Positron annihilation lifetime spectroscopy was also used to estimate the size and number density of free volume sites in the material. The spectra were analyzed in terms of continuous distributions of free volume size. The results suggest an increase of the lower free volume size when cross linking takes place. Both techniques give similar results for the dependence of free volume on the time of cure of the polymer.
12. Positron annihilation induced Auger electron spectroscopy
NASA Technical Reports Server (NTRS)
Weiss, Alex; Koymen, A. R.; Mehl, David; Jensen, K. O.; Lei, Chun; Lee, K. H.
1990-01-01
Recently, Weiss et al. have demonstrated that it is possible to excite Auger transitions by annihilating core electrons using a low energy (less than 30eV) beam of positrons. This mechanism makes possible a new electron spectroscopy, Positron annihilation induced Auger Electron Spectroscopy (PAES). The probability of exciting an Auger transition is proportional to the overlap of the positron wavefunction with atomic core levels. Since the Auger electron energy provides a signature of the atomic species making the transition, PAES makes it possible to determine the overlap of the positron wavefunction with a particular element. PAES may therefore provide a means of detecting positron-atom complexes. Measurements of PAES intensities from clean and adsorbate covered Cu surfaces are presented which indicate that approx. 5 percent of positrons injected into CU at 25eV produce core annihilations that result in Auger transitions.
13. Positron Annihilation Spectroscopy Study of Barnett Shale Core
Ameena, Fnu; Alsleben, Helge; Quarles, Carroll A.
14. Positron Annihilation in the Bipositronium Ps2
SciTech Connect
Bailey, David H.; Frolov, Alexei M.
2005-07-01
The electron-positron-pair annihilation in the bipositronium PS2 is considered. In particular, the two-, three-, one- and zero-photon annihilation rates are determined to high accuracy. The corresponding analytical expressions are also presented. Also, a large number of bound state properties have been determined for this system.
15. Nondestructive examination using neutron activated positron annihilation
DOEpatents
Akers, Douglas W.; Denison, Arthur B.
2001-01-01
A method is provided for performing nondestructive examination of a metal specimen using neutron activated positron annihilation wherein the positron emitter source is formed within the metal specimen. The method permits in situ nondestructive examination and has the advantage of being capable of performing bulk analysis to determine embrittlement, fatigue and dislocation within a metal specimen.
16. Characterization of a sucrose/starch matrix through positron annihilation lifetime spectroscopy: unravelling the decomposition and glass transition processes.
PubMed
Sharma, Sandeep Kumar; Roudaut, Gaëlle; Fabing, Isabelle; Duplâtre, Gilles
2010-11-14
The triplet state of positronium, o-Ps, is used as a probe to characterize a starch-20% w/w sucrose matrix as a function of temperature (T). A two-step decomposition (of sucrose, and then starch) starts at 440 K as shown by a decrease in the o-Ps intensity (I(3)) and lifetime (τ(3)), the latter also disclosing the occurrence of a glass transition. Upon sucrose decomposition, the matrix acquires properties (reduced size and density of nanoholes) that are different from those of pure starch. A model is successfully established, describing the variations of both I(3) and τ(3) with T and yields a glass transition temperature, T(g) = (446 ± 2) K, in spite of the concomitant sucrose decomposition. Unexpectedly, the starch volume fraction (as probed through thermal gravimetry) decreases with T at a higher rate than the free volume fraction (as probed through PALS).
17. Positron annihilation in solid and liquid Ni
SciTech Connect
Fluss, M.J.; Smedskjaer, L.C.; Chakraborty, B.; Chason, M.K.
1982-03-01
New techniques have been developed for the study of metals via positron annihilation which provide for the in-situ melting of the samples and subsequent measurements via Doppler broadening of positron-annihilation radiation. Here we report these metods currently in use at our laboratory; ion implantation of /sup 58/Co and the use of Al/sub 2/O/sub 3/ crucibles for in-situ melting followed by the decomposition of the Doppler-broadened spectrum into a parabolic and a Gaussian component. Our earliest results obtained for pure Ni in the polycrystalline solid and in the liquid state are compared. An interesting similarity is reported for the distributions of the high-momentum (Gaussian) component for positrons annihilating in vacancies at high temperatures and those annihilating in liquid Ni.
18. Defects in metals. [Positron annihilation spectroscopy
SciTech Connect
Siegel, R.W.
1982-06-01
The application of positron annihilation spectroscopy (PAS) to the study of defects in metals has led to increased knowledge on lattice-defect properties during the past decade in two areas: the determination of atomic defect properties, particularly those of monovacancies, and the monitoring and characterization of vacancy-like microstructure development during post-irradiation and post-quench annealing. The study of defects in metals by PAS is reviewed within the context of the other available techniques for defect studies. The strengths and weaknesses of PAS as a method for the characterization of defect microstructures are considered. The additional possibilities for using the positron as a localized probe of the atomic and electronic structures of atomic defects are discussed, based upon theoretical calculations of the annihilation characteristics of defect-trapped positrons and experimental observations. Finally, the present status and future potential of PAS as a tool for the study of defects in metals is considered. 71 references, 9 figures.
19. Positron beam lifetime spectroscopy at Lawrence Livermore National Laboratory
SciTech Connect
Howell, R.H.; Cowan, T.E.; Hartley, J.H.; Stern, P.A. |
1996-10-01
Defect analysis is needed for samples ranging in thickness from thin films to large engineering parts. We are meeting that need with two positron beam lifetime spectrometers: on on a 3 MeV electrostatic accelerator and the second on our high current linac beam. The high energy beam spectrometer performs positron lifetime analysis on thick samples which can be encapsulated for containment or for in situ measurements in controlled environments. At our high current beam, we are developing a low energy, microscopically focused, pulsed positron beam to enable positron annihilation lifetime spectroscopy for defect specific, 3-D maps with sub-micron location resolution. The data from these instruments with the aid of first principles calculations of defect specific positron lifetimes.
20. Role of vibrational dynamics in resonant positron annihilation on molecules.
PubMed
Jones, A C L; Danielson, J R; Natisin, M R; Surko, C M
2013-05-31
Vibrational Feshbach resonances are dominant features of positron annihilation for incident positron energies in the range of the molecular vibrations. Studies in relatively small molecules are described that elucidate the role of intramolecular vibrational energy redistribution into near-resonant multimode states, and the subsequent coupling of these modes to the positron continuum, in suppressing or enhancing these resonances. The implications for annihilation in other molecular species, and the necessary ingredients of a more complete theory of resonant positron annihilation, are discussed.
1. Apparatus for photon activation positron annihilation analysis
DOEpatents
Akers, Douglas W.
2007-06-12
Non-destructive testing apparatus according to one embodiment of the invention comprises a photon source. The photon source produces photons having predetermined energies and directs the photons toward a specimen being tested. The photons from the photon source result in the creation of positrons within the specimen being tested. A detector positioned adjacent the specimen being tested detects gamma rays produced by annihilation of positrons with electrons. A data processing system operatively associated with the detector produces output data indicative of a lattice characteristic of the specimen being tested.
2. Application of positron annihilation in materials science
SciTech Connect
Siegel, R.W.; Fluss, M.J.; Smedskjaer, L.C.
1984-05-01
Owing to the ability of the positron to annihilate from a variety of defect-trapped states, positron annihilation spectroscopy (PAS) has been applied increasingly to the characterization and study of defects in materials in recent years. In metals particularly, it has been demonstrated that PAS can yield defect-specific information which, by itself or in conjunction with more traditional experimental techniques, has already made a significant impact upon the determination of atomic-defect properties and the monitoring and characterization of vacancy-like microstructure development, as occurs during post-irradiation annealing. The applications of PAS are now actively expanding to the study of more complex defect-related phenomena in irradiated or deformed metals and alloys, phase transformations and structural disorder, surfaces and near-surface defect characterization. A number of these applications in materials science are reviewed and discussed with respect to profitable future directions.
3. Positron scattering and annihilation from hydrogenlike ions
SciTech Connect
Novikov, S.A.; Bromley, M.W.J.; Mitroy, J.
2004-05-01
The Kohn variational method is used with a configuration-interaction-type wave function to determine the J=0 and J=1 phase shifts and annihilation parameter Z{sub eff} for positron-hydrogenic ion scattering. The phase shifts are within 1-2% of the best previous calculations. The values of Z{sub eff} are small and do not exceed unity for any of the momenta considered. At thermal energies Z{sub eff} is minute with a value of order 10{sup -50} occurring for He{sup +} at k=0.05a{sub 0}{sup -1}. In addition to the variational calculations, analytic expressions for the phase shift and annihilation parameters within the Coulomb wave Born approximation are derived and used to help elucidate the dynamics of positron collisions with positive ions.
4. Positron annihilation study of P implanted Si
SciTech Connect
Asoka-Kumar, P.; Au, H.L.; Lynn, K.G. ); Sferlazzo, P. . SED Division)
1992-01-01
High-energy ion implantation (above 200 keV) is now commonly used in a variety of VLSI processes. The high energy required for these implants is often achieved by implanting multiply charged ions, which inevitably brings in the problem of low-energy ion contamination. The low-energy contamination is difficult to diagnose and detect. Positron annihilation spectroscopy is used to examine the defect distributions in these high energy implants with varying degrees of contamination.
5. Positron annihilation study of P implanted Si
SciTech Connect
Asoka-Kumar, P.; Au, H.L.; Lynn, K.G.; Sferlazzo, P.
1992-12-01
High-energy ion implantation (above 200 keV) is now commonly used in a variety of VLSI processes. The high energy required for these implants is often achieved by implanting multiply charged ions, which inevitably brings in the problem of low-energy ion contamination. The low-energy contamination is difficult to diagnose and detect. Positron annihilation spectroscopy is used to examine the defect distributions in these high energy implants with varying degrees of contamination.
6. On the method of positron lifetime measurement
NASA Technical Reports Server (NTRS)
Nishiyama, F.; Shizuma, K.; Nasai, H.; Nishi, M.
1983-01-01
A fast-slow coincidence system was constructed for the measurement of positron lifetimes in material. The time resolution of this system was 270 ps for the (60)Co gamma rays. Positron lifetime spectra for 14 kinds of alkali halides were measured with this system. Two lifetime components and their intensities were derived from analyses of the lifetime spectra.
7. Correlation of Gas Permeability in a Metal-Organic Framework MIL-101(Cr)-Polysulfone Mixed-Matrix Membrane with Free Volume Measurements by Positron Annihilation Lifetime Spectroscopy (PALS).
PubMed
Jeazet, Harold B Tanh; Koschine, Tönjes; Staudt, Claudia; Raetzke, Klaus; Janiak, Christoph
2013-10-25
Hydrothermally stable particles of the metal-organic framework MIL-101(Cr) were incorporated into a polysulfone (PSF) matrix to produce mixed-matrix or composite membranes with excellent dispersion of MIL-101 particles and good adhesion within the polymer matrix. Pure gas (O2, N2, CO2 and CH4) permeation tests showed a significant increase of gas permeabilities of the mixed-matrix membranes without any loss in selectivity. Positron annihilation lifetime spectroscopy (PALS) indicated that the increased gas permeability is due to the free volume in the PSF polymer and the added large free volume inside the MIL-101 particles. The trend of the gas transport properties of the composite membranes could be reproduced by a Maxwell model.
8. Correlation of Gas Permeability in a Metal-Organic Framework MIL-101(Cr)–Polysulfone Mixed-Matrix Membrane with Free Volume Measurements by Positron Annihilation Lifetime Spectroscopy (PALS)
PubMed Central
Jeazet, Harold B. Tanh; Koschine, Tönjes; Staudt, Claudia; Raetzke, Klaus; Janiak, Christoph
2013-01-01
Hydrothermally stable particles of the metal-organic framework MIL-101(Cr) were incorporated into a polysulfone (PSF) matrix to produce mixed-matrix or composite membranes with excellent dispersion of MIL-101 particles and good adhesion within the polymer matrix. Pure gas (O2, N2, CO2 and CH4) permeation tests showed a significant increase of gas permeabilities of the mixed-matrix membranes without any loss in selectivity. Positron annihilation lifetime spectroscopy (PALS) indicated that the increased gas permeability is due to the free volume in the PSF polymer and the added large free volume inside the MIL-101 particles. The trend of the gas transport properties of the composite membranes could be reproduced by a Maxwell model. PMID:24957061
9. Surfaces of colloidal PbSe nanocrystals probed by thin-film positron annihilation spectroscopy
SciTech Connect
Chai, L.; Schut, H.; Schaarenburg, L. C. van; Eijt, S. W. H.; Al-Sawai, W.; Barbiellini, B.; Bansil, A.; Gao, Y.; Houtepen, A. J.; Mijnarends, P. E.; Huis, M. A. van; Ravelli, L.; Egger, W.; Kaprzyk, S.
2013-08-01
Positron annihilation lifetime spectroscopy and positron-electron momentum density (PEMD) studies on multilayers of PbSe nanocrystals (NCs), supported by transmission electron microscopy, show that positrons are strongly trapped at NC surfaces, where they provide insight into the surface composition and electronic structure of PbSe NCs. Our analysis indicates abundant annihilation of positrons with Se electrons at the NC surfaces and with O electrons of the oleic ligands bound to Pb ad-atoms at the NC surfaces, which demonstrates that positrons can be used as a sensitive probe to investigate the surface physics and chemistry of nanocrystals inside multilayers. Ab initio electronic structure calculations provide detailed insight in the valence and semi-core electron contributions to the positron-electron momentum density of PbSe. Both lifetime and PEMD are found to correlate with changes in the particle morphology characteristic of partial ligand removal.
10. Evaluation of the reactor pressure vessel steels by positron annihilation
Slugeň, V.; Hein, H.; Sojak, S.; Simeg Veterníková, J.; Petriska, M.; Sabelová, V.; Pavúk, M.; Hinca, R.; Stacho, M.
2013-11-01
This paper presents a comparison of commercially used German and Russian reactor pressure vessel steels from the positron annihilation spectroscopy (PAS) point of view, having in mind knowledge obtained also from other techniques from the last decades. The second generation of Russian RPV steels seems to be fully comparable with German steels and their quality allows prolongation of NPP operating lifetime over projected 40 years. The embrittlement of CrMoV steels is relatively low due to effect of higher temperature which implies partial in situ annealing of primary microstructural point defects and therefore delays the degradation processes caused by neutron irradiation.
11. Pore Topology Effects in Positron Annihilation Spectroscopy of Zeolites.
PubMed
Zubiaga, Asier; Warringham, Robbie; Mitchell, Sharon; Gerchow, Lars; Cooke, David; Crivelli, Paolo; Pérez-Ramírez, Javier
2016-12-14
Positron annihilation spectroscopy (PAS) is a powerful method to study the size and connectivity of pores in zeolites. The lifetime of positronium within the host material is commonly described by the Tao-Eldrup model. However, one of its largest limitations arises from the simple geometries considered for the shape of the pores, which cannot describe accurately the complex topologies in zeolites. Here, an atomic model that combines the Tao potential with the crystallographic structure is introduced to calculate the distribution and lifetime of Ps intrinsic to a given framework. A parametrization of the model is undertaken for a set of widely applied zeolite framework types (*BEA, FAU, FER, MFI, MOR, UTL), before extending the model to all known structures. The results are compared to structural and topological descriptors, and to the Tao-Eldrup model adapted for zeolites, demonstrating the intricate dependence of the lifetime on the pore architecture.
12. Effect of magnetic field on positron lifetimes of Fe, Co and Ni.
PubMed
Li, H; Maekawa, M; Kawasuso, A; Tanimura, N
2015-06-24
Positron lifetime spectra of Fe, Co and Ni were measured under magnetic field using a (22)Na source. Very small but distinguishable difference of positron lifetime upon magnetic field reversal was observed suggesting the existence of two bulk lifetimes associated with majority and minority spin electrons. Using two spin-dependent Fe bulk lifetimes, the difference Doppler broadening of annihilation radiation spectra between majority and minority spin electrons were also examined. Agreement between experiment and theory indicates that spin-polarized positron annihilation spectroscopy may have potential in investigation of spin-aligned electron momentum distribution.
13. Slow positron beam generator for lifetime studies
NASA Technical Reports Server (NTRS)
Singh, Jag J. (Inventor); Eftekhari, Abe (Inventor); St.clair, Terry L. (Inventor)
1991-01-01
A slow positron beam generator uses a conductive source residing between two test films. Moderator pieces are placed next to the test film on the opposite side of the conductive source. A voltage potential is applied between the moderator pieces and the conductive source. Incident energetic positrons: (1) are emitted from the conductive source; (2) are passed through test film; and (3) isotropically strike moderator pieces before diffusing out of the moderator pieces as slow positrons, respectively. The slow positrons diffusing out of moderator pieces are attracted to the conductive source which is held at an appropriate potential below the moderator pieces. The slow positrons have to pass through the test films before reaching the conductive source. A voltage is adjusted so that the potential difference between the moderator pieces and the conductive source forces the positrons to stop in the test films. Measurable annihilation radiation is emitted from the test film when positrons annihilate (combine) with electrons in the test film.
14. Materials analysis using positron beam lifetime spectroscopy
SciTech Connect
Hartley, J.; Howell, R. H., Asoka-Kumar, P.; Sterne, P.; Stoeffl, W.
1998-11-12
We are using a defect analysis capabilities based on two positron beam lifetime spectrometers: the first is based on a 3 MeV electrostatic accelerator and the second on our high current linac beam. The high energy beam lifetime spectrometer is routinely used to perform positron lifetime analysis with a 3 MeV positron beam on thick sample specimens. It is being used for bulk sample analysis and analysis of samples encapsulated in controlled environments for in situ measurements. A second, low energy, microscopically focused, pulsed positron beam for defect analysis by positron lifetime spectroscopy is under development at the LLNL high current positron source. This beam will enable defect-specific, 3-dimensional maps of defect concentration with sub-micron location resolution. When coupled with first principles calculations of defect specific positron lifetimes it will enable new levels of defect concentration mapping and defect identification.
15. Positron-annihilation study of radiation defects in sodium azide
SciTech Connect
Etin, G.I.; Ryabykh, S.M.
1987-07-01
Annihilation-photon angular correlation has been used to examine radiation defects in sodium azide capable of trapping positrons. The calculated and measured characteristics have been determined for various defects, including micropores filled by radiolytic nitrogen. The positron annihilation rates have been determined for the regions around radiation defects.
16. Positron Annihilation Spectroscopy of High Performance Polymer Films under CO2 Pressure
SciTech Connect
C.A. Quarles; John R. Klaehn; Eric S. Peterson; Jagoda M. Urban-Klaehn
2010-08-01
Positron annihilation Lifetime and Doppler broadening measurements are reported for six polymer films as a function of carbon dioxide absolute pressure ranging from 0 to 45 psi. Since the polymer films were thin and did not absorb all positrons, corrections were made in the lifetime analysis for the absorption of positrons in the positron source and sample holder using the Monte Carlo transport code MCNP. Different polymers are found to behave differently. Some polymers studied form positronium and some, such as the polyimide structures, do not. For those samples that form positronium an interpretation in terms of free volume is possible; for those that don’t form positronium, further work is needed to determine how best to describe the behavior in terms of the bulk positron annihilation parameters. Some polymers exhibit changes in positron lifetime and intensity under CO2 pressure which may be described by the Henry or Langmuir sorption models, while the positron response of other polymers is rather insensitive to the CO2 pressure. The results demonstrate the usefulness of positron annihilation spectroscopy in investigating the sorption of CO2 into various polymers at pressures up to about 3 atm.
17. Positron Annihilation Spectroscopy Of High Performance Polymer Films Under CO{sub 2} Pressure
SciTech Connect
Quarles, C. A.; Klaehn, John R.; Peterson, Eric S.; Urban-Klaehn, Jagoda M.
2011-06-01
Positron annihilation Lifetime and Doppler broadening measurements are reported for six polymer films as a function of carbon dioxide (CO{sub 2}) absolute pressure ranging from 0 to 45 psi. Since the polymer films were thin and did not absorb all positrons, corrections were made in the lifetime analysis for the absorption of positrons in the positron source and sample holder using the Monte Carlo transport code MCNP. The studied polymers are found to behave differently from each other. Some polymers form positronium and others, such as the polyimide structures, do not. For those polymers that form positronium an interpretation in terms of free volume is possible; for those that don't form positronium, further work is needed to determine how best to describe the behavior in terms of the bulk positron annihilation parameters. A few of the studied polymers exhibit changes in positron lifetime and intensity under CO{sub 2} pressure which may be described by the Henry or Langmuir sorption models, while the positron response of other polymers is rather insensitive to the CO{sub 2} pressure. The results demonstrate the usefulness of positron annihilation spectroscopy in investigating the sorption of CO{sub 2} into various polymers at pressures up to about 3 atm (45psi).
18. Sensitivity of positron annihilation to hydrogen in Zr
SciTech Connect
Hood, G.M.; Schultz, R.J.
1982-01-01
Positron annihilation spectroscopy has been applied to the quantitative determination of hydrogen in zirconium. The sensitivity of the positron annihilation was noted to be influenced not only by the presence of hydrogen but also by the heat treatment of the hydrided samples. The positron is attracted to the relatively negative, or ion-core-deficient regions of the metal, F regions commonly associated with vacancies, voids and dislocations. It was found to be very difficult to gauge the relative effects which hydrides and dislocations might have on the positron annihilation in zirconium. (BLM)
19. Positron annihilation investigations on poly(methyl methacrylate)
Mohamed, Hamdy F. M.; Abd-Elsadek, Gomaa G.
2000-06-01
Positron lifetime and Doppler broadened annihilation radiation were measured for seven different samples of poly(methyl methacrylate) at room temperature in vacuum. The polymerisation of methyl methacrylate was carried out as a bulk polymerisation in the presence of benzoyl peroxide as an initiator. The effect of the amount of the initiator on the viscosity-average molecular weight was studied. It was found that the viscosity-average molecular weight decreased with increasing amount of the initiator. The average lifetime and intensity of ortho-positronium ( o-Ps) increased with increasing viscosity-average molecular weight up to 6.85 × 10 4 and remained constant after that. The S-parameter showed a similar behaviour as that of the o-Ps intensity.
20. Resolvability of defect ensembles with positron annihilation studies
SciTech Connect
Fluss, M.J.; Howell, R.H.; Rosenberg, I.J.; Meyer, P.
1984-11-12
Recent advances in the use of positron annihilation to study defect ensembles in and on the surfaces of metals, are pointing the way towards studies where particular positron-electron annihilation modes may be identified and studied in the presence of one another. Although a great deal is understood about the annihilation of positrons in ostensibly defect-free metals, much less is understood when the positron annihilates in complex defect systems such as liquid metals, amorphous solids, or at or near the vacuum-solid interface. In this paper the results of three experiments, all of which demonstrate means by which we can resolve various poistron annihilation channels from one another, are discussed.
1. Positron-annihilation spectroscopy of vacancy defects in aluminum
SciTech Connect
Chakraborty, B.; Berko, S.; Fluss, M.J.; Hoffmann, K.; Lippel, P.; Siegel, R.W.
1982-06-01
Positron-annihilation characteristics in a monovacancy and a divacancy in aluminium have been calculated self-consistently using a local density functional formalism, into which the many-body enhancement effects have been incorporated. Results for the theoretical two-dimensional angular correlation of annihilation radiation spectra are compared to experimental results obtained from an aluminum single crystal at 20/sup 0/C, where positrons annihilate from a Bloch-state, and at higher temperatures, 500/sup 0/C and 630/sup 0/C, where they annihilate primarily from vacancy-trapped states.
2. Resonances and Bound States in Positron Annihilation on Molecules
Surko, C. M.
2007-10-01
Positron annihilation is important in such diverse areas as study of metabolic processes in the human brain and the characterization of materials. Annihilation on molecules has been a subject of keen interest for decades. In particular, annihilation rates can be orders of magnitude greater than those expected for simple collisions. Recent results put our understanding of many aspects of this long-standing problem on a firm footing. We now understand that the annihilation proceeds by vibrational Feshbach resonances (VFR). A prerequisite for the existence of these VFR is that the positron binds to the target. The annihilation energy spectra provide the best measures to date of positron binding energies. Predictions of a new theory of VFR-enhanced annihilation in small molecules (methyl halides) [1] show excellent, quantitative agreement with experiment. New data and analyses for larger molecules (e.g., hydrocarbons with more than two carbon atoms) show that annihilation rates depend strongly on the number of vibrational degrees of freedom but, surprisingly, only weakly on positron binding energy. This places important constraints on theories of annihilation in these molecules. Results for second bound (i.e., positronically excited) states and overtone and combination-mode VFR, as well as outstanding questions, will also be discussed. This work is done in collaboration with Jason Young. [1] G. F. Gribakin and C. M. R. Lee, Phys. Rev. Lett. 97, 193201 (2006).
3. Iodine-doped polyvinylalcohol using positron annihilation spectroscopy
Lobo, Blaise; Ranganath, M. R.; Chandran, T. S. G. Ravi; Venugopal Rao, G.; Ravindrachary, V.; Gopal, S.
1999-06-01
Iodine-doped polyvinylalcohol, doped up to 52 wt %, was studied using positron annihilation lifetime technique and Doppler broadening of annihilation radiation. Three component, free fit analysis was used for the lifetime spectra. It is found that I3 drops sharply on initial iodine doping, whereas decrease in τ3 is small, indicating inhibition of positronium formation by the dopant. The S parameter, on iodine doping, initially shows a drastic increase due to the decrease in crystallinity of the doped sample. Differential scanning calorimetry (DSC) and x-ray diffraction curves confirm that doping results in decreased crystallinity of the sample. τ3 increases beyond 23 wt % doping level due to structural changes induced by formation of polyiodide complexes, which is confirmed by UV-Vis spectra, for moderately and highly doped samples. The drop in τ3 at higher levels of doping (>44 wt %) suggests chemical quenching of positronium, probably due to iodine aggregation. DSC confirms formation of iodine aggregates, as revealed by a large endotherm at 185 °C, for doping levels beyond 47 wt %.
4. Positron annihilation study on free volume of amino acid modified, starch-grafted acrylamide copolymer
Mahmoud, K. R.; Al-Sigeny, S.; Sharshar, T.; El-Hamshary, H.
2006-05-01
5. Positron annihilation in the near surface of room temperature ionic liquids
Hirade, T.; O’Rourke, B. E.; Kobayashi, Y.
2017-01-01
Positronium (Ps; a bound state of an electron and a positron) formation in insulating materials is explained by the spur reaction model. According to the model, electron and/or positron mobility affects the yield of Ps formation. A vertical slow positron beam was used to investigate the surface of a room temperature ionic liquid, N,N,N-trimethyl-N-propylammonium bis(trifluoromethanesulfonyl)imide (TMPA-TFSI). Measurement of positron lifetimes indicated a higher Ps formation probability in near surface of TMPA-TFSI than in the bulk. This result suggests that the electron (and positron) mobility in the near surface may be larger than that in the bulk. Moreover, the longest annihilation lifetime of triplet Ps (ortho-Ps) in the near surface was found to be shorter than that measured in the bulk liquid. Ortho-Ps lifetimes in liquids are well correlated with the surface tension with a shorter lifetime corresponding to higher surface tension. The higher Ps formation yield and the shorter ortho-Ps annihilation lifetime were probably caused by the layered structure in near surface of TMPA-TFSI. A vertical slow positron beam is a strong tool to investigate the surface of room temperature ionic liquids.
6. Positron annihilation characteristics in mesostructural silica films with various porosities
SciTech Connect
Xiong, Bangyun; Mao, Wenfeng; Tang, Xiuqin; He, Chunqing
2014-03-07
Porous silica films with various porosities were prepared via a sol-gel method using a nonionic amphiphilic triblock copolymer F127 as the structure-directing agent. Doppler broadening of positron annihilation radiation (DBAR) spectra were collected for the prepared films using a variable energy slow positron beam. Different linear relationships between positron annihilation line shape parameters S and W are found for the as-deposited films and calcined ones, indicative of the decomposition of the copolymer porogen in the as-deposited films upon calcination. This also reveals the variation of positron annihilation sites as a function of F127 loading or porosity. Strong correlations between positronium 3γ annihilation fraction, S parameter and porosity of the mesoporous silica films with isolated pores are obtained, which may provide a complementary method to determine closed porosities of mesoporous silica films by DBAR.
7. Positron annihilation characteristics in mesostructural silica films with various porosities
Xiong, Bangyun; Mao, Wenfeng; Tang, Xiuqin; He, Chunqing
2014-03-01
Porous silica films with various porosities were prepared via a sol-gel method using a nonionic amphiphilic triblock copolymer F127 as the structure-directing agent. Doppler broadening of positron annihilation radiation (DBAR) spectra were collected for the prepared films using a variable energy slow positron beam. Different linear relationships between positron annihilation line shape parameters S and W are found for the as-deposited films and calcined ones, indicative of the decomposition of the copolymer porogen in the as-deposited films upon calcination. This also reveals the variation of positron annihilation sites as a function of F127 loading or porosity. Strong correlations between positronium 3γ annihilation fraction, S parameter and porosity of the mesoporous silica films with isolated pores are obtained, which may provide a complementary method to determine closed porosities of mesoporous silica films by DBAR.
8. Positron annihilation studies of moisture in graphite-reinforced composites
NASA Technical Reports Server (NTRS)
Singh, J. J.; Holt, W. H.; Mock, W., Jr.; Buckingham, R. D.
1980-01-01
The positron lifetime technique of monitoring absorbed moisture is applied to several composites, including graphite/polymides which are candidates for high-temperature (over 260 C) applications. The experimental setup is a conventional fast-slow coincidence system wherein the positron lifetime is measured with respect to a reference time determined by the detection of a nuclear gamma ray emitted simultaneously with the positron. From the experiments, a rate of change of positron mean lifetime per unit mass of water can be determined for each type of specimen. Positron lifetime spectra are presented for a graphite/polyimide composite and for a pure polyimide.
9. Moisture dependence of positron annihilation spectra in nylon-6
NASA Technical Reports Server (NTRS)
Singh, J. J.; St. Clair, T. L.; Holt, W. H.; Mock, W., Jr.
1984-01-01
Positron annihilation time spectra have been measured in nylon-6 samples as a function of their moisture content. The measured average long life component lifetime values are: 1722 + or - 47 ps (dry), 1676 + or - 40 ps (14.6 percent saturation value), 1719 + or - 26 ps (29.3 percent saturation value), 1720 + or - 35 ps (50 percent of saturation value), 1857 + or - 35 ps (78.1 percent saturation value), and 1936 + or - 57 ps (saturated). It appears that nylon-6 has a special affinity for water at low concentration levels where H2O molecules enter between the (C = O - H-N) chemical bonds between nylon molecular chains. As the water concentration increases beyond a critical level, nylon-6 specimens start trapping H2O molecules in other bond sites or potential wells. The trapped water increases the free volume in the test specimens and reduces Ps atom formation as well as its subsequent decay rate.
10. Positron annihilation studies of zirconia doped with metal cations of different valence
Prochazka, I.; Cizek, J.; Melikhova, O.; Konstantinova, T. E.; Danilenko, I. A.; Yashchishyn, I. A.; Anwand, W.; Brauer, G.
2013-06-01
New results obtained by applying positron annihilation spectroscopy to the investigation of zirconia-based nanomaterials doped with metal cations of different valence are reported. The slow-positron implantation spectroscopy combined with Doppler broadening measurements was employed to study the sintering of pressure-compacted nanopowders of tetragonal yttria-stabilised zirconia (t-YSZ) and t-YSZ with chromia additive. Positronium (Ps) formation in t-YSZ was proven by detecting 3γ-annihilations of ortho-Ps and was found to gradually decrease with increasing sintering temperature. A subsurface layer with enhanced 3γ-annihilations, compared to the deeper regions, could be identified. Addition of chromia was found to inhibit Ps formation. In addition, first results of positron lifetime measurements on nanopowders of zirconia phase-stabilised with MgO and CeO2 are presented.
11. Positron annihilation and magnetic properties studies of copper substituted nickel ferrite nanoparticles
Kargar, Z.; Asgarian, S. M.; Mozaffari, M.
2016-05-01
Single phase copper substituted nickel ferrite Ni1-xCuxFe2O4 (x = 0.0, 0.1, 0.3 and 0.5) nanoparticles were synthesized by the sol-gel method. TEM images of the samples confirm formation of nano-sized particles. The Rietveld refinement of the X-ray diffraction patterns showed that lattice constant increase with increase in copper content from 8.331 for x = 0.0 to 8.355 Å in x = 0.5. Cation distribution of samples has been determined by the occupancy factor, using Rietveld refinement. The positron lifetime spectra of the samples were convoluted into three lifetime components. The shortest lifetime is due to the positrons that do not get trapped by the vacancy defects. The second lifetime is ascribed to annihilation of positrons in tetrahedral (A) and octahedral (B) sites in spinel structure. It is seen that for x = 0.1 and 0.3 samples, positron trapped within vacancies in A sites, but for x = 0.0 and 0.5, the positrons trapped and annihilated within occupied B sites. The longest lifetime component attributed to annihilation of positrons in the free volume between nanoparticles. The obtained results from coincidence Doppler broadening spectroscopy (CDBS) confirmed the results of positron annihilation lifetime spectroscopy (PALS) and also showed that the vacancy clusters concentration for x = 0.3 is more than those in other samples. Average defect density in the samples, determined from mean lifetime of annihilated positrons reflects that the vacancy concentration for x = 0.3 is maximum. The magnetic measurements showed that the saturation magnetization for x = 0.3 is maximum that can be explained by Néel's theory. The coercivity in nanoparticles increased with increase in copper content. This increase is ascribed to the change in anisotropy constant because of increase of the average defect density due to the substitution of Cu2+ cations and magnetocrystalline anisotropy of Cu2+ cations. Curie temperature of the samples reduces with increase in copper content which
12. Irradiation damage from low-dose high-energy protons on mechanical properties and positron annihilation lifetimes of Fe-9Cr alloy
Xu, Q.; Fukumoto, K.; Ishi, Y.; Kuriyama, Y.; Uesugi, T.; Sato, K.; Mori, Y.; Yoshiie, T.
2016-01-01
Nuclear reactions in accelerator-driven systems (ADS) result in the generation of helium within the ADS materials. The amount of helium produced in this way is approximately one order of magnitude higher than that generated by nuclear fusion. As helium is well-known to induce degradation in the mechanical properties of metals, its effect on ADS materials is an important factor to assess. The results obtained in this study show that low-dose proton irradiation (11 MeV at 573 K to 9.0 × 10-4 dpa and 150 MeV at room temperature to 2.6 × 10-6 dpa) leads to a decrease in yield stress and ultimate tensile strength in a Fe-9Cr alloy. Moreover, interstitial helium and hydrogen atoms, as well as the annihilation of dislocation jogs, were identified as key factors that determine the observed softening of the alloy.
13. Positron lifetime spectrometer using a DC positron beam
DOEpatents
Xu, Jun; Moxom, Jeremy
2003-10-21
An entrance grid is positioned in the incident beam path of a DC beam positron lifetime spectrometer. The electrical potential difference between the sample and the entrance grid provides simultaneous acceleration of both the primary positrons and the secondary electrons. The result is a reduction in the time spread induced by the energy distribution of the secondary electrons. In addition, the sample, sample holder, entrance grid, and entrance face of the multichannel plate electron detector assembly are made parallel to each other, and are arranged at a tilt angle to the axis of the positron beam to effectively separate the path of the secondary electrons from the path of the incident positrons.
14. Photoluminescence and positron annihilation spectroscopic investigation on a H(+) irradiated ZnO single crystal.
PubMed
Sarkar, A; Chakrabarti, Mahuya; Sanyal, D; Bhowmick, D; Dechoudhury, S; Chakrabarti, A; Rakshit, Tamita; Ray, S K
2012-08-15
15. Positron Annihilation Studies In Polymer Nano-Composites
SciTech Connect
Chen, H. M.; Awad, Somia; Jean, Y. C.; Yang, J.; Lee, L. James
2011-06-01
Positron annihilation spectroscopy coupled with a variable mono-energy positron beam has been applied to study nanoscale polymeric nanocomposites. New information about multilayer depth profiles and structures, interfacial free-volume and open space properties have been obtained in polystyrene/carbon nano fiber composites. The S parameter in Doppler Broadening Energy Spectra combined slow positron beam is used to quantitatively represent the free volume, open spaces, and interactions in the interface between polystyrene matrix and carbon nanofibers.
16. Detecting positron-atom bound states through resonant annihilation.
PubMed
Dzuba, V A; Flambaum, V V; Gribakin, G F
2010-11-12
A method is proposed for detecting positron-atom bound states by observing enhanced positron annihilation due to electronic Feshbach resonances at electron-volt energies. The method is applicable to a range of open-shell transition-metal atoms which are likely to bind the positron: Fe, Co, Ni, Tc, Ru, Rh, Sn, Sb, Ta, W, Os, Ir, and Pt. Estimates of their binding energies are provided.
17. Positron annihilation spectroscopy investigation of vacancy defects in neutron-irradiated 3 C -SiC
Hu, Xunxiang; Koyanagi, Takaaki; Katoh, Yutai; Wirth, Brian D.
2017-03-01
Positron annihilation spectroscopy characterization results for neutron-irradiated 3 C -SiC are described here, with a specific focus on explaining the size and character of vacancy clusters as a complement to the current understanding of the neutron irradiation response of 3 C -SiC. Positron annihilation lifetime spectroscopy was used to capture the irradiation temperature and dose dependence of vacancy defects in 3 C -SiC following neutron irradiation from 0.01 to 31 dpa in the temperature range from 380°C to 790°C . The neutral and negatively charged vacancy clusters were identified and quantified. The results suggest that the vacancy defects that were measured by positron annihilation spectroscopy technique contribute very little to the transient swelling of SiC. In addition, coincidence Doppler broadening measurement was used to investigate the chemical identity surrounding the positron trapping sites. It was found that silicon vacancy-related defects dominate in the studied materials and the production of the antisite defect CSi may result in an increase in the probability of positron annihilation with silicon core electrons.
18. New insights into the nanostructure of innovative thin film solar cells gained by positron annihilation spectroscopy
Eijt, S. W. H.; Shi, W.; Mannheim, A.; Butterling, M.; Schut, H.; Egger, W.; Dickmann, M.; Hugenschmidt, C.; Shakeri, B.; Meulenberg, R. W.; Callewaert, V.; Saniz, R.; Partoens, B.; Barbiellini, B.; Bansil, A.; Melskens, J.; Zeman, M.; Smets, A. H. M.; Kulbak, M.; Hodes, G.; Cahen, D.; Brück, E.
2017-01-01
Recent studies showed that positron annihilation methods can provide key insights into the nanostructure and electronic structure of thin film solar cells. In this study, positron annihilation lifetime spectroscopy (PALS) is applied to investigate CdSe quantum dot (QD) light absorbing layers, providing evidence of positron trapping at the surfaces of the QDs. This enables one to monitor their surface composition and electronic structure. Further, 2D-Angular Correlation of Annihilation Radiation (2D-ACAR) is used to investigate the nanostructure of divacancies in photovoltaic-high-quality a-Si:H films. The collected momentum distributions were converted by Fourier transformation to the direct space representation of the electron-positron autocorrelation function. The evolution of the size of the divacancies as a function of hydrogen dilution during deposition of a-Si:H thin films was examined. Finally, we present a first positron Doppler Broadening of Annihilation Radiation (DBAR) study of the emerging class of highly efficient thin film solar cells based on perovskites.
19. Proposed parameter-free model for interpreting the measured positron annihilation spectra of materials using a generalized gradient approximation.
PubMed
Barbiellini, Bernardo; Kuriplach, Jan
2015-04-10
Positron annihilation spectroscopy is often used to analyze the local electronic structure of materials of technological interest. Reliable theoretical tools are crucial to interpret the measured spectra. Here, we propose a parameter-free gradient correction scheme for a local-density approximation obtained from high-quality quantum Monte Carlo data. The results of our calculations compare favorably with positron affinity and lifetime measurements, opening new avenues for highly precise and advanced positron characterization of materials.
20. Limiting factors of room-temperature nonradiative photoluminescence lifetime in polar and nonpolar GaN studied by time-resolved photoluminescence and slow positron annihilation techniques
Chichibu, S. F.; Uedono, A.; Onuma, T.; Sota, T.; Haskell, B. A.; DenBaars, S. P.; Speck, J. S.; Nakamura, S.
2005-01-01
Room-temperature nonradiative lifetime (τnr) of the near-band-edge excitonic photoluminescence (PL) peak in {0001} polar, (112¯0), (11¯00), and (001) nonpolar GaN was shown to increase with the decrease in density or size of Ga vacancies (VGa) and with the decrease in gross density of point defects including complexes, leading to the increase in the PL intensity. As the edge threading dislocation density decreased, density or size of VGa tended to decrease and τnr tended to increase. However, there existed remarkable exceptions. The results indicate that nonradiative recombination process is governed not by single point defects, but by certain defects introduced with the incorporation of VGa, such as VGa-defect complexes.
1. Positron annihilation behavior in several corrosion protective polymeric coatings
Leidheiser, Henry; Szeles, Csaba; Vértes, Attila
1987-04-01
Positron annihilation was studied in a vinyl ester and four epoxy coatings on steel. Measurements were made on coatings in equilibrium with air at approximately 50% relative humidity and on coatings immersed in liquid water for 24 h. Three spectral components were identified: a short-lived component associated with annihilation largely in the steel substrate; a medium-lived component associated with annihilation in small voids in the coating; and a long-lived component associated with annihilation of o-positronium in the polymer matrix and within large voids in the polymer and at the polymer/metal interface. An excellent correlation was observed between the effect of water exposure on the annihilation spectra and the protective properties of the coating in an aggressive H 2SO 4 environment. Other correlations between the annihilation spectra and the protective properties were also identified.
2. Effect of positron source irradiation on positronium annihilation in fine powdered alumina
Liu, Z. W.; Chen, Z. Q.
2016-09-01
3. Application of positron annihilation and Raman spectroscopies to the study of perovskite type materials
Grebennikov, D.; Ovchar, O.; Belous, A.; Mascher, P.
2010-12-01
Defect properties of perovskite type materials, Ba3B'Nb2O9 (where B'=Mg, Zn, or Co), with near-stoichiometric compositions were studied by positron annihilation and Raman spectroscopies. Theoretical simulations of stoichiometric perovskites revealed a dependence of the positron bulk lifetime on the degree of ordering. In Ba3MgNb2O9 (BMN) the positron bulk lifetime for a completely disordered structure is 195 ps versus 237 ps for a completely ordered one. The predicted bulk lifetimes for Ba3ZnNb2O9 (BZN) and Ba3CoNb2O9 (BCN), with Pm3¯m symmetries are 193 ps and 194 ps, respectively. It was found that deviation from stoichiometry results in the appearance of secondary Ba- and Nb-rich phases, which according to theoretical simulations have bulk lifetimes much longer than that of the host material. Positron lifetime spectroscopy was used to monitor changes in the concentration of these second phases. The difference between predicted defect lifetimes and the bulk values for the studied perovskites was less than 70 ps. This and the likely small concentrations made it impossible to discern the presence of point defects in the samples. Raman measurements demonstrated the presence of a particular mode that could be attributed to the formation of a 1:1 phase, the size of which is limited by requirements for charge compensation. The existence of an internal electric field between charged 1:1 nanoregions and the rest of material creates conditions for preferential positron annihilation that influence the obtained positron lifetime values. For BZN type materials it was found that the degree of 1:2 cation ordering decreases by increasing the sintering temperature to above 1400 °C.
4. Detection of Mg17Al12 precipitates in deformed thermal-aged AZ91 alloy by positron annihilation spectroscopy
Ortega, Y.; Del Río, J.
2004-02-01
Positron-annihilation lifetime measurements are used to study the influence of Mg17Al12 precipitates in mechanical properties of deformed magnesium alloys containing 9 wt% Al and 1wt% Zn. Deformations are performed at room temperature on untreated and thermal-aged samples, and the response of the positron lifetime to the deformation degree is studied. Measurements reveal that changes in the average positron lifetime are very small on both samples. The slight increase of positron lifetime in deformed samples, seems to be related with the unfavourable orientation of Mg17Al12 precipitates in the magnesium matrix to produce work hardening, as it has shown by other authors through TEM observations. Further isothermal annealing experiments, on samples that are previously deformed, illustrate almost a complete recovery of the positron lifetime on untreated samples at 375 K and on age-hardened samples at 433 K.
5. Optical and microstructural characterization of porous silicon using photoluminescence, SEM and positron annihilation spectroscopy
Cheung, C. K.; Nahid, F.; Cheng, C. C.; Beling, C. D.; Fung, S.; Ling, C. C.; Djurisic, A. B.; Pramanik, C.; Saha, H.; Sarkar, C. K.
2007-12-01
We have studied the dependence of porous silicon morphology and porosity on fabrication conditions. N-type (100) silicon wafers with resistivity of 2-5 Ω cm were electrochemically etched at various current densities and anodization times. Surface morphology and the thickness of the samples were examined by scanning electron microscopy (SEM). Detailed information of the porous silicon layer morphology with variation of preparation conditions was obtained by positron annihilation spectroscopy (PAS): the depth-defect profile and open pore interconnectivity on the sample surface has been studied using a slow positron beam. Coincidence Doppler broadening spectroscopy (CDBS) was used to study the chemical environment of the samples. The presence of silicon micropores with diameter varying from 1.37 to 1.51 nm was determined by positron lifetime spectroscopy (PALS). Visible luminescence from the samples was observed, which is considered to be a combination effect of quantum confinement and the effect of Si = O double bond formation near the SiO2/Si interface according to the results from photoluminescence (PL) and positron annihilation spectroscopy measurements. The work shows that the study of the positronium formed when a positron is implanted into the porous surface provides valuable information on the pore distribution and open pore interconnectivity, which suggests that positron annihilation spectroscopy is a useful tool in the porous silicon micropores' characterization.
6. Free Volume Structure of Acrylic-Type Dental Nanocomposites Tested with Annihilating Positrons.
PubMed
Shpotyuk, Olha; Ingram, Adam; Shpotyuk, Oleh
2016-12-01
Positron annihilation spectroscopy in lifetime measuring mode exploring conventional fast-fast coincidence ORTEC system is employed to characterize free volume structure of commercially available acrylic-type dental restorative composite Charisma® (Heraeus Kulzer GmbH, Germany). The measured lifetime spectra for uncured and light-cured composites are reconstructed from unconstrained x3-term fitting and semi-empirical model exploring x3-x2-coupling decomposition algorithm. The governing channel of positron annihilation in the composites studied is ascribed to mixed positron-Ps trapping, where Ps decaying in the third component is caused entirely by input from free-volume holes in polymer matrix, while the second component is defined by free positron trapping in interfacial free-volume holes between filler nanoparticles and surrounded polymer matrix. Microstructure scenario of the photopolymerization shrinkage includes cross-linking of structural chains in polymer matrix followed by conversion of bound positron-electron (positronium) traps in positron-trapping interfacial free-volume voids in a vicinity of agglomerated filler nanoparticles.
7. Free Volume Structure of Acrylic-Type Dental Nanocomposites Tested with Annihilating Positrons
Shpotyuk, Olha; Ingram, Adam; Shpotyuk, Oleh
2016-11-01
Positron annihilation spectroscopy in lifetime measuring mode exploring conventional fast-fast coincidence ORTEC system is employed to characterize free volume structure of commercially available acrylic-type dental restorative composite Charisma® (Heraeus Kulzer GmbH, Germany). The measured lifetime spectra for uncured and light-cured composites are reconstructed from unconstrained x3-term fitting and semi-empirical model exploring x3-x2-coupling decomposition algorithm. The governing channel of positron annihilation in the composites studied is ascribed to mixed positron-Ps trapping, where Ps decaying in the third component is caused entirely by input from free-volume holes in polymer matrix, while the second component is defined by free positron trapping in interfacial free-volume holes between filler nanoparticles and surrounded polymer matrix. Microstructure scenario of the photopolymerization shrinkage includes cross-linking of structural chains in polymer matrix followed by conversion of bound positron-electron (positronium) traps in positron-trapping interfacial free-volume voids in a vicinity of agglomerated filler nanoparticles.
8. Mechanical durability of polymeric coatings studied by positron annihilation spectroscopy: correlation between cyclic loading and free volumes
Chen, H.; Peng, Q.; Huang, Y. Y.; Zhang, R.; Mallon, P. E.; Zhang, J.; Li, Y.; Wu, Y.; Richardson, J. R.; Sandreczki, T. C.; Jean, Y. C.; Suzuki, R.; Ohdaira, T.
2002-06-01
9. Positron annihilation in TiBe/sub 2/
SciTech Connect
Manuel, A.A.; Hoffmann, L.; Singh, A.K.; Jarlborg, T.; Peter, M.; Smith, J.L.; Fisk, Z.; Pecora, L.M.; Ehrlich, A.C.
1988-01-01
We report positron annihilation measurements on TiBe/sub 2/. Calculations using LMTO band structure method are also presented. The good agreement with the experimental data leads to the conclusion that the unusual magnetic properties of this compound can be well explained in terms of its electronic structure. A reconstruction of the electron-positron momentum distribution from calculated and measured 2D-ACPAR is discussed. 10 refs., 3 figs.
10. Thermal Stability of MgyTi1-y Thin Films Investigated by Positron Annihilation Spectroscopy
Anastasopol, A.; Eijt, S. W. H.; Schut, H.; Mulder, F. M.; Plazaola, F.; Dam, B.
Mg-Ti compounds are attractive candidates as hydrogen storage materials for their fast sorption kinetics and high storage capacity. In this context, an investigation of their thermal stability is of great importance. The thermal stability of MgyTi1-y thin films was investigated using positron annihilation spectroscopy. Despite the positive enthalpy of mixing of Mg and Ti, positron Doppler Broadening of Annihilation Radiation (DBAR) depth profiling showed that Mg0.9Ti0.1 films are stable up to 300°C. However, for Mg0.7Ti0.3 films, segregation of Mg and Ti was observed at 300oC by the appearance of a clear Ti signature in the S-W diagrams and in the Doppler broadening depth profiles analyzed using VEPFIT. The thickness of the 250-300 nm thin films remained unchanged during the heating treatments. We further present ab-initio calculations of positron lifetimes of the corresponding metal and metal hydride phases for comparison to our previous positron annihilation lifetime spectroscopy (PALS) study.
11. Si nanocrystals and nanocrystal interfaces studied by positron annihilation
Kujala, J.; Slotte, J.; Tuomisto, F.; Hiller, D.; Zacharias, M.
2016-10-01
Si nanocrystals embedded in a SiO 2 matrix were studied with positron annihilation and photoluminescence spectroscopies. Analysis of the S- and W-parameters for the sample annealed at 800 °C reveals a positron trap at the interface between the amorphous nanodots and the surrounding matrix. Another trap state is observed in the 1150 °C heat treated samples where nanodots are in a crystalline form. Positrons are most likely trapped to defects related to dangling bonds at the surface of the nanocrystals. Passivation of the samples results on one hand in the decrease of the S-parameter implying a decrease in the open volume of the interface state and, on the other hand, in the strengthening of the positron annihilation signal from the interface. The intensity of the photoluminescence signal increases with the formation of the nanocrystals. Passivation of samples strengthens the photoluminescence signal, further indicating a successful deactivation of luminescence quenching at the nanocrystal surface. Strengthening of the positron annihilation signal and an increase in the photoluminescence intensity in passivated silicon nanocrystals suggests that the positron trap at the interface does not contribute to a significant extent to the exciton recombination in the nanocrystals.
12. Characterizing microstructural changes in ferritic steels by positron annihilation spectroscopy: Studies on modified 9Cr-1Mo steel
Hari Babu, S.; Rajkumar, K. V.; Hussain, S.; Amarendra, G.; Sundar, C. S.; Jayakumar, T.
2013-01-01
Applicability of positron annihilation spectroscopy in probing the microstructural changes in ferritic steels has been investigated with thermal treatment studies on modified 9Cr-1Mo steel, during 300-1273 K. Positron lifetime results are compared with those of ultrasonic velocity and hardness techniques with two initial microstructural conditions i.e., normalized and tempered condition as well as only normalized condition. In first case, positron lifetime is found to be sensitive to small changes in metal carbide precipitation which could not be probed by other two techniques. In later case, positron lifetime is found to be sensitive to defect annealing until 673 K and in distinguishing the growth and coarsening of metal carbide precipitation stages during 773-1073 K. The present study suggests that by combining positron lifetime, ultrasonic velocity and hardness measurements, it is possible to distinguish distinct microstructures occurring at different stages.
13. Positron annihilation spectroscopy study of materials for reactor vessels
Grafutin, V. I.; Prokop'ev, E. P.; Krsjak, V.; Burcl, R.; Hähner, P.; Zeman, A.; Ilyukhina, O. V.; Erak, D.; Mogilevskyi, M. A.; Myasischeva, G. G.; Funtikov, Yu. V.
2011-02-01
Steels used in the nuclear industry have been experimentally studied by positron annihilation spectroscopy. Analysis of the experimental results and their comparison with the existing data make it possible to reveal vacancy defects, in particular, those caused by neutron radiation, and to determine their size.
14. Study of radiation damage in ODS steels by positron annihilation spectroscopy
Bartošová, I.; Bouhaddane, A.; Dománková, M.; Slugeň, V.; Wall, D.; Selim, F. A.
2016-01-01
Microstructure of various oxide-dispersion-strengthened (ODS) steels with 15% chromium content was studied in term of vacancy defects presence and their accumulation after defined irradiation treatment, respectively. Studied materials originated from Kyoto University and studied via IAEA collaborative project. Samples were characterized “as received” by positron annihilation lifetime spectroscopy and their microstructure was examined by transmission electron microscopy as well. Samples were afterwards irradiated in Washington State University Nuclear Radiation Center via a strong gamma source (6TBq). Damage induced by gamma irradiation was evaluated by positron lifetime measurements in emphasis on defect accumulation in the materials. We have demonstrated strong defect production induced by gamma irradiation which results from positron measurement data.
15. Probing sub-nano level molecular packing and correlated positron annihilation characteristics of ionic cross-linked chitosan membranes using positron annihilation spectroscopy.
PubMed
Xia, Rui; Cao, Xingzhong; Gao, Meizhen; Zhang, Peng; Zeng, Minfeng; Wang, Baoyi; Wei, Long
2017-02-01
16. Positron annihilation studies of recrystallization in the subsurface zone induced by friction in magnesium—effect of the inhomogeneity on measured positron annihilation characteristics
Dryzek, Jerzy
2014-02-01
The discussion of the positron annihilation studies of crystal structure defects, like vacancies, dislocations, grain boundaries and the defect depth profile, is presented. The role of the positron implantation depth and positron diffusion in such studies has been considered in detail. For description of the measured annihilation characteristics the proposed theoretical models take into account both effects. The annealing studies of defects created in pure magnesium by compression or dry sliding-wear were used for demonstration of the discussed thesis. The positron lifetime measurements were applied for monitoring open volume defects behavior. It was demonstrated that annealing at the temperature of about 300 °C removes the defects created by compression. Application of the proposed model to description of the data obtained allows to determine the activation energy of the grain boundary mobility in pure magnesium equal to Q=0.56±0.18 eV. However, defects created by the dry sliding are not completely annealed up to the temperature of 500 °C. The defect depth profile induced by dry sliding evolves with the annealing temperature in such a way that at the worn surface concentration of defects gradually decreases but at the depth between 60 and 100 μm the generation of new defects takes place at temperature of 150 and 225 °C. Above 300 °C the defects still are extended up to the depth of about 80 μm.
17. Effect of metal ions on positron annihilation characteristics in metal ion containing epoxies
NASA Technical Reports Server (NTRS)
Singh, J. J.; St. Clair, A. K.; Stoakley, D. M.; Holt, W. H.; Mock, W., Jr.
1984-01-01
In the course of developing improved moisture-resistant epoxy resins, two different types of epoxy resins containing variable mole ratios of chromium ions per polymer repeat unit were developed. Positron annihilation characteristics have been investigated in these resins as a function of their metal ion content. In both cases, the presence of metal ions reduces the lifetime as well as the intensity of the long life component. The long life component intensity reduction is considerably more pronounced than the lifetime reduction. These results have been discussed in terms of increased unpaired electron density at Ps formation sites due to the presence of chromium ions in the matrix.
18. Positron Annihilation Studies in Search of Fine Precipitates in Fe-9Cr alloys
SciTech Connect
Babu, S. Hari; Rajaraman, R.; Govindaraj, R.; Amarendra, G.; Sundar, C. S.
2011-07-15
Positron annihilation lifetime studies were carried out on cold worked pure Fe and Fe-9Cr alloy subjected to isochronal annealing in the temperature range from 300 to 1323 K. The measured lifetimes of Fe-9Cr alloy showed three distinct annealing stages as compared to pure Fe viz., initial annealing of defects, a plateau between 623 K and 873 K and noticeable increase beyond 1123 K. The second annealing stage is likely due to the formation of chromium rich nanoclusters. Third annealing stage beyond 1123 K is attributed to highly defected martensitic phase formation during cooling from y-phase.
19. Positron annihilation study of vacancy-type defects in Al single crystal foils with the tweed structures across the surface
SciTech Connect
Kuznetsov, Pavel; Cizek, Jacub Hruska, Petr; Anwad, Wolfgang; Bordulev, Yuri; Lider, Andrei; Laptev, Roman; Mironov, Yuri
2015-10-27
The vacancy-type defects in the aluminum single crystal foils after a series of the cyclic tensions were studied using positron annihilation. Two components were identified in the positron lifetime spectra associated with the annihilation of free positrons and positrons trapped by dislocations. With increasing number of cycles the dislocation density firstly increases and reaches a maximum value at N = 10 000 cycles but then it gradually decreases and at N = 70 000 cycles falls down to the level typical for the virgin samples. The direct evidence on the formation of a two-phase system “defective near-surface layer/base Al crystal” in aluminum foils at cyclic tension was obtained using a positron beam with the variable energy.
20. Positron annihilation study of cavities in black Au films
Melikhova, O.; Čížek, J.; Hruška, P.; Vlček, M.; Procházka, I.; Anwand, W.; Novotný, M.; Bulíř, J.
2017-01-01
Defects in a black Au film were studied using variable energy positron annihilation spectroscopy. Black Au films exhibit porous morphology similar to cauliflower. This type of structure enhances the optical absorption due to a multiple reflections in the micro-cavities. A nanostructured black Au film was compared with conventional smooth Au films with high reflectivity. The black Au film exhibited a remarkably enhanced S-parameter in sub-surface region. This is caused by a narrow para-Positronium contribution to the annihilation peak.
1. A study of vacancy defects related to gray tracks in KTiOPO{sub 4} (KTP) using positron annihilation
SciTech Connect
Zhang, Yang; Li, Jing; Wang, Jiyang Jiang, Huaidong; Cao, Xingzhong; Yang, Jing
2014-12-15
For the first time to our knowledge, positron annihilation spectroscopy (PAS) was used to study vacancy defects in KTiOPO{sub 4} (KTP) single crystals. Positron annihilation lifetime spectroscopy combined with dielectric measurements identified the existence of oxygen vacancies and reflected the concentration of vacancy defects in three samples. The vacancy defects in KTP do not consist of monovacancies, but rather vacancy complexes. Doppler broadening indicates that the vacancy defects are distributed uniformly. A relationship is established where a crystal with a low oxygen vacancy concentration and a highly balanced stoichiometry has a higher resistance to gray track formation.
2. Annihilation of positrons trapped at the alkali-metal-covered transition-metal surface
SciTech Connect
Fazleev, N.G.; Fry, J.L.; Kuttler, K.H.; Koymen, A.R.; Weiss, A.H.
1995-08-15
Recent studies of the Cu(100) surface covered with submonolayers of Cs revealed that the normalized intensity of the positron-annihilation-induced Cu {ital M}{sub 2,3}{ital VV} Auger signal remains nearly constant at the clean Cu(100) surface value until the Cs coverage reaches approximately 0.7 physical monolayer, at which coverage the signal intensity drops precipitously. We present a microscopic analysis of this unusual behavior of the Cu {ital M}{sub 2,3}{ital VV} Auger signal based on a treatment of a positron as a single charged particle trapped in a correlation well in the proximity of the surface atoms. The image-potential-induced positron surface states are calculated using the corrugated-mirror model in a full three-dimensional geometry. These states are studied for the clean Cu(100) surface and for various ordered structures of the Cs adsorbate on the Cu(100) surface below and above the critical alkali-metal coverage of approximately 0.7 physical monolayer. Calculations show that whereas the positron surface state is localized in the region of the Cs/Cu(100) interface for Cs coverages below the critical alkali-metal coverage, at a Cs coverage corresponding to one physical monolayer the positron surface state is localized on the vacuum side of the Cs overlayer. The probabilities for a positron trapped in a surface state to annihilate with relevant Cu and Cs core-level electrons as well as the positron surface-state lifetimes are computed for various alkali-metal structures on the Cu(100) surface and compared with experimental positron-annihilation-induced Auger-electron-spectroscopy data. It is shown that a shift in localization of the positron surface state from the Cs/Cu(100) interface to the vacuum side of the alkali-metal overlayer results in a sharp decrease in the positron-annihilation probabilities with Cu 3{ital s} and 3{ital p} core-level electrons, in agreement with experiment.
3. Positron states and annihilation characteristics of surface-trapped positrons at the oxidized Cu(110) surface
Fazleev, N. G.; Olenga, Antoine; Weiss, A. H.
2013-03-01
The process by which oxide layers are formed on metal surfaces is still not well understood. In this work we present the results of theoretical studies of positron states and annihilation characteristics of surface-trapped positrons at the oxidized Cu(110) surface. An ab-initio investigation of stability and associated electronic properties of different adsorption phases of oxygen on Cu(110) has been performed on the basis of density functional theory and using DMOl3 code. The changes in the positron work function and the surface dipole moment when oxygen atoms occupy on-surface and sub-surface sites have been attributed to charge redistribution within the first two layers, buckling effects within each layer and interlayer expansion. The computed positron binding energy, positron surface state wave function, and annihilation probabilities of surface trapped positrons with relevant core electrons demonstrate their sensitivity to oxygen coverage, elemental content, atomic structure of the topmost layers of surfaces, and charge transfer effects. Theoretical results are compared with experimental data obtained from studies of oxidized transition metal surfaces using positron annihilation induced Auger electron spectroscopy. This work was supported in part by the National Science Foundation Grant DMR-0907679.
4. Positron annihilation spectroscopy of biological tissue in 11C irradiation.
PubMed
Sakurai, Hiroshi; Itoh, Fumitake; Hirano, Yoshiyuki; Nitta, Munetaka; Suzuki, Kosuke; Kato, Daisuke; Yoshida, Eiji; Nishikido, Fumihiko; Wakizaka, Hidekatsu; Kanai, Tatsuaki; Yamaya, Taiga
2014-11-21
Positron annihilation spectroscopy (PAS) spectra of biological tissue in 11C irradiation are reported and spatial resolution coefficient of positron emission tomography (PET) obtained from the PAS spectrum is discussed for 11C irradiation. A PAS spectrum of the biological tissue with water is the same as that of the water pool phantom in 11C irradiation. However, a PAS spectrum of the biological tissue with less water differs from that of the water pool phantom. The PET spatial resolution coefficient depends on the kind of biological tissue. However, the PET spatial resolution coefficient, 0.00243±0.00014, can be used as a common value of maximum limit.
5. Photon induced positron annihilation spectroscopy: A nondestructive method for assay of defects in large engineering materials
Pujari, P. K.; Sudarshan, K.; Tripathi, R.; Dutta, D.; Maheshwari, P.; Sharma, S. K.; Srivastava, D.; Krause-Rehberg, R.; Butterling, M.; Anwand, W.; Wagner, A.
2012-01-01
This paper describes a new methodology for volumetric assay of defects in large engineering materials nondestructively. It utilizes high energy photons produced by nuclear reaction to create positrons in situ whose fate is followed using conventional positron spectroscopic techniques. The photon induced positron annihilation (PIPA) spectroscopy system has been set-up using a Folded Tandem Ion Accelerator (FOTIA). Possibility of using prompt γ-rays produced in nuclear reactions 27Al( 1H,γ) 28Si and 19F( 1H,αγ) 16O has been examined. The reaction 19F( 1H,αγ) 16O is seen to provide higher photon flux (and positron yield) and measurements have been carried out in large samples of metals and polymers. We could establish good sensitivity of the technique as well as reproducibility in a number of measurements. This technique has been used to carry out defect studies in cold worked zircaloy-2 plates. The measured S-parameter, indicative of defect concentration, was seen to correlate well with the measured residual stress using X-ray technique. The results were validated by γ-induced positron annihilation lifetime measurements at ELBE LINAC based GiPS facility.
6. Characterization of vacancy defects in Cu(In,Ga)Se2 by positron annihilation spectroscopy
Elsharkawy, M. R. M.; Kanda, G. S.; Yakushev, M. V.; Abdel-Hady, E. E.; Keeble, D. J.
2016-12-01
The photovoltaic performance of Cu(In1-x,Gax)Se2 (CIGS) materials is commonly assumed to be degraded by the presence of vacancy-related defects. However, experimental identification of specific vacancy defects remains challenging. In this work we report positron lifetime measurements on CIGS crystals with x = 0, and x = 0.05, saturation trapping to two dominant vacancy defect types, in both types of crystal, is observed and found to be independent of temperature between 15-300 K. Atomic superposition method calculations of the positron lifetimes for a range of vacancy defects in CIS and CGS are reported. The calculated lifetimes support the assignment of the first experimental lifetime component to monovacancy or divacancy defects, and the second to trivacancies, or possibly the large In-Se divacancy. Further, the calculated positron parameters obtained here provide evidence that positron annihilation spectroscopy has the capability to identify specific vacancy-related defects in the Cu(In1-x,Gax)Se2 chalcogenides.
7. A modified positron lifetime spectrometer as method of non-destructive testing in materials
Chen, Z. Q.; Shi, J. J.; Jiang, J.; Liu, X. B.; Wang, R. S.; Wu, Y. C.
2015-02-01
This paper aims to develop a new non-destructive testing (NDT) method using positron annihilation spectroscopy, a powerful tool to detect vacancy-type defects and defect's chemical environment. A positron NDT system was designed and constructed by modifying the "sandwich" structure of sample-source-sample in the conventional positron lifetime spectrometer. The positron lifetime spectra of one single sample can be measured and analyzed by subtracting the contribution of a reference sample. The feasibility and reliability of the positron NDT system have been tested by analyzing nondestructively deformation damage caused by mechanical treatment in metals and steels. This system can be used for detecting defects and damage in thick or large-size samples without cutting off the sample materials, as well as for detecting two-dimensional distribution of defects.
8. Analysis of positron lifetime spectra in polymers
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Mall, Gerald H.; Sprinkle, Danny R.
1988-01-01
A new procedure for analyzing multicomponent positron lifetime spectra in polymers was developed. It requires initial estimates of the lifetimes and the intensities of various components, which are readily obtainable by a standard spectrum stripping process. These initial estimates, after convolution with the timing system resolution function, are then used as the inputs for a nonlinear least squares analysis to compute the estimates that conform to a global error minimization criterion. The convolution integral uses the full experimental resolution function, in contrast to the previous studies where analytical approximations of it were utilized. These concepts were incorporated into a generalized Computer Program for Analyzing Positron Lifetime Spectra (PAPLS) in polymers. Its validity was tested using several artificially generated data sets. These data sets were also analyzed using the widely used POSITRONFIT program. In almost all cases, the PAPLS program gives closer fit to the input values. The new procedure was applied to the analysis of several lifetime spectra measured in metal ion containing Epon-828 samples. The results are described.
9. Speciation of uranium and doping induced defects in Gd1.98U0.02Zr2O7: Photoluminescence, X-ray photoelectron and positron annihilation lifetime spectroscopy
Gupta, Santosh K.; Reghukumar, C.; Pathak, Nimai; Sudarshan, K.; Tyagi, D.; Mohapatra, M.; Pujari, P. K.; Kadam, R. M.
2017-02-01
Based on photoluminescence spectroscopy it was inferred that uranium stabilizes as both U(IV) as well as U(VI) in Gd2Zr2O7 which was also corroborated using X-ray photo electron spectroscopy (XPS). Absence of equidistant vibronic structure in emission spectrum of Gd1.98U0.02Zr2O7 confirmed that U(VI) stabilizes in the form of UO66-. Based on luminescence lifetime it was inferred that majority of UO66- stabilizes at both Gd3+/Zr4+ whereas U4+ stabilizes only at Zr4+ sites. The positron lifetime doesn't change on uranium doping indicating the formation of antisite defect. Infact it is this antisite defect in Gd1.98U0.02Zr2O7 which favours the stabilization of its fluorite phase.
10. Morphology of Thermoset Polyimides by Positron Annihilation Spectroscopy
NASA Technical Reports Server (NTRS)
Ranganathaiah, C.; Pater, R. H.; Sprinkle, D. R.; Baugher, A. H.; Eftekhari, A.; Singh, J. J.
1994-01-01
Thermoset polyimides have great potential for successfully meeting tough stress and temperature challenges in the advanced aircraft development program. However, studies of structure/property relationships in these materials have not been very successful so far. Positron annihilation spectroscopy has been used to investigate free volumes and associated parameters. It has been noted that the free volume correlates well with the molecular weight, cross-link density and thermal coefficient of expansion of these materials. Currently no other techniques are available for direct measurement of these parameters. Experimental results and their interpretations will be discussed.
11. Fatigue damage in superalloys determined using Doppler broadening positron annihilation
NASA Technical Reports Server (NTRS)
Hoeckelman, Donald; Leighly, H. P., Jr.
1990-01-01
Axial fatigue specimens of three superalloys, Inconel 718, Incoloy 903 and Haynes 188, were machined from solution-heat-treated material and artificially aged. They were subjected to cyclic loading for a selected number of cycles after which the S parameter was determined using Doppler broadening positron annihilation. Initially, the S parameter decreased, followed by a large increase and a subsequent decline leading to fracture. This has been interpreted as the removal of residual vacancies, the introduction of new defects by cyclic loading, and, finally, a clustering of the defects as microcracks which grow to cause failure.
12. Development of positron annihilation spectroscopy for characterizing neutron irradiated tungsten
SciTech Connect
C.N. Taylor; M. Shimada; D.W. Akers; M.W. Drigert; B.J. Merrill; Y. Hatano
2013-05-01
Tungsten samples (6 mm diameter, 0.2 mm thick) were irradiated to 0.025 and 0.3 dpa with neutrons in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. Samples were then exposed to deuterium plasma in the tritium plasma experiment (TPE) at 100, 200 and 500ºC to a total fluence of 1 x 1026 m-2. Nuclear reaction analysis (NRA) and Doppler broadening positron annihilation spectroscopy (DB-PAS) were performed at various stages to characterize damage and retention. We present the first known results of neutron damaged tungsten characterized by DB-PAS in order to study defect concentration. Two positron sources, 22Na and 68Ge, probe ~58 µm and through the entire 200 µm thick samples, respectively. DB-PAS results reveal clear differences between the various irradiated samples. These results, and the calibration of DB-PAS to NRA data are presented.
13. Positron-annihilation spectroscopy of defects in metals: an assessment
SciTech Connect
Siegel, R.W.
1982-06-01
Positron annihilation spectroscopy (PAS) has made significant contributions to our knowledge regarding lattice defects in metals in two areas: (i) the determination of atomic defect properties, particularly those of monovacancies, and (ii) the monitoring and characterization of vacancy-like microstructure development during post-irradiation of post-quench annealing. The application of PAS to the study of defects in metals is selectively reviewed and critically assessed within the context of other available techniques for such investigations. Possibilities for using the positron as a localized probe of the structure of atomic defects are discussed. Finally, the present status and future potential of PAS as a tool for the study of defects in metals are considered relative to other available techniques. 92 references, 20 figures.
14. Effects of process parameters on the defects in graphene oxide-polyaniline composites investigated by positron annihilation spectroscopy.
PubMed
Rana, Utpal; Nambissan, P M G; Malik, Sudip; Chakrabarti, Kuntal
2014-02-21
Graphene oxide (GO)-polyaniline (PANI) composites were prepared with different relative abundance of PANI and GO by in situ polymerization of aniline in the presence of GO and ammonium persulphate at different temperatures. In the process, GO also got reduced to graphene. Positron lifetimes and coincidence Doppler broadening of the electron-positron annihilation gamma ray spectra originating from the composite samples were measured and the results are reported. The positron lifetimes indicated the presence of very large size defects in the form of vacancy clusters within the samples. Another interesting observation was the increase of relative intensity of the defect specific positron lifetime component when an increase in relative abundance of PANI led to increased reduction of GO to graphene. The reduction also shrank the volume occupied by GO and the free volume thereby released added to the overall defect concentration, resulting in a simultaneous increase of the intensity of the positron lifetime component. The variation of the positron lifetime and its intensity with the synthesis temperature suggested an optimum temperature suitable for the process. The above observations are corroborated by other experimental investigations like electron microscopy, X-ray diffraction and electrical conductivity.
15. Defects in nitride-based semiconductors probed by positron annihilation
Uedono, A.; Sumiya, M.; Ishibashi, S.; Oshima, N.; Suzuki, R.
2014-04-01
Point defects in InxGa1-xN grown by metal organic chemical vapor deposition were studied by a monoenergetic positron beam. Measurements of Doppler broadening spectra of the annihilation radiation as a function of incident positron energy for InxGa1-xN (x = 0.08 and 0.14) showed that vacancy-type defects were introduced with increasing InN composition. From comparisons between coincidence Doppler broadening spectra and the results calculated using the projector augmented-wave method, the major defect species was identified as the complexes between a cation vacancy and nitride vacancies. The concentration of the defects was found to be suppressed by Mg doping. An effect of Mg-doping on the positron diffusion properties in GaN and InN was also discussed. The momentum distribution of electrons at the InxGa1-xN/GaN interface was close to that in defect-free GaN or InxGa1-xN, which was attributed to the localization of positrons at the interface due to the electric field caused by polarizations.
16. Resolving Nuclear Reactor Lifetime Extension Questions: A Combined Multiscale Modeling and Positron Characterization approach
SciTech Connect
Wirth, B; Asoka-Kumar, P; Denison, A; Glade, S; Howell, R; Marian, J; Odette, G; Sterne, P
2004-04-06
The objective of this work is to determine the chemical composition of nanometer precipitates responsible for irradiation hardening and embrittlement of reactor pressure vessel steels, which threaten to limit the operating lifetime of nuclear power plants worldwide. The scientific approach incorporates computational multiscale modeling of radiation damage and microstructural evolution in Fe-Cu-Ni-Mn alloys, and experimental characterization by positron annihilation spectroscopy and small angle neutron scattering. The modeling and experimental results are
17. Positron annihilation study of Fe-ion irradiated reactor pressure vessel model alloys
Chen, L.; Li, Z. C.; Schut, H.; Sekimura, N.
2016-01-01
The degradation of reactor pressure vessel steels under irradiation, which results from the hardening and embrittlement caused by a high number density of nanometer scale damage, is of increasingly crucial concern for safe nuclear power plant operation and possible reactor lifetime prolongation. In this paper, the radiation damage in model alloys with increasing chemical complexity (Fe, Fe-Cu, Fe-Cu-Si, Fe-Cu-Ni and Fe-Cu-Ni-Mn) has been studied by Positron Annihilation Doppler Broadening spectroscopy after 1.5 MeV Fe-ion implantation at room temperature or high temperature (290 oC). It is found that the room temperature irradiation generally leads to the formation of vacancy-type defects in the Fe matrix. The high temperature irradiation exhibits an additional annealing effect for the radiation damage. Besides the Cu-rich clusters observed by the positron probe, the results show formation of vacancy-Mn complexes for implantation at low temperatures.
18. HEAO 3 measurements of the atmospheric positron annihilation line
SciTech Connect
Mahoney, W.A.; Ling, J.C.; Jacobson, A.S.
1981-12-01
All spectra measured with the High Energy resolution Gamma-Ray Spectroscopy Experiment (HEAO C-1) on the third High Energy Astronomy Observatory (HEAO 3) contain a strong line at 511 keV resulting from positron annihilation. This line originates in the instrument itself, the earth's atmosphere, and cosmic sources, possibly including the diffuse cosmic background. In order to understand the emission from cosmic sources, the atmospheric positron annihilation line emission has been determined as a function of geomagnetic latitude and zenith angle. Although the intensity of the line increases with increasing latitude, it was found that variations with zenith angle can be satisfactorily explained only if the atmospheric emission exhibits significant limb darkening. The atmospheric line has an energy of 511.07 +- 0.10 keV and a net width of 2.29 +- 0.30 keV FWHM. Characteristics of the instrument background have allowed an upper limit of 9.4 x 10/sup -3/ photons/cm/sup 2/-sec-sr to be placed on any narrow (< or approx. =3 keV) diffuse cosmic emission at 511 keV.
19. Moisture determination in composite materials using positron lifetime techniques
NASA Technical Reports Server (NTRS)
Singh, J. J.; Holt, W. R.; Mock, W., Jr.
1980-01-01
A technique was developed which has the potential of providing information on the moisture content as well as its depth in the specimen. This technique was based on the dependence of positron lifetime on the moisture content of the composite specimen. The positron lifetime technique of moisture determination and the results of the initial studies are described.
20. Positron-annihilation study of the equilibrium vacancy ensemble in aluminum
SciTech Connect
Fluss, M.J.; Berko, S.; Chakraborty, B.; Hoffmann, K.; Lippel, P.; Siegel, R.W.
1982-06-01
A preliminary report is presented of a positron-annihilation study of the equilibrium vacancy ensemble in aluminum using one- and two-dimensional angular correlation of annihilation radiation (ACAR) measurements versus temperature. The annihilation characteristics of a positron from the Bloch state, and the monovancy- and divacancy-trapped states have been calculated self-consistently within a supercell, including many-body enhancement effects, and are compared with experiment. 4 figures.
1. Positron and gamma-ray signatures of dark matter annihilation and big-bang nucleosynthesis
SciTech Connect
Hisano, Junji; Kawasaki, Masahiro; Kohri, Kazunori; Nakayama, Kazunori
2009-03-15
The positron excess observed by the PAMELA experiment may come from dark matter annihilation, if the annihilation cross section is large enough. We show that the dark matter annihilation scenarios to explain the positron excess may also be compatible with the discrepancy of the cosmic lithium abundances between theory and observations. The winolike neutralino in the supersymmetric standard model is a good example for it. This scenario may be confirmed by Fermi satellite experiments.
2. Determination and applications of enhancement factors for positron and ortho-positronium annihilations
SciTech Connect
Mitroy, J.
2005-12-15
Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the 1s electron in H, He{sup +}, He, Li{sup 2+}, and Li{sup +}. The enhancement factor for a free positron annihilating with He{sup +} and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of 1.47a{sub 0} for Ps-He scattering. Further, enhancement factors for e{sup +}-Ne and e{sup +}-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of 1.46a{sub 0} for Ps-Ne scattering and 1.75a{sub 0} for Ps-Ar scattering.
3. Positron Annihilation Spectroscopy and Small Angle Neutron Scattering Characterization of Nanostructural Features in Irradiated Fe-Cu-Mn Alloys
SciTech Connect
Wirth, B D; Asoka-Kumar, P; Howell, R H; Odette, G R; Sterne, P A
2001-01-01
Radiation embrittlement of nuclear reactor pressure vessel steels results from a high number density of nanometer sized Cu-Mn-Ni rich precipitates (CRPs) and sub-nanometer matrix features, thought to be vacancy-solute cluster complexes (VSC). However, questions exist regarding both the composition of the precipitates and the defect character and composition of the matrix features. We present results of positron annihilation spectroscopy (PAS) and small angle neutron scattering (SANS) characterization of irradiated and thermally aged Fe-Cu and Fe-Cu-Mn alloys. These complementary techniques provide insight into the composition and character of both types of nanoscale features. The SANS measurements indicate populations of CRPs and VSCs in both alloys. The CRPs are coarser in the Fe-Cu alloy and the number densities of CRP and VSC increase with the addition of Mn. The PAS involved measuring both the positron lifetimes and the Doppler broadened annihilation spectra in the high momentum region to provide elemental sensitivity at the annihilation site. The spectra in Fe-Cu-Mn specimens thermally aged to peak hardness at 450 C and irradiated at 288 C are nearly identical to elemental Cu. Positron lifetime and spectrum measurements in Fe-Cu specimens irradiated at 288 C clearly show the existence of long lifetime ({approx}500 ps) open volume defects, which also contain Cu. Thus the SANS and PAS provide a self-consistent picture of nanostructures composed of CRPs and VSCs and tend to discount high Fe concentrations in the CRPs.
4. Temperature dependence of o-Ps annihilation lifetime in non-uniform cylindrical pores in comparison with ETE model
2017-04-01
Ortho-positronium (o-Ps) annihilation lifetime was calculated in non-uniform cylinder-shaped pores by solving Schrodinger equation using a well-known multi-physics program called COMSOL. The o-Ps annihilation lifetime variation in terms of temperature was calculated on the basis of ETE model via a numerical method. The COMSOL simulations indicate that as long as the pore is uniform cylinder-shaped, the results agree with those of two-dimensional ETE model, whereas deformations in the cylinder shape (indentation or protrusion) change the temperature behavior of ETE model and, thereby, higher values are predicted for o-Ps lifetime in the pore at lower temperatures. The geometry of the non-uniform cylinder-shaped pores, which is accompanied by empirical evidence, can be used for the analysis of empirical results obtained from positron lifetime spectroscopy in different temperatures.
5. Positron Annihilation Spectroscopy as a Probe of Microscopic Structure and Physical Aging in Polymer.
Yu, Minzi
Positron annihilation is studied as a characterization method for the properties of polymers. Previous studies indicate that the ortho-positronium lifetime tau _3 and intensity I_3 is correlated to the free volume "hole" size and number density of holes in a polymer. Positron annihilation lifetime (PAL) studies in polymers measure the change in free volume, and they are sensitive to different physical environments. PAL studies of the temperature dependence of a bisphenol-A polycarbonate shows that the free volume increases with increasing temperature, and it also obtains the transition temperatures T_{rm g} and T_beta^', from the tau_3 curve and the I_3 curve, respectively. The isothermal aging in polycarbonate shows that: I_3 decreases while tau_3 remains constant during a long-time annealing at a temperature far below T_{rm g}; and I_3 remains constant while tau_3 goes through a "over shooting" in the first few hours after quenching and annealing at a temperature just below T_{rm g}. The free volume in polycarbonate increases (as a result of an increase in tau_3 ) with applied tensile strain up to 4%, then levels off. Similarly, the free volume in polymethyl methacrylate (PMMA) decreases (as the result of tau_3 ) with applied compressional strain also up to -4% then levels off. A negative change in both tau_3 and I _3 has been observed when polycarbonate is under 3% tensile strain and after release of strain. A more advance technique of positron annihilation, PAL-momentum correlation which can give more detailed information about free volume structure in polymers, has also been studied and improved. Two 5-cm-diameter, 5-cm-long CsF scintillation detectors for lifetime measurement, and a 30-cm-diameter Anger camera whose y-analog pulse gives one-dimensional ACAR information, comprise a new experimental arrangement of PAL-momentum correlation system. Its triple -coincidence counting rate is about 2.5 per minute per microcurie of positron source and system time
6. Structural transition in rare earth doped zirconium oxide: A positron annihilation study
SciTech Connect
Chakraborty, Keka; Bisoi, Abhijit
2012-11-15
Graphical abstract: New microstructural analysis and phase transition of rare earth doped mixed oxide compounds such as: Sm{sub 2−x}Dy{sub x}Zr{sub 2}O{sub 7} (where x = 0.0 ≤ x ≥ 2.0) that are potentially useful as solid oxide fuels, ionic conductors, optoelectronic materials and most importantly as radiation resistant host for high level rad-waste disposal, structural transition in the system is reported through positron annihilation spectroscopy as there is an indication in the X-ray diffraction analysis. Highlights: ► Zirconium oxide material doped with rare earth ions. ► The method of positron annihilation spectroscopy suggests a phase transition in the system. ► The crystal structure transformation from pure pyrochlore to defect fluorite type of structure is shown by X-ray diffraction results. -- Abstract: A series of compounds with the general composition Sm{sub 2−x}Dy{sub x}Zr{sub 2}O{sub 7} (where 0 ≤ x ≥ 2.0) were synthesized by chemical route and characterized by powder X-ray diffraction (XRD) analysis. The rare earth ion namely Sm{sup +3} in the compound was gradually replaced with another smaller and heavier ion, Dy{sup +3} of the 4f series, there by resulting in order–disorder structural transition, which has been studied by positron annihilation lifetime and Doppler broadening spectroscopy. This study reveals the subtle electronic micro environmental changes in the pyrochlore lattice (prevalent due to the oxygen vacancy in anti-site defect structure of the compound) toward its transformation to defect fluorite structure as found in Dy{sub 2}Zr{sub 2}O{sub 7}. A comparison of the changes perceived with PAS as compared to XRD analysis is critically assayed.
7. Positron annihilation studies of 4-n-butyl-4'-isothiocyanato-1,1'-biphenyl.
PubMed
Dryzek, E; Juszyńska, E; Zaleski, R; Jasińska, B; Gorgol, M; Massalska-Arodź, M
2013-08-01
Positron annihilation lifetime spectroscopy (PALS) measurements were performed between 93 and 293 K in order to study the supercooled smectic-E (Sm-E) phase of 4-n-butyl-4'-isothiocyanato-1,1'-biphenyl (4TCB), the ordered molecular crystal of 4TCB, and the phase transition between the Sm-E phase and the ordered molecular crystal of 4TCB. The phase transition was well reflected in the abrupt increase of the ortho-positronium (o-Ps) lifetime and intensity. The value of the o-Ps lifetime in the Sm-E liquid crystalline phase of 4TCB, i.e., 2.21 ns at room temperature, was explained by the formation of bubbles induced by Ps atoms, which are created due to a liquidlike state of the butyl chains of 4TCB molecules in the Sm-E phase. The temperature dependence of the o-Ps intensity for the supercooled Sm-E phase can be explained by thermal generation of sites where bubbles are formed; an activation energy equal to 0.30±0.02 eV was estimated. This value was compared with the activation energies of molecular motions. The o-Ps lifetime in the ordered molecular crystal was interpreted as originating from the annihilation of o-Ps confined in molecular vacancy-type imperfections in the crystal lattice. The value of the o-Ps pickoff annihilation between 1.8 and 1.9 ns is in accordance with the size of the molecular vacancy for the 4TCB crystal lattice. Its intensity is lower than 5%. The isothermal crystallization of the 4TCB Sm-E phase was observed by PALS. The low-dimensional crystal growth was concluded from the Avrami equation fitted to the time dependence of the o-Ps intensity, which resulted in an Avrami exponent equal to 1.73.
8. Neutron irradiation and post annealing effect on sapphire by positron annihilation.
PubMed
Han, Jie-cai; Zhang, Hai-liang; Zhang, Ming-fu; Wang, Bao-yi; Li, Zhuo-xin; Xu, Cheng-hai; Guo, Huai-xin
2010-09-01
Sapphire single crystals grown by an improved Kyropoulos-like method are irradiated by fast neutron flux. The irradiated doses of neutron are 10(18) and 10(19)n/cm(2). The infrared transmission spectra of sapphire were studied before and after irradiation. The irradiated samples were annealed at 200, 400, 600, 800 and 1000 degrees C for 10min in ambient atmosphere. Positron annihilation studies have been carried out before and after neutron irradiation. The experimentally measured positron lifetime in the pristine specimen is 143ps. There were aluminum vacancies produced in sapphire crystals after neutron irradiation. The positron lifetime increased with the dose of neutron flux. A longer value tau(2) was found after annealing at 600 degrees C, which indicated vacancies were aggregated with each other. The second long-time component tau(2) has been found to increase with the annealing temperature. There was almost no change in peak position of the CDB spectra after neutron irradiation and isothermal annealing. The chemical environment of core in sapphire did not change greatly after neutron irradiation.
9. Optimisation of the thickness of the moderator for positron annihilation process study in Ar gas
Oka, Toshitaka; Sano, Yosuke; Kino, Yasushi; Sekine, Tsutomu
2014-06-01
To investigate the deceleration and annihilation processes of positron in noble gas, we attempted to optimise the thickness of the positron moderator. The results of the decreasing trend of free positron intensity and ortho-positronium intensity with the thickness, and the annihilation rate suggest that the energy of almost all the positrons passed through the metal foils was much above the positronium formation threshold of 9 eV. Total thickness of 0.1 g cm-2 of the moderator and the Ar gas was required to stop almost all the positron in Ar gas.
10. Evaluation of irradiated pressure vessel steel by mechanical tests and positron annihilation lineshape analysis
SciTech Connect
Nakamura, Noriko; Ohta, Yoshio; Yoshida, Kazuo; Maeda, Noriyoshi
1999-10-01
Mechanical test and positron annihilation lineshape analysis have been performed on neutron irradiated pressure vessel steels, A533B1 steel and the weld metal. Marked changes in the mechanical properties were observed for both metals after the neutron exposure. S-parameters, the positron annihilation parameters, also increased after the neutron irradiation but only the small change was observed in the different levels of neutron fluence. The change in S-parameter and the mechanical properties were well correlated. It is concluded that changes in embrittlement induced by radiation can be monitored by positron annihilation lineshape analysis but detectability is dependent on the materials.
11. On the potential of positron lifetime spectroscopy for the study of early stages of zeolites formation from their amorphous precursors
Bosnar, S.; Kosanović, C.; Subotić, B.; Bosnar, D.; Kajcsos, Zs.; Liszkay, L.; Lohonyai, L.; Molnár, B.; Lázár, K.
2007-02-01
The applicability of positron lifetime (LT) spectroscopy to the study of progress of formation of Secondary Building Units (SBU) in gels yielding in FAU and LTA type zeolites was investigated. Samples were prepared from aluminosilicate gels with various degrees of local structural order. LT measurements were performed at room temperature in air and in vacuum. Coexistence of annihilation modi with long lifetime components was shown; a correlation with precursors of nucleation and type of exchanged ions was also indicated.
12. High energy oxygen irradiation-induced defects in Fe-doped semi-insulating indium phosphide by positron annihilation technique
Pan, S.; Mandal, A.; Sohel, Md. A.; Saha, A. K.; Das, D.; Sen Gupta, A.
2017-02-01
13. Positron lifetime calculation for the elements of the periodic table.
PubMed
Campillo Robles, J M; Ogando, E; Plazaola, F
2007-04-30
Theoretical positron lifetime values have been calculated systematically for most of the elements of the periodic table. Self-consistent and non-self-consistent schemes have been used for the calculation of the electronic structure in the solid, as well as different parametrizations for the positron enhancement factor and correlation energy. The results obtained have been studied and compared with experimental data, confirming the theoretical trends. As is known, positron lifetimes in bulk show a periodic behaviour with atomic number. These calculations also confirm that monovacancy lifetimes follow the same behaviour. The effects of enhancement factors used in calculations have been commented upon. Finally, we have analysed the effects that f and d electrons have on positron lifetimes.
14. Comment on "Gamma-ray spectra from low-energy positron annihilation processes in molecules"
Green, D. G.; Gribakin, G. F.
2017-03-01
In the article by Ma et al. [Phys. Rev. A 94, 052709 (2016), 10.1103/PhysRevA.94.052709], γ -ray spectra for positron annihilation on molecules were calculated in the independent-particle approximation with the positron wave function set to unity. Based on comparisons with experimental data, they concluded that inner valence electrons play a dominant role in positron annihilation. These conclusions are incorrect and resulted from fallacious analysis that ignored the known effect of the positron wave function on the spectra.
15. Positron line radiation from halo WIMP annihilations as a dark matter signature
NASA Technical Reports Server (NTRS)
Turner, Michael S.; Wilczek, Frank
1989-01-01
We suggest a new signature for dark matter annihilation in the halo: high energy positron line radiation. Because the cosmic ray positron spectrum falls rapidly with energy, e+'s from halo WIMP annihilations can be a significant, clean signal for very massive WIMP's (approx. greater than 30 GeV). In the case that the e+e- annihilation channel has an appreciable branch, the e+ signal should be above background in a future detector, such as have been proposed for ASTROMAG, and of potential importance as a dark matter signature. A significant e+e- branching ratio can occur for neutralinos or Dirac neutrinos. High-energy, continuum positron radiation may also be an important signature for massive neutralino annihilations, especially near or above the threshold of the W+W- and ZoZo annihilation channels.
16. Neutrino emissivity from electron-positron annihilation in hot matter in a strong magnetic field
SciTech Connect
Amsterdamski, P.; Haensel, P. )
1990-10-15
The neutrino emissivity due to electron-positron annihilation in a strong magnetic field is computed. A strong magnetic field can significantly increase the neutrino emissivity at {ital T}{similar to}10{sup 9} K.
17. Relative Defect Density Measurements of Laser Shock Peened 316L Stainless Steel Using Positron Annihilation Spectroscopy
SciTech Connect
Marcus A. Gagliardi; Bulent H. Sencer; A. W. Hunt; Stuart A. Maloy; George T. Gray III
2011-12-01
The surface of an annealed 316L stainless steel coupon was laser shock peened and Vickers hardness measurements were subsequently taken of its surface. This Vickers hardness data was compared with measurements taken using the technique of positron annihilation Doppler broadening spectroscopy. When compared, a correlation was found between the Vickers hardness data measurements and those made using Doppler broadening spectroscopy. Although materials with a high defect density can cause the S-parameter measurements to saturate, variations in the Sparameter measurements suggest that through further research the Doppler broadening technique could be used as a viable alternative to measuring a material's hardness. In turn, this technique, could be useful in industrial settings where surface hardness and surface defects are used to predict lifetime of components.
18. Synthesis and characterization of magnesium oxide nanocrystallites and probing the vacancy-type defects through positron annihilation studies
Das, Anjan; Mandal, Atis Chandra; Roy, Soma; Prashanth, Pendem; Ahamed, Sk Izaz; Kar, Subhrasmita; Prasad, Mithun S.; Nambissan, P. M. G.
2016-09-01
Magnesium oxide nanocrystallites exhibit certain abnormal characteristics when compared to those of other wide band gap oxide semiconductors in the sense they are most prone to water absorption and formation of a hydroxide layer on the surface. The problem can be rectified by heating and pure nanocrystallites can be synthesized with controllable sizes. Inevitably the defect properties are distinctly divided between two stages, the one with the hydroxide layer (region I) and the other after the removal of the layer by annealing (region II). The lattice parameters, the optical band gap and even the positron annihilation characteristics are conspicuous by their distinct behavior in the two stages of the surface configurations of nanoparticles. While region I was specific with the formation of positronium-hydrogen complexes that drastically altered the defect-specific positron lifetimes, pick-off annihilation of orthopositronium atoms marked region II. The vacancy clusters within the nanocrystallites also trapped positrons. They agglomerated due to the effect of the higher temperatures and resulted in the growth of the nanocrystallites. The coincidence Doppler broadening spectroscopic measurements supported these findings and all the more indicated the trapping of positrons additionally into the neutral divacancies and negatively charged trivacancies. This is apart from the Mg2+ monovacancies which acted as the dominant trapping centers for positrons.
19. Synthesis and characterization of highly conductive charge-transfer complexes using positron annihilation spectroscopy.
PubMed
Adam, Abdel Majid A; Refat, Moamen S; Sharshar, T; Heiba, Z K
2012-09-01
Molecular charge-transfer complexes of the tetramethylethylenediamine (TMEDA) with picric acid (Pi-OH), benzene-1,4-diol (QL), tin(IV) tetrachloride (SnCl(4)), iodine, bromine, and zinc chloride (ZnCl(2)) have been synthesized and investigated by elemental and thermal analysis, electronic, infrared, Raman and proton-NMR, energy-dispersive X-ray spectroscopy, X-ray powder diffraction and positron annihilation lifetime spectroscopy, and scanning electron microscopy. In this work, three types of acceptors π-acceptors (Pi-OH and QL), σ-acceptors (iodine and bromine), and vacant orbital acceptors (SnCl(4) and ZnCl(2)) were covered. The results of elemental analysis indicated that the CT complexes were formed with ratios 1:1 and 1:2 for QL, SnCl(4), and ZnCl(2) acceptors and iodine, Pi-OH, and Br(2) acceptors, respectively. The type of chelating between the TMEDA donor and the mentioned acceptors depends upon the behavior of both items. The positron annihilation lifetime parameters were found to be dependent on the structure, electronic configuration, and the power of acceptors. The correlation between these parameters and the molecular weight and biological activities of studied complexes was also observed. Regarding the electrical properties, the AC conductivity and the dielectric coefficients were measured as a function of frequency at room temperature. The TMEDA charge-transfer complexes were screened against antibacterial (Escherichia coli, Staphylococcus aureus, Bacillus subtilis, and Pseudomonas aeruginosa) and antifungal (Aspergillus flavus and Candida albicans) activities.
20. Low-temperature positron lifetime and Doppler-broadening measurements for single-crystal nickel oxide containing cation vacancies
SciTech Connect
Waber, J.T.; Snead, C.L. Jr.; Lynn, K.G.
1985-01-01
Lifetime and Doppler-broadening measurements for positron annihilation in substoichiometric nickelous oxide have been made concomitantly from liquid-helium to room temperature. The concentration of cation vacancies is readily controlled by altering the ambient oxygen pressure while annealing the crystals at 1673/sup 0/K. It was found that neither of the three lifetimes observed or their relative intensities varied significantly with the oxygen pressure, and the bulk rate only increased slightly when the specimen was cooled from room to liquid-helium temperatures. These results are interpreted as indicating that some of the positrons are trapped by the existing cation vacancies and a smaller fraction by vacancy clusters.
1. Positron lifetime studies in thermoplastic polyimide test specimens
NASA Technical Reports Server (NTRS)
Singh, J. J.; Stclair, T. L.; Holt, W. H.; Mock, W., Jr.
1982-01-01
Positron lifetime measurements were made in two thermoplastic polyimide materials recently developed at Langley. The long component lifetime values in polyimidesulfone samples are 847 + or - 81 Ps (dry) and 764 + or - 91 Ps (saturated). The corresponding values in LARC thermoplastic imides are 1080 + or - 139 Ps (dry) and 711 + or - 96 Ps (saturated). Clearly, the presence of moisture has greater effect on positron lifetime in LARC thermoplastic imides than in the case of polyimidesulfones. This result is consistent with the photomicrographic observations made on frozen water saturated specimens of these materials.
2. Positron annihilation study for cadmium (electronic structure and enhancement effect)
Hamid, A.
2003-12-01
The three dimensional electron density in momentum space ρ(p) and in wave vector space n(k) was reconstructed for cadmium (Cd). The measurements were performed using the two dimensional angular correlation of annihilation radiation (2D-ACAR) technique. Enhanced contributions in the spectra were observed around 5.5 mrad, discussed in terms of a Kahana-like enhancement effect. From another viewpoint, Fermi radii were analyzed in the (λM K), (ALM) and (AHK) planes, and they showed a maximum deviation of about 4% from the free electron Fermi radius. Moreover, comparisons to a radio-frequency size effect (RFSE) experiment and theoretical band structure calculations (using augmented plane wave (APW), linear combination of atomic orbital (LCAO) and linear muffin tin orbital (LMTO) methods) were examined. The results showed a qualitative agreement with both APW and LCAO calculations. However, a favorable agreement with the APW method was determined via Fermi surface dimensions. The differences of bands' occupation of n(k) between the current work and the APW method were argued in view of positron wave function in Cd.
3. Investigations of Positron Annihilation with Atoms and Molecules using PsARS
Kauppila, W. E.; Edwards, J. J.; Miller, E. G.; Stein, T. S.; Surdutovich, E.
2006-03-01
Positrons, being the antiparticles of electrons, ultimately annihilate either directly with electrons (that are free or attached to atoms or molecules), or via the formation of positronium (Ps, a short-lived atom composed of a positron and an electron) with subsequent annihilation. In this work we have developed positronium annihilation ratio spectroscopy (PsARS), and are using PsARS to investigate the formation and destruction of Ps [1], as well as positron attachment to molecules. For this experiment a 3 to 100 eV positron beam obtained from a sodium-22 radioactive source is passed through a gas scattering cell and resulting annihilation gamma rays of different energies are detected in coincidence. Annihilation measurements, such as these, have astrophysical relevance since characteristic positron annihilation gamma rays have been observed from various extraterrestrial sources (e.g., solar flares and the direction towards the center of our galaxy). [1] W.E. Kauppila, E.G. Miller, H.F.M. Mohamed, K. Pipinos, T.S. Stein and E. Surdutovich, Phys. Rev. Lett. 93, 113401 (2004).
4. Investigation of Positron-CO scattering using Positronium Annihilation Ratio Spectroscopy
Kauppila, W. E.; Edwards, J. J.; Miller, E. G.; Stein, T. S.; Surdutovich, E.
2006-05-01
We are using the technique [1] of positronium annihilation ratio spectroscopy (PsARS) to study the annihilation of 6 - 13 eV positrons colliding with CO. In this method we detect in coincidence (a) two 511 keV annihilation gamma rays, and simultaneously (b) two 300 - 460 keV gamma rays from the three gamma decay of ortho-Ps. The ratio of these signals R3γ/2γ versus positron impact energy reveals anomalous behavior for CO when compared with other gases [1] suggesting that some other mechanism than Ps formation is contributing to positron annihilation at an energy about 1 eV above the Ps formation threshold of 7.2 eV. Recognizing that the threshold for electronic excitation by positron impact is located where the anomalous R3γ/2γ behavior occurs suggests that we may be observing an effect where the positron is electronically exciting CO and temporarily binding to the molecule in a resonance-like state from which the positron can annihilate with an electron producing an enhanced 511 keV coincidence signal consistent with our measurements. [1] W.E. Kauppila, E.G. Miller, H.F.M. Mohamed, K. Pipinos, T.S. Stein and E. Surdutovich, Phys. Rev. Lett. 93, 113401 (2004).
5. Gamma-ray spectra from low-energy positron annihilation processes in molecules
Ma, Xiaoguang; Wang, Meishan; Zhu, Yinghao; Liu, Yang; Yang, Chuanlu; Wang, Dehua
2016-11-01
The theoretical γ -ray spectra from positron-electron annihilation process in a wide variety of atoms and molecules are studied. The theoretical Doppler broadened γ -ray spectra for core, inner valence, and outer valence electrons of these molecules are studied systematically. The present results show that the experimental γ -ray spectra agree well with inner valence electrons, especially the lowest occupied valence orbital electrons rather than the outer valence electrons. These inner valence electrons show a strong correlation with the corresponding available experimental measurements. These findings are interesting because the outer valence electrons have been supposed to have larger probability annihilating with positrons rather than the inner valence electrons. The present work also suggests that the accurate positron wave functions must be involved to identify the dominance of the bound electrons clearly in positron-electron annihilation process.
6. Diffusion of permanent liquid dye molecules in human hair investigated by positron lifetime spectroscopy.
PubMed
Chandrashekara, M N; Ranganathaiah, C
2009-02-15
The diffusion behavior of a commercial permanent liquid hair dye in human hair has been investigated using positron annihilation lifetime spectroscopy (PALS) and gravimetric sorption method. The positron technique makes it possible to non-invasively characterize the angstrom sized free volume holes in hair, which are supposed to be express pathways for diffusion of small molecules. The o-Ps lifetime parameters tau3 and I3 decrease rapidly during the first 60 min of sorption time. The overall decrease in o-Ps lifetime (tau3) was well over 200 ps and o-Ps intensity (I3) drops by 3.5%. These positron results are explained in terms of dye molecules filling the free volume holes and hair morphology. The dye penetrates the cuticle rapidly, but slowly in cortex. The first hour of dyeing appears to be the most effective period of deposition of dye molecules within hair. These results are well corroborated by the sorption results which suggest that the dye diffusion is essentially a diffusion controlled (i.e. Fickian) process, with no observable relaxation effects. In the latter part of the sorption, where positron parameters remain almost constant, mass increase might be due to surface adhesion. These two stages of sorption are well separated by the positron technique. The sorption curve also yielded an average value of apparent diffusivity of the dye in hair. From this study, we conclude that the free volume theory and positron technique, widely used in polymer research, may expediently be used to understand hair properties, more importantly diffusion of dye molecules.
7. Ultra Fine-Grained Metals Prepared by Severe Plastic Deformation: A Positron Annihilation Study
Čížek, J.; Procházka, I.; Kužel, R.; Matĕj, Z.; Cherkaska, V.; Cieslar, M.; Smola, B.; Stulíková, I.; Brauer, G.; Anwand, W.; Islamgaliev, R. K.; Kulyasova, O.
2005-05-01
Recent investigations of ultra fine-grained metals (Cu, Fe, Ni) performed within a Prague-Rossendorf-Ufa collaboration will be reviewed. The specimens were prepared by severe plastic deformation: the high-pressure torsion and equal channel angular pressing. Positron annihilation spectroscopy was used as the main method including (i) the conventional lifetime and the Doppler broadening measurements with 22Na and (ii) the slow-positron implantation spectroscopy with the Doppler broadening measurement. Other methods were also involved: transmission electron microscopy, X-ray diffraction, and microhardness. First, the mean grain size was determined and defects were identified in the as-deformed materials. Defects concentration and spatial distribution were studied in detail. Dislocations situated in distorted regions along grain boundaries, and a few-vacancy clusters distributed homogeneously inside dislocations-free grains, were observed in the ultra fine-grained Cu, Fe, and Ni. Subsequently, the thermal evolution of the ultra fine-grained structures during isochronal annealing was studied.
8. Positron lifetime measurements in chiral nematic liquid crystals
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Eftekhari, Abe; Parmar, Devendra S.
1991-01-01
Positron lifetimes in the isotropic phases of chiral nematic liquid crystal formulations and their mixtures up to the racemic level were measured. The lifetime spectra for all liquid crystal systems were analyzed into three components. Although the individual spectra in the left- and right-handed components are identical, their racemic mixtures exhibit much larger orthopositronium lifetimes; these larger lifetimes indicate the presence of larger microvoids. This result is consistent with the reportedly higher thermodynamic stability and color play range in the racemic mixtures of chiral nematic liquid crystals.
9. Monte Carlo modelling of the propagation and annihilation of nucleosynthesis positrons in the Galaxy
Alexis, A.; Jean, P.; Martin, P.; Ferrière, K.
2014-04-01
Aims: We want to estimate whether the positrons produced by the β+-decay of 26Al, 44Ti, and 56Ni synthesised in massive stars and supernovae are sufficient to explain the 511 keV annihilation emission observed in our Galaxy. Such a possibility has often been put forward in the past. In a previous study, we showed that nucleosynthesis positrons cannot explain the full annihilation emission. Here, we extend this work using an improved propagation model. Methods: We developed a Monte Carlo Galactic propagation code for ~MeV positrons in which the Galactic interstellar medium, the Galactic magnetic field, and the propagation are finely described. This code allows us to simulate the spatial distribution of the 511 keV annihilation emission. We tested several Galactic magnetic fields models and several positron escape fractions from type-Ia supernova for 56Ni positrons to account for the large uncertainties in these two parameters. We considered the collisional/ballistic transport mode and then compared the simulated 511 keV intensity spatial distributions to the INTEGRAL/SPI data. Results: Regardless of the Galactic magnetic field configuration and the escape fraction chosen for 56Ni positrons, the 511 keV intensity distributions are very similar. The main reason is that ~MeV positrons do not propagate very far away from their birth sites in our model. The direct comparison to the data does not allow us to constrain the Galactic magnetic field configuration and the escape fraction for 56Ni positrons. In any case, nucleosynthesis positrons produced in steady state cannot explain the full annihilation emission. The comparison to the data shows that (a) the annihilation emission from the Galactic disk can be accounted for; (b) the strongly peaked annihilation emission from the inner Galactic bulge can be explained by positrons annihilating in the central molecular zone, but this seems to require more positron sources than the population of massive stars and type Ia
10. The Effects of Surface Reconstruction and Electron-Positron Correlation on the Annihilation Characteristics of Positrons Trapped at Semiconductor Surfaces
SciTech Connect
Fazleev, N. G.; Jung, E.; Weiss, A. H.
2009-03-10
Experimental positron annihilation induced Auger electron spectroscopy (PAES) data from Ge(100) and Ge(111) surfaces display several strong Auger peaks corresponding to M{sub 4,5}N{sub 1}N{sub 2,3}, M{sub 2,3}M{sub 4,5}M{sub 4,5}, M{sub 2,3}M{sub 4,5}V, and M{sub 1}M{sub 4,5}M{sub 4,5} Auger transitions. The integrated peak intensities of Auger transitions have been used to obtain experimental annihilation probabilities for the Ge 3d and 3p core electrons. The experimental data were analyzed by performing theoretical studies of the effects of surface reconstructions and electron-positron correlations on image potential induced surface states and annihilation characteristics of positrons trapped at the reconstructed Ge(100) and Ge(111) surfaces. Calculations of positron surface states and annihilation characteristics have been performed for Ge(100) surface with (2x1), (2x2), and (4x2) reconstructions, and for Ge(111) surface with c(2x8) reconstruction. Estimates of the positron binding energy and annihilation characteristics reveal their sensitivity to the specific atomic structure of the topmost layers of the semiconductor and to the approximations used to describe electron-positron correlations. The results of these theoretical studies are compared with the ones obtained for the reconstructed Si(100)-(2x1) and Si(111)-(7x7) surfaces.
11. Positron annihilation spectroscopy of vacancy type defects in submicrocrystalline copper under annealing
Kuznetsov, Pavel V.; Lider, Andrey M.; Bordulev, Yuriy S.; Laptev, Roman S.; Mironov, Yuriy P.; Rakhmatulina, Tanzilya V.; Korznikov, Alexandr V.
2016-11-01
The annealing of submicrocrystalline copper produced by the equal channel angular pressing followed by rolling was studied using positron annihilation and XRD analysis. In as-prepared samples, positrons are trapped at vacancies, concentration of which is very high (˜1.6 × 10-4) and dislocation type defects; however, a few percent of positrons annihilate from a free state. Increasing annealing temperature leads to the formation of vacancy complexes. The main positron trap centers in the temperature range ΔT = 20-300°C are vacancies and their small complexes of two or three vacancies. The dominant centers of positron trapping in the temperature range ΔT = 300-670°C are dislocation-type defects.
12. Rectifying barrier at GaN/SiC hetero-junction studied with positron annihilation spectroscopy
Hu, Yi-Fan; Beling, D. C.
2005-11-01
Positron annihilation spectroscopy on GaN films grown on SiC substrate with MBE are presented. It is shown that the GaN/SiC interface is rectifying towards positrons, such that positrons can only travel from SiC to GaN and not vice versa. Potential steps seen by the positron at the GaN/SiC interface are calculated from experimental values of electron and positron work function. This rectifying'' effect has been successfully mimicked by inserting a thin region of very high electric field in the Variable Energy Positron Fit (VEPF) analysis. The built-in electric field is attributed to different positron affinities, dislocation and/or interface defects at the GaN/SiC interface.
13. The annihilation of positrons in the cold phase of the interstellar medium revisited
NASA Technical Reports Server (NTRS)
Wallyn, P.; Durouchoux, PH.; Chapuis, C.; Leventhal, M.
1994-01-01
The positron cross sections in H and H2 media are reevaluated, taking into account new experimental results. Using a Monte Carlo simulation, we find a positronium fraction before thermalization of 0.90 for H2, in good agreement with the previous experimental result given by Brown et al. (1986). For H we obtain an upper limit of 0.98. We study the behavior of the charge exchange annihilation in a cold phase (molecular cloud). We calculate a formula for the slowing-down time t, before annihilation lasting Delta t, via charge exchange, of a positron beam with a given energy for different medium densities and initial energies. An upper limit of 0.7 MeV for the initial energy of the positrons, annihilating in the molecular cloud G0.86 - 0.08 near the gamma ray source positronium and gives new time constraints on their possible observation.
14. Positron lifetime studies in vinyl polymers of medical importance
Ferreira Marques, M. F.; Gordo, P. M.; Gil, C. Lopes; Kajcsos, Zs.; Gil, M. H.; Mariz, M. J.; de Lima, A. P.
2003-10-01
Vinyl polymers used as artificial lens implants in ophthalmology were investigated by positron lifetime spectroscopy. The structure of these polymers with free volumes offers the possibility of charging them with anti-inflammatory drugs for sustained release. A correlation between the amount of normalised free volume and the ratio of the methyl methacrylate to ethyl-hexyl-acrylate, used as polymerisation monomers, was found.
15. Positron annihilation study in SmFeAsO and SmFeAsO0.82F0.18
Hao, Y. P.; Chen, X. L.; Liu, R. H.; Kong, W.; Cheng, B.; Xu, H. X.; Chen, X. H.; Han, R. D.; Weng, H. M.; Du, H. J.; Ye, B. J.
2010-02-01
SmFeAsO1-xFx polycrystalline samples were first studied by positron annihilation lifetime spectroscopy and Doppler-broadening spectroscopy, combined with the calculated results of positron lifetime. The experimental results agree well with the calculated positron bulk lifetime in SmFeAsO and SmFeAsF crystals. The temperature dependence of S-parameter shows a remarkable difference between the parent and superconductor. An abrupt jump of S-parameter is detected around 150 K in parent sample, however, two different slopes were shown below and above superconducting transition. The linearity S-T plot determines one-type of defects through the superconducting transition which must play an important role in superconductivity.
16. Silicide phase formation in Ni/Si system: Depth-resolved positron annihilation and Rutherford backscattering study
SciTech Connect
Abhaya, S.; Amarendra, G.; Panigrahi, B.K.; Nair, K.G.M.
2006-02-01
Silicidation in Ni/Si thin-film junction has been investigated using depth-resolved positron annihilation spectroscopy (PAS) and Rutherford backscattering spectrometry (RBS). Identification of various silicide phases from an analysis of the positron annihilation parameters is consistent with the RBS results. Absence of vacancy defects in the silicide region is clearly brought out by PAS00.
17. Mössbauer and positron annihilation studies of pharmaceutically important iron-dextran complexes
Oshtrakh, M. I.; Kopelyan, E. A.; Semionkin, V. A.; Livshits, A. B.; Krylova, V. E.; Kozlov, A. A.
1993-04-01
Iron-dextran complexes are pharmaceutically important models of iron-storage protein ferritin. These complexes are used for treatment of iron-deficiency anemias. In this work we present the results of the study of various iron-dextran complexes by Mössbauer spectroscopy and the positron annihilation technique. Mössbauer spectroscopy indicated the differences between the electronic and magnetic structures of iron cores in iron-dextran complexes while positron annihilation showed variations of dextran shells in those complexes. Both techniques appeared to be useful to study microstructural variations in iron-dextran complexes.
18. γ-Ray spectra and enhancement factors for positron annihilation with core electrons.
PubMed
Green, D G; Gribakin, G F
2015-03-06
Many-body theory is developed to calculate the γ spectra for positron annihilation in noble-gas atoms. Inclusion of electron-positron correlation effects and core annihilation gives spectra in excellent agreement with experiment [K. Iwata et al., Phys. Rev. Lett. 79, 39 (1997)]. The calculated correlation enhancement factors γ_{nl} for individual electron orbitals nl are found to scale with the ionization energy I_{nl} (in eV), as γ_{nl}=1+sqrt[A/I_{nl}]+(B/I_{nl})^{β}, where A≈40 eV, B≈24 eV, and β≈2.3.
19. Positron annihilation studies in the field induced depletion regions of metal-oxide-semiconductor structures
SciTech Connect
Asoka-Kumar, P.; Leung, T.C.; Lynn, K.G.; Nielsen, B.; Forcier, M.P. ); Weinberg, Z.A.; Rubloff, G.W. )
1992-06-01
The centroid shifts of positron annihilation spectra are reported from the depletion regions of metal-oxide-semiconductor (MOS) capacitors at room temperature and at 35 K. The centroid shift measurement can be explained using the variation of the electric field strength and depletion layer thickness as a function of the applied gate bias. An estimate for the relevant MOS quantities is obtained by fitting the centroid shift versus beam energy data with a steady-state diffusion-annihilation equation and a derivative-gaussian positron implantation profile. Inadequacy of the present analysis scheme is evident from the derived quantities and alternate methods are required for better predictions.
20. Jet algorithms in electron-positron annihilation: perturbative higher order predictions
Weinzierl, Stefan
2011-02-01
This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti- k t , as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are N3LO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rates and LO for the five-jet rates.
1. Positron-annihilation 2D-ACAR studies of disordered and defected alloys
SciTech Connect
Bansil, A.; Prasad, R.; Smedskjaer, L.C.; Benedek, R.; Mijnarends, P.E.
1987-09-01
Theoretical and experimental progess in connection with 2D-ACAR positron annihilation studies of ordered, disordered, and defected alloys is discussed. We present, in particular, some of the recent developments concerning the electronic structure of disordered alloys, and the work in the area of annihilation from positrons trapped at vacancy-type defects in metals and alloys. The electronic structure and properties of a number of compounds are also discussed briefly; we comment specifically on high T/sub c/ ceramic superconductors, Heusler alloys, and transition-metal aluminides. 58 refs., 116 figs.
2. Asymmetric 511 keV Positron Annihilation Line Emission from the Inner Galactic Disk
NASA Technical Reports Server (NTRS)
Skinner, Gerry; Weidenspointner, Georg; Jean, Pierre; Knodlseder, Jurgen; Ballmoos, Perer von; Bignami, Giovanni; Diehl, Roland; Strong, Andrew; Cordier, Bertrand; Schanne, Stephane; Winkler, Christoph
2008-01-01
A recently reported asymmetry in the 511 keV gamma-ray line emission from the inner galactic disk is unexpected and mimics an equally unexpected one in the distribution of LMXBs seen at hard X-ray energies. A possible conclusion is that LMXBs are an important source of the positrons whose annihilation gives rise to the line. We will discuss these results, their statistical significance and that of any link between the two. The implication of any association between LMXBs and positrons for the strong annihilation radiation from the galactic bulge will be reviewed.
3. Construction of a surface positronium lifetime spectroscopy apparatus with a spin-polarized low energy positron beam
Maekawa, M.; Wada, K.; Miyashita, A.; Kawasuso, A.
2017-01-01
We have developed a surface positronium (Ps) lifetime spectrometer. A spin-polarized slow positron beam is generated by a sodium-22 source and a solid krypton moderator and transported to the sample chamber by electrostatic lenses. The incident energy is adjusted by a retarding potential using a deceleration tube. For the lifetime measurement, the start signal is obtained from a secondary-electron detector installed in front of the sample. The stop signal is detected by a scintillation detector for annihilation gamma rays. As a performance test, Ps lifetime measurements were carried out and clear decay curves derived from ortho-Ps self-annihilation were successfully observed. This system might be used for the estimation of the spin polarization at the surface of ferromagnetic materials.
4. Positron distribution contribution to changes in annihilation characteristics across Tc in high-temperature superconductors
SciTech Connect
Bharathi, A.; Sundar, C.S.; Ching, W.Y.; Jean, Y.C. ); Hor, P.H.; Xue, Y.Y.; Chu, C.W. )
1990-12-01
In this paper we present detailed calculations of the positron distribution in a host of high-temperature superconductors using the electron densities and potentials obtained from self-consistent orthogonalized linear combination of atomic orbitals band-structure calculations. The positron and electron densities obtained from the calculations are used to evaluate the electron-positron overlap function, which reveals that the major contribution to positron annihilation in these materials is from the oxygen atoms. A systematic correlation between the nature of this overlap function within the Cu-O cluster and the experimentally observed temperature dependence of the annihilation characteristics in the superconducting state is established: A decrease in positron annihilation parameters, below {Tc}, is observed when the overlap is predominantly from the apical oxygen atom, whereas an increase is observed if the overlap is predominantly from the planar oxygen atom. The observed temperature dependence of the positron parameters below {Tc} in all the high-{Tc} superconductors is understood in terms of an electron density transfer from the planar oxygen atoms to the apical oxygen atoms. These results are discussed in the light of charge-transfer models of superconductivity in the cuprate superconductors.
5. Miscibility and crystallization behavior of poly (3-hydroxybutyrate) and poly (ethylene glycol) blends studied by positron annihilation spectroscopy
Abdel-Hady, E. E.; Abdel-Hamed, M. O.; Hammam, A. M.
2011-01-01
Positron annihilation Lifetime (PAL) spectroscopy has been used to study the effect of PEG concentrations on the free volume properties of PHB. The data revealed that the ortho-positronium (o-Ps) lifetime τPs increases with 20% increase in concentration, decrease as the concentration increases to 40%, then rapid increase at 50% concentration of PEG. The o-Ps intensity, I3, shows a linear dependence as the concentration increases with a discontinuity at 20% concentration of PEG. Furthermore, the results presented and discussed in this work show that the PHB and PEG are miscible up to 40% of PEG but greater than 40%, the blend is immiscible. In addition, the mechanical properties of PHB are well improved by the addition of PEG with a low concentration up to 20%, while at higher concentration the blend becomes waxy.
6. Centroid shift of. gamma. rays from positron annihilation in the depletion region of metal-oxide-semiconductor structures
SciTech Connect
Leung, T.C.; Kong, Y.; Lynn, K.G.; Nielsen, B. ); Weinberg, Z.A.; Rubloff, G.W. )
1991-01-07
Using metal-oxide-semiconductor (MOS) structures, the shift of centroid (peak) of {gamma}-ray energy distributions emitted from positron annihilation has been measured as a function of incident positron energy. The Doppler centroid shift was found to be consistent with the positron motion in the MOS depletion region. The results are described by a one-dimensional positron diffusion model, and provide information on effective'' positron diffusion length under applied field.
7. Whole-Pattern Fitting and Positron Annihilation Studies of Magnetic PVA/α-Fe2O3 Nanocomposites
Prashanth, K. S.; Mahesh, S. S.; Prakash, M. B. Nanda; Ningaraju, S.; Ravikumar, H. B.; Somashekar, R.; Nagabhushana, B. M.
2016-06-01
A low-temperature solution combustion method was used to synthesize α-Fe2O3 nanoparticles. Magnetic polyvinyl alcohol (PVA)/α-Fe2O3/NaCl nanocomposites were prepared by solvent cast method. The Fourier transform infrared (FTIR) spectroscopy and scanning electron microscopy (SEM) results are in confirmation with X-ray diffraction (XRD) results indicating the formation of nanocomposites. The microcrystalline parameters, crystallite size ( ), lattice strain ( g in %), stacking faults ( α d ), and twin faults ( β) of prepared polymer nanocomposites were evaluated by whole-pattern fitting technique. The refinement was carried out using the computed microstructural parameters in which the twin faults and stacking faults did not vary much and statistical deviation was less than 5 %. Positron annihilation lifetime spectroscopy (PALS) was used for microstructural characterization. PALS results show that the ortho-positronium (o-Ps) lifetime (τ3) increases gradually as a function of nanoparticle concentration and about 219 ps increase observed from1.50 to1.71 ns at 3 wt%. This indicates the increase of free volume hole size ( V f ) from 54.47 to 72.18 Å3. The o-Ps intensities ( I 3) decrease indicating the inhibition of o-Ps formation upon incorporation of nanoparticles into PVA. The increase in I 2 values suggests the increased annihilation at the interface region. Positron lifetime parameters, viz., o-Ps lifetime, and its intensities indicate the effect of quenching and inhibition upon incorporation of metal oxide nanoparticles and inorganic salt into PVA.
8. Theoretical studies of positron states and annihilation characteristics at the oxidized Cu(100) surface
SciTech Connect
Fazleev, N. G.; Weiss, A. H.
2013-04-19
In this work we present the results of theoretical studies of positron surface and bulk states and annihilation probabilities of surface-trapped positrons with relevant core electrons at the oxidized Cu(100) surface under conditions of high oxygen coverage. An ab-initio study of the electronic properties of the Cu(100) missing row reconstructed surface at various on surface and sub-surface oxygen coverages has been performed on the basis of the density functional theory (DFT) using the Dmol3 code and the generalized gradient approximation (GGA). Surface structures in calculations have been constructed by adding oxygen atoms to various surface hollow and sub-surface octahedral sites of the 0.5 monolayer (ML) missing row reconstructed phase of the Cu(100) surface with oxygen coverages ranging from 0.5 to 1.5 ML. The charge redistribution at the surface and variations in atomic structure and chemical composition of the topmost layers associated with oxidation and surface reconstruction have been found to affect the spatial extent and localization of the positron surface state wave function and annihilation probabilities of surface trapped positrons with relevant core electrons. Theoretical results are compared with experimental data obtained from studies of oxidation of the Cu(100) surface using positron annihilation induced Auger electron spectroscopy (PAES). It has been shown that positron annihilation probabilities with Cu 3s and 3p core electrons decrease when total (on-surface and sub-surface) oxygen coverage of the Cu(100) surface increases up to 1 ML. The calculations show that for high oxygen coverage when total oxygen coverage is 1. 5 ML the positron is not bound to the surface.
9. A positron annihilation spectroscopic investigation of europium-doped cerium oxide nanoparticles.
PubMed
Thorat, Atul V; Ghoshal, Tandra; Holmes, Justin D; Nambissan, P M G; Morris, Michael A
2014-01-07
Doping in ceria (CeO2) nanoparticles with europium (Eu) of varying concentrations (0, 0.1, 0.5, …, 50 atom%) is studied using complementary experimental techniques and novel observations were made during the investigation. The immediate observable effect was a distinct reduction in particle sizes with increasing Eu concentration attributed to the relaxation of strain introduced due to the replacement of Ce(4+) ions by Eu(3+) ions of larger radius. However, this general trend was reversed in the doping concentration range of 0.1-1 atom% due to the reduction of Ce(4+) to Ce(3+) and the formation of anion vacancies. Quantum confinement effects became evident with the increase of band gap energy when the particle sizes reduced below 7-8 nm. Positron annihilation studies indicated the presence of vacancy type defects in the form of vacancy clusters within the nanoparticles. Some positron annihilation was also seen on the surface of crystallites as a result of diffusion of thermalized positrons before annihilation. Coincidence Doppler broadening measurements indicated the annihilation of positrons with electrons of different species of atoms and the characteristic S-W plot showed a kink-like feature at the particle sizes where quantum confinement effects began.
10. Positron annihilation process in Ni/sub c/Cu/sub 1-c/ alloys
SciTech Connect
Szotek, Z.; Gyorffy, B.L.; Stocks, G.M.; Temmerman, W.M.
1982-01-01
New, accurate, calculations of the electron momentum distribution function for the Cu/sub 60/Ni/sub 40/ random solid solution are presented and the role played by the positron wavefunction in determining the Angular Correlation of the Annihilation Radiation (ACAR) is discussed in quantitative terms.
11. Positron annihilation spectroscopy of vacancy-type defects hierarchy in submicrocrystalline nickel during annealing
SciTech Connect
Kuznetsov, Pavel V.; Mironov, Yuri P. E-mail: [email protected] Tolmachev, Aleksey I. E-mail: [email protected] Rakhmatulina, Tanzilya V. E-mail: [email protected]; Bordulev, Yuri S. E-mail: [email protected] Laptev, Roman S. E-mail: [email protected] Lider, Andrey M. E-mail: [email protected] Mikhailov, Andrey A. E-mail: [email protected]; Korznikov, Alexander V.
2014-11-14
Positron annihilation and X-ray diffraction analysis have been used to study submicrocrystalline nickel samples prepared by equal channel angular pressing. In the as-prepared samples the positrons are trapped at dislocation-type defects and in vacancy clusters that can include up to 5 vacancies. The study has revealed that the main positron trap centers at the annealing temperature of ΔT= 20°C-180°C are low-angle boundaries enriched by impurities. At ΔT = 180°C-360°C, the trap centers are low-angle boundaries providing the grain growth due to recrystallization in-situ.
12. Desorption of water from hydrophilic MCM-41 mesopores: positron annihilation, FTIR and MD simulation studies.
PubMed
Maheshwari, Priya; Dutta, D; Muthulakshmi, T; Chakraborty, B; Raje, N; Pujari, P K
2017-02-08
The desorption mechanism of water from the hydrophilic mesopores of MCM-41 was studied using positron annihilation lifetime spectroscopy (PALS) and attenuated total reflection Fourier transform infrared spectroscopy supplemented with molecular dynamics (MD) simulation. PALS results indicated that water molecules do not undergo sequential evaporation in a simple layer-by-layer manner during desorption from MCM-41 mesopores. The results suggested that the water column inside the uniform cylindrical mesopore become stretched during desorption and induces cavitation (as seen in the case of ink-bottle type pores) inside it, keeping a dense water layer at the hydrophilic pore wall, as well as a water plug at both the open ends of the cylindrical pore, until the water was reduced to a certain volume fraction where the pore catastrophically empties. Before being emptied, the water molecules formed clusters inside the mesopores. The formation of molecular clusters below a certain level of hydration was corroborated by the MD simulation study. The results are discussed.
13. Desorption of water from hydrophilic MCM-41 mesopores: positron annihilation, FTIR and MD simulation studies
Maheshwari, Priya; Dutta, D.; Muthulakshmi, T.; Chakraborty, B.; Raje, N.; Pujari, P. K.
2017-02-01
The desorption mechanism of water from the hydrophilic mesopores of MCM-41 was studied using positron annihilation lifetime spectroscopy (PALS) and attenuated total reflection Fourier transform infrared spectroscopy supplemented with molecular dynamics (MD) simulation. PALS results indicated that water molecules do not undergo sequential evaporation in a simple layer-by-layer manner during desorption from MCM-41 mesopores. The results suggested that the water column inside the uniform cylindrical mesopore become stretched during desorption and induces cavitation (as seen in the case of ink-bottle type pores) inside it, keeping a dense water layer at the hydrophilic pore wall, as well as a water plug at both the open ends of the cylindrical pore, until the water was reduced to a certain volume fraction where the pore catastrophically empties. Before being emptied, the water molecules formed clusters inside the mesopores. The formation of molecular clusters below a certain level of hydration was corroborated by the MD simulation study. The results are discussed.
14. JRQ and JPA irradiated and annealed reactor pressure vessel steels studied by positron annihilation
Slugeň, Vladimír; Gokhman, Oleksandr; Pecko, Stanislav; Sojak, Stanislav; Bergner, Frank
2016-03-01
The paper is focused on a comprehensive study of JRQ and JPA reactor pressure vessel steels from the positron annihilation lifetime spectroscopy (PALS) point of view. Based on our more than 20 years' experience with characterization of irradiated reactor steels, we confirmed that defects after irradiation start to grow and/or merge into bigger clusters. Experimental results shown that JPA steel is more sensitive to the creation of irradiation-induced defects than JRQ steel. It is most probably due to high copper content (0.29 wt.% in JPA) and copper precipitation has a major impact on neutron-induced defect creation at the beginning of the irradiation. Based on current PALS results, no large vacancy clusters were formed during irradiation, which could cause dangerous embrittlement concerning operation safety of nuclear power plant. The combined PALS, small angle neutron scattering and atomic probe tomography studies support the model for JRQ and JPA steels describing the structure of irradiation-induced clusters as agglomerations of vacancy clusters (consisting of 2-6 vacancies each) and are separated from each other by a distribution of atoms.
15. Radiation defects induced by helium implantation in gold-based alloys investigated by positron annihilation spectroscopy
Thome, T.; Grynszpan, R. I.
2006-06-01
The formation of gas bubbles in metallic materials may result in drastic degradation of in-service properties. In order to investigate this effect in high density and medium-low melting temperature ( T-M ) alloys, positron annihilation spectroscopy measurements were performed on helium-implanted gold-silver solid solutions after isochronal annealing treatments. Three recovery stages are observed, attributed to the migration and elimination of defects not stabilized by helium atoms, helium bubble nucleation and bubble growth. Similarities with other metals are found for the recovery stages involving bubble nucleation and growth processes. Lifetime measurements indicate that He implantation leads to the formation of small and over-pressurized bubbles that generate internal stresses in the material. A comprehensive picture is drawn for possible mechanisms of helium bubble evolution. Two values of activation energy (0.26 and 0.53 eV) are determined below and above 0.7 T-M , respectively, from the variation of the helium bubble radius during the bubble growth stage. The migration and coalescence mechanism, which accounts for these very low activation energies, controls the helium bubble growth.
16. Measuring electron-positron annihilation radiation from laser plasma interactions
SciTech Connect
Chen, Hui; Tommasini, R.; Seely, J.; Szabo, C. I.; Feldman, U.; Pereira, N.; Gregori, G.; Falk, K.; Mithen, J.; Murphy, C. D.
2012-10-15
We investigated various diagnostic techniques to measure the 511 keV annihilation radiations. These include step-wedge filters, transmission crystal spectroscopy, single-hit CCD detectors, and streaked scintillating detection. While none of the diagnostics recorded conclusive results, the step-wedge filter that is sensitive to the energy range between 100 keV and 700 keV shows a signal around 500 keV that is clearly departing from a pure Bremsstrahlung spectrum and that we ascribe to annihilation radiation.
17. Bulk Materials Analysis Using High-Energy Positron Beams
SciTech Connect
Glade, S C; Asoka-Kumar, P; Nieh, T G; Sterne, P A; Wirth, B D; Dauskardt, R H; Flores, K M; Suh, D; Odette, G R
2002-11-11
This article reviews some recent materials analysis results using high-energy positron beams at Lawrence Livermore National Laboratory. We are combining positron lifetime and orbital electron momentum spectroscopic methods to provide electron number densities and electron momentum distributions around positron annihilation sites. Topics covered include: correlation of positron annihilation characteristics with structural and mechanical properties of bulk metallic glasses, compositional studies of embrittling features in nuclear reactor pressure vessel steel, pore characterization in Zeolites, and positron annihilation characteristics in alkali halides.
18. A novel design for a variable energy positron lifetime spectrometer
Chen, D.; Zhang, J. D.; Cheng, C. C.; Beling, C. D.; Fung, S.
2008-10-01
We present computer simulations of a new design of a variable energy positron lifetime beam that uses for a start signal the secondary electron emission from a 25-nm thick carbon foil (C-foil) located in front of the sample. A needle of ˜30 μm diameter is positioned on-axis right behind the foil, creating a radial electric field that deflects the secondary electrons radially outward so as to miss the sample and to hit the micro-channel plate (MCP) detector placed down beam. The MCP signal provides the start signal for the positron lifetime spectrometer. A grid can be further introduced between the sample holder and the MCP to yield a cleaner signal by preventing the positrons with large transmitted scattering angle from hitting the MCP. The cylindrical symmetry of this design reduces the experimental complexity and offers good timing resolution. We show that the design is robust against the transmitted energy and angle of the secondary electrons and positrons.
19. Mn-Doping in NiO Nanoparticles: Defects-Modifications and Associated Effects Investigated Through Positron Annihilation Spectroscopy.
PubMed
Das, Anjan; Mandal, Atis Chandra; Roy, Soma; Nambissan, P M G
2016-04-01
Manganese-doped nickel oxide (Ni1-xMnxO) nanoparticulate samples with x in the range 0 (undoped sample) to 0.35 were synthesized by sol-gel method involving chemical reactions between the solutions of nickel nitrate hexahydrate and manganese acetate tetrahydrate. The nanocrystallites obtained after annealing of the precipitates for different durations were characterized by X-ray diffraction and high resolution transmission electron microscopy. The samples showed high degree of purity with no secondary phase up to 35 at.% (x = 0.35) of Mn-doping. At the initial doping concentrations, the crystallite sizes increased due to vacancy type defects being recombined with some of the doped Mn2+ ions. However, substitution-induced strain soon overtook the crystallite dynamics and the sizes rapidly started reducing again as an indirect consequence of the necessity to accommodate majority of the doped cations on the surfaces of the nanocrystallites. There was conspicuous changes in the lattice parameter too which could again be attributed to the strain and charge effects. The average sizes of the crystallites were obtained in the range 5.5 nm to 13.1 nm for the different samples. UV-Vis absorption studies indicated the formation of excitonic states in NiO on Mn-doping. The band gap energy (Eg) derived from the optical absorption spectra showed a continuous increase with increase of Mn-doping of the samples. Positron lifetime and Doppler broadening spectroscopic studies were carried out on those samples to characterize the vacancy type defects and defect clusters/complexes. There were also indications to suggest positron annihilation at the crystallite surfaces owing to their sizes of nanometer order. Positron lifetimes decreased upon increase of Mn-doping. The coincidence Doppler broadened ratio curves indicated definite shifts of the prominent oxygen-electron-annihilation peak and the variation of the lineshape parameter S also indicated clearly the effects of Mn-doping.
20. Correlation of soft magnetic properties with free volume and medium range ordering in metallic glasses probed by fluctuation microscopy and positron annihilation technique
Srivastava, A. P.; Srivastava, D.; Sudarshan, K.; Sharma, S. K.; Pujari, P. K.; Majumdar, B.; Suresh, K. G.; Dey, G. K.
2012-08-01
Amorphous ribbons of different thicknesses of Co64.5Fe3.5Si16B14Ni2 alloy were synthesized using the melt spinning technique by varying wheel speed. The effect of cooling rate on the ribbon thickness and their soft magnetic properties have been studied. The amorphous structure has been characterized in terms of structural free volume and medium range order (MRO) by positron annihilation spectroscopy and fluctuation electron microscopy techniques. Positron lifetime spectra of amorphous samples showed two lifetime components. The first component was found to be correlated with MRO whereas, the second lifetime component was found to be associated with nanovoid type of defects, and the second component was strongly dependent on processing conditions. It could be established that the coercivity of the amorphous samples produced by the rapid solidification technique mainly depends on the defects formed during processing rather than change induced in MRO.
1. Electron momentum distribution and singlet-singlet annihilation in the organic anthracene molecular crystals using positron 2D-ACAR and fluorescence spectroscopy.
PubMed
Selvakumar, Sellaiyan; Sivaji, Krishnan; Arulchakkaravarthi, Arjunan; Sankar, Sambasivam
2014-08-14
We present the mapping of electron momentum distribution (EMD) in a single crystal of anthracene by two-dimensional angular correlation of positron annihilation radiation (2D-ACAR). The projected EMD is explained on the basis of the crystallographic features of the material. The EMD spectra provide information about the positron states and their behavior and also about the hindrance of the positronium (Ps) formation in this material. The EMD has exhibited evidence for the absence of free volume defects. The characteristic EMD features regarding the delocalized electronic states are explained. Further, scintillation characteristics such as fluorescence and time-correlated single photon counting have also been studied. The emission peaks are attributed to vibrational bands of fluorescence emission from the singlet excitons and lifetime components are observed to be due to singlet fission and the singlet-singlet excitons annihilation.
2. On positron annihilation in concentrated random alloys and superconducting cuprates
SciTech Connect
Szotek, Z.; Temmerman, W.M.; Gyorffy, B.L.; Stocks, G.M.
1988-01-01
We discuss an application of a generalisation of the Lock-Crisp-West theorem to concentrated random alloys. Using a theory developed for binary random alloys we explore a possibility of positron localisation in the new high temperature superconductors. 7 refs., 1 fig.
3. Annihilation momentum density of positrons trapped at vacancy-type defects in metals and alloys
SciTech Connect
Bansil, A.; Prasad, R.; Benedek, R.
1988-01-01
Positron annihilation, especially the angular correlation of annihilation radiation, is a powerful tool for investigating the electronic spectra of ordered as well as defected materials. The tendency of positrons to trap at vacancy-type defects should enable this technique to study the local environment of such defects. However, we need to develop a theoretical basis for calculating the two-photon annihilation momentum density rho/sub 2gamma/(p-vector). We have recently formulated and implemented a theory of rho/sub 2gamma/(p-vector) from vacancy-type defects in metals and alloys. This article gives an outline of our approach together with a few of our results. Section 2 summarizes the basic equations for evaluating rho/sub 2gamma/(p-vector). Our Green's function-based approach is nonperturbative and employs a realistic (one-particle) muffin-tin Hamiltonian for treating electrons and positrons. Section 3 presents and discusses rho/sub 2gamma/(p-vector) results for a mono-vacancy in Cu. We have neglected the effects of electron-positron correlations and of lattice distortion around the vacancy. Section 4 comments briefly on the question of treating defects such as divacancies and metal-impurity complexes in metals and alloys. Finally, in Section 5, we remark on the form of rho/sub 2gamma/(p-vector) for a mono-vacancy in jellium. 2 figs.
4. Study of PRIMAVERA steel samples by a positron annihilation spectroscopy technique
Grafutin, V.; Ilyukhina, O.; Krsjak, V.; Burcl, R.; Hähner, P.; Erak, D.; Zeman, A.
2010-11-01
In the present article, a positron annihilation spectroscopy investigation of VVER-440/230 weld materials is discussed. Important characteristics of metals such as Fermi energy, concentration of electrons in the conduction band, size and concentration of defects were experimentally determined for three model materials with higher level of copper (0.16 wt.%) and phosphorus (0.027-0.038 wt.%). The impact of neutron irradiation and subsequent annealing on crystal lattice parameters was investigated. The experiments with the angular correlation of positron annihilation radiation (ACAR) complement the published positron annihilation spectroscopy (PAS) studies of the radiation treated VVER materials as well as previous experiments on PRIMAVERA materials. The availability of the experimental reactor to prepare strong 64Cu positron sources provided for unique experimental conditions, such as good resolution of spectra (0.4 mrad) and reasonable short time of measurement (36 h). The present paper aims to contribute to further understanding of RPV (reactor pressure vessel) steels behaviour under irradiation conditions as well as annealing recovery procedures, which have already been applied at several VVER NPP units in Europe.
5. Photoinduced dehydrogenation of defects in undoped a-si:H using positron annihilation spectroscopy.
PubMed
Zou, X; Chan, Y C; Webb, D P; Lam, Y W; Hu, Y F; Beling, C D; Fung, S; Weng, H M
2000-01-24
We report changes in variable-energy positron annihilation spectroscopy measurements on undoped hydrogenated amorphous silicon films after light soaking. The change, seen predominantly in the high momentum band of the annihilation radiation, is not reversed by thermal annealing. We suggest, following recent models of the Staebler-Wronski effect, that light exposure induces hydrogen trapped in vacancylike defects to become mobile in the Si network. The observations place constraints on models of hydrogen motion fitting macroscopic Staebler-Wronski effect kinetics and may help to achieve a definitive description of metastability in a-Si:H.
6. Time of flight spectrometer for background-free positron annihilation induced Auger electron spectroscopy.
PubMed
Mukherjee, S; Shastry, K; Anto, C V; Joglekar, P V; Nadesalingam, M P; Xie, S; Jiang, N; Weiss, A H
2016-03-01
We describe a novel spectrometer designed for positron annihilation induced Auger electron spectroscopy employing a time-of-flight spectrometer. The spectrometer's new configuration enables us to implant monoenergetic positrons with kinetic energies as low as 1.5 eV on the sample while simultaneously allowing for the detection of electrons emitted from the sample surface at kinetic energies ranging from ∼500 eV to 0 eV. The spectrometer's unique characteristics made it possible to perform (a) first experiments demonstrating the direct transition of a positron from an unbound scattering state to a bound surface state and (b) the first experiments demonstrating that Auger electron spectra can be obtained down to 0 eV without the beam induced secondary electron background obscuring the low energy part of the spectra. Data are presented which show alternative means of estimating positron surface state binding energy and background-free Auger spectra.
7. Development and Testing of the Positron Identification By Coincident Annihilation Photons (PICAP) System
Tran, D.; Connell, J. J.; Lopate, C.; Bickford, B.
2014-12-01
Moderate energy positrons (~few to 10 MeV) have seldom been observed in the Heliosphere, due primarily to there not having been dedicated instruments for such measurements. Their detection would have implications in the study of Solar energetic particle events and the transport and modulation of the Solar wind and Galactic cosmic rays. The Positron Identification by Coincident Annihilation Photons (PICAP) system is designed specifically to measure these moderate energy positrons by simultaneously detecting the two 511-keV γ-ray photons that result from a positron stopping in the instrument and the subsequent electron-positron annihilation. This method is also expected to effectively discriminate positrons from protons by measuring the amount of energy deposited in the detectors (dE/dx versus residual energy). PICAP offers a low-mass, low-power option for measuring positrons, electrons, and ions in space. Following Monte Carlo modeling, a PICAP laboratory prototype, adaptable to a space-flight design, was designed, built, and tested. This instrument is comprised of (Si) solid-state detectors, plastic scintillation detectors, and high-Z BGO crystal scintillator suitable for detecting the 511-keV γ rays. The prototype underwent preliminary laboratory testing and calibration using radioactive sources for the purpose of establishing functionality. It has since been exposed to beams of energetic protons (up to ~200 MeV) at Massachusetts General Hospital's Francis H. Burr Proton Beam Therapy Center and positrons and electrons (up to ~10 MeV) at Idaho State University's Idaho Accelerator Center. The goal is to validate modeling and determine the performance of the instrument concept. We will present a summary of modeling calculations and analysis of data taken at the accelerator tests. This work is 95% supported by NASA Grant NNX10AC10G.
8. Positron annihilation signatures associated with the outburst of the microquasar V404 Cygni.
PubMed
Siegert, Thomas; Diehl, Roland; Greiner, Jochen; Krause, Martin G H; Beloborodov, Andrei M; Bel, Marion Cadolle; Guglielmetti, Fabrizia; Rodriguez, Jerome; Strong, Andrew W; Zhang, Xiaoling
2016-03-17
Microquasars are stellar-mass black holes accreting matter from a companion star and ejecting plasma jets at almost the speed of light. They are analogues of quasars that contain supermassive black holes of 10(6) to 10(10) solar masses. Accretion in microquasars varies on much shorter timescales than in quasars and occasionally produces exceptionally bright X-ray flares. How the flares are produced is unclear, as is the mechanism for launching the relativistic jets and their composition. An emission line near 511 kiloelectronvolts has long been sought in the emission spectrum of microquasars as evidence for the expected electron-positron plasma. Transient high-energy spectral features have been reported in two objects, but their positron interpretation remains contentious. Here we report observations of γ-ray emission from the microquasar V404 Cygni during a recent period of strong flaring activity. The emission spectrum around 511 kiloelectronvolts shows clear signatures of variable positron annihilation, which implies a high rate of positron production. This supports the earlier conjecture that microquasars may be the main sources of the electron-positron plasma responsible for the bright diffuse emission of annihilation γ-rays in the bulge region of our Galaxy. Additionally, microquasars could be the origin of the observed megaelectronvolt continuum excess in the inner Galaxy.
9. Positron annihilation signatures associated with the outburst of the microquasar V404 Cygni
Siegert, Thomas; Diehl, Roland; Greiner, Jochen; Krause, Martin G. H.; Beloborodov, Andrei M.; Bel, Marion Cadolle; Guglielmetti, Fabrizia; Rodriguez, Jerome; Strong, Andrew W.; Zhang, Xiaoling
2016-03-01
Microquasars are stellar-mass black holes accreting matter from a companion star and ejecting plasma jets at almost the speed of light. They are analogues of quasars that contain supermassive black holes of 106 to 1010 solar masses. Accretion in microquasars varies on much shorter timescales than in quasars and occasionally produces exceptionally bright X-ray flares. How the flares are produced is unclear, as is the mechanism for launching the relativistic jets and their composition. An emission line near 511 kiloelectronvolts has long been sought in the emission spectrum of microquasars as evidence for the expected electron-positron plasma. Transient high-energy spectral features have been reported in two objects, but their positron interpretation remains contentious. Here we report observations of γ-ray emission from the microquasar V404 Cygni during a recent period of strong flaring activity. The emission spectrum around 511 kiloelectronvolts shows clear signatures of variable positron annihilation, which implies a high rate of positron production. This supports the earlier conjecture that microquasars may be the main sources of the electron-positron plasma responsible for the bright diffuse emission of annihilation γ-rays in the bulge region of our Galaxy. Additionally, microquasars could be the origin of the observed megaelectronvolt continuum excess in the inner Galaxy.
10. Surface states and positron annihilation spectroscopy: results and prospects from a first-principles approach
Callewaert, V.; Saniz, R.; Barbiellini, B.; Partoens, B.
2017-01-01
The trapping of positrons at the surface of a material can be exploited to study quite selectively the surface properties of the latter by means of positron annihilation spectroscopy techniques. To support these, it is desirable to be able to theoretically predict the existence of such positronic surface states and to describe their annihilation characteristics with core or valence surface electrons in a reliable way. Here, we build on the well-developed first-principles techniques for the study of positrons in bulk solids as well as on previous models for surfaces, and investigate two schemes that can improve the theoretical description of the interaction of positrons with surfaces. One is based on supplementing the local-density correlation potential with the corrugated image potential at the surface, and the other is based on the weighted-density approximation to correlation. We discuss our results for topological insulators, graphene layers, and quantum dots, with emphasis on the information that can be directly related to experiment. We also discuss some open theoretical problems that should be addressed by future research.
11. J-PET detector system for studies of the electron-positron annihilations
Pawlik-Niedźwiecka, M.; Khreptak, O.; Gajos, A.; Wieczorek, A.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Głowacz, B.; Gupta-Sharma, N.; Gorgol, M.; Hiesmayr, B. C.; Jasińska, B.; Kamińska, D.; Korcyl, G.; Kowalski, P.; Krzmień, W.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Niedźwiecki, Sz.; Raczyński, L.; Rudy, Z.; Silarski, M.; Wiślicki, W.; Zgardzińska, B.; Zieliński, M.; Moskal, P.
2016-11-01
Jagiellonian Positron Emission Tomograph (J-PET) has been recently constructed at the Jagiellonian University as a prototype of a cost-effective scanner for the metabolic imaging of the whole human body. J-PET detector is optimized for the measurement of momentum and polarization of photons from the electron-positron annihilations. It is built out of strips of plastic scintillators, forming three cylindrical layers. As detector of gamma quanta it will be used for studies of discrete symmetries and multiparticle entanglement of photons originating from the decays of ortho-positronium atoms.
12. Positron annihilation studies of the electronic structure and fermiology of the high-{Tc} superconductors
SciTech Connect
Smedskjaer, L.C.; Bansil, A.
1992-09-01
We discuss the application of the positron annihilation angular correlation (ACAR) spectroscopy for investigating the electronic structure and Fermiology of the high-T{sub c} superconductors, with focus on the YBa{sub 2}Cu{sub 3}O{sub 7} system where most of the experimental and theoretical work has to date been concentrated. Comparisons between measured 2D-ACAR positron spectra and band theory predictions show a remarkable agreement (for the normal state), indicating that the electronic structure and Fermi surface of this material is described reasonably by the conventional picture.
13. Positron annihilation studies of the electronic structure and fermiology of the high-[Tc] superconductors
SciTech Connect
Smedskjaer, L.C. ); Bansil, A. . Dept. of Physics)
1992-09-01
We discuss the application of the positron annihilation angular correlation (ACAR) spectroscopy for investigating the electronic structure and Fermiology of the high-T[sub c] superconductors, with focus on the YBa[sub 2]Cu[sub 3]O[sub 7] system where most of the experimental and theoretical work has to date been concentrated. Comparisons between measured 2D-ACAR positron spectra and band theory predictions show a remarkable agreement (for the normal state), indicating that the electronic structure and Fermi surface of this material is described reasonably by the conventional picture.
14. Characterization of Densified Fully-Stabilized Nanometric Zirconia by Positron Annihilation Spectroscopy
SciTech Connect
Garay, J E; Glade, S C; Asoka-Kumar, P; Anselmi-Tamburini, U; Munir, Z A
2005-04-05
Fully-stabilized nanometric zirconia samples with varying degrees of porosity and grain sizes were analyzed using the coincidence Doppler broadening mode of the positron annihilation spectroscopy (PAS). A decrease in the low momentum fraction was observed and coincided with a decrease in porosity. In addition to pores, it is proposed that defects in the negatively charges grain boundary space region act as positron trapping centers; their effectiveness decreases with an increase in grain size. It is shown that PAS is sensitive to small grain size differences within the nanometric regime in these oxide materials.
15. Positron beam lifetime spectroscopy of atomic scale defect distributions in bulk and microscopic volumes
SciTech Connect
Howell, R.H.; Cowan, T.E.; Hartley, J.; Sterne, P.; Brown, B.
1996-05-01
We are developing a defect analysis capability based on two positron beam lifetime spectrometers: the first is based on a 3 MeV electrostatic accelerator and the second on our high current linac beam. The high energy beam lifetime spectrometer is operational and positron lifetime analysis is performed with a 3 MeV positron beam on thick samples. It is being used for bulk sample analysis and analysis of samples encapsulated in controlled environments for {ital in}{ital situ} measurements. A second, low energy, microscopically focused, pulsed positron beam for defect analysis by positron lifetime spectroscopies is under development at the LLNL high current positron source. This beam will enable defect specific, 3-D maps of defect concentration with sub-micron location resolution and when coupled with first principles calculations of defect specific positron lifetimes it will enable new levels of defect concentration mapping and defect identification.
16. Resonant two-photon annihilation of an electron-positron pair in a pulsed electromagnetic wave
Voroshilo, A. I.; Roshchupkin, S. P.; Nedoreshta, V. N.
2016-09-01
Two-photon annihilation of an electron-positron pair in the field of a plane low-intensity circularly polarized pulsed electromagnetic wave was studied. The conditions for resonance of the process which are related to an intermediate particle that falls within the mass shell are studied. In the resonant approximation the probability of the process was obtained. It is demonstrated that the resonant probability of two-photon annihilation of an electron-positron pair may be several orders of magnitude higher than the probability of this process in the absence of the external field. The obtained results may be experimentally verified by the laser facilities of the international megaprojects, for example, SLAC (National Accelerator Laboratory), FAIR (Facility for Antiproton and Ion Research), and XFEL (European X-Ray Free-Electron Laser).
17. Macromolecular conformation in solution. Study of carbonic anhydrase by the positron annihilation technique.
PubMed Central
Handel, E D; Graf, G; Glass, J C
1980-01-01
The structural features of carbonic anhydrase (carbonate hydro-lyase; EC 4.2.1.1) in aqueous solution were probed by the positron annihilation technique. The data obtained under varying conditions of temperature, pH, and enzyme concentration were interpreted in terms of the free volume model. The change of enzymic activity with temperature is accompanied by a change in free volume of the protein. Upon thermal denaturation an irreversible change in free volume of the molecule occurred. At low temperatures the protein-water interactions were investigated. These results are discussed in terms of current concepts of structure-function relationships in proteins. This study shows the sensitivity of the positron annihilation method toward the structure of proteins related to their overall conformation and to the nature of bound water. PMID:6789901
18. Calculation of the positron annihilation rate in PsH with the positronic extension of the explicitly correlated nuclear-electronic orbital method.
PubMed
Pak, Michael V; Chakraborty, Arindam; Hammes-Schiffer, Sharon
2009-04-23
The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) method is modified and extended to study electron-positron quantum systems. The NEO-XCHF method is more computationally efficient than the explicitly correlated methods previously applied to positron systems because only the electron-positron dynamical correlation is treated explicitly in NEO-XCHF. As a result, the form of the wave function is much simpler with fewer parameters, and the variational optimization of the molecular orbital parameters is performed through an iterative scheme rather than a stochastic optimization. The NEO-XCHF approach is used to calculate the positron annihilation rate for positronium hydride (PsH). The resulting annihilation rate for PsH is within 20% of the most accurate values available and is calculated at a fraction of the computational cost. These results suggest that qualitatively accurate positron annihilation rates can be calculated treating only electron-positron correlation explicitly, leading to significant computational savings by neglecting electron-electron dynamical correlation. Thus, the NEO-XCHF approach could potentially enable the calculation of qualitatively accurate positron annihilation rates for larger positron systems.
19. INTEGRAL/SPI Observations of Electron-Positron Annihilation Radiation from our Galaxy
NASA Technical Reports Server (NTRS)
Teegarden, B. J.; Watanabe, K.; Knoedlseder, J.; Jean, P.; Lonjou, V.; Weidenspointer, G.; Skinner, G.; Vedrenne, G.; Roques, J.-P.; Schanne, S.; Schoenfelder, V.
2005-01-01
The spectrometer on INTEGRAL (SPI) is a coded-aperture gamma-ray telescope with moderate angular resolution (3 deg) and superior energy resolution (2 keV at 511 kev). One of it's principal science goals is the detailed study of 511 keV electron-positron annihilation from our Galaxy. The origin of this radiation remains a mystery, however current morphological studies suggest an older stellar population. There has also been recent speculation on the possibility of the existence of light (< 100 MeV) dark matter particles whose annihilation or decay could produce the observed 511 keV emission. In this paper we summarize the current results from SPI, compare them with previous results and discuss their implication on possible models for the production of the annihilation radiation.
20. INTEGRAL/SPI Limits on Electron-Positron Annihilation Radiation from the Galactic Plane
NASA Technical Reports Server (NTRS)
Teegarden, B. J.; Watanabe, K.; Jean, P.; Knoedlseder, J.; Lonjou, V.; Roques, J. P.; Skinner, G. K.; vonBallmoos, P.; Weidenspointner, G.; Bazzano, A.
2005-01-01
The center of our Galaxy is a known strong source of electron-positron 511- keV annihilation radiation. Thus far, however, there have been no reliable detections of annihilation radiation outside of the central radian of our Galaxy. One of the primary objectives of the INTEGRAL (INTErnational Gamma-RAy Astrophysics Laboratory) mission, launched in Oct. 2002, is the detailed study of this radiation. The Spectrometer on INTEGRAL (SPI) is a high resolution coded-aperture gamma-ray telescope with an unprecedented combination of sensitivity, angular resolution and energy resolution. We report results from the first 10 months of observation. During this period a significant fraction of the observing time was spent in or near the Galactic Plane. No positive annihilation flux was detected outside of the central region (|l| greater than 40 degrees) of our Galaxy. In this paper we describe the observations and data analysis methods and give limits on the 511-keV flux.
1. Prediction of positron-annihilation parameters for vacancy-type defects in ternary alloy semiconductors by data-scientific approach
Ishibashi, Shoji; Kino, Hiori; Uedono, Akira; Miyake, Takashi; Terakura, Kiyoyuki
2017-01-01
We calculated positron annihilation parameters for mono- and di-vacancies in ternary semiconductors Al0.5Ga0.5N and In0.5Ga0.5N. It has been found that the obtained annihilation parameters are well correlated with structural parameters. By constructing multiple linear regression models using selected (about 1/4 of the total) datasets as training sets in order to reduce computational cost, we could predict annihilation parameters for the rest.
2. Search for positron annihilation line and continuum radiation from the Galactic Center
NASA Technical Reports Server (NTRS)
Maccallum, C. J.; Leventhal, M.
1985-01-01
Our balloon-borne germain gamma-ray telescope was flown over Alice Springs, Australia, on 1984 November 20 to search for the 511 keV positron annihilation line from the Galactic Center. The measured line flux at Earth was (0.6 + or - 4.4) x 0.001 ph/sq cm/s indicating that the source was still in a low or off state.
3. P -wave coupled channel effects in electron-positron annihilation
Du, Meng-Lin; Meißner, Ulf-G.; Wang, Qian
2016-11-01
P -wave coupled channel effects arising from the D D ¯, D D¯ *+c .c . , and D*D¯* thresholds in e+e- annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the P -wave interactions in the e+e- annihilations, and then be employed to investigate possible isosinglet P -wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers JPC=1-+ . In the mass region of the D D ¯, D D¯ *+c .c . , and D*D¯* thresholds, there are two quark model bare states, i.e. the ψ (3770 ) and ψ (4040 ), which are assigned as (13D1) and (31S1) states, respectively. By an overall fit of the cross sections of e+e-→D D ¯, D D¯ *+c .c . , D*D¯*, we determine the physical coupling constants to each channel and extract the pole positions of the ψ (3770 ) and ψ (4040 ). The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the D and the D*. Besides the two poles, we also find a pole a few MeV above the D D¯ *+c .c . threshold which can be related to the so-called G (3900 ) observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the D*D¯* channel with high luminosity experiments.
4. Extragalactic Inverse Compton Light from Dark Matter annihilation and the Pamela positron excess
SciTech Connect
Profumo, Stefano; Jeltema, Tesla E. E-mail: [email protected]
2009-07-01
We calculate the extragalactic diffuse emission originating from the up-scattering of cosmic microwave photons by energetic electrons and positrons produced in particle dark matter annihilation events at all redshifts and in all halos. We outline the observational constraints on this emission and we study its dependence on both the particle dark matter model (including the particle mass and its dominant annihilation final state) and on assumptions on structure formation and on the density profile of halos. We find that for low-mass dark matter models, data in the X-ray band provide the most stringent constraints, while the gamma-ray energy range probes models featuring large masses and pair-annihilation rates, and a hard spectrum for the injected electrons and positrons. Specifically, we point out that the all-redshift, all-halo inverse Compton emission from many dark matter models that might provide an explanation to the anomalous positron fraction measured by the Pamela payload severely overproduces the observed extragalactic gamma-ray background.
5. Quantification of Stress History in Type 304L Stainless Steel Using Positron Annihilation Spectroscopy
SciTech Connect
Thomas W. Walters
2011-04-01
Five type 304L stainless steel specimens were subjected to incrementally increasing values of plastic strain. At each value of strain, the associated static stress was recorded and the specimen was subjected to Positron Annihilation Spectroscopy (PAS) using the Doppler Broadening method. A calibration curve for the ‘S’ parameter as a function of stress was developed based on the five specimens. Seven different specimens (blind specimens labeled B1-B7) of 304L stainless steel were subjected to values of stress inducing plastic deformation. The values of stress ranged from 310-517 MPa. The seven specimens were subjected to Positron Annihilation Spectroscopy post loading using the Doppler Broadening method, and the results were compared against the developed curve from the previous five specimens to determine feasibility of applying the curve to materials in order to non-destructively quantify stress history in materials based only on the ‘S’ parameter extracted from the Positron Annihilation Spectroscopy. Results for the calibration set of specimens indicated that calibration development is possible.
6. Characterization of interfaces in Binary and Ternary Polymer Blends by Positron Lifetime Spectroscopy
Ranganathaiah, C.
2015-06-01
A miscible blend is a single-phase system with compact packing of the polymeric chains/segments due configuration/conformational changes upon blending. Differential Scanning Calorimetry (DSC) is the most employed method to ascertain whether the blend is miscible or immiscible. Positron Lifetime Spectroscopy (PLS) has been employed in recent times to study miscibility properties of polymer blends by monitoring the ortho-Positronium annihilation lifetimes as function of composition. However, just free volume monitoring and the DSC methods fail to provide the composition dependent miscibility of blends. To overcome this limitation, an alternative approach based on hydrodynamic interactions has been developed to derive this information using the same o-Ps lifetime measurements. This has led to the development of a new method of measuring composition dependent miscibility level in binary and ternary polymer blends. Further, the new method also provides interface characteristics for immiscible blends. The interactions between the blend components has a direct bearing on the strength of adhesion at the interface and hence the hydrodynamic interaction. Understanding the characteristic of interfaces which decides the miscibility level of the blend and their end applications is made easy by the present method. The efficacy of the present method is demonstrated for few binary and ternary blends.
7. Positron lifetime spectroscopy for investigation of thin polymer coatings
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Sprinkle, Danny R.; Eftekhari, Abe
1993-01-01
In the aerospace industry, applications for polymer coatings are increasing. They are now used for thermal control on aerospace structures and for protective insulating layers on optical and microelectronic components. However, the effectiveness of polymer coatings depends strongly on their microstructure and adhesion to the substrates. Currently, no technique exists to adequately monitor the quality of these coatings. We have adapted positron lifetime spectroscopy to investigate the quality of thin coatings. Results of measurements on thin (25-micron) polyurethane coatings on aluminum and steel substrates have been compared with measurements on thicker (0.2-cm) self-standing polyurethane discs. In all cases, we find positron lifetime groups centered around 560 psec, which corresponds to the presence of 0.9-A(exp 3) free-volume cells. However, the number of these free-volume cells in thin coatings is larger than in thick discs. This suggests that some of these cells may be located in the interfacial regions between the coatings and the substrates. These results and their structural implications are discussed in this report.
8. Studies Of Oxidation And Thermal Reduction Of The Cu(100) Surface Using Positron Annihilation Induced Auger Electron Spectroscopy
SciTech Connect
2011-06-01
Positron annihilation induced Auger electron spectroscopy (PAES) measurements from the surface of an oxidized Cu(100) single crystal show a large increase in the intensity of the annihilation induced Cu M2,3VV Auger peak as the sample is subjected to a series of isochronal anneals in vacuum up to annealing temperature 300 deg. C. The PAES intensity then decreases monotonically as the annealing temperature is increased to {approx}550 deg. C. Experimental positron annihilation probabilities with Cu 3p and O 1s core electrons are estimated from the measured intensities of the positron annihilation induced Cu M{sub 2,3}VV and O KLL Auger transitions. PAES results are analyzed by performing calculations of positron surface states and annihilation probabilities of the surface-trapped positrons with relevant core electrons taking into account the charge redistribution at the surface and various surface structures associated with low and high oxygen coverages. The variations in atomic structure and chemical composition of the topmost layers of the oxidized Cu(100) surface are found to affect localization and spatial extent of the positron surface state wave function. The computed positron binding energy and annihilation characteristics reveal their sensitivity to charge transfer effects, atomic structure and chemical composition of the topmost layers of the oxidized Cu(100) surface. Theoretical positron annihilation probabilities with Cu 3p and O 1s core electrons computed for the oxidized Cu(100) surface are compared with experimental ones. The obtained results provide a demonstration of thermal reduction of the copper oxide surface after annealing at 300 deg. C followed by re-oxidation of the Cu(100) surface at higher annealing temperatures presumably due to diffusion of subsurface oxygen to the surface.
9. Single crystal growth of Ga[subscript 2](Se[subscript x]Te[subscript 1;#8722;x])[subscript 3] semiconductors and defect studies via positron annihilation spectroscopy
SciTech Connect
Abdul-Jabbar, N.M.; Bourret-Courchesne, E.D.; Wirth, B.D.
2012-12-10
Small single crystals of Ga{sub 2}(Se{sub x}Te{sub 1-x}){sub 3} semiconductors, for x = 0.1, 0.2, 0.3, were obtained via modified Bridgman growth techniques. High resolution powder x-ray diffractometry confirms a zincblende cubic structure, with additional satellite peaks observed near the (111) Bragg line. This suggests the presence of ordered vacancy planes along the [111] direction that have been previously observed in Ga{sub 2}Te{sub 3}. Defect studies via positron annihilation spectroscopy show an average positron lifetime of {approx} 400 ps in bulk as-grown specimens. Such a large lifetime suggests that the positron annihilation sites in these materials are dominated by defects. Moreover, analyzing the electron momenta via coincidence Doppler broadening measurements suggests a strong presence of large open-volume defects, likely to be vacancy clusters or voids.
10. Hunting for glueballs in electron-positron annihilation
SciTech Connect
Stanley Brodsky; Alfred Scharff Goldhaber; Jungil Lee
2003-05-01
We calculate the cross section for the exclusive production of J{sup PC} = 0{sup ++} glueballs G{sub 0} in association with the J/{psi} in e{sup +}e{sup -} annihilation using the pQCD factorization formalism. The required long-distance matrix element for the glueball is bounded by CUSB data from a search for resonances in radiative {Upsilon} decay. The cross section for e{sup +}e{sup -} {yields} J/{psi} + G{sub 0} at {radical}s = 10.6 GeV is similar to exclusive charmonium-pair production e{sup +}e{sup -} {yields} J/{psi} + h for h = {eta}{sub c} and {chi}{sub c0}, and is larger by a factor 2 than that for h = {eta}{sub c}(2S). As the subprocesses {gamma}* {yields} (c {bar c}) (c {bar c}) and {gamma}* {yields} (c {bar c}) (g g) are of the same nominal order in perturbative QCD, it is possible that some portion of the anomalously large signal observed by Belle in e{sup +}e{sup -} {yields} J/{psi} X may actually be due to the production of charmonium-glueball J/{psi} G{sub J} pairs.
11. The 511 keV emission from positron annihilation in the Galaxy
SciTech Connect
Prantzos, N.; Boehm, C.; Bykov, A. M.; Diehl, R.; Ferriere, K.; Guessoum, N.; Jean, P.; Knoedlseder, J.; Marcowith, A.; Moskalenko, I. V.; Strong, A.; Weidenspointner, G.
2011-07-01
The first {gamma}-ray line originating from outside the Solar System that was ever detected is the 511 keV emission from positron annihilation in the Galaxy. Despite 30 years of intense theoretical and observational investigation, the main sources of positrons have not been identified up to now. Observations in the 1990s with OSSE/CGRO (Oriented Scintillation Spectrometer Experiment on GRO satellite/Compton Gamma Ray Observatory) showed that the emission is strongly concentrated toward the Galactic bulge. In the 2000s, the spectrometer SPI aboard the European Space Agency's (ESA) International Gamma Ray Astrophysics Laboratory (INTEGRAL) allowed scientists to measure that emission across the entire Galaxy, revealing that the bulge-to-disk luminosity ratio is larger than observed at any other wavelength. This mapping prompted a number of novel explanations, including rather ''exotic'' ones (e.g., dark matter annihilation). However, conventional astrophysical sources, such as type Ia supernovae, microquasars, or x-ray binaries, are still plausible candidates for a large fraction of the observed total 511 keV emission of the bulge. A closer study of the subject reveals new layers of complexity, since positrons may propagate far away from their production sites, making it difficult to infer the underlying source distribution from the observed map of 511 keV emission. However, in contrast to the rather well-understood propagation of high-energy (>GeV) particles of Galactic cosmic rays, understanding the propagation of low-energy ({approx}MeV) positrons in the turbulent, magnetized interstellar medium still remains a formidable challenge. The spectral and imaging properties of the observed 511 keV emission are reviewed and candidate positron sources and models of positron propagation in the Galaxy are critically discussed.
12. Positron Annihilation Study of Ternary Sb2Te3-x Se x for Its Tuning Electrical and Thermal Properties
Zheng, Wenwen; Yang, Dongwang; Bi, Peng; He, Chunqing; Liu, Fengming; Shi, Jing; Ding, Yi; Wang, Ziyu; Xiong, Rui
2016-10-01
Atomic scale point defects play important roles in tuning the carrier concentration and ultimately influencing electrical and thermal properties. Herein, we fabricated the ternary Sb2Te3-x Se x alloys to study the intimate relationship of internal point defects and thermoelectric performance. The Se substitution of Te atoms in the Sb2Te3 lattice decreased the electrical conductivity from 2.2 × 105 S/m to 6.4 × 104 S/m owing to the reduced holes concentration. The declined point defects, including antisite defects and vacancies in materials, gave rise to the decrease in carrier concentration. The Seebeck coefficient of the ternary Sb2Te3-x Se x exhibited an increase with doping of Se atoms. Simultaneously, the thermal conductivity behaved a fallihg trend as well as increasing Se content. As a result, the ZT value reached the maximum from the corresponding Sb2Te2.9Se0.1 pellet. Positron annihilation measurement revealed that the average positron lifetime showed a monotonic decrease with Se addition, demonstrating the reduced point defects, which was in agreement with the thermoelectric performance.
13. Novel time-of-flight spectrometer for the analysis of positron annihilation induced Auger electrons
SciTech Connect
Hugenschmidt, Christoph; Legl, Stefan
2006-10-15
Positron annihilation induced Auger-electron spectroscopy (PAES) has several advantages over conventional Auger-electron spectroscopy such as extremely high surface sensitivity and outstanding signal-to-noise ratio at the Auger-transition energy. In order to benefit from these prominent features a low-energy positron beam of high intensity is required for surface sensitive PAES studies. In addition, an electron energy analyzer is required, which efficiently detects the Auger electrons with acceptable energy resolution. For this reason a novel time-of-flight (TOF) spectrometer has been developed at the intense positron source NEPOMUC that allows PAES studies within short measurement time. This TOF-PAES setup combines a trochoidal filter and a flight tube in a Faraday cage in order to achieve an improved energy resolution of about 1 eV at high electron energies up to E{approx_equal}1000 eV. The electron flight time is the time between the annihilation radiation at the sample and when the electron hits a microchannel plate detector at the end of the flight tube.
14. Microstructure Evaluation of Fe-BASED Amorphous Alloys Investigated by Doppler Broadening Positron Annihilation Technique
Lu, Wei; Huang, Ping; Wang, Yuxin; Yan, Biao
2013-07-01
Microstructure of Fe-based amorphous and nanocrystalline soft magnetic alloy has been investigated by X-ray diffraction (XRD), transmission electronic microscopy (TEM) and Doppler broadening positron annihilation technique (PAT). Doppler broadening measurement reveals that amorphous alloys (Finemet, Type I) which can form a nanocrystalline phase have more defects (free volume) than alloys (Metglas, Type II) which cannot form this microstructure. XRD and TEM characterization indicates that the nanocrystallization of amorphous Finemet alloy occurs at 460°C, where nanocrystallites of α-Fe with an average grain size of a few nanometers are formed in an amorphous matrix. With increasing annealing temperature up to 500°C, the average grain size increases up to around 12 nm. During the annealing of Finemet alloy, it has been demonstrated that positron annihilates in quenched-in defect, crystalline nanophase and amorphous-nanocrystalline interfaces. The change of line shape parameter S with annealing temperature in Finemet alloy is mainly due to the structural relaxation, the pre-nucleation of Cu nucleus and the nanocrystallization of α-Fe(Si) phase during annealing. This study throws new insights into positron behavior in the nanocrystallization of metallic glasses, especially in the presence of single or multiple nanophases embedded in the amorphous matrix.
15. Measurement of the hadronic cross section in electron-positron annihilation
SciTech Connect
Clearwater, S.
1983-11-01
This thesis describes the most precise measurement to date of the ratio R, the hadronic cross section in lowest order electron-positron annihilation to the cross section for muon pair production in lowest order electron-positron annihilation. This experiment is of interest because R is a fundamental parameter that tests in a model independent way the basic assumptions of strong interaction theories. According to the assumptions of one of these theories the value of R is determined simply from the electric charges, spin, and color assignments of the produced quark-pairs. The experiment was carried out with the MAgnetic Calorimeter using collisions of 14.5 GeV electrons and positrons at the 2200m circumference PEP storage ring at SLAC. The MAC detector is one of the best-suited collider detectors for measuring R due to its nearly complete coverage of the full angular range. The data for this experiment were accumulated between February 1982 and April 1983 corresponding to a total event sample of about 40,000 hadronic events. About 5% of the data were taken with 14 GeV beams and the rest of the data were taken with 14.5 GeV beams. A description of particle interactions and experimental considerations is given.
16. Novel time-of-flight spectrometer for the analysis of positron annihilation induced Auger electrons
Hugenschmidt, Christoph; Legl, Stefan
2006-10-01
Positron annihilation induced Auger-electron spectroscopy (PAES) has several advantages over conventional Auger-electron spectroscopy such as extremely high surface sensitivity and outstanding signal-to-noise ratio at the Auger-transition energy. In order to benefit from these prominent features a low-energy positron beam of high intensity is required for surface sensitive PAES studies. In addition, an electron energy analyzer is required, which efficiently detects the Auger electrons with acceptable energy resolution. For this reason a novel time-of-flight (TOF) spectrometer has been developed at the intense positron source NEPOMUC that allows PAES studies within short measurement time. This TOF-PAES setup combines a trochoidal filter and a flight tube in a Faraday cage in order to achieve an improved energy resolution of about 1eV at high electron energies up to E ≈1000eV. The electron flight time is the time between the annihilation radiation at the sample and when the electron hits a microchannel plate detector at the end of the flight tube.
17. Positron annihilation study of proton-irradiated reactor pressure vessel steels
Liu, Xiangbing; Wang, Rongshan; Ren, Ai; Huang, Ping; Wu, Yichu; Jiang, Jing; Zhang, Chonghong; Wang, Xitao
2012-10-01
The microstructures, irradiation-induced defects and changes of mechanical property of Chinese domestic A508-3 steels after proton irradiation were investigated by TEM, positron lifetime, slow positron beam Doppler broadening spectroscopy and hardness measurements. The defects were induced by 240 keV proton irradiation with fluences of 1.25×1017 ions cm-2 (0.26 dpa), 2.5×1017 ions cm-2 (0.5 dpa), and 5.0×1017 ions cm-2 (1.0 dpa). The TEM observation revealed that the as-received steel had typical bainitic-ferritic microstructures. It was also observed that Doppler broadening S-parameter and average lifetime increased with dose level owing to the formation of defects and voids induced by proton irradiation. The correlation between positron parameters and hardness was found.
18. Local electron-electron interaction strength in ferromagnetic nickel determined by spin-polarized positron annihilation.
PubMed
Ceeh, Hubert; Weber, Josef Andreas; Weber, Josef Andreass; Böni, Peter; Leitner, Michael; Benea, Diana; Chioncel, Liviu; Ebert, Hubert; Minár, Jan; Vollhardt, Dieter; Hugenschmidt, Christoph
2016-02-16
We employ a positron annihilation technique, the spin-polarized two-dimensional angular correlation of annihilation radiation (2D-ACAR), to measure the spin-difference spectra of ferromagnetic nickel. The experimental data are compared with the theoretical results obtained within a combination of the local spin density approximation (LSDA) and the many-body dynamical mean-field theory (DMFT). We find that the self-energy defining the electronic correlations in Ni leads to anisotropic contributions to the momentum distribution. By direct comparison of the theoretical and experimental results we determine the strength of the local electronic interaction U in ferromagnetic Ni as 2.0 ± 0.1 eV.
19. Enhanced Dark Matter Annihilation Rate for Positron and Electron Excesses from Q-Ball Decay
SciTech Connect
McDonald, John
2009-10-09
We show that Q-ball decay in Affleck-Dine baryogenesis models can account for dark matter when the annihilation cross section is sufficiently enhanced to explain the positron and electron excesses observed by PAMELA, ATIC, and PPB-BETS. For Affleck-Dine baryogenesis along a d=6 flat direction, the reheating temperature is approximately 30 GeV and the Q-ball decay temperature is in the range of 10-100 MeV. The lightest supersymmetric particles produced by Q-ball decay annihilate down to the observed dark matter density if the cross section is enhanced by a factor approx10{sup 3} relative to the thermal relic cross section.
20. Local electron-electron interaction strength in ferromagnetic nickel determined by spin-polarized positron annihilation
PubMed Central
Ceeh, Hubert; Weber, Josef Andreass; Böni, Peter; Leitner, Michael; Benea, Diana; Chioncel, Liviu; Ebert, Hubert; Minár, Jan; Vollhardt, Dieter; Hugenschmidt, Christoph
2016-01-01
We employ a positron annihilation technique, the spin-polarized two-dimensional angular correlation of annihilation radiation (2D-ACAR), to measure the spin-difference spectra of ferromagnetic nickel. The experimental data are compared with the theoretical results obtained within a combination of the local spin density approximation (LSDA) and the many-body dynamical mean-field theory (DMFT). We find that the self-energy defining the electronic correlations in Ni leads to anisotropic contributions to the momentum distribution. By direct comparison of the theoretical and experimental results we determine the strength of the local electronic interaction U in ferromagnetic Ni as 2.0 ± 0.1 eV. PMID:26879249
1. Cosmic-ray antiprotons, positrons, and gamma rays from halo dark matter annihilation
NASA Technical Reports Server (NTRS)
Rudaz, S.; Stecker, F. W.
1988-01-01
The subject of cosmic ray antiproton production is reexamined by considering other choices for the nature of the Majorana fermion chi other than the photino considered in a previous article. The calculations are extended to include cosmic-ray positrons and cosmic gamma rays as annihilation products. Taking chi to be a generic higgsino or simply a heavy Majorana neutrino with standard couplings to the Z-zero boson allows the previous interpretation of the cosmic antiproton data to be maintained. In this case also, the annihilation cross section can be calculated independently of unknown particle physics parameters. Whereas the relic density of photinos with the choice of parameters in the previous paper turned out to be only a few percent of the closure density, the corresponding value for Omega in the generic higgsino or Majorana case is about 0.2, in excellent agreement with the value associated with galaxies and one which is sufficient to give the halo mass.
2. Solid Eu(III) complexes studied by positron annihilation, optical and Mössbauer spectroscopies: insights on the positronium formation mechanism.
PubMed
Fulgêncio, F; de Oliveira, F C; Ivashita, F F; Paesano, A; Windmöller, D; Marques-Netto, A; Magalhães, W F; Machado, J C
2012-06-15
In this work, positron annihilation lifetime (PALS), Doppler broadening annihilation radiation lineshape (DBARL), Mössbauer and optical spectroscopies measurements were performed in Eu(III) dipivaloylmetanate complex, Eu(dpm)(3), at 295 and 80 K. The Eu(dpm)(3) complex is not luminescent at 298 K and does not form positronium. On the other hand, it is highly luminescent at 80K, but still does not form positronium. The absence of positronium formation at 80K cannot be explained by a ligand/metal charge transfer process. We found strong evidences that the electronic delocalization does not occur at both temperatures. Despite the Mössbauer results being inconclusive regarding the Eu(III)/Eu(II) reduction hypothesis, previous results showing positronium formation in other Eu(III) complexes suggest that this process is not occurring. Thus, more studies are needed to explain the absence of positronium in Eu(III) complexes.
3. Solid Eu(III) complexes studied by positron annihilation, optical and Mössbauer spectroscopies: Insights on the positronium formation mechanism
Fulgêncio, F.; de Oliveira, F. C.; Ivashita, F. F.; Paesano, A.; Windmöller, D.; Marques-Netto, A.; Magalhães, W. F.; Machado, J. C.
In this work, positron annihilation lifetime (PALS), Doppler broadening annihilation radiation lineshape (DBARL), Mössbauer and optical spectroscopies measurements were performed in Eu(III) dipivaloylmetanate complex, Eu(dpm)3, at 295 and 80 K. The Eu(dpm)3 complex is not luminescent at 298 K and does not form positronium. On the other hand, it is highly luminescent at 80 K, but still does not form positronium. The absence of positronium formation at 80 K cannot be explained by a ligand/metal charge transfer process. We found strong evidences that the electronic delocalization does not occur at both temperatures. Despite the Mössbauer results being inconclusive regarding the Eu(III)/Eu(II) reduction hypothesis, previous results showing positronium formation in other Eu(III) complexes suggest that this process is not occurring. Thus, more studies are needed to explain the absence of positronium in Eu(III) complexes.
4. Gamma-ray lines from novae. [relationship to radioactive decay and positron annihilation
NASA Technical Reports Server (NTRS)
Clayton, D. D.; Hoyle, F.
1974-01-01
An appropriate gamma-ray telescope could detect the gamma-rays associated with radioactive decays. The observable lines would be the annihilation radiation following the positron emission of N-13, O-14, O-15, and Na-22 and the 2.312-MeV line emitted following the O-14 decay and the 1.274-MeV line emitted following the Na-22 decay. The experimental possibility should be borne in mind for the occurrence of novae within a few kiloparsecs.
5. Positron annihilation spectroscopy techniques applied to the study of an HPGe detector
SciTech Connect
Nascimento, E. do; Vanin, V. R.; Maidana, N. L.; Silva, T. F.; Rizzutto, M. A.; Fernandez-Varea, J. M.
2013-05-06
Doppler Broadening Spectroscopy of the large Ge crystal of an HPGe detector was performed using positrons from pair production of 6.13 MeV {gamma}-rays from the {sup 19}F(p,{alpha}{gamma}){sup 16}O reaction. Two HPGe detectors facing opposite sides of the Ge crystal acting as target provided both coincidence and singles spectra. Changes in the shape of the annihilation peak were observed when the high voltage applied to the target detector was switched on or off, amounting to somewhat less than 20% when the areas of equivalent energy intervals in the corresponding normalized spectra are compared.
6. Production of {omega}{pi}{sup 0} pairs in electron-positron annihilation
SciTech Connect
Arbuzov, A. B.; Kuraev, E. A.; Volkov, M. K.
2011-04-15
The process of electron-positron annihilation into a pair of {pi}{sup 0} and {omega} mesons is considered in the framework of the SU(2)xSU(2) Nambu-Jona-Lasinio model. Contributions of intermediate photons, {rho}(770) and {rho}{sup '}(1450) vector mesons are taken into account. It is shown that the bulk of the cross section at energies below 2 GeV is provided by the process with intermediate {rho}{sup '}(1450) state. The contribution due to single photon and {rho}(770) exchange is in agreement with the vector meson dominance model. Numerical results are compared with experimental data.
7. The effect of vacancies on the microwave surface resistance of niobium revealed by positron annihilation spectroscopy
Romanenko, A.; Edwardson, C. J.; Coleman, P. G.; Simpson, P. J.
2013-06-01
Using variable-energy positron annihilation spectroscopy, we demonstrate that a different near-surface vacancy concentration accompanies drastic differences in surface resistance of superconducting niobium cavities for particle acceleration. Our data suggest that vacuum baking at 120 °C leads to the doping of a near-surface layer with vacancy-hydrogen complexes, and that higher vacancy-type defect concentration distinguishes electropolished from chemically etched cavities. Our findings may help to explain a strong dependence of cavity performance on heat and chemical treatments, and may be of interest to other physics fields including cavity quantum electrodynamics (QED), microresonators, and single photon detectors.
8. Electronic correlations in vanadium revealed by electron-positron annihilation measurements
Weber, Josef Andreas; Benea, Diana; Appelt, Wilhelm H.; Ceeh, Hubert; Kreuzpaintner, Wolfgang; Leitner, Michael; Vollhardt, Dieter; Hugenschmidt, Christoph; Chioncel, Liviu
2017-02-01
The electronic structure of vanadium measured by angular correlation of electron-positron annihilation radiation (ACAR) is compared with the predictions of the combined density functional and dynamical mean-field theory (DMFT). Reconstructing the momentum density from five two-dimensional projections we were able to determine the full Fermi surface and found excellent agreement with the DMFT calculations. In particular, we show that the local, dynamic self-energy corrections contribute to the anisotropy of the momentum density and need to be included to explain the experimental results.
9. AC Dielectric Properties and Positron Annihilation Study on Co and Ti Substitution Effect on Ca-Sr M-Hexaferrites
Mahmoud, K. R.; Eraky, M. R.
2016-06-01
The dependence of AC conductivity σ AC, dielectric constant έ, and dielectric loss tangent tan δ on frequency and composition have been investigated at room temperature for polycrystalline Ca0.5Sr0.5Co x Ti x Fe12 - 2 x O19 (where 0.0 ≤ x ≤ 0.8) hexaferrites. It was found that the parameters σ AC, ɛ ', and tan δ have maximum values at x = 0.4 of the Co and Ti substitution. The behavior of σ AC, ɛ ', and tan δ with frequency and composition was explained on the basis of the hopping conduction mechanism and the Koops model. Positron annihilation lifetime spectroscopy (PALS) was used to investigate the defects and changes in electron density for hexaferrite samples. The PAL parameters ( τ 1, I 1, τ 2, I 2, and mean lifetime) show that altering the doping percentage of the Co and Ti ions affects the size and concentration of defects. The results reveal that there are some large voids in the studied samples. The obtained results indicate the high sensitivity of the PALS technique to the enhanced structure changes with changing composition of the investigated samples and correlate the results with the measured electrical parameters.
10. Possible presence of hydrophilic SO3H nanoclusters on the surface of dry ultrathin Nafion® films: a positron annihilation study.
PubMed
Mohamed, Hamdy F M; Kuroda, S; Kobayashi, Y; Oshima, N; Suzuki, R; Ohira, A
2013-02-07
Solutions of Nafion® with an ion exchange capacity (IEC) of 0.91 meq g(-1), which are on the verge of the formation of SO(3)H nanoclusters, were spin coated on silicon (Si), glassy carbon (GC) and platinum/silicon (Pt/Si) substrates to form films of up to 256 nm thickness. Nanostructure of the films was studied using Doppler broadening of annihilation radiation (DBAR), positron annihilation lifetime (PAL), X-ray photoelectron spectroscopy (XPS), an atomic force microscope (AFM) and contact angle measurements. Contact angles as low as 10 degrees indicate that the surface of dry ultrathin Nafion® films on Si is highly hydrophilic. XPS data of 10 nm thick, ultrathin film on Si show that oxygen concentration is enhanced and the SO(3)H group concentration, in other words, IEC on the surface is much higher than other films. The S parameter measured by DBAR of an ultrathin Nafion® film on Si is much higher than that of the films on the other substrates. We consider that a large number of hydrophilic, reversed micelle like SO(3)H groups are on the surface of the ultrathin Nafion® film on Si but not on the surface of other films. Positrons implanted into the film are trapped by the SO(3)H clusters, annihilating with the electrons of oxygen and exhibit the high S parameter. The SO(3)H concentration on the surface of thin Nafion® films on GC and Pt/Si substrates may not be so high as the threshold for the formation of a large number of SO(3)H clusters. Positrons implanted into the films annihilate mostly with fluorine atoms, resulting in a low S parameter. The film-substrate interaction plays an essential role in nanostructuring of Nafion® thin films, which may also be the case for Nafion® on the catalysts of polymer electrolyte fuel cells.
11. Positron annihilation in (Ga, Mn)N: A study of vacancy-type defects
SciTech Connect
Yang, X. L.; Zhu, W. X.; Wang, C. D.; Fang, H.; Yu, T. J.; Yang, Z. J.; Zhang, G. Y.; Qin, X. B.; Yu, R. S.; Wang, B. Y.
2009-04-13
The vacancy-type defects in (Ga,Mn)N films grown by metal organic chemical vapor deposition were studied by positron annihilation technique. Doppler broadening spectra were measured for the films. Compared to the undoped GaN film, the positron trapping defects in the (Ga,Mn)N films have been changed to a new type defects and its concentration increases with the increasing Mn concentration. By analyzing the S-W correlation plots and our previous results, we identify this type defects in the (Ga,Mn)N as V{sub N}-Mn{sub Ga} complex. This type of defects should be considered when understand the magnetic properties in a real (Ga,Mn)N system.
12. Thermal annealing of C ion irradiation defects in nuclear graphite studied by positron annihilation
Shi, C. Q.; Schut, H.; Li, Z. C.
2016-01-01
In order to investigate the thermal behaviour of radiation induced point defects in nuclear graphite, ETU10 graphite was implanted with 350 keV C+ ion to doses of 1015 and 1016 cm-2. The point defects introduced by the implantation were characterized by Positron Annihilation Doppler Broadening (PADB) and their thermal behaviour was studied during “in situ” annealing at Delft Variable Energy Positron beam (VEP). The annealing was performed for 5 minutes at temperatures ranging from 300 K (as implanted) to 1500 K in steps of 100 K. For both doses, an annealing stage at around 450 K is observed followed by a second stage around 700 K. For the high dose implantation vacancy complexes are found which are stable up to a temperature around 1400K.
13. Evidence of Positron Annihilation at Electronic Excitation Threshold for N2 ^*
Miller, E. G.; Edwards, J. J.; Kauppila, W. E.; Stein, T. S.; Surdutovich, E.
2006-05-01
We are investigating Positronium (Ps) formation for < 20 eV positrons interacting with N2 in a gas scattering cell. The technique [1] of Ps annihilation ratio spectroscopy (PsARS) is used to obtain the ratios of coincidence signals for two of the three gamma rays (S3γ) in the photon energy window 300 to 460 keV resulting from ortho-Ps decay to that for two 511 keV gamma rays (S2γ) arising from para-Ps decay and other processes. By comparing these ratios of S3 γ/S2γ for N2 to those for Ar it is found that N2 exhibits strikingly anomalous behavior near and below the Ps formation threshold. Typically, this ratio remains constant within 2 eV above the Ps threshold. For N2, this ratio decreases to zero at the threshold and an S2 γ signal remains for an energy of ˜0.3 eV below. Since N2 has an electronic excitation threshold for positron impact that opens up at ˜0.3 eV below the Ps threshold, the present results strongly suggest that the incident positron is electronically exciting N2 and then binding to the excited N2 in a temporary resonance-like state from which the bound positron annihilates with a molecular electron. ^*Research supported by NSF Grant PHY 99-88093.[1] W.E. Kauppila, E.G. Miller, H. F.M. Mohamed, K. Pipinos, T. S. Stein, and E. Surdutovich, Phys. Rev. Lett. 93, 113401 (2004).
14. Modification of steel surfaces induced by turning: non-destructive characterization using Barkhausen noise and positron annihilation
Čížek, J.; Neslušan, M.; Čilliková, M.; Mičietová, A.; Melikhova, O.
2014-11-01
This paper deals with the characterization of sub-surface damage caused by the machining of 100Cr6 roll bearing steel. The samples turned using tools with variable flank wears were characterized by two non-destructive techniques sensitive to defects introduced by plastic deformation: magnetic Barkhausen noise and positron annihilation. These techniques were combined with light and electron microscopy, x-ray diffraction and microhardness testing. The results of the experiment showed that damage in the sub-surface region increases with increasing flank wear, but from a certain critical value dynamic recovery takes place. The intensity of Barkhausen noise strongly decreases with increasing flank wear due to the increasing density of the dislocations pinning the Bloch walls and suppressing their motion. This was confirmed by positron annihilation spectroscopy, which enables the determination of the dislocation density directly. Hence, a good correlation between Barkhausen noise emission and positron annihilation spectroscopy was found.
15. First-principles calculations of momentum distributions of annihilating electron-positron pairs in defects in UO2
Wiktor, Julia; Jomard, Gérald; Torrent, Marc; Bertolus, Marjorie
2017-01-01
We performed first-principles calculations of the momentum distributions of annihilating electron-positron pairs in vacancies in uranium dioxide. Full atomic relaxation effects (due to both electronic and positronic forces) were taken into account and self-consistent two-component density functional theory schemes were used. We present one-dimensional momentum distributions (Doppler-broadened annihilation radiation line shapes) along with line-shape parameters S and W. We studied the effect of the charge state of the defect on the Doppler spectra. The effect of krypton incorporation in the vacancy was also considered and it was shown that it should be possible to observe the fission gas incorporation in defects in UO2 using positron annihilation spectroscopy. We suggest that the Doppler broadening measurements can be especially useful for studying impurities and dopants in UO2 and of mixed actinide oxides.
16. Configuration interaction calculations of potential curves and annihilation rates for positronic complexes of alkali monoxides.
PubMed
Buenker, Robert J; Liebermann, Heinz-Peter
2009-09-21
Ab initio multireference single- and double-excitation configuration interaction calculations have been carried out to compute the potential curves and annihilation rates (ARs) of positronic molecular complexes of a series of alkali monoxides. The dissociation limit for the lowest states of these systems consists of the positive alkali ion ground state (M(+)) and the OPs (e(+)O(-)) complex formed by attaching the positron to O(-), even though the ground state of the corresponding neutral molecule always correlates with uncharged fragments (M+O). The positron affinity of the neutral oxide (2)Pi state is greater than that of (2)Sigma(+) in each case, so that the e(+)MO ground state always has (3,1)Pi symmetry, despite the fact that both KO and RbO have (2)Sigma(+) ground states. The bonding in the positronic systems is highly ionic at all internuclear distances and this causes their ARs to decrease gradually as the positive alkali ion approaches the OPs fragment.
17. Positron annihilation studies of defects in molecular beam epitaxy grown III-V layers
SciTech Connect
Umlor, M.T.; Keeble, D.J.; Asoka-Kumar, P.; Lynn, K.G.; Cooke, P.W.
1994-08-01
A summary of recent positron annihilation experiments on molecular beam epitaxy (MBE) grown III-V layers is Presented. Variable energy positron beam measurements on Al{sub 0.32}Ga{sub 0.68}As undoped and Si doped have been completed. Positron trapping at a open volume defect in Al{sub 0.32}Ga{sub 0.68}:Si for temperatures from 300 to 25 K in the dark was observed. The positron trap was lost after 1.3 eV illumination at 25K. These results indicate an open volume defect is associated with the local structure of the deep donor state of the DX center. Stability of MBE GaAs to thermal annealing war, investigated over the temperature range of 230 to 700{degrees}C, Proximity wafer furnace anneals in flowing argon were used, Samples grown above 450{degrees}C were shown to be stable but for sample below this temperature an anneal induced vacancy related defect was produced for anneals between 400 and 500{degrees}C. The nature of the defect was shown to be different for material grown at 350 and 230{degrees}C. Activation energies of 2.5 eV to 2.3 eV were obtained from isochronal anneal experiments for samples grown at 350 and 230{degrees}C, respectively.
18. Positron Annihilation Induced Auger Electron Spectroscopy of Inner Shell Transitions Using Time-Of Technique
Xie, Shuping; Jiang, Neng; Weiss, A. H.
2003-03-01
Positron annihilation induced Auger electron spectroscopy (PAES) has been shown to have unique advantages over conventional electron collision induced Auger techniques, including the ability to eliminate the secondary electron background and selectively probe the top-most atomic layer on the sample surface. Here we report on the development of a new time-of-flight (TOF) spectrometer which combines features high efficiency magnetic transport and parrallel energy measurment with high resolution by using an innovative timing method. The new TOF-PAES system, was used to make the first quantitative comparative measurements of the Auger intensities associated with the annihilation of positrons with the deep core levels (1s) of S KLL (180eV), C KLL (270eV), N KLL (360eV), and O KLL (510eV). Experimental results of Auger probabilities at outer core level (3s, 3P) of Cu M2,3VV (60eV), M1VV (105eV) are compared with the theoretical value of Jensen and Weiss. Quantitatively study the surface adsorbate process on Cu is performed and concentration changes of surface components are obtained. These results demonstrate that TOF-PAES can be used to obtain quantitative,top-layer specific, information from chemically important elements including those with relatively deep core levels (e.g. C and O).
19. Quantification of stress history in type 304L stainless steel using positron annihilation spectroscopy
SciTech Connect
Walters, Thomas W.; Walters, Leon C.; Schoen, Marco P.; Naidu, D. Subbaram; Dickerson, Charles; Perrenoud, Ben C.
2011-04-15
Five Type 304L stainless steel specimens were subjected to incrementally increasing values of plastic strain. At each value of strain, the associated static stress was recorded and the specimen was subjected to positron annihilation spectroscopy (PAS) using the Doppler Broadening method. A calibration curve for the 'S' parameter as a function of stress was developed based on the five specimens. Seven different specimens (blind specimens labeled B1-B7) of 304L stainless steel were subjected to values of stress inducing plastic deformation. The values of stress ranged from 310 to 517 MPa. The seven specimens were subjected to PAS post-loading using the Doppler Broadening method, and the results were compared against the developed curve from the previous five specimens. It was found that a strong correlation exists between the 'S' parameter, stress, and strain up to a strain value of 15%, corresponding to a stress value of 500 MPa, beyond which saturation of the 'S' parameter occurs. Research Highlights: {yields} Specimens were initially in an annealed/recrystallized condition. {yields} Calibration results indicate positron annihilation measurements yield correlation. {yields} Deformation produced by cold work was likely larger than the maximum strain.
20. The gamma-ray spectra of 5-carbon alkane isomers in the positron annihilation process
Ma, Xiaoguang; Zhu, Yinghao; Liu, Yang
2016-05-01
The gamma-ray spectra of pentane (C5H12) and its two isomers, i.e., 2-Methylbutane (CH3C(CH3)HC2H5) and 2,2-Dimethylpropane (C(CH3)4) have been studied theoretically in the present work. The recent experimental gamma-ray spectra of these three molecules show that they have the same Doppler shifts, although their molecular structures are dramatically different. In order to reveal why the gamma-ray spectra of these molecules are less sensitive to the molecular structures, the one-dimensional gamma-ray spectra and spherically averaged momentum (SAM) distributions, the two-dimensional angular correlation of annihilation radiation (ACAR), and the three-dimensional momentum distributions of the positron-electron pair are studied. The one-centered momentum distributions of the electrons are found to play more important role than the multi-centered coordinate distributions. The present theoretical predictions have confirmed the experimental findings for the first time. The dominance of the inner valence electrons in the positron-electron annihilation process has also been suggested in the present work.
1. A Positron Annihilation Study of Corrosion of Aluminum and Aluminum Alloy by NaOH
Wu, Y. C.; Zhai, T.; Coleman, P. G.
2012-08-01
Corrosion of fully-annealed pure aluminum and a continuous-cast AA2037 aluminum alloy (solutionized and water quenched) in a 1M NaOH solution for various periods of time were analyzed with positron beam-based Doppler broadening spectroscopy. By varying the energy of the incident positron beam, corrosion-induced defects at different depths from the surface were detected. It was found that the Doppler-broadened annihilation line-width parameter was significantly increased near the surface of pure aluminum after corrosion, probably due to the interaction between positrons and nanometer-sized voids formed near the aluminum surface during corrosion. Examination by atomic force microscopy indicated that many pits were formed on the aluminum surface after corrosion. In contrast, a significant decrease in the line-width parameter was observed in AA2037 alloy after corrosion and interpreted as being caused by copper enrichment at the metal-oxide interface during corrosion; such enrichment at large cavity sites was confirmed by energy dispersion spectrometry.
2. On-ground detection of an electron-positron annihilation line from thunderclouds
Umemoto, D.; Tsuchiya, H.; Enoto, T.; Yamada, S.; Yuasa, T.; Kawaharada, M.; Kitaguchi, T.; Nakazawa, K.; Kokubun, M.; Kato, H.; Okano, M.; Tamagawa, T.; Makishima, K.
2016-02-01
Thunderclouds can produce bremsstrahlung gamma-ray emission, and sometimes even positrons. At 00:27:00 (UT) on 13 January 2012, an intense burst of gamma rays from a thundercloud was detected by the GROWTH experiment, located in Japan, facing the Sea of Japan. The event started with a sharp gamma-ray flash with a duration of <300 ms coincident with an intracloud discharge, followed by a decaying longer gamma-ray emission lasting for ˜60 s. The spectrum of this prolonged emission reached ˜10 MeV, and contained a distinct line emission at 508 ±3 (stat .)±5 (sys .) keV, to be identified with an electron-positron annihilation line. The line was narrow within the instrumental energy resolution (˜80 keV) , and contained 520 ±50 photons which amounted to ˜10 % of the total signal photons of 5340 ±190 detected over 0.1-10 MeV. As a result, the line equivalent width reached 280 ±40 keV, which implies a nontrivial result. The result suggests that a downward positron beam produced both the continuum and the line photons.
3. On-ground detection of an electron-positron annihilation line from thunderclouds.
PubMed
Umemoto, D; Tsuchiya, H; Enoto, T; Yamada, S; Yuasa, T; Kawaharada, M; Kitaguchi, T; Nakazawa, K; Kokubun, M; Kato, H; Okano, M; Tamagawa, T; Makishima, K
2016-02-01
Thunderclouds can produce bremsstrahlung gamma-ray emission, and sometimes even positrons. At 00:27:00 (UT) on 13 January 2012, an intense burst of gamma rays from a thundercloud was detected by the GROWTH experiment, located in Japan, facing the Sea of Japan. The event started with a sharp gamma-ray flash with a duration of <300 ms coincident with an intracloud discharge, followed by a decaying longer gamma-ray emission lasting for ∼60 s. The spectrum of this prolonged emission reached ∼10 MeV, and contained a distinct line emission at 508±3(stat.)±5(sys.) keV, to be identified with an electron-positron annihilation line. The line was narrow within the instrumental energy resolution (∼80keV), and contained 520±50 photons which amounted to ∼10% of the total signal photons of 5340±190 detected over 0.1-10 MeV. As a result, the line equivalent width reached 280±40 keV, which implies a nontrivial result. The result suggests that a downward positron beam produced both the continuum and the line photons.
4. Moments of event shapes in electron-positron annihilation at next-to-next-to-leading order
SciTech Connect
Weinzierl, Stefan
2009-11-01
This article gives the perturbative next-to-next-to-leading order results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter and the Durham three-to-two-jet transition variable.
5. Accounting for the lack of nano-effect in a thermoset/clay nanocomposite: A positron annihilation study
Rath, S. K.; Sudarshan, K.; Patri, M.; Pujari, P. K.
2015-06-01
The effect of nanoclay dispersion on the thermo-mechanical properties of an unsaturated polyester thermoset resin was studied by flexural and dynamic mechanical property measurements. Transmission electron microscopy studies revealed intercalated clay dispersion morphology in the nanocomposites. The thermomechanical measurements showed a steady decrease in the flexural strength and a relaxation temperature, with only moderate increase in the storage modulus at 1% clay loading, followed by a drop at higher clay loadings. In order to understand the absence of nano-effect in this case, free volume measurements were carried out by using positron annihilation lifetime spectroscopy. A bimodal distribution of o-Ps life times was observed. Nanoclay loading resulted in the increase of the o-Ps intensity corresponding to the longest life time as well as free volume fraction suggesting diminished chain packing efficiency in the nanocomposites. We posit that nanoclay induced decreased chain packing efficiency and the presence of higher free volume size elements might cause deterioration in mechanical properties of the nanocomposites.
6. Structural analysis of IPC zeolites and related materials using positron annihilation spectroscopy and high-resolution argon adsorption.
PubMed
Jagiello, J; Sterling, M; Eliášová, P; Opanasenko, M; Zukal, A; Morris, R E; Navaro, M; Mayoral, A; Crivelli, P; Warringham, R; Mitchell, S; Pérez-Ramírez, J; Čejka, J
2016-06-01
The advanced investigation of pore networks in isoreticular zeolites and mesoporous materials related to the IPC family was performed using high-resolution argon adsorption experiments coupled with the development of a state-of-the-art non-local density functional theory approach. The optimization of a kernel for model sorption isotherms for materials possessing the same layer structure, differing only in the interlayer connectivity (e.g. oxygen bridges, single- or double-four-ring building units, mesoscale pillars etc.) revealed remarkable differences in their porous systems. Using high-resolution adsorption data, the bimodal pore size distribution consistent with crystallographic data for IPC-6, IPC-7 and UTL samples is shown for the first time. A dynamic assessment by positron annihilation lifetime spectroscopy (PALS) provided complementary insights, simply distinguishing the enhanced accessibility of the pore network in samples incorporating mesoscale pillars and revealing the presence of a certain fraction of micropores undetected by gas sorption. Nonetheless, subtle differences in the pore size could not be discriminated based on the widely-applied Tao-Eldrup model. The combination of both methods can be useful for the advanced characterization of microporous, mesoporous and hierarchical materials.
7. Vacancy trapping by solute atoms during quenching in Cu-based dilute alloys studied by positron annihilation spectroscopy
Yabuuchi, A.; Yamamoto, Y.; Ohira, J.; Sugita, K.; Mizuno, M.; Araki, H.; Shirai, Y.
2009-11-01
Frozen-in vacancies and the recovery have been investigated in some Cu-based dilute alloys by using positron annihilation lifetime spectroscopy. Cu-0.5at%Sb, Cu-0.5at%Sn and Cu-0.5at%In dilute bulk alloys were quenched to ice water from 1223 K. A pure-Cu specimen was also quenched from the same temperature. As a result, no frozen-in vacancies have been detected in as-quenched pure-Cu specimen. On the other hand, as-quenched Cu-0.5at%Sb alloy contained frozen-in thermal equilibrium vacancies with concentration of 3 × 10-5. Furthermore, these frozen-in vacancies in Cu-0.5at%Sb alloy were stable until 473 K, and began to migrate at 523 K. Finally, the Cu-Sb alloy were recovered to the fully annealed state at 823 K. This thermal stability clearly implies some interaction exists between a vacancy and Sb atom and due to the interaction, thermal equilibrium vacancies are trapped by Sb atoms during quenching.
8. Positron annihilation on defects in silicon irradiated with 15 MeV protons.
PubMed
Arutyunov, N Y; Elsayed, M; Krause-Rehberg, R; Emtsev, V V; Oganesyan, G A; Kozlovski, V V
2013-01-23
Microstructure and thermal stability of the radiation defects in n-FZ-Si ([P] ≈ 7 × 10(15) cm(-3)) single crystals have been investigated. The radiation defects have been induced by irradiation with 15 MeV protons and studied by means of both the positron lifetime spectroscopy and low-temperature measurements of the Hall effect. At each step of the isochronal annealing over the temperature range ∼60-700 °C the positron lifetime has been measured for the temperature interval ∼30-300 K, and for samples-satellites the temperature dependences of the charge carriers and mobility have been determined over the range ∼4.2-300 K. It is argued that as-grown impurity centers influence the average positron lifetime by forming shallow (E(b) ≈ 0.013 eV) positron states. The radiation-induced defects were also found to trap positrons into weakly bound (E(b) ≤ 0.01 eV) states. These positron states are observed at cryogenic temperatures during the isochronal annealing up to T(anneal.) = 340 °C. The stages of annealing in the temperature intervals ∼60-180 °C and ∼180-260 °C reflect the disappearance of E-centers and divacancies, respectively. Besides these defects the positrons were found to be localized at deep donor centers hidden in the process of annealing up to the temperature T(anneal.) ≈ 300 °C. The annealing of the deep donors occurs over the temperature range ∼300-650 °C. At these centers positrons are estimated to be bound with energies E(b) ≈ 0.096 and 0.021 eV within the temperature intervals ∼200-270 K and ∼166-66 K, respectively. The positron trapping coefficient from these defects increases from ∼1.1 × 10(16) to ∼6.5 × 10(17) s(-1) over the temperature range ∼266-66 K, thus substantiating a cascade phonon-assisted positron trapping mechanism whose efficiency is described by ≈T(-3) law. It is argued that the value of activation energy of the isochronal annealing E(a) ≈ 0.74-0.59 eV is due to dissociation of the
9. Positron annihilation spectroscopy of vacancy-related defects in CdTe:Cl and CdZnTe:Ge at different stoichiometry deviations.
PubMed
Šedivý, L; Čížek, J; Belas, E; Grill, R; Melikhova, O
2016-02-10
Positron annihilation spectroscopy (PAS) was used to examine the effect of defined Cd-rich and Te-rich annealing on point defects in Cl-doped CdTe and Ge-doped CdZnTe semi-insulating single crystals. The as-grown crystals contain open-volume defects connected with Cd vacancies . It was found that the Cd vacancies agglomerate into clusters coupled with Cl in CdTe:Cl, and in CdZnTe:Ge they are coupled with Ge donors. While annealing in Cd pressure reduces of the density, subsequent annealing in Te pressure restores . The CdTe:Cl contains negatively-charged shallow traps interpreted as Rydberg states of A-centres and representing the major positron trapping sites at low temperature. Positrons confined in the shallow traps exhibit lifetime, which is shorter than the CdTe bulk lifetime. Interpretation of the PAS data was successfully combined with electrical resistivity, Hall effect measurements and chemical analysis, and allowed us to determine the principal point defect densities.
10. Positron annihilation spectroscopy of vacancy-related defects in CdTe:Cl and CdZnTe:Ge at different stoichiometry deviations
PubMed Central
Šedivý, L.; Čížek, J.; Belas, E.; Grill, R.; Melikhova, O.
2016-01-01
Positron annihilation spectroscopy (PAS) was used to examine the effect of defined Cd-rich and Te-rich annealing on point defects in Cl-doped CdTe and Ge-doped CdZnTe semi-insulating single crystals. The as-grown crystals contain open-volume defects connected with Cd vacancies . It was found that the Cd vacancies agglomerate into clusters coupled with Cl in CdTe:Cl, and in CdZnTe:Ge they are coupled with Ge donors. While annealing in Cd pressure reduces of the density, subsequent annealing in Te pressure restores . The CdTe:Cl contains negatively-charged shallow traps interpreted as Rydberg states of A-centres and representing the major positron trapping sites at low temperature. Positrons confined in the shallow traps exhibit lifetime, which is shorter than the CdTe bulk lifetime. Interpretation of the PAS data was successfully combined with electrical resistivity, Hall effect measurements and chemical analysis, and allowed us to determine the principal point defect densities. PMID:26860684
11. Positron annihilation studies of fluorine-vacancy complexes in Si and SiGe
SciTech Connect
Edwardson, C. J.; Coleman, P. G.; El Mubarek, H. A. W.; Gandy, A. S.
2012-04-01
The formation of fluorine-vacancy (FV) complexes in strained Si-SiGe-Si multilayer structures and relaxed SiGe layers of varying Ge content has been investigated using variable-energy positron annihilation spectroscopy, including Doppler-broadened spectra ratio curves. It has been found that in all sample types there are two distinct regions defined only by the damage created by the implanted F ions. The first, shallower region (from the surface to a depth of {approx}200 nm) was found to contain a mixture of undecorated vacancies and FV complexes; there is no correlation between the vacancy or F concentration in this region and the Ge content. The multi-layer samples may also have O contamination that is not present in the relaxed samples. The second region (at depths {approx}200-440 nm) contains primarily FV complexes in all samples. In the multi-layer samples secondary ion mass spectrometry (SIMS) results show peaks of F accumulating in, or at the interfaces of, each SiGe multi-layer; the FV complexes, however, are distributed over depths similar to those in the relaxed samples, with some localization at the SiGe layer located within the second region. The positron response is primarily to FV complexes formed by the F implant in all samples. The F: FV ratios are approximately 3-7: 1 in the relaxed samples. Positrons appear to be relatively insensitive to the largest of the F SIMS peaks which lies beyond the second region. This is probably because the F has filled all the open volume at the SiGe layer, leaving no positron trapping sites.
12. Study of nitrogen implanted amorphous hydrogenated carbon thin films by variable-energy positron annihilation spectroscopy
SciTech Connect
Freire, F.L. Jr.; Franceschini, D.F.; Brusa, R.S.; Karwasz, G.R.; Mariotto, G.; Zecca, A.; Achete, C.A.
1997-03-01
Hard amorphous hydrogenated carbon ({ital a}-C:H) films deposited by self-bias glow discharge were implanted at room temperature with 70 keV nitrogen ions at fluences between 2.0 and 9.0{times}10{sup 16} N/cm{sup 2}. The implanted samples were analyzed by positron Doppler broadening annihilation spectroscopy to determine the voids distribution. For samples implanted with 2.0{times}10{sup 16} N/cm{sup 2} the defect distribution is broader than the vacancies depth profile predicted by Monte Carlo simulation. For higher fluences we observed a reduction of the defect density. These results are discussed in terms of a competition between two processes: ion induced defects and structural modifications induced in the films due to ion implantation. {copyright} {ital 1997 American Institute of Physics.}
13. Doppler broadening of annihilation radiation measurements on 3d and 4f ferromagnets using polarized positrons
Kawasuso, A.; Maekawa, M.; Fukaya, Y.; Yabuuchi, A.; Mochizuki, I.
2012-01-01
We measured the Doppler broadening of annihilation radiation (DBAR) spectra of 3d (Fe, Co, and Ni) and 4f (Gd, Tb, and Dy) ferromagnets under a magnetic field by using spin-polarized positrons from a 68Ge-68Ga source. The results showed that the DBAR spectra of these metals have notably different magnetic-field dependences. The differences among Fe, Co, and Ni reflect that the upper minority spin bands of Fe and Co are nearly empty while those of Ni are still mostly occupied. For the rare-earth metals instead of the inner 4f electrons, 5d electrons that mediate the exchange interaction of the 4f electrons are primarily responsible for the magnetic-field effects on the DBAR spectra. Furthermore, the magnetic-field effects on the DBAR spectra of Gd, Tb, and Dy vanished above the Curie temperatures of the magnetic-phase transition for these metals.
14. Spatially resolved positron annihilation spectroscopy on friction stir weld induced defects
Hain, Karin; Hugenschmidt, Christoph; Pikart, Philip; Böni, Peter
2010-04-01
A friction stir welded (FSW) Al alloy sample was investigated by Doppler broadening spectroscopy (DBS) of the positron annihilation line. The spatially resolved defect distribution showed that the material in the joint zone becomes completely annealed during the welding process at the shoulder of the FSW tool, whereas at the tip, annealing is prevailed by the deterioration of the material due to the tool movement. This might be responsible for the increased probability of cracking in the heat affected zone of friction stir welds. Examination of a material pairing of steel S235 and the Al alloy Silafont36 by coincident Doppler broadening spectroscopy (CDBS) indicates the formation of annealed steel clusters in the Al alloy component of the sample. The clear visibility of Fe in the CDB spectra is explained by the very efficient trapping at the interface between steel cluster and bulk.
15. Spatially resolved positron annihilation spectroscopy on friction stir weld induced defects
PubMed Central
Hain, Karin; Hugenschmidt, Christoph; Pikart, Philip; Böni, Peter
2010-01-01
A friction stir welded (FSW) Al alloy sample was investigated by Doppler broadening spectroscopy (DBS) of the positron annihilation line. The spatially resolved defect distribution showed that the material in the joint zone becomes completely annealed during the welding process at the shoulder of the FSW tool, whereas at the tip, annealing is prevailed by the deterioration of the material due to the tool movement. This might be responsible for the increased probability of cracking in the heat affected zone of friction stir welds. Examination of a material pairing of steel S235 and the Al alloy Silafont36 by coincident Doppler broadening spectroscopy (CDBS) indicates the formation of annealed steel clusters in the Al alloy component of the sample. The clear visibility of Fe in the CDB spectra is explained by the very efficient trapping at the interface between steel cluster and bulk. PMID:27877329
16. Spatially resolved positron annihilation spectroscopy on friction stir weld induced defects.
PubMed
Hain, Karin; Hugenschmidt, Christoph; Pikart, Philip; Böni, Peter
2010-04-01
A friction stir welded (FSW) Al alloy sample was investigated by Doppler broadening spectroscopy (DBS) of the positron annihilation line. The spatially resolved defect distribution showed that the material in the joint zone becomes completely annealed during the welding process at the shoulder of the FSW tool, whereas at the tip, annealing is prevailed by the deterioration of the material due to the tool movement. This might be responsible for the increased probability of cracking in the heat affected zone of friction stir welds. Examination of a material pairing of steel S235 and the Al alloy Silafont36 by coincident Doppler broadening spectroscopy (CDBS) indicates the formation of annealed steel clusters in the Al alloy component of the sample. The clear visibility of Fe in the CDB spectra is explained by the very efficient trapping at the interface between steel cluster and bulk.
17. Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas
SciTech Connect
Andreev, Pavel A.
2015-06-15
We discuss the complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular to an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction.
18. PREFACE: The 16th International Conference on Positron Annihilation (ICPA-16)
Alam, Ashraf; Coleman, Paul; Dugdale, Stephen; Roussenova, Mina
2013-06-01
The 16th International Conference on Positron Annihilation (ICPA-16) was held at the University of Bristol, United Kingdom during 19-24 August, 2012. This triennial conference is the foremost gathering of the Positron Annihilation Physics community and it was hosted in the UK for the first time since the series of meetings first started back in 1965. The University of Bristol, the Alma Mater of Paul Dirac, is situated at the heart of the city, and it has established a worldwide reputation in research and teaching. Many of the topics which were discussed during ICPA-16 form an integral part of the research themes in the schools of Physics, Chemistry and Engineering of this University. ICPA-16 attracted a diverse audience, both from academic and industrial institutions, with over 200 participants from 29 countries. It continued the long held tradition of showcasing novel research in the field of positron annihilation and a total of 170 papers were presented as talks and posters. The papers reported studies of metallic and semi-conducting solids, polymers and soft matter, porous materials, surfaces and interfaces, as well as advances in experimental, analytical and biomedical applications. The high quality of the presented work, coupled with the enthusiastic exchange of ideas, provided an invaluable forum, especially for younger researchers and postgraduate students. The excellence of student presentations was acknowledged by the award of prizes for the best student posters, which were received by David Billington (University of Bristol, UK), Moussa Sidibe (CEMHTI, France) and Hongxia Xu (Tohoku University, Japan). All papers published in the Conference Proceedings were reviewed by ICPA-16 participants. We are indebted to all reviewers who contributed their time and intellectual resources, allowing the refereeing and editing process to move smoothly toward the compilation of the Proceedings. Our sincere thanks and gratitude go to everyone who contributed to the
19. Development of an Electron-Positron Source for Positron Annihilation Lifetime Spectroscopy
DTIC Science & Technology
2009-12-19
coherent processes were sponsored by the NSF Quasi- monoenergetic MeV electron spectra emitted by an SiO2 plasma with (red) and without...adhering to the target surface. Aspects of this work that were directed toward neutron production were sponsored by the NRL. High-order
20. Ar irradiated Cr rich Ni alloy studied using positron annihilation spectroscopy
Saini, Sanjay; Menon, Ranjini; Sharma, S. K.; Srivastava, A. P.; Mukherjee, S.; Nabhiraj, P. Y.; Pujari, P. K.; Srivastava, D.; Dey, G. K.
2016-10-01
The present study focuses on understanding the effect of Ar ion irradiation at room temperature on Cr rich Ni-Cr alloy. The alloy is irradiated with Ar9+ ions (energy 315 keV) for total dose varying from 9.3 × 1014 to 2.3 × 1016 ion/cm2. The changes in the microstructure of the irradiated samples have been characterized by depth dependent Doppler broadening of annihilation radiation (DBAR) measurements using a slow positron beam facility. The variation in S-E profiles as a function of total dose corroborated with S-W curves indicates that the type of defects is also varied with the increase in total dose. The S-E profiles have been fitted using variable energy positron fit (VEPFIT) program considering a three layer structure for the irradiated samples. Estimated displacement damage profile as a function of increasing dose has been analyzed and a possible mechanism has been attributed to explain the observations made from S-parameter variation.
1. Calculations of the interference of annihilation radiations with positron spectra in a Ge detector
Avignone, F. T.; Noma, H.; Moltz, D. M.; Toth, K. S.
1981-10-01
The distortion of the Kurie plots of allowed positron spectra due to annihilation radiations was calculated by a simple Monte-Carlo technique for a small intrinsic Ge detector. The experimentally observed non-linearity near the end point is accurately reproduced by the calculations. Corrections were calculated for 15 theoretical allowed spectra with end-point energies ranging from 2.5 to 10 MeV for one small detector 1.6 cm in diameter and 0.7 cm thick and one larger detector 4.0 cm in diameter and 1.0 cm thick. The major effect of this interference is to shift the end-point up in energy from 182 keV at 2.5 MeV and to 204 keV at 9 MeV in the small detector and from 279 keV at 2.5 MeV and to 321 keV at 9 MeV in the larger detector. The method was used to correct the end-point energies of the two positron branches in the decay of 82Sr. The corrected data give values of (3.19 ± 0.02) and (2.42 ± 0.02) MeV. The resulting Q-value is (4.21 ± 0.02) MeV.
2. Defect Characterization in SiGe/SOI Epitaxial Semiconductors by Positron Annihilation
Ferragut, R.; Calloni, A.; Dupasquier, A.; Isella, G.
2010-12-01
The potential of positron annihilation spectroscopy (PAS) for defect characterization at the atomic scale in semiconductors has been demonstrated in thin multilayer structures of SiGe (50 nm) grown on UTB (ultra-thin body) SOI (silicon-on-insulator). A slow positron beam was used to probe the defect profile. The SiO2/Si interface in the UTB-SOI was well characterized, and a good estimation of its depth has been obtained. The chemical analysis indicates that the interface does not contain defects, but only strongly localized charged centers. In order to promote the relaxation, the samples have been submitted to a post-growth annealing treatment in vacuum. After this treatment, it was possible to observe the modifications of the defect structure of the relaxed film. Chemical analysis of the SiGe layers suggests a prevalent trapping site surrounded by germanium atoms, presumably Si vacancies associated with misfit dislocations and threading dislocations in the SiGe films.
3. Gamma Spectra Resulting From the Annihilation of Positrons with Electrons in Single, Selected Core Levels of Cu, Ag and Au
SciTech Connect
Kim, S; Eshed, A; Goktepeli, S; Sterne, P A; Koymen, A R; Chen, W C; Weiss, A H
2005-07-25
The {gamma}-ray energy spectra due to positron annihilation with the 3p core-level of Cu, the 4p core-level of Ag, and 5p core level of Au were obtained separately from the total annihilation spectrum by measuring the energies of {gamma}-rays time coincident with Auger electrons emitted as a result of filling the core-hole left by annihilation. The results of these measurements are compared to the total annihilation spectra and with LDA based theoretical calculations. A comparison of area normalized momentum distributions with the individual cores extracted from the Doppler measurements shows good qualitative agreement, however, in all three spectra, the calculated values of the momentum density appears to fall below the measured values as the momentum increases. The discrepancies between theory and experiment are well outside the statistical uncertainties of the experiment and become more pronounced with increasing Z going down the column from Cu to Ag to Au. The comparison with the experimental results clearly indicates that the calculations are not predicting the correct ratio of high momentum to low momentum spectral weight and suggest the need to improve the treatment of many body electron-positron correlation effects in annihilation as they pertain to core levels.
4. A slow positron beam generator for lifetime studies
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Eftekhari, Abe; St.clair, Terry L.
1989-01-01
A slow positron beam generator using well-annealed polycrystalline tungsten moderators and a Na-22 positron source was developed. A 250 micro c source, deposited on a 2.54 micron thick aluminized mylar, is sandwiched between two (2.54 cm x 2.54 cm x 0.0127 cm) tungsten pieces. Two (2.54 cm x 2.54 cm x t cm) test polymer films insulate the two tungsten moderator pieces from the aluminized mylar source holder (t=0.00127 to 0.0127). A potential difference of 10 to 100 volts--depending on the test polymer film thickness (t)--is applied between the tungsten pieces and the source foil. Thermalized positrons diffusing out of the moderator pieces are attracted to the source foil held at an appropriate potential below the moderator pieces. These positrons have to pass through the test polymer films before they can reach the source foil. The potential difference between the moderator pieces and the aluminized mylar is so adjusted as to force the positrons to stop in the test polymer films. Thus the new generator becomes an effective source of positrons for assaying thin polymer films for their molecular morphology.
5. Positron annihilation spectroscopic studies of Mn substitution-induced cubic to tetragonal transformation in ZnFe2-xMnxO4 (x = 0.0-2.0) spinel nanocrystallites
Cyriac, Jincemon; Mundiyaniyil Thankachan, Rahul; Raneesh, B.; Nambissan, P. M. G.; Sanyal, D.; Kalarikkal, Nandakumar
2015-12-01
The replacement of cations at the B-sites in the spinel ferrite ZnFe2O4 by Mn3+ ions brings in several interesting changes, the most striking among them being a transformation from the spinel cubic structure to a body-centered tetragonal one. Concomitantly, there are variations in the nanocrystallite sizes and also in the lattice parameters. These are examined through high-precision X-ray diffraction measurements and transmission electron microscopic analysis. A more interesting aspect is the success of positron annihilation spectroscopy comprising of the measurements of positron lifetime and coincidence Doppler broadening measurements in understanding the effects of cation replacement and the resultant generation of vacancy-type defects. There are definite changes in the positron lifetimes and intensities which show positron trapping in trivacancy-type defect clusters and the nanocrystallite surfaces. The presence of ortho-positronium atoms within the extended intercrystallite region is also identified, although in small concentrations. The cubic to tetragonal transformation is indicated through definite decrease in the values of the positron lifetimes. We also performed a model analysis to predict the expected effect of substitution on the positron lifetime in the bulk of the sample and the experimentally obtained positron lifetimes significantly differed, indirectly hinting at the possibility of a structural transformation. Finally, Mössbauer spectroscopic studies have indicated a ferromagnetic nature for one of the samples, i.e. the one with Mn3+ doping concentration x = 0.4, which incidentally had the lowest crystallite size ~10 nm.
6. Positron annihilation spectroscopic study of high performance semi-interpenetrating network polyimids
NASA Technical Reports Server (NTRS)
Ray, Asit K.
1995-01-01
Semi-interpenetrating (S-IPN) network polyimids were made from different proportions of LaRC RP46 (a thermosetpolyimid) and LaRC BDTA-ODA (a thermoplastic polyimid). The ultimate goal of this networking is to improve the mechanical properties of the thermoset polyimid. Positron lifetime study was made to calculate lifetime based on second component of the life time spectra and the free volume & microvoid size. All these properties tend to decrease steadily with increasing thermoset content except at the 50 percent thermoset level where these properties show sudden drop. This result contradicts with the initial expectation that the blend properties should change gradually if it were a solid solution of thermoset (TSP) and thermoplastic (TPP) components. Thermal analyses (TMA, DSC, DMA & TGA) were run to complement the positron life time studies. The TMA and DSC studies confirm the contradiction mentioned above. Further experimentation with S-IPN polymers made at TSP/TTP content around 50/50 level are being conducted to explain this anomaly. Scanning electron microscope study of the S-IPN polyimid samples is under way in order to detect morphological differences which might help explain the phenomenon mentioned above.
7. Graphene networks and their influence on free-volume properties of graphene-epoxidized natural rubber composites with a segregated structure: rheological and positron annihilation studies.
PubMed
He, Canzhong; She, Xiaodong; Peng, Zheng; Zhong, Jieping; Liao, Shuangquan; Gong, Wei; Liao, Jianhe; Kong, Lingxue
2015-05-14
Epoxidized natural rubber-graphene (ENR-GE) composites with segregated GE networks were successfully fabricated using the latex mixing combined in situ reduced technology. The rheological behavior and electrical conductivity of ENR-GE composites were investigated. At low frequencies, the storage modulus (G') became frequency-independent suggesting a solid-like rheological behavior and the formation of GE networks. According to the percolation theory, the rheological threshold of ENR-GE composites was calculated to be 0.17 vol%, which was lower than the electrical threshold of 0.23 vol%. Both percolation thresholds depended on the evolution of the GE networks in the composites. At low GE concentrations (<0.17 vol%), GE existed as individual units, while a "polymer-bridged GE network" was constructed in the composites when GE concentrations exceeded 0.17 vol%. Finally, a "three-dimensional GE network" with percolation conductive paths was formed with a GE concentration of 0.23 vol%, where a remarkable increase in the conductivity of ENR-GE composites was observed. The effect of GE on the atom scale free-volume properties of composites was further studied by positron annihilation lifetime spectroscopy and positron age momentum correlation measurements. The motion of ENR chains was retarded by the geometric confinement of "GE networks", producing a high-density interfacial region in the vicinity of GE nanoplatelets, which led to a lower ortho-positronium lifetime intensity and smaller free-volume hole size.
8. Interstitial oxygen related defects and nanovoids in Au implanted a-SiO2 glass depth profiled by positron annihilation spectroscopy
Ravelli, L.; Macchi, C.; Mariazzi, S.; Mazzoldi, P.; Egger, W.; Hugenschmidt, C.; Somoza, A.; Brusa, R. S.
2015-12-01
Samples of amorphous silica were implanted with Au ions at an energy of 190 keV and fluences of 1× {{10}14} ions cm-2and 5× {{10}14} ions cm-2 at room temperature. The damage produced by ion implantation and its evolution with the thermal treatment at 800 °C for one hour in nitrogen atmosphere was depth profiled using three positron annihilation techniques: Doppler broadening spectroscopy, positron annihilation lifetime spectroscopy and coincidence Doppler broadening spectroscopy. Around the ion projected range of {{R}\\text{p}}=67 nm, a size reduction of the silica matrix intrinsic nanovoids points out a local densification of the material. Oxygen related defects were found to be present at depths four times the ion projected range, showing a high mobility of oxygen molecules from the densified and stressed region towards the bulk. The 800 °C thermal treatment leads to a recovery of the silica intrinsic nanovoids only in the deeper damaged region and the defect distribution, probed by positrons, shrinks around the ion projected range where the Au atoms aggregate. Open volume defects at the interface between Au and the amorphous matrix were evidenced in both the as implanted and in the thermal treated samples. A practically complete disappearance of the intrinsic nanovoids was observed around {{R}\\text{p}} when the implantation fluence was increased by two orders of magnitude (3× {{10}16} ions cm-2). In this case, the oxygen defects move to a depth five times larger than {{R}\\text{p}} .
9. Detection of helium in irradiated Fe9Cr alloys by coincidence Doppler broadening of slow positron annihilation
Cao, Xingzhong; Zhu, Te; Jin, Shuoxue; Kuang, Peng; Zhang, Peng; Lu, Eryang; Gong, Yihao; Guo, Liping; Wang, Baoyi
2017-03-01
An element analysis method, coincidence Doppler broadening spectroscopy of slow positron annihilation, was employed to detect helium in ion-irradiated Fe9Cr alloys. Spectra with higher peak to background ratio were recorded using a two-HPGe detector coincidence measuring system. It means that information in the high-momentum area of the spectra can be used to identify helium in metals. This identification is not entirely dependent on the helium concentration in the specimens, but is related to the structure and microscopic arrangement of atoms surrounding the positron annihilation site. The results of Doppler broadening spectroscopy and transmission electron microscopy show that vacancies and dislocations were formed in ion-irradiated specimens. Thermal helium desorption spectrometry was performed to obtain the types of He traps.
10. Implications of an astrophysical interpretation of PAMELA and Fermi-LAT data for future searches of a positron signal from dark matter annihilations
Choi, Ki-Young; Yaguna, Carlos E.
2010-01-01
The recent data from PAMELA and Fermi-LAT can be interpreted as evidence of new astrophysical sources of high energy positrons. In that case, such astrophysical positrons constitute an additional background against the positrons from dark matter annihilation. In this paper, we study the effect of that background on the prospects for the detection of a positron dark matter signal in future experiments. In particular, we determine the new regions in the (mass, ⟨σv⟩) plane that are detectable by the AMS-02 experiment for several dark matter scenarios and different propagation models. We find that, due to the increased background, these regions feature annihilation rates that are up to a factor of 3 larger than those obtained for the conventional background. That is, an astrophysical interpretation of the present data by PAMELA and Fermi-LAT implies that the detection of positrons from dark matter annihilation is slightly more challenging than previously believed.
11. Positron lifetime studies on 8 MeV electron-irradiated n-type 6H silicon carbide
Lam, C. H.; Lam, T. W.; Ling, C. C.; Fung, S.; Beling, C. D.; De-Sheng, Hang; Huimin, Weng
2004-11-01
The positron lifetime technique was employed to study vacancy-type defects in 8 MeV electron-irradiated n-type 6H silicon carbide. A long-lifetime component having a characteristic lifetime of 223-232 ps was observed in the irradiated sample and was attributed to the VCVSi divacancy. Other positron traps, which dominated at low temperatures, were observed to compete with the VCVSi for trapping positrons. A positron trapping model involving a positron shallow trap, a negatively charged monovacancy and the VCVSi divacancy was found to give a good description of the temperature-dependent positron lifetime data of the 1200 °C annealed sample. The identity of the monovacancy could not be unambiguously determined, but its lifetime was found to be in the range 160-172 ps.
12. A study of defects in iron-based binary alloys by the Mössbauer and positron annihilation spectroscopies
SciTech Connect
Idczak, R. Konieczny, R.; Chojcan, J.
2014-03-14
The room temperature positron annihilation lifetime spectra and {sup 57}Fe Mössbauer spectra were measured for pure Fe as well as for iron-based Fe{sub 1−x}Re{sub x}, Fe{sub 1−x}Os{sub x}, Fe{sub 1−x}Mo{sub x}, and Fe{sub 1−x}Cr{sub x} solid solutions, where x is in the range between 0.01 and 0.05. The measurements were performed in order to check if the known from the literature, theoretical calculations on the interactions between vacancies and solute atoms in iron can be supported by the experimental data. The vacancies were created during formation and further mechanical processing of the iron systems under consideration so the spectra mentioned above were collected at least twice for each studied sample synthesized in an arc furnace— after cold rolling to the thickness of about 40 μm as well as after subsequent annealing at 1270 K for 2 h. It was found that only in Fe and the Fe-Cr system the isolated vacancies thermally generated at high temperatures are not observed at the room temperature and cold rolling of the materials leads to creation of another type of vacancies which were associated with edge dislocations. In the case of other cold-rolled systems, positrons detect vacancies of two types mentioned above and Mössbauer nuclei “see” the vacancies mainly in the vicinity of non-iron atoms. This speaks in favour of the suggestion that in iron matrix the solute atoms of Os, Re, and Mo interact attractively with vacancies as it is predicted by theoretical computations and the energy of the interaction is large enough for existing the pairs vacancy-solute atom at the room temperature. On the other hand, the corresponding interaction for Cr atoms is either repulsive or attractive but smaller than that for Os, Re, and Mo atoms. The latter is in agreement with the theoretical calculations.
13. Development of positron annihilation spectroscopy for investigating deuterium decorated voids in neutron-irradiated tungsten
Taylor, C. N.; Shimada, M.; Merrill, B. J.; Akers, D. W.; Hatano, Y.
2015-08-01
The present work is a continuation of a recent research to develop and optimize positron annihilation spectroscopy (PAS) for characterizing neutron-irradiated tungsten. Tungsten samples were exposed to neutrons in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory and damaged to 0.025 and 0.3 dpa. Subsequently, they were exposed to deuterium plasmas in the Tritium Plasma Experiment (TPE) at Idaho National Laboratory. The implanted deuterium was desorbed through sample heating to 900 °C, and Doppler broadening (DB)-PAS was performed both before and after heating. Results show that deuterium impregnated tungsten is identified as having a smaller S-parameter. The S-parameter increases after deuterium desorption. Microstructural changes also occur during sample heating. These effects can be isolated from deuterium desorption by comparing the S-parameters from the deuterium-free back face with the deuterium-implanted front face. The application of using DB-PAS to examine deuterium retention in tungsten is examined.
14. Moessbauer and Positron Annihilation Spectroscopy Applied to WWER-1000 RPV Steels
SciTech Connect
Slugen, V.; Lipka, J.; Zeman, A.; Debarberis, L.
2005-04-26
Moessbauer spectroscopy (MS) and Positron annihilation spectroscopy (PAS) were applied in the evaluation of the microstructure parameters and degradation processes of nuclear reactor pressure vessel (RPV) steel surveillance specimens. Study was oriented to the material investigation of Russian WWER-1000 steels (15Kh2MNFAA and 12Kh2N2MAA) with higher Ni content (1.26 wt.% in base metal and 1.7 wt.% in weld). For comparison, the WWER-440 weld metal (Sv10KhMFT) without Ni was measured too. Specimens were studied in as received form, after irradiation in LVR-15 experimental reactor to the neutron fluence F(E>0.5 MeV) = 1.47x1024 m-2s-1 and after annealing process in vacuum at 475 deg. C/2h. Changes due to different chemical composition and due to irradiation were registered using MS. Post-irradiation thermal treatment and annealing of defects was well detected by different PAS techniques. Results confirm the hypothesis that Ni affects size (decrease) and distribution (more homogeneous) of the Cu- and P-rich clusters and MxCx carbides.
15. Vacancy analysis in a Ni-Nb-Zr-H glassy alloy by positron annihilation spectroscopy
Fukuhara, Mikio
2012-02-01
The positron lifetimes of Ni36Nb24Zr40 and (Ni0.36Nb0.24Zr0.40)90H10 glassy alloys are almost the same but longer than those of pure Zr, Nb, and Ni crystals, indicating that they have higher density of vacancies with smaller size than in crystals. The coincidence Doppler broadening spectrum for both specimens shows that the contribution of Ni around the vacancies is lower than that of Zr and Nb, suggesting that hydrogen atoms favour to exist between Ni atoms comprising neighboring distorted icosahedral Zr5Ni5Nb3 clusters. Thus, these results provide a substitute model of quantum dot tunneling along Ni-H-Ni atomic bond arrays among the clusters.
16. Detection of vacancy defects in gallium arsenide by positron lifetime spectroscopy
SciTech Connect
Saarinen, K.; Kuisma, S.; Hautojaervi, P.
1996-12-01
Vacancy-related native defects were studied in semi-insulating GaAs by positron life-time measurements. Both gallium and arsenic vacancies are observed at concentrations of 10{sup 15} - 10{sup 16} cm{sup -3}. The experiments in the dark after illumination manifest the vacancy nature of the metastable state of the EL2 center.
17. Calculation of Positron Binding Energies and Electron-Positron Annihilation Rates for Atomic Systems with the Reduced Explicitly Correlated Hartree-Fock Method in the Nuclear-Electronic Orbital Framework.
PubMed
Brorsen, Kurt R; Pak, Michael V; Hammes-Schiffer, Sharon
2017-01-19
Although the binding of a positron to a neutral atom has not been directly observed experimentally, high-level theoretical methods have predicted that a positron will bind to a neutral atom. In the present study, the binding energies of a positron to lithium, sodium, beryllium, and magnesium, as well as the electron-positron annihilation rates for these systems, are calculated using the reduced explicitly correlated Hartree-Fock (RXCHF) method within the nuclear-electronic orbital (NEO) framework. Due to the lack of explicit electron-positron correlation, NEO Hartree-Fock and full configuration interaction calculations with reasonable electronic and positronic basis sets do not predict positron binding to any of these atoms. In contrast, the RXCHF calculations predict positron binding energies and electron-positron annihilation rates in qualitative agreement with previous highly accurate but computationally expensive stochastic variational method calculations. These results illustrate that the RXCHF method can successfully describe the binding of a positron to a neutral species with no dipole moment. Moreover, the RXCHF method will be computationally tractable for calculating positron binding to molecular systems. The RXCHF approach offers a balance of accuracy and computational tractability for studying these types of positronic systems.
18. Post-irradiation annealing behavior of microstructure and hardening of a reactor pressure vessel steel studied by positron annihilation and atom probe tomography
Kuramoto, A.; Toyama, T.; Takeuchi, T.; Nagai, Y.; Hasegawa, M.; Yoshiie, T.; Nishiyama, Y.
2012-06-01
Post-irradiation annealing (PIA) behavior of irradiation-induced microstructural changes and hardening of an A533B (0.16 wt.% Cu) steel after neutron-irradiation of 3.9 × 1019 n cm-2 (0.061 displacement per atom (dpa)) at 290 °C was studied by positron annihilation spectroscopy (PAS), atom probe tomography (APT) and Vickers microhardness measurements. Coincidence Doppler broadening and positron lifetime measurements clearly reveal two recovery stages; (i) as-irradiated state to annealing at 450 °C and (ii) annealing from 450 to 600 °C. The first stage is due to annealing out of the most of irradiation-induced vacancy-related defects, while the second stage corresponds to dissolving of irradiation-induced solute nanoclusters (SCs). APT observations reveal that the SCs are enriched with Cu, Mn, Ni and Si and that their number densities decrease with increasing annealing temperature without coarsening to give almost complete recovery at 550 °C. The experimental hardening is almost twice the SC hardening estimated by the Russell-Brown model below 350 °C, whereas it is almost the same as that estimated in the range 400-550 °C.
19. Positron annihilation study for enhanced nitrogen-vacancy center formation in diamond by electron irradiation at 77 K
SciTech Connect
Tang, Z.; Chiba, T.; Nagai, Y.; Inoue, K.; Toyama, T.; Hasegawa, M.
2014-04-28
A compact ensemble of high density nitrogen-vacancy (NV) centers in diamond is essential to sense various external fields with a high precision at the nanoscale. Here, defects in type IIa and type Ib diamonds induced by 28 MeV electron irradiation at 77 K were studied by combining the positron annihilation spectroscopy and first-principles calculations. It is shown that the electron irradiation at 77 K can significantly enhance the NV center formation by directly converting 24% vacancies into the NV centers, indicating that it is an efficient way to produce the high density NV centers in the type Ib diamond.
20. Positron annihilation and constant photocurrent method measurements on a-Si:H films: A comparative approach to defect identification
Gordo, P. M.; Ferreira Marques, M. F.; Lopes Gil, C.; de Lima, A. P.; Lavareda, G.; Nunes de Carvalho, C.; Amaral, A.; Kajcsos, Zs.
2007-02-01
Defect structure of hydrogenated amorphous silicon thin-films was studied by positron annihilation spectroscopy (PAS), whereas the density of states below the Fermi level was measured by constant photocurrent method (CPM). Divacancies and large vacancy clusters were identified as the main defects present in these films, with relative concentrations strongly dependent on the rf-power. Correlation between PAS, CPM results and I( V) characteristics of solar cells suggests the creation of energy levels above the Fermi energy, not observable by CPM, related to large vacancy clusters.
1. Defect formation and annealing behaviors of fluorine-implanted GaN layers revealed by positron annihilation spectroscopy
Wang, M. J.; Yuan, L.; Cheng, C. C.; Beling, C. D.; Chen, K. J.
2009-02-01
Defect formation and annealing behaviors of fluorine-implanted, unintentionally doped GaN layers were studied by positron annihilation spectroscopy (PAS). Single Ga vacancies (VGa) were identified as the main vacancy-type defects detected by PAS after fluorine implantation at 180 keV with a dose of 1×1015 cm-2. Implantation-induced VGa tend to aggregate and form vacancy clusters after postimplantation annealing in N2 ambient at 600 °C. Fluorine ions tend to form F-vacancy complexes quickly after thermal annealing, which is consistent with the proposed diffusion model that predicts the behaviors of fluorine in GaN.
2. Revealing the nano-level molecular packing in chitosan-NiO nanocomposite by using positron annihilation spectroscopy and small-angle X-ray scattering.
PubMed
Sharma, Sandeep K; Bahadur, Jitendra; Patil, Pushkar N; Maheshwari, Priya; Mukherjee, Saurabh; Sudarshan, Kathi; Mazumder, Subhasish; Pujari, Pradeep K
2013-04-02
Chitosan-NiO nanocomposite (CNC) is shown to be a potential dielectric material with promising properties. CNCs containing NiO nanoparticles (0.2, 0.6, 1, 2, 5 wt %) are prepared through chemical methods. The inclusion of NiO nanoparticles in the chitosan matrix is confirmed by scanning electron microscopy (SEM) and X-ray diffraction. The morphology of the NiO nanoparticles and the nanocomposites is investigated by transmission electron microscopy and SEM, respectively. Positron annihilation lifetime spectroscopy (PALS) and the coincidence Doppler broadening (CDB) technique are used to quantify the free volume and molecular packing in the nanocomposites. The triplet-state positronium lifetime and the corresponding intensity show the changes in nanohole size, density, and size distribution as a function of NiO loading. Small-angle X-ray scattering indicates that the NiO aggregates are identical in all the CNCs. The momentum density distribution obtained from CDB measurements excludes the possibility of a contribution of vacant spaces (pores) available in NiO aggregates to the free volume of nanocomposites upon determination by using PALS. The results show systematic variation in free-volume properties and nano-level molecular packing as a function of NiO loading, which is presumed to play a vital role in determining the various properties of the nanocomposites.
3. Investigation of Oxygen-Induced Quenching of Phosphorescence in Photoexcited Aromatic Molecules by Positron Annihilation Spectroscopy
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Eftekhari, Abe
1996-01-01
Platinum OctaEthyl Porphyrin (Pt.OEP) is an efficient phosphor under ultraviolet excitation. The phosphorescent triplet state P(T(Sup 1)) is readily quenched by the oxygen O2 molecules. This phenomenon is being utilized as the basis for global air pressure measurements in aerodynamic facilities at various laboratories. The exact mechanism by which O2 molecules quench the P(T(Sup 1) approaches P(S(Sub O)) transitions is still unknown. The diamagnetic singlet states P(S(Sub n)), which feed P(T(Sub 1)) states via intersystem crossings, would presumably not be affected by O2. It must be only the magnetic P(T(Sub 1)) states, which can interact with the paramagnetic O2 molecules, that are affected. However, our positron lifetime and Doppler broadening studies suggest the formation of O2P(S(Sub n)), complexes which can also eventually reduce the population of the P(T(Sub 1)) states (i.e., quench phosphorescence). This reduction is possible because higher triplet states in (Pt.OEP) are admixed with the P(S(Sub 1)), states via spin orbit interactions. The experimental procedures and the results of various measurements are presented in this paper.
4. Mechanism of phosphorescence quenching in photomagnetic molecules determined by positron annihilation spectroscopy
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Eftekhari, A.; Naidu, S. V. N.
1994-01-01
Platinum Octaethyl Porphyrin (Pt.OEP) is an efficient phosphor under ultraviolet excitation. The phosphorescent triplet state (T(sub 1)) is readily quenched by the oxygen (O2) molecules. This phenomenon is being utilized as the basis for global air pressure measurements in aerodynamic facilities at various laboratories. The exact mechanism by which O2 molecules quench the (T(sub 1)-S(sub 0)) transitions is still unknown. The diamagnetic S(sub n) singlet states, which feed T(sub 1) states via intersystem crossings, would presumably not be affected by O2. It must be the magnetic T(sub 1) states, which can interact with the paramagnetic O2 molecules, that are affected. However, our positron lifetime and Doppler broadening studies suggest the formation of (S(sub n).02) complexes which can also eventually reduce the population of the T(sub 1) states (i.e. quench phosphorescence). This is possible since higher triplet states in (Pt-OEP) are admixed with the S(sub n) states via spin orbit interactions. The experimental procedures and the results of various measurements are discussed in this paper.
5. Mechanism of phosphorescence quenching in photomagnetic molecules determined by positron annihilation spectroscopy
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Eftekhari, A.; Naidu, S. V. N.
1994-01-01
Platinum Octaethyl Porphyrin (Pt.OEP) is an efficient phosphor under ultraviolet excitation. The phosphorescent triplet state (T(sub 1)) is readily quenched by the oxygen (O2) molecules. This phenomenon is being utilized as the basis for global air pressure measurements in aerodynamic facilities at various laboratories. The exact mechanism by which O2 molecules quench the (T(sub 1) - S(sub 0)) transitions is still unknown. The diamagnetic S(sub n) singlet states, which feed T(sub 1) states via intersystem crossings, would presumably not be affected by O2. It must be the magnetic T(sub 1) states, which can interact with the paramagnetic O2 molecules, that are affected. However, our positron lifetime and Doppler broadening studies suggest the formation of (S(sub n) central dot O2) complexes which can also eventually reduce the population of the T(sub 1) states (i.e. quench phosphorescence). This is possible since higher triplet states in (Pt.OEP) are admixed with the S(sub n) states via spin orbit interactions. The experimental procedures and the results of various measurements are discussed in this paper.
6. Influence of O-Co-O layer thickness on the thermal conductivity of Na{sub x}Co{sub 2}O{sub 4} studied by positron annihilation
SciTech Connect
Li, H. Q.; Zhao, B.; Zhang, T.; Li, X. F.; He, H. F.; Chen, Z. Q.; Su, X. L.; Tang, X. F.
2015-07-21
Nominal stoichiometric Na{sub x}Co{sub 2}O{sub 4} (x = 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0) polycrystals were synthesized by a solid-state reaction method. They were further pressed into pellets by the spark plasma sintering. The crystal structure and morphology of Na{sub x}Co{sub 2}O{sub 4} samples were characterized by X-ray diffraction and scanning electron microscopy measurements. Good crystallinity and layered structures were observed for all the samples. Positron annihilation measurements were performed for Na{sub x}Co{sub 2}O{sub 4} as a function of Na content. Two lifetime components are resolved. τ{sub 1} is attributed mainly to positron annihilation in the O-Co-O layers and shifts to Na layers only in the H3 phase. The second lifetime τ{sub 2} is due to positron annihilation in vacancy clusters which may exist in the Na layers or grain boundary region. The size of vacancy clusters grow larger but their concentration decreases with increasing Na content in the range of 1.0 < x < 1.8. The thickness of O-Co-O layer also shows continuous increase with increasing Na content, which is reflected by the increase of τ{sub 1}. The thermal conductivity κ, on the other hand, shows systematic decrease with increasing Na content. This suggests that the increasing spacing of O-Co-O layer could effectively reduce the thermal conductivity of Na{sub x}Co{sub 2}O{sub 4}.
7. Structural transition of partially Ba-filled thermoelectric CoSb{sub 3} investigated by positron annihilation spectroscopy
SciTech Connect
Zhang, T.; Li, X. F.; Chen, Z. Q.; Zhou, K.; Su, X. L.; Tang, X. F.
2015-02-07
Microstructure of unfilled and Ba-filled CoSb{sub 3} has been studied by positron lifetime measurements together with theoretical calculation. Positron trapping in intrinsic voids is observed in the CoSb{sub 3}, which contributes a positron lifetime of 263 ± 2 ps. After filling Ba atoms with content up to x = 0.4, the positron lifetime shows continuous increase. By comparing the experimental results with calculation following the phase diagram of Ba{sub x}Co{sub 4}Sb{sub 12} with x in the range of 0–0.5, it is found that when the Ba content is lower than 0.16, the filling of Ba atoms is in a phase of solid solution. At x = 0.2, γ phase is formed, which is mixed with solid solution. At x > 0.25, transition from γ phase to a mixture of γ and α phases is confirmed.
8. Reply to "Comment on Gamma-ray spectra from low-energy positron annihilation processes in molecules' "
Ma, Xiaoguang; Wang, Meishan; Zhu, Yinghao; Yang, Chuanlu
2017-03-01
In reply to the Comment of Green et al. [Phys. Rev. A 95, 036701 (2017)., 10.1103/PhysRevA.95.036701] on our paper [Phys. Rev. A 94, 052709 (2016), 10.1103/PhysRevA.94.052709], we reconfirm that all the conclusions are based on the observation and the comparisons of the theoretical and experimental data. One criticism of Green et al. [Phys. Rev. A 95, 036701 (2017)., 10.1103/PhysRevA.95.036701] concerns the positrophilic electrons and the inner valence electrons. The inner valence electrons or positrophilic electrons show most agreeable widths with the corresponding experimental measurements due to their narrowest momentum distributions for all 59 molecules. However, we agree with the criticism of Green et al. [Phys. Rev. A 95, 036701 (2017)., 10.1103/PhysRevA.95.036701] and reconfirm that this agreement does not represent the dominance of the inner valence in the annihilation process. In this Reply, we will clarify the difference between agreement and dominance and illustrate with some figures. Another criticism is about the approximation used in our paper. We emphasize that the averaged discrepancy of 34.2% for these molecules of the theoretical γ -ray spectra from the experimental measurements is due to the neglect of the positron-electron correlations, vibrational couplings, virtual-state formation, even tunneling of core electrons not the neglect of the positron wave function. In this Reply, we will show, even in this zero-order approximation, these positron-induced effects in the electron-positron annihilation process of molecules can also be analyzed with more corrections and explanations.
9. Simultaneous existence of defects and mesopores in nanosized ZSM-5 zeolite studied by positron annihilation and X-ray diffraction spectroscopies
Anh Tuyen, L.; Quang Hung, N.; Chi Cuong, L.; Duy Khiem, D.; Trong Phuc, P.; Ly Nguyen, L.; Ngoc Hue, N. T.; Thi Hue, P.; Van Phuc, D.
2017-02-01
Crystallization, formation, and accumulation of defects and mesopores in the ZSM-5 zeolite samples, which are synthesized from the gel composition of 1.2Na2O 0.1Al2O3 0.8 tetra-propylammonium hydroxide (TPAOH) 6SiO2 400H2O at a temperature of 140 degree Celsius (°C) in 10, 15, and 18 h, are studied by using the Positron annihilation lifetime (PALS) and X-ray diffraction (XRD) spectroscopies. The XRD is used for investigating the crystalline concentration and nano-crystal size of ZSM-5 during the crystallizing process, whereas the PALS is performed in order to determine the presence of templates, defects, and mesopores in the zeolite samples. The latter are calcined in air during 1, 2, and 3 h at a temperature of 600 °C before being measured. The results obtained indicate that there exist clusters of small crystals in the early crystalline stages of the samples. The size of these crystals increases with time and reaches approximately 100 nm after 18 h of reaction. In addition, the template (TPAOH) is found to exist not only in the channels inside the framework but also in the mesopores outside it. Finally, by analyzing the Positron lifetime spectra, we have found for the first time the simultaneous existence of defects and mesopores, which are formatted and accumulated during the crystallization of ZSM-5. Those important results contribute significantly to our understanding of the internal structure of the synthetic zeolite ZSM-5 as well as the synthetic processes for producing zeolites with special features.
10. Measurement of the spectra of low energy electrons resulting from Auger transitions induced by the annihilation of low energy positrons implanted at The Ag (100) surface
Shastry, Karthik; Joglekar, Prasad; Weiss, A. H.; Fazleev, N. G.
2013-04-01
A few percent of positrons bound to a solid surface annihilate with core electrons resulting in highly excited atoms containing core holes. These core holes may be filled in an auto-ionizing process in which a less tightly bound electron drops into the hole and the energy difference transferred to an outgoing "Auger electron." Because the core holes are created by annihilation and not impact it is possible to use very low energy positron beams to obtain annihilation induced Auger signals. The Auger signals so obtained have little or none of the large impact induced secondary electron background that interferes with measurements of the low energy Auger spectra obtained using the much higher incident energies necessary when using electron or photon beams. Here we present the results of measurements of the energy spectrum of low energy electrons emitted as a result of Positron Annihilation Induce Auger Electron Emission [1] from a clean Ag (100) surface. The measurements were performed using the University of Texas Arlington Time of Flight Positron Annihilation induced Auger Electron Spectrometer (T-O-F-PAES) System [2]. A strong double peak was observed at ˜35eV corresponding to the N2VV and N3VV Auger transitions in agreement with previous PAES studies [3].
11. Optical and positron annihilation spectroscopic studies on PMMA polymer doped by rhodamine B/chloranilic acid charge transfer complex: Special relevance to the effect of γ-ray irradiation.
PubMed
Hassan, H E; Refat, Moamen S; Sharshar, T
2016-04-15
Polymeric sheets of poly (methylmethaclyerate) (PMMA) containing charge transfer (CT) complex of rhodamine B/chloranilic acid (Rho B/CHA) were synthesized in methanol solvent at room temperature. The systematic analysis done on the Rho B and its CT complex in the form of powder or polymeric sheets confirmed their structure and thermal stability. The IR spectra interpreted the charge transfer mode of interaction between the CHA central positions and the terminal carboxylic group. The polymer sheets were irradiated with 70 kGy of γ radiation using (60)Co source to study the enhanced changes in the structure and optical parameters. The microstructure changes of the PMMA sheets caused by γ-ray irradiation were analyzed using positron annihilation lifetime (PAL) and positron annihilation Doppler broadening (PADB) techniques. The positron life time components (τ(i)) and their corresponding intensities (I(i)) as well as PADB line-shape parameters (S and W) were found to be highly sensitive to the enhanced disorder occurred in the organic chains of the polymeric sheets due to γ-irradiation.
12. Optical and positron annihilation spectroscopic studies on PMMA polymer doped by rhodamine B/chloranilic acid charge transfer complex: Special relevance to the effect of γ-ray irradiation
Hassan, H. E.; Refat, Moamen S.; Sharshar, T.
2016-04-01
Polymeric sheets of poly (methylmethaclyerate) (PMMA) containing charge transfer (CT) complex of rhodamine B/chloranilic acid (Rho B/CHA) were synthesized in methanol solvent at room temperature. The systematic analysis done on the Rho B and its CT complex in the form of powder or polymeric sheets confirmed their structure and thermal stability. The IR spectra interpreted the charge transfer mode of interaction between the CHA central positions and the terminal carboxylic group. The polymer sheets were irradiated with 70 kGy of γ radiation using 60Co source to study the enhanced changes in the structure and optical parameters. The microstructure changes of the PMMA sheets caused by γ-ray irradiation were analyzed using positron annihilation lifetime (PAL) and positron annihilation Doppler broadening (PADB) techniques. The positron life time components (τi) and their corresponding intensities (Ii) as well as PADB line-shape parameters (S and W) were found to be highly sensitive to the enhanced disorder occurred in the organic chains of the polymeric sheets due to γ-irradiation.
13. OSSE observations of Galactic 511 keV positron annihilation radiation - Initial phase 1 results. [Oriented Scintillation Spectrometer Experiment
NASA Technical Reports Server (NTRS)
Purcell, W. R.; Grabelsky, D. A.; Ulmer, M. P.; Johnson, W. N.; Kinzer, R. L.; Kurfess, J. D.; Strickman, M. S.; Jung, G. V.
1993-01-01
The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma-Ray Observatory (GRO) has performed numerous observations of the Galactic plane and Galactic center region to measure the distribution of Galactic 511 keV positron annihilation radiation and to search for time variability of the emission. The initial 511 keV line fluxes for the observations performed during the first 18 months of the GRO mission are presented. The 511 keV line flux for a typical Galactic center observation is (2.5 +/- 0.3) x 10 exp -4 gamma/sq cm per sec, where the quoted uncertainty represents the 1 sigma statistical uncertainty. No statistically significant time variability of the line flux has been observed; the 3 sigma upper limit to daily variations from the mean is 3 x 10 exp -4 gamma/sq cm per sec. The distribution of Galactic 511 keV positron annihilation radiation implied by the OSSE observations is discussed and compared with observations by other instruments.
14. Physical Selectivity of Molecularly Imprinted polymers evaluated through free volume size distributions derived from Positron Lifetime Spectroscopy
Pasang, T.; Ranganathaiah, C.
2015-06-01
The technique of imprinting molecules of various sizes in a stable structure of polymer matrix has derived multitudes of applications. Once the template molecule is extracted from the polymer matrix, it leaves behind a cavity which is physically (size and shape) and chemically (functional binding site) compatible to the particular template molecule. Positron Annihilation Lifetime Spectroscopy (PALS) is a well known technique to measure cavity sizes precisely in the nanoscale and is not being used in the field of MIPs effectively. This method is capable of measuring nanopores and hence suitable to understand the physical selectivity of the MIPs better. With this idea in mind, we have prepared molecular imprinted polymers (MIPs) with methacrylicacid (MAA) as monomer and EGDMA as cross linker in different molar ratio for three different size template molecules, viz. 4-Chlorophenol (4CP)(2.29 Å), 2-Nephthol (2NP) (3.36 Å) and Phenolphthalein (PP) (4.47Å). FTIR and the dye chemical reactions are used to confirm the complete extraction of the template molecules from the polymer matrix. The free volume size and its distribution have been derived from the measured o-Ps lifetime spectra. Based on the free volume distribution analysis, the percentage of functional cavities for the three template molecules are determined. Percentage of functional binding cavities for 4-CP molecules has been found out to be 70.2% and the rest are native cavities. Similarly for 2NP it is 81.5% and nearly 100% for PP. Therefore, PALS method proves to be very precise and accurate for determining the physical selectivity of MIPs.
15. The Distribution of Galactic 511 keV Positron Annihilation Radiation
DTIC Science & Technology
1994-01-01
and 44Sc, this positron production rate implies a limit to the present rate of Galactic iron nucleosynthesis of 0:7 M per 100 years (see Ramaty...constraints on the positron production rate for the disk and spheroidal components, and on the present rate of Galactic nucleosynthesis of +-unstable
16. Electron irradiated liquid encapsulated Czochralski grown undoped gallium antimonide studied by positron lifetime spectroscopy and photoluminescence
Ma, S. K.; Lui, M. K.; Ling, C. C.; Fung, S.; Beling, C. D.; Li, K. F.; Cheah, K. W.; Gong, M.; Hang, H. S.; Weng, H. M.
2004-09-01
Electron irradiated undoped liquid encapsulated Czochralski (LEC) grown GaSb samples were studied by positron lifetime spectroscopy (PLS) and photoluminescence (PL). In addition to the 315 ps component reported in the previous studies, another defect with a lifetime of 280 ps was also identified in the present electron irradiated samples. The bulk lifetime of the GaSb material was found to be 258 ps. The VGa,280 ps and the VGa,315 ps defects were associated with two independent Ga vacancy related defects having different microstructures. The well known 777 meV PL signal (usually band A) was also observed in the electron irradiated undoped GaSb samples. The band A intensity decreases with increasing electron irradiation dosage and it disappears after the 300 °C annealing regardless of the irradiation dosage. The origin of the band A signal is also discussed.
17. Free volume in imidazolium triflimide ([C{sub 3}MIM][NTf{sub 2}]) ionic liquid from positron lifetime: Amorphous, crystalline, and liquid states
SciTech Connect
Dlubek, G.; Beichel, W.; Bulut, S.; Pogodina, N.; Krossing, I.; Friedrich, Ch.
2010-09-28
Positron annihilation lifetime spectroscopy (PALS) is used to study the ionic liquid 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide [C{sub 3}MIM][NTf{sub 2}] in the temperature range between 150 and 320 K. The positron decay spectra are analyzed using the routine LifeTime-9.0 and the size distribution of local free volumes (subnanometer-size holes) is calculated. This distribution is in good agreement with Fuerth's classical hole theory of liquids when taking into account Fuerth's hole coalescence hypothesis. During cooling, the liquid sample remains in a supercooled, amorphous state and shows the glass transition in the ortho-positronium (o-Ps) lifetime at 187 K. The mean hole volume varies between 70 A{sup 3} at 150 K and 250 A{sup 3} at 265-300 K. From a comparison with the macroscopic volume, the hole density is estimated to be constant at 0.20x10{sup 21} g{sup -1} corresponding to 0.30 nm{sup -3} at 265 K. The hole free volume fraction varies from 0.023 at 185 K to 0.073 at T{sub m}+12 K=265 K and can be estimated to be 0.17 at 430 K. It is shown that the viscosity follows perfectly the Cohen-Turnbull free volume theory when using the free volume determined here. The heating run clearly shows crystallization at 200 K by an abrupt decrease in the mean <{tau}{sub 3}> and standard deviation {sigma}{sub 3} of the o-Ps lifetime distribution and an increase in the o-Ps intensity I{sub 3}. The parameters of the second lifetime component <{tau}{sub 2}> and {sigma}{sub 2} behave parallel to the o-Ps parameters, which also shows the positron's (e{sup +}) response to structural changes. During melting at 253 K, all lifetime parameters recover to the initial values of the liquid. An abrupt decrease in I{sub 3} is attributed to the solvation of e{sup -} and e{sup +} particles. Different possible interpretations of the o-Ps lifetime in the crystalline state are briefly discussed.
18. Positron annihilation studies of the AlO{sub x}/SiO{sub 2}/Si interface in solar cell structures
SciTech Connect
Edwardson, C. J.; Coleman, P. G.; Li, T.-T. A.; Cuevas, A.; Ruffell, S.
2012-03-01
Film and film/substrate interface characteristics of 30 and 60 nm-thick AlO{sub x} films grown on Si substrates by thermal atomic layer deposition (ALD), and 30 nm-thick AlO{sub x} films by sputtering, have been probed using variable-energy positron annihilation spectroscopy (VEPAS) and Doppler-broadened spectra ratio curves. All samples were found to have an interface which traps positrons, with annealing increasing this trapping response, regardless of growth method. Thermal ALD creates an AlO{sub x}/SiO{sub x}/Si interface with positron trapping and annihilation occurring in the Si side of the SiO{sub x}/Si boundary. An induced positive charge in the Si next to the interface reduces diffusion into the oxides and increases annihilation in the Si. In this region there is a divacancy-type response (20 {+-} 2%) before annealing which is increased to 47 {+-} 2% after annealing. Sputtering seems to not produce samples with this same electrostatic shielding; instead, positron trapping occurs directly in the SiO{sub x} interface in the as-deposited sample, and the positron response to it increases after annealing as an SiO{sub 2} layer is formed. Annealing the film has the effect of lowering the film oxygen response in all film types. Compared to other structural characterization techniques, VEPAS shows larger sensitivity to differences in film preparation method and between as-deposited and annealed samples.
19. Effect of annealing on Cu precipitates in H ion irradiated Fe-0.6%Cu studied by positron annihilation
Jin, Shuoxue; Zhang, Peng; Lu, Eryang; Wang, Baoyi; Yuan, Daqing; Wei, Long; Cao, Xingzhong
2016-10-01
Fe-0.6%Cu alloy was irradiated with H ions to 0.1 dpa, and then annealed for 30 min from 150 °C to 500 °C. We focused the evolution of Cu precipitates in irradiated Fe-0.6%Cu alloy after the isochronal annealing from the perspective of positron annihilation. The ΔW parameters after thermal annealing (400 °C and 500 °C) were much larger than that induced by 0.1 dpa H irradiation. Annealing could promote the aggregation of the Cu-vacancy complexes, and form the Cu cluster-vacancies complexes. When the vacancy-like defects recovered around 500 °C, it meant the formation and growing of the defect-free Cu precipitates.
Hareesh, K.; Pandey, A. K.; Meghala, D.; Ranganathaiah, C.; Sanjeev, Ganesh
2013-02-01
The free volume properties of pristine and UV irradiated Lexan polycarbonate have been investigated using Positron Lifetime Spectroscopy (PLS). The decrease in o-Ps life time and free volume size of irradiated sample is attributed to free volume modification and formation of more stable free radicals. These free radicals are formed due to the breakage of C-O bonds in Lexan polycarbonate after irradiation. This is also supported by the decrease in the intensity of C-O bond after exposure to UV-radiation as studied from Fourier Transform Infrared (FTIR) spectroscopy and it also shows that benzene ring does not undergo any changes after irradiation.
1. Structural and defect characterization of Gd-doped GaN films by X-ray diffraction and positron annihilation
Yabuuchi, A.; Oshima, N.; O'Rourke, B. E.; Suzuki, R.; Ito, K.; Sano, S.; Higashi, K.; Zhou, Y.-K.; Hasegawa, S.
2014-04-01
Molecular-beam-epitaxy-grown Ga1-xGdxN films were investigated by X-ray diffraction and slow positron beams. From the positron lifetime results, N-vacancy-related defects may be expected in the Ga0.9Gd0.1N film grown under Ga-rich conditions which exhibits a lattice expansion in the c-axis direction. In contrast, Ga vacancies more than 1019 cm-3 were detected in the Ga0.9Gd0.1N film grown under N-rich conditions which does not exhibit the lattice expansion, implying that the highly-concentrated Ga vacancies contribute to a relaxation of the lattice distortion caused by incorporating oversized Gd atoms.
2. High energy beam lifetime analysis
SciTech Connect
Howell, R.H.; Sterne, P.A.; Hartley, J.; Cowan, T.E.
1997-05-01
We have developed a positron lifetime defect analysis capability based on a 3 MeV electrostatic accelerator. The high energy beam lifetime spectrometer is operational with a 60 mCi {sup 22}Na source providing a current of 7 10{sup 5} positrons per second. Lifetime data are derived from a thin plastic transmission detector providing an implantation time and a BaF{sub 2} detector to determine the annihilation time. Positron lifetime analysis is performed with a 3 MeV positron beam on thick sample specimens at counting rates in excess of 2000 per second. The instrument is being used for bulk sample analysis and analysis of samples encapsulated in controlled environments for in situ measurements.
3. CHARACTERIZATION OF PLASTICALLY-INDUCED STRUCTURAL CHANGES IN A Zr-BASED BULK METALLIC GLASS USING POSITRON ANNIHILATION SPECTROCOPY
SciTech Connect
Flores, K M; Kanungo, B P; Glade, S C; Asoka-Kumar, P
2005-09-16
Flow in metallic glasses is associated with stress-induced cooperative rearrangements of small groups of atoms involving the surrounding free volume. Understanding the details of these rearrangements therefore requires knowledge of the amount and distribution of the free volume and how that distribution evolves with deformation. The present study employs positron annihilation spectroscopy to investigate the free volume change in Zr{sub 58.5}Cu{sub 15.6}Ni{sub 12.8}Al{sub 10.3}Nb{sub 2.8} bulk metallic glass after inhomogeneous plastic deformation by cold rolling and structural relaxation by annealing. Results indicate that the size distribution of open volume sites is at least bimodal. The size and concentration of the larger group, identified as flow defects, changes with processing. Following initial plastic deformation the size of the flow defects increases, consistent with the free volume theory for flow. Following more extensive deformation, however, the size distribution of the positron traps shifts, with much larger open volume sites forming at the expense of the flow defects. This suggests that a critical strain is required for flow defects to coalesce and form more stable nanovoids, which have been observed elsewhere by high resolution TEM. Although these results suggest the presence of three distinct open volume size groups, further analysis indicates that all groups have the same line shape parameter. This is in contrast to the distinctly different interactions observed in crystalline materials with multiple defect types. This similarity may be due to the disordered structure of the glass and positron affinity to particular atoms surrounding open-volume regions.
4. Microstructural Characterization of Semi-Interpenetrating Polymer Networks by Positron Lifetime Spectroscopy
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Pater, Ruth H.; Eftekhari, Abe
1996-01-01
Thermoset and thermoplastic polyimides have complementary physical and mechanical properties. Whereas thermoset polyimides are brittle and generally easier to process, thermoplastic polyimides are tough but harder to process. A combination of these two types of polyimides may help produce polymers more suitable for aerospace applications. Semi-Interpenetrating Polymer Networks (S-IPN) of thermoset LaRC(TM)-RP46 and thermoplastic LaRC(TM)-IA polyimides were prepared in weight percent ratios ranging from 100:0 to 0:100. Positron lifetime measurements were made in these samples to correlate their free volume features with physical and mechanical properties. As expected, positronium atoms are not formed in these samples. The second lifetime component has been used to infer the positron trap dimensions. The 'free volume' goes through a minimum at a ratio of about 50:50, and this suggests that S-IPN samples are not merely solid solutions of the two polymers. These data and related structural properties of the S-IPN samples are discussed.
5. Positron States at Li- and O-adsorbed Fe(001) Ferromagnetic Surfaces Studied by Two-Component Density Functional Theory
Hagiwara, Satoshi; Watanabe, Kazuyuki
2016-11-01
The positron states for Li- and O-adsorbed Fe(001) ferromagnetic surfaces are studied by using two-component density functional theory. Positron surface lifetimes and positron binding energies are found to be sensitive to changes in the surface structure and the dipole barrier induced by adatoms, which can be understood by the positron density distribution and surface potential. Spin-dependent positron lifetime fractions are in excellent agreement with spin-polarization fractions at the topmost surface, because the localized positrons at the surface are sensitive to the surface magnetic state. Therefore, the present results show that spin-polarized positron annihilation spectroscopy can extract the outermost surface magnetic state.
6. Positron Annihilation Ratio Spectroscopy (PsARS) Applied to Positronium Formation Studies
DTIC Science & Technology
2010-03-01
experimentation within the chemical hood, and Lt. Nick Herr for sharing his hard earned expertise on the AFM machine. I would also like to especially...Positrons in Metals. Hodges , Stott. 1, s.l. : Physical Review B, Vol. 7. 21. Experimental studies on positronium negative ions. Nagashima. s.l
7. Evaluation of a microchannel-plate PMT as a potential timing detector suitable for positron lifetime measurements
Kosev, K.; Butterling, M.; Anwand, W.; Cowan, T.; Hartmann, A.; Heidel, K.; Jungmann, M.; Krause-Rehberg, R.; Massarczyk, R.; Schilling, K. D.; Schwengner, R.; Wagner, A.
2010-12-01
This paper focuses on the evaluation of a microchannel-plate photomultiplier tube (MCP-PMT) as a candidate detector, suitable for positron lifetime studies. Several properties of MCP-PMTs, such as their fast time response, compact size, low susceptibility to magnetic fields, relatively high gain and the low power consumption make them attractive for positron lifetime spectroscopy. The preliminary tests were performed with a 85001-501 Burle Planacon TM photomultiplier tube assembly. Initial measurements were conducted with a pulsed Picosecond Injection Laser (PiLas) system. The engineering sample of the 85001 exhibits a transit-time-spread (TTS) of 110 ps (FWHM). Further timing experiments showing the suitability of the device as Cherenkov detector are presented. For the first time, a conventional positron lifetime spectrum of a Cz-Si probe measured with a spectrometer, where an MCP-PMT detector is included, has been demonstrated.
8. Collins effect in semiinclusive deeply inelastic scattering and in electron-positron-annihilation
SciTech Connect
Efremov, A.V.; Goeke, K.; Schweitzer, P.
2006-05-01
The Collins fragmentation function is extracted from HERMES data on azimuthal single spin asymmetries in semi-inclusive deeply inelastic scattering, and BELLE data on azimuthal asymmetries in e{sup +}e{sup -}-annihilations. A Gaussian model is assumed for the distribution of transverse parton momenta and predictions are used from the chiral quark-soliton model for the transversity distribution function. We find that the HERMES and BELLE data yield a consistent picture of the Collins fragmentation function which is compatible with COMPASS data and the information previously obtained from an analysis of DELPHI data. Estimates for future experiments are made.
9. Positron Annihilation Ratio Spectroscopy Study of Electric Fields Applied to Positronium at Material Interfaces
DTIC Science & Technology
2011-03-01
positron and neutrino are 14 emitted. When Na-22 decays, 90.4% of the time it decays via β + to an excited state of Ne-22. 3.7 psec after the...of Na-22 [12:7]. 22 22 11 10Na Ne e (8) where γ is the gamma ray and ν is the neutrino . Due to the fact that the neutrino can
10. Spectroscopic, Elemental and Thermal Analysis, and Positron Annihilation Studies on Ca(II), Sr(II), Ba(II), Pb(II), and Fe(III) Penicillin G Potassium Complexes
Refat, M. S.; Sharshara, T.
2015-11-01
The [Pb(Pin)2] · 3H2O, [M(Pin)(H2O)2(Cl)] · nH2O (M = SrII, CaII or BaII; n = 0-1), and [Fe(Pin)2(Cl)(H2O)] · H2O penicillin G potassium (Pin) complexes were synthesized and characterized using elemental analyses, molar conductivity, thermal analysis and electronic spectroscopy techniques. The positron annihilation lifetime (PAL) and Doppler broadening (DB) techniques have been employed to probe the defects and structural changes of Pin ligand and its complexes. The PAL and DB line-shape parameters were discussed in terms of the structure, molecular weight, ligand-metal molar ratio, and other properties of the Pin complexes.
11. An evaluation of algorithms for the deconvolution of Doppler broadening positron annihilation radiation spectroscopy spectra
Woo, Teresa K. C.; Cheng, Vincent K. W.; Beling, Christopher D.; Ng, Michael K. P.
2005-06-01
Two least squares minimization methods for the deconvolution of 1D Doppler Broadening Annihilation Radiation Spectroscopy (DBARS) spectra have been tested with spectra generated by Monte Carlo simulation according to the following functional forms: inverted triangle, inverted parabola, Laplace, Lorentz and a model DBARS spectrum for a metal composed of an inverted parabola and a Gaussian function. These reference spectra were firstly convoluted with a Gaussian broadening factor and then restored to its original form with the algorithms. The method with Tikhonov regularizer and non-negativity constraint still failed to restore the sharp features of these spectral functions although the negative signal found in an earlier study was removed. On the other hand, the method with the Huber regularizer was successful. Optimization of the deconvolution in terms of regularization parameters is necessary to achieve good deconvolution. The optimization of the deconvolution was checked with visual matching and a quality factor which takes into account the number of counts in the spectrum.
12. Defects versus grain size effects on the ferromagnetism of ZrO2 nanocrystals clarified by positron annihilation
Wang, D. D.; Qi, N.; Jiang, M.; Chen, Z. Q.
2013-01-01
Undoped ZrO2 nanocrystals were annealed in open air from 100 °C to 1300 °C. X-ray diffraction and transmission electron microscope were used to study the structure change and grain growth. Both the methods reveal that the ZrO2 grain size has very slight increase after annealing up to 900 °C. Positron annihilation measurements reveal a high concentration of vacancy defects which most probably exist in the grain boundary region. Thermal annealing above 500 °C causes recovery of these defects, and after annealing at 1200 °C, most of them are removed. Room temperature ferromagnetism is observed for the sample annealed at 100 °C and 500 °C. The magnetization becomes very weak after the nanocrystals are annealed at 700 °C, and it almost disappears at 1000 °C. It is clear that the intrinsic ferromagnetism in our ZrO2 nanocrystals is mostly related with the interfacial defects instead of grain size effects.
13. A comparative study on ferromagnetic C/O-implanted GaN films by positron annihilation spectroscopy
Xu, Juping; Li, Qiang; Liu, Jiandang; Ye, Bangjiao
2016-05-01
Room temperature ferromagnetism was observed in both C- and O-implanted GaN films, which were irradiated by 80 keV C/O-ions with respective dose of 5 × 1016 and 2 × 1017 ions/cm2. Positron annihilation spectroscopy was used to explore the magnetic origin and the correlation between the magnetism and structural features. The results reveal that carbon-ions play an important role in the stable ferromagnetism in C-implanted GaN films, while oxygen has no effect on the magnetic properties, even than a weak hysteresis loop was observed in O-implanted sample. This weak ferromagnetism is demonstrated as originated from Ga-related vacancies which induced by implantation. With first-principle calculations, we confirmed that substitutional C-ion at N-site can introduce magnetic moment for 0.8 μB and stabilize ferromagnetic coupling with adjacent Ga-vacancy at room temperature. Moreover, the effect of O-ions was clearly ruled out. Our discussion gives an experimental and theoretical insight of the different origin of ferromagnetism between acceptor and donor non-metal-doped GaN materials.
14. Impacts of B-factory measurements on determination of fragmentation functions from electron-positron annihilation data
Hirai, M.; Kawamura, H.; Kumano, S.; Saito, K.
2016-11-01
Fragmentation functions are determined for the pion and kaon by global analyses of charged-hadron production data in electron-positron annihilation. Accurate measurements were reported by the Belle and BaBar collaborations for the fragmentation functions at the center-of-mass energies of 10.52 and 10.54 GeV, respectively, at the KEK and SLAC B factories, whereas other available ee measurements were mostly done at higher energies, mainly at the Z mass of 91.2 GeV. There is a possibility that gluon fragmentation functions, as well as quark fragmentation functions, are accurately determined by scaling violation. We report our global analysis of the fragmentation functions especially to show impacts of the B-factory measurements on the fragmentation function determination. Our results indicate that the fragmentation functions are determined more accurately not only by the scaling violation but also by the high-statistical nature of the Belle and BaBar data. However, there are some tensions between the Belle and BaBar data in comparison with previous measurements. We also explain how the flavor dependence of quark fragmentation functions and the gluon function are separated by using measurements at different Q values. In particular, the electric and weak charges are different depending on the quark type, so that a light-quark flavor separation also became possible in principle due to the precise data at both √s ≃10.5 and 91.2 GeV.
15. Measurement of the Total Cross Section and Energy - Correlations for Electron-Positron Annihilation Into Hadrons at 29 GEV.
Heltsley, Brian Keith
This work describes measurements of the total cross section and the energy-energy correlation cross section for hadronic events produced in electron-positron annihilation at a center-of-mass energy of 29 GeV. The performance of the MAC detector at PEP, featuring total absorption calorimetry and charged particle tracking over nearly the full solid angle, is examined and found to meet the original design requirements. The unique and optimal features of MAC are fully exploited to reduce the systematics involved in both measurements, resulting in significant quantitative tests of the theory of quantum chromodynamics. Special attention is focussed on radiative corrections to the total cross section, which constitute a critical component of the acceptance determination, and for the first time the effects of higher order than (alpha)('3) QED processes are included. The total cross section measurement yields R = 3.91 with a total error of (+OR-)2.7%, an accuracy not previously attained by other experiments. For the energy-energy correlation cross section, the consequences of combining pure quantum chromodynamics with contrasting fragmentation models are explored and compared with the data, and result in different values for the strong coupling constant, (alpha)(,s) (TURNEQ) 0.13 (+OR-) 0.02 for incoherent jet formation and 0.24 (+OR-) 0.04 in the string model.
16. Positronics of radiation-induced effects in chalcogenide glassy semiconductors
SciTech Connect
Shpotyuk, O.; Kozyukhin, S. A.; Shpotyuk, M.; Ingram, A.; Szatanik, R.
2015-03-15
Using As{sub 2}S{sub 3} and AsS{sub 2} glasses as an example, the principal possibility of using positron annihilation spectroscopy methods for studying the evolution of the free volume of hollow nanoobjects in chalcogenide glassy semiconductors exposed to radiation is shown. The results obtained by measurements of the positron annihilation lifetime and Doppler broadening of the annihilation line in reverse chronological order are in full agreement with the optical spectroscopy data in the region of the fundamental absorption edge, being adequately described within coordination defect-formation and physical-aging models.
17. Helium-Implantation-Induced Damage in NHS Steel Investigated by Slow-Positron Annihilation Spectroscopy
Li, Yuan-Fei; Shen, Tie-Long; Gao, Xing; Gao, Ning; Yao, Cun-Feng; Sun, Jian-Rong; Wei, Kong-Fang; Li, Bing-Sheng; Zhang, Peng; Cao, Xing-Zhong; Zhu, Ya-Bin; Pang, Li-Long; Cui, Ming-Huan; Chang, Hai-Long; Wang, Ji; Zhu, Hui-Ping; Wang, Dong; Song, Peng; Sheng, Yan-Bin; Zhang, Hong-Peng; Hu, Bi-Tao; Wang, Zhi-Guang
2014-03-01
Evolutions of defects and helium contained defects produced by atomic displacement and helium deposition with helium implantation at different temperatures in novel high silicon (NHS) steel are investigated by a slow positron beam. Differences of the defect information among samples implanted by helium to a fluence of 1 × 1017 ions/cm2 at room temperature, 300°C, 450°C and 750°C are discussed. It is found that the mobility of vacancies and vacancy clusters, a recombination of vacancy-type defects and the formation of the He-V complex lead to the occurrence of these differences. At high temperature irradiations, a change of the diffusion mechanism of He atoms/He bubbles might be one of the reasons for the change of the S-parameter.
18. Analysis of exclusive kT jet algorithms in electron-positron annihilation
Chay, Junegone; Kim, Chul; Kim, Inchol
2015-10-01
We study the factorization of the dijet cross section in e+e- annihilation using the generalized exclusive jet algorithm which includes the cone-type, the JADE, the kT, the anti-kT and the Cambridge/Aachen jet algorithms as special cases. In order to probe the characteristics of the jet algorithms in a unified way, we consider the generalized kT jet algorithm with an arbitrary weight of the energies, in which various types of the kT-type algorithms are included for specific values of the parameter. We show that the jet algorithm respects the factorization property for the parameter α <2 . The factorized jet function and the soft function are well defined and infrared safe for all the jet algorithms except the kT algorithm. The kT algorithm (α =2 ) breaks the factorization since the jet and the soft functions are infrared divergent and are not defined for α =2 , though the dijet cross section is infrared finite. In the jet algorithms which enable factorization, we give a phenomenological analysis using the resummed and the fixed-order results.
19. Investigation of free volume and the interfacial, and toughening behavior for epoxy resin/rubber composites by positron annihilation
Minfeng, Zeng; Xudong, Sun; Huiquan, Xiao; Genzhong, Ji; Xuewen, Jiang; Baoyi, Wang; Chenze, Qi
2008-03-01
An epoxy resin (EP) matrix has been modified with carboxyl-randomized butadiene-acrylonitrile (CRBN) rubber and hydroxyl-terminated butadiene-acrylonitrile rubber (HTBN). When the rubber content was low (⩽5%), the free volume size varied slowly, meanwhile, the free volume size of EP/HTBN system was smaller than EP/CRBN system. With further addition of rubber component (⩾7%), the free volume size of the composite increased quickly. In this case, the free volume size of EP/HTBN system was larger than EP/CRBN system. The intermediate positron lifetime component ( I2) was affected by the structure of the interface layer between rubber particles and EP matrix. The different free volume properties could be attributed to the compatibility between rubber and EP.
20. Hard photon processes in electron-positron annihilation at 29 GeV
SciTech Connect
Gold, M.S.
1986-11-01
The hard photon processes ..mu mu gamma.. and hadrons + ..gamma.. in e/sup +/e/sup -/ annihilation at 29 GeV have been studied. The study is based on an integrated luminosity of 226 pb/sup -1/ taken at PEP with the Mark II detector. For the ..mu mu gamma.. process, a small fraction of non-planar events are observed with missing momentum along the beam direction. The resulting missing energy spectrum is consistent with that expected from higher order effects. The observed cross section is consistent with the predicted cross section for this process, sigma/sup exp/sigma/sup th/ = .90 +- .05 +- .06. The observed hard photon energy spectrum and mass distributions are found to be in agreement with O(..cap alpha../sup 3/) QED. The measured charge asymmetry is in good agreement with the predicted value, A/sub exp/A/sub th/ = .83 +- .25 +- .12. The ..mu gamma.. invariant mass distribution is used to place a limit on a possible excited muon coupling G..gamma../M* for excited muon masses in the range 1 < M* < 21 GeV of (G..gamma../M*)/sup 2/ < 10/sup -5/ GeV/sup -2/ at a 95% confidence level. In the hadrons + ..gamma.. process, evidence for final state radiation is found in an excess of events over that predicted from initial state radiation alone of 253 +- 54 +- 60 events. Further evidence for final state radiation is found in a large hadronic charge asymmetry A/sub Had+..gamma../= (-24.6 +- 5.5)%.
1. Free volumes in bulk nanocrystalline metals studied by the complementary techniques of positron annihilation and dilatometry
Würschum, Roland; Oberdorfer, Bernd; Steyskal, Eva-Maria; Sprengel, Wolfgang; Puff, Werner; Pikart, Philip; Hugenschmidt, Christoph; Pippan, Reinhard
2012-07-01
Free-volume type defects, such as vacancies, vacancy-agglomerates, dislocations, and grain boundaries represent a key parameter in the properties of ultrafine-grained and nanocrystalline materials. Such free-volume type defects are introduced in high excess concentration during the processes of structural refinement by severe plastic deformation. The direct method of time-differential dilatometry is applied in the present work to determine the total amount and the kinetics of free volume by measuring the irreversible length change upon annealing of bulk nanocrystalline metals (Fe, Cu, Ni) prepared by high-pressure torsion (HPT). In the case of HPT-deformed Ni and Cu, distinct substages of the length change upon linear heating occur due to the loss of grain boundaries in the wake of crystallite growth. The data on dilatometric length change can be directly related to the fast annealing of free-volume type defects studied by in situ Doppler broadening measurements performed at the high-intensity positron beam of the FRM II (Garching, Munich, Germany).
2. Positron annihilation Doppler broadening spectroscopy study on Fe-ion irradiated NHS steel
Zhu, Huiping; Wang, Zhiguang; Gao, Xing; Cui, Minghuan; Li, Bingsheng; Sun, Jianrong; Yao, Cunfeng; Wei, Kongfang; Shen, Tielong; Pang, Lilong; Zhu, Yabin; Li, Yuanfei; Wang, Ji; Song, Peng; Zhang, Peng; Cao, Xingzhong
2015-02-01
3. Positron annihilation study of defects in electron-irradiated single crystal zinc oxide
To, C. K.; Yang, B.; Beling, C. D.; Fung, S.; Ling, C. C.; Gong, M.
2011-01-01
Pressurized melt grown zinc oxide (ZnO) single crystals purchased from Cermet Inc. were irradiated by 2MeV electrons with fluence of 6x1017cm-2. Isochronal annealing from 100°C-800°C was performed on the crystals under argon and air ambience. Variable Energy Doppler Broadening Spectroscopy (VEDBS) was carried out on both the as-grown and the irradiated samples at each annealing step. The migration, agglomeration and annealing of grown-in and irradiated-introduced defects were studied. It was observed that the grown-in vacancy-type defects concentration decreased at 300°C and 600 °C. For the irradiated sample annealed in argon, the positron trapping vacancy-type defect concentration decreased at 300°C and 600°C. Further annealing the as-grown and irradiated samples in argon increased the S parameter further. For the irradiated sample annealed in air, the vacancy-type defect concentration decreases at 300°C and 700°C.
4. Free volumes in bulk nanocrystalline metals studied by the complementary techniques of positron annihilation and dilatometry.
PubMed
Würschum, Roland; Oberdorfer, Bernd; Steyskal, Eva-Maria; Sprengel, Wolfgang; Puff, Werner; Pikart, Philip; Hugenschmidt, Christoph; Pippan, Reinhard
2012-07-15
Free-volume type defects, such as vacancies, vacancy-agglomerates, dislocations, and grain boundaries represent a key parameter in the properties of ultrafine-grained and nanocrystalline materials. Such free-volume type defects are introduced in high excess concentration during the processes of structural refinement by severe plastic deformation. The direct method of time-differential dilatometry is applied in the present work to determine the total amount and the kinetics of free volume by measuring the irreversible length change upon annealing of bulk nanocrystalline metals (Fe, Cu, Ni) prepared by high-pressure torsion (HPT). In the case of HPT-deformed Ni and Cu, distinct substages of the length change upon linear heating occur due to the loss of grain boundaries in the wake of crystallite growth. The data on dilatometric length change can be directly related to the fast annealing of free-volume type defects studied by in situ Doppler broadening measurements performed at the high-intensity positron beam of the FRM II (Garching, Munich, Germany).
5. Defects in virgin and N+ -implanted ZnO single crystals studied by positron annihilation, Hall effect, and deep-level transient spectroscopy
Brauer, G.; Anwand, W.; Skorupa, W.; Kuriplach, J.; Melikhova, O.; Moisson, C.; von Wenckstern, H.; Schmidt, H.; Lorenz, M.; Grundmann, M.
2006-07-01
High-quality single crystals of ZnO in the as-grown and N+ ion-implanted states have been investigated using a combination of three experimental techniques—namely, positron lifetime/slow positron implantation spectroscopy accompanied by theoretical calculations of the positron lifetime for selected defects, temperature-dependent Hall (TDH) measurements, and deep level transient spectroscopy (DLTS). The positron lifetime in bulk ZnO is measured to be (151±2)ps and that for positrons trapped in defects (257±2)ps . On the basis of theoretical calculations the latter is attributed to Zn+O divacancies, existing in the sample in neutral charge state, and not to the Zn vacancy proposed in previous experimental work. Their concentration is estimated to be 3.7×1017cm-3 . From TDH measurements the existence of negatively charged intrinsic defects acting as compensating acceptors is concluded which are invisible to positrons—maybe interstitial oxygen. This view is supported from TDH results in combination with DLTS which revealed the creation of the defect E1 , and an increase in concentration of the defect E3 after N+ ion implantation, and peculiarities in the observation of the defect E4 .
6. General relativistic ray-tracing algorithm for the determination of the electron-positron energy deposition rate from neutrino pair annihilation around rotating neutron and quark stars
Kovács, Z.; Harko, T.
2011-11-01
We present a full general relativistic numerical code for estimating the energy-momentum deposition rate (EMDR) from neutrino pair annihilation (?). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour-flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino-antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino-antineutrino pair annihilation around compact stellar objects, as measured at infinity.
7. Positron spectroscopy for materials characterization
SciTech Connect
1988-01-01
One of the more active areas of research on materials involves the observation and characterization of defects. The discovery of positron localization in vacancy-type defects in solids in the 1960's initiated a vast number of experimental and theoretical investigations which continue to this day. Traditional positron annihilation spectroscopic techniques, including lifetime studies, angular correlation, and Doppler broadening of annihilation radiation, are still being applied to new problems in the bulk properties of simple metals and their alloys. In addition new techniques based on tunable sources of monoenergetic positron beams have, in the last 5 years, expanded the horizons to studies of surfaces, thin films, and interfaces. In the present paper we briefly review these experimental techniques, illustrating with some of the important accomplishments of the field. 40 refs., 19 figs.
8. A Study of Double-Charm and Charm-Strange Baryons inElectron-Positron Annihilations
SciTech Connect
2007-10-15
In this dissertation I describe a study of double-charm and charm-strange baryons based on data collected with the BABAR Detector at the Stanford Linear Accelerator Center. In this study I search for new baryons and make precise measurements of their properties and decay modes. I seek to verify and expand upon double-charm and charm-strange baryon observations made by other experiments. The BABAR Detector is used to measure subatomic particles that are produced at the PEP-II storage rings. I analyze approximately 300 million e+e- {yields} c{bar c} events in a search for the production of double-charm baryons. I search for the double-charm baryons {Xi}{sup +}{sub cc} (containing the quarks ccd) and {Xi}{sup ++}{sub cc} (ccu) in decays to {Lambda}{sup +}{sub c}K{sup -}{pi}{sup +} and {Lambda}{sup +}{sub c}K{sup -}{pi}{sup +}{pi}{sup +}, respectively. No statistically significant signals for their production are found, and upper limits on their production are determined. Statistically significant signals for excited charm-strange baryons are observed with my analysis of approximately 500 million e+e- {yields} c{bar c} events. The charged charm-strange baryons {Xi}{sub c}(2970){sup +}, {Xi}{sub c}(3055){sup +}, {Xi}{sub c}(3123){sup +} are found in decays to {Lambda}{sup +}{sub c}K{sup -}{pi}{sup +}, the same decay mode used in the {Xi}{sup +}{sub cc} search. The neutral charm-strange baryon {Xi}{sub c}(3077){sup 0} is observed in decays to {Lambda}{sup +}{sub c}K{sub 8}{pi}{sup -}. I also search for excited charm-strange baryon decays to {Lambda}{sup +}{sub c}K{sub 8}, {Lambda}{sup +}{sub c}K{sup -}, {Lambda}{sup +}{sub c}K{sub 8}{pi}{sup -}{pi}{sup +}, and {Lambda}{sup +}{sub c}K{sup -}{pi}{sup -}{pi}{sup +}. No significant charm-strange baryon signals a f h these decay modes. For each excited charm-strange baryon state that I observe, I measure its mass, natural width (lifetime), and production rate. The properties of these excited charm-strange baryons and their
9. Observation of the electron ridge Fermi surface in YBa{sub 2}Cu{sub 3}O{sub 7-x} by positron annihilation
SciTech Connect
Smedskjaer, L.C.; Fang, Y.; Bailey, K.G.; Welp, U.; Bansil, A.
1991-04-01
Positron annihilation (two-dimensional-angular-correlation) experiments on an untwinned single crystal of metallic YBa{sub 2}Cu{sub 3}O{sub 7{minus}x} sample are reported in the c-projection. The measurements were carried out at room temperature and involved 94 Mcounts. An analysis of the spectra reveals clearly for the first time the presence of the electron ridge Fermi surface associated with the one-dimensional chain bands, and orthorhombic anisotropies in momentum density in good agreement with the band theory predictions.
10. Diffuse galactic annihilation radiation from supernova nucleosynthesis
NASA Technical Reports Server (NTRS)
Higdon, J. C.
1985-01-01
The propagation of MeV positrons in the outer ejecta of type I supernovae was investigated. It was found that the positrons created at times of approx 100 days propagated along magnetic field lines in the outer ejecta without any appreciable pitch-angle scattering or excitation of hydromagnetic waves. The lack of significant pitch-angle scattering is well consistent with models of wave excitation and scattering by resonant interactions. This occurs because time periods to scatter the particles or to excite waves are significantly longer than escape times. Thus it is expected that, when positrons are not coupled to the ejecta by Coulomb collisions, they escape from the relatively cold, dense ejecta and reside predominantly in the tenuous, hotter, shock-heated interstellar gas. In the tenuous shock-heated gas the positron lifetime against annihilation is much greater than lifetimes in the dense ejectra. Thus the production of steady-state diffuse annihilation radiation by some fraction of these escaped positrons seems probable.
11. Ab initio study of the positronation of the CaO and SrO molecules including calculation of annihilation rates.
PubMed
Buenker, Robert J; Liebermann, Heinz-Peter
2012-07-15
Ab initio multireference single- and double-excitation configuration interaction calculations have been performed to compute potential curves for ground and excited states of the CaO and SrO molecules and their positronic complexes, e(+)CaO, and e(+)SrO. The adiabatic dissociation limit for the (2)Σ(+) lowest states of the latter systems consists of the positive metal ion ground state (M(+)) and the OPs complex (e(+)O(-)), although the lowest energy limit is thought to be e(+)M + O. Good agreement is found between the calculated and experimental spectroscopic constants for the neutral diatomics wherever available. The positron affinity of the closed-shell X (1)Σ(+) ground states of both systems is found to lie in the 0.16-0.19 eV range, less than half the corresponding values for the lighter members of the alkaline earth monoxide series, BeO and MgO. Annihilation rates (ARs) have been calculated for all four positronated systems for the first time. The variation with bond distance is generally similar to what has been found earlier for the alkali monoxide series of positronic complexes, falling off gradually from the OPs AR value at their respective dissociation limits. The e(+)SrO system shows some exceptional behavior, however, with its AR value reaching a minimum at a relatively large bond distance and then rising to more than twice the OPs value close to its equilibrium distance.
12. Voids and other neutron-produced microstructure in Mo and Mo-0. 5 at. % Ti as studied by positron-annihilation techniques
SciTech Connect
Snead, Jr, C L; Lynn, K G; Jean, Y; Wiffen, F W; Schultz, P
1980-01-01
Specimens of Mo and Mo-0.5 at. % Ti which have been irradiated with neutrons (approx. 10/sup 22/ n/cm/sup 2/, E > 0.1 MeV) at temperatures between 425 and 1500/sup 2/C have been studied using both lifetime and Doppler-broadening measurements. Both the shape parameter and the intensity of the lifetime component from positrons trapped at voids define swelling as a function of temperature in a way that is independent of the neutron fluence. The relative swelling as a function of irradiation temperature and the swelling peak (approx. 750/sup 0/C) are well defined, but no information on the magnitude of the void volume is obtainable. In the determination of the shape and peak of the derived swelling curve, the positron analysis is more definitive than similar determinations using transmission electron microscopy.
13. Positron bunching and electrostatic transport system for the production and emission of dense positronium clouds into vacuum
Aghion, S.; Amsler, C.; Ariga, A.; Ariga, T.; Belov, A. S.; Bonomi, G.; Bräunig, P.; Bremer, J.; Brusa, R. S.; Cabaret, L.; Caccia, M.; Caravita, R.; Castelli, F.; Cerchiari, G.; Chlouba, K.; Cialdi, S.; Comparat, D.; Consolati, G.; Demetrio, A.; Di Noto, L.; Doser, M.; Dudarev, A.; Ereditato, A.; Evans, C.; Fesel, J.; Fontana, A.; Forslund, O. K.; Gerber, S.; Giammarchi, M.; Gligorova, A.; Gninenko, S.; Guatieri, F.; Haider, S.; Holmestad, H.; Huse, T.; Jernelv, I. L.; Jordan, E.; Kaltenbacher, T.; Kellerbauer, A.; Kimura, M.; Koetting, T.; Krasnicky, D.; Lagomarsino, V.; Lebrun, P.; Lansonneur, P.; Lehner, S.; Liberadzka, J.; Malbrunot, C.; Mariazzi, S.; Marx, L.; Matveev, V.; Mazzotta, Z.; Nebbia, G.; Nedelec, P.; Oberthaler, M.; Pacifico, N.; Pagano, D.; Penasa, L.; Petracek, V.; Pistillo, C.; Prelz, F.; Prevedelli, M.; Ravelli, L.; Rienäcker, B.; Røhne, O. M.; Rosenberger, S.; Rotondi, A.; Sacerdoti, M.; Sandaker, H.; Santoro, R.; Scampoli, P.; Sorrentino, F.; Spacek, M.; Storey, J.; Strojek, I. M.; Testera, G.; Tietje, I.; Vamosi, S.; Widmann, E.; Yzombard, P.; Zavatarelli, S.; Zmeskal, J.
2015-11-01
We describe a system designed to re-bunch positron pulses delivered by an accumulator supplied by a positron source and a Surko-trap. Positron pulses from the accumulator are magnetically guided in a 0.085 T field and are injected into a region free of magnetic fields through a μ -metal field terminator. Here positrons are temporally compressed, electrostatically guided and accelerated towards a porous silicon target for the production and emission of positronium into vacuum. Positrons are focused in a spot of less than 4 mm FWTM in bunches of ∼8 ns FWHM. Emission of positronium into the vacuum is shown by single shot positron annihilation lifetime spectroscopy.
14. Vacancy defects and defect clusters in alkali metal ion-doped MgO nanocrystallites studied by positron annihilation and photoluminescence spectroscopy
Sellaiyan, S.; Uedono, A.; Sivaji, K.; Janet Priscilla, S.; Sivasankari, J.; Selvalakshmi, T.
2016-10-01
Pure and alkali metal ion (Li, Na, and K)-doped MgO nanocrystallites synthesized by solution combustion technique have been studied by positron lifetime and Doppler broadening spectroscopy methods. Positron lifetime analysis exhibits four characteristic lifetime components for all the samples. Doping reduces the Mg vacancy after annealing to 800 °C. It was observed that Li ion migrates to the vacancy site to recover Mg vacancy-type defects, reducing cluster vacancies and micropores. For Na- and K-doped MgO, the aforementioned defects are reduced and immobile at 800 °C. Coincidence Doppler broadening studies show the positron trapping sites as vacancy clusters. The decrease in the S parameter is due to the particle growth and reduction in the defect concentration at 800 °C. Photoluminescence study shows an emission peak at 445 nm and 498 nm, associated with F2 2+ and recombination of higher-order vacancy complexes. Further, annealing process is likely to dissociate F2 2+ to F+ and this F+ is converted into F centers at 416 nm.
15. Study of Submonolayer Films of GOLD/COPPER(100) and PALLADIUM/COPPER(100) Using Positron Annihilation Induced Auger Electron Spectroscopy
Lee, Keunho
Positron Annihilation induced Auger Electron Spectroscopy (PAES), Electron induced Auger Electron Spectroscopy (EAES), and Low Energy Electron Diffraction (LEED) have been used to study the surface composition, surface alloying and overlayer formation of ultrathin films of Au and Pd on Cu(100). This is the first systematic application of PAES to the study of the surface properties of ultrathin layers of metals on metal substrates. Temperature induced changes in the top layer surface compositions in Au/Cu(100) and Pd/Cu(100) are directly observed using PAES, while EAES spectra indicate only minor changes. The surface alloying of the Au/Cu(100) and Pd/Cu(100) systems are demonstrated using PAES in conjunction with LEED. The PAES intensity measurements also provide evidence for positron trapping at surface defects such as steps, kinks and isolated adatoms. The PAES intensity was found to be strongly dependent on surface defects introduced by ion sputtering. The surface defect dependence of the PAES intensity is interpreted in terms of the surface atomic diffusion and positron trapping at surface defects in Au/Cu(100) and Pd/Cu(100). In both systems the shapes of the PAES intensity versus coverage curves for submonolayer coverages at 173K are quite distinct indicating differences in overlayer growth and diffusion behavior of Au and Pd adatoms on the Cu(100) surface. PAES intensities for both Au and Pd are saturated at 1 monolayer demonstrating the extreme surface selectivity of PAES.
16. Positronium lifetime in supercooled 1-butanol: Search for polyamorphism
Zgardzińska, B.; Paluch, M.; Goworek, T.
2010-05-01
Isothermal transformations of supercooled 1-butanol were observed by positron lifetime spectroscopy. Transformation rate is the highest near 150 K, whereas below 140 K it slows down becoming undetectable below 120 K. At the temperature range of 123-135 K the ortho-positronium lifetime achieves the final value which is higher than the one observed for crystalline phase. This is an indication of transition to a new (meta)stable structure, in which the ortho-positronium lifetime and intensity reach values that are intermediate between liquid and crystal phases. Consistency of positron annihilation data with the concept of two coexisting phases is discussed.
17. Direct Observation of the Surface Segregation of Cu in Pd by Time-Resolved Positron-Annihilation-Induced Auger Electron Spectroscopy
SciTech Connect
Mayer, J.; Hugenschmidt, C.; Schreckenbach, K.
2010-11-12
Density functional theory calculations predict the surface segregation of Cu in the second atomic layer of Pd which has not been unambiguously confirmed by experiment so far. We report measurements on Pd surfaces covered with three and six monolayers of Cu using element selective positron-annihilation-induced Auger electron spectroscopy (PAES) which is sensitive to the topmost atomic layer. Moreover, time-resolved PAES, which was applied for the first time, enables the investigation of the dynamics of surface atoms and hence the observation of the segregation process. The time constant for segregation was experimentally determined to {tau}=1.38(0.21) h, and the final segregated configuration was found to be consistent with calculations. Time-dependent PAES is demonstrated to be a novel element selective technique applicable for the investigation of, e.g., heterogeneous catalysis, corrosion, or surface alloying.
18. Formation of isolated Zn vacancies in ZnO single crystals by absorption of ultraviolet radiation: a combined study using positron annihilation, photoluminescence, and mass spectroscopy.
PubMed
Khan, Enamul H; Weber, Marc H; McCluskey, Matthew D
2013-07-05
Positron annihilation spectra reveal isolated zinc vacancy (V(Zn)) creation in single-crystal ZnO exposed to 193-nm radiation at 100 mJ/cm(2) fluence. The appearance of a photoluminescence excitation peak at 3.18 eV in irradiated ZnO is attributed to an electronic transition from the V(Zn) acceptor level at ~100 meV to the conduction band. The observed V(Zn) density profile and hyperthermal Zn(+) ion emission support zinc vacancy-interstitial Frenkel pair creation by exciting a wide 6.34 eV Zn-O antibonding state at 193-nm photon-a novel photoelectronic process for controlled V(Zn) creation in ZnO.
19. Positron Lifetime Modulation by Electric Field Induced Positronium Formation on a Gold Surface
DTIC Science & Technology
2012-03-22
to optimize the resolution for the gamma spectra generated by the NaI ring detector. The decays calculated for each PMT were all slightly...annihilation. 26 Gamma spectra were generated on each channel from data collected for 1 hour from each isotope one at a time. Key features were...identified in the spectra such as full energy peaks and Compton continua. Figure 7. Gamma spectrum of Na-22 generated in Igor Pro from the
20. A comparison of the doppler-broadened positron annihilation spectra of neutron irradiated Al 2O 3 and MgAl 2O 3
Jones, P. L.; Schaffer, J. P.; Cocks, F. H.; Clinard, F. W.; Hurley, G. F.
1985-01-01
Radiation damage studies of oxides and ceramics have become of increasing importance due to the projected use of these materials in thermonuclear fusion reactors as electronic insulators and first wall materials. In addition these materials are important in RAD waste disposal. As part of a study of the defect structure in radiation damaged ceramics Doppler-broadened positron annihilation spectra have been obtained for a series of single crystal sapphire (α-Al 2O 3) and polycrystal (1:1) and (1:2) magnesium aluminate spinel (MgO·Al 2O 3 and MgO-2Al 2O 3) samples. These samples were irradiated in EBR-II to a fluence of 3 × 10 25 n/m 2 (E > 0.1 MeV) at 740°C, and 2 × 10 26 n/m 2 (E > 0.1 MeV) at ~ 550°C respectively. Positron annihilation spectra lineshapes for the irradiated, annealed, and as-received samples of both materials were compared using S parameter analysis. These calculations were made on deconvoluted gamma ray spectra that were free of any instrumental broadening effects. In this way, absolute S parameter changes could be calculated. The observed changes in the S parameter are consistent with independent volume swelling measurements for both the α-A1 2O 3 and the (1:2) MgAl 2O 4 samples. However, the change in S parameter measured for the (1:1) spinel is contrary to the measured volume change. This apparent anomaly indicates a predominence of interstitial as opposed to vacancy type defects in this material.
1. Positron annihilation study of structural relaxation and crystallization in a metallic glass Al80Fe8Mo7Ni5 alloy
Abo-Elsoud, M.
2013-04-01
Kinetic transformations induced in the metallic glass Al80Fe8Mo7Ni5 by thermal treatments from the amorphous to the crystallized state, following the variation of the Doppler broadening of the positron annihilation line-shaped S-and W-parameters were reported. The behavior of the annihilation line-shape shows reversible and non-reversible contributions. Crystallization of the sample appears as a three-stage process. The corresponding crystallization process consists of only one activation enthalpy, Eai. The mean value obtained for Eai is: Eam=(3.65±0.14) eV. In-situ high-temperature X-ray diffraction showed that the crystallization was a complex involving growth of the Al7Fe8Mo crystalline phase along with crystallization of the amorphous matrix Al phase at T ≈500 °C. Electron micrograph with image analysis of the scanning electron microscopy pictures confirmed the presence of fcc-Al and Al7Fe8Mo crystalline phase.
2. Contributions to cosmic reionization from dark matter annihilation and decay
Liu, Hongwan; Slatyer, Tracy R.; Zavala, Jesús
2016-09-01
Dark matter annihilation or decay could have a significant impact on the ionization and thermal history of the universe. In this paper, we study the potential contribution of dark matter annihilation (s -wave- or p -wave-dominated) or decay to cosmic reionization, via the production of electrons, positrons and photons. We map out the possible perturbations to the ionization and thermal histories of the universe due to dark matter processes, over a broad range of velocity-averaged annihilation cross sections/decay lifetimes and dark matter masses. We have employed recent numerical studies of the efficiency with which annihilation/decay products induce heating and ionization in the intergalactic medium, and in this work extended them down to a redshift of 1 +z =4 for two different reionization scenarios. We also improve on earlier studies by using the results of detailed structure formation models of dark matter haloes and subhaloes that are consistent with up-to-date N -body simulations, with estimates on the uncertainties that originate from the smallest scales. We find that for dark matter models that are consistent with experimental constraints, a contribution of more than 10% to the ionization fraction at reionization is disallowed for all annihilation scenarios. Such a contribution is possible only for decays into electron/positron pairs, for light dark matter with mass mχ≲100 MeV , and a decay lifetime τχ˜1 024- 1 025 s .
3. Measuring Positron Annihilation in NaI(Tl) Detectors as the Final Stage in a Carbon Diagnostic.
Braaten, Melissa; Brown, Cassarah; Padalino, Stephen; Glebov, Vladimir; Sangster, T. Craig; Duffy, Timothy
2007-11-01
This study was performed to increase the detection efficiency of 511 keV annihilation radiation from decaying C-11 by indentifying and eliminating different forms of background radiation originating from the source and the ambient background in the gamma ray coincidence spectrum. Cu-64 was substituted for C-11 in this investigation since it could be easily made from Cu-63 via neutron capture using a PuBe neutron source. Using Cu-64, the effect of ambient background and source induced radiation in the NaI detectors was examined in three coincidence spectra. The spectra were generated by pairing the output signals of the three NaI(Tl) detectors and displaying them as two dimensional spectra. Different gamma ray background contributions to the coincidence spectrum were studied, including annihilation radiation from pair production in the detectors and the lead shielding. Detector geometries and source materials which modified the Compton scattering background were also investigated.
4. Structure and sublimation of water ice films grown in vacuo at 120-190 K studied by positron and positronium annihilation.
PubMed
Townrow, S; Coleman, P G
2014-03-26
The crystalline structure of ∼ 5-20 μm water ice films grown at 165 and 172 K has been probed by measuring the fraction of positrons forming ortho-positronium (ortho-Ps) and decaying into three gamma photons. It has been established that films grown at slower rates (water vapour pressure ≥ 1 mPa) have lower concentrations of lattice defects and closed pores, which act as Ps traps, than those grown at higher rates (vapour pressure ∼ 100 mPa), evidenced by ortho-Ps diffusion lengths being approximately four times greater in the former. By varying the growth temperature between 162 and 182 K it was found that films become less disordered at temperatures above ∼ 172 K, with the ortho-Ps diffusion length rising by ∼ 60%, in this range. The sublimation energy for water ice films grown on copper has been measured to be 0.462(5) eV using the time dependence of positron annihilation parameters from 165 to 195 K, in agreement with earlier studies and with no measurable dependence on growth rate and thermal history.
5. Thermal and optical excitation of trapped electrons in high-density polyethylene (HDPE) studied through positron annihilation
Nahid, F.; Zhang, J. D.; Yu, T. F.; Ling, C. C.; Fung, S.; Beling, C. D.
2011-04-01
Positronium (Ps) formation in high-density polyethylene (HDPE) has been studied below the glass transition temperature. The formation probability increases with positron irradiation time due to an increasing number of inter-track trapped electrons becoming available for positron capture. The temperature variation of the saturated Ps level is discussed in different models. The quenching of trapped electrons by light has been studied and the optical de-trapping cross-section for different photon energies has been estimated over the visible region.
6. Positron sensing of distribution of defects in depth materials
Kupchishin, A. I.; Kupchishin, A. A.; Voronova, N. A.; Kirdyashkin, V. I.
2016-02-01
It was developed a non-destructive method of positron sensing, which allows to determine the distribution of defects in the depth of the material. From the analysis we can conclude that the angular distribution curves of annihilation photons (well as and on the characteristics in experiments on the lifetime, 3γ - angular correlation, Doppler effect) is influenced by three main factors: a) The distribution of defects in the depth of the material, their dimensions as well as parameters of the interaction of positrons with defects. With increasing the concentration of defects the intensity Jγ(a, ξ) varies more; b) Modification of the energy spectrum of slow positrons due to the influence of defects, wherein the spectrum of positrons becomes softer, and the average energy of the positron annihilation is reduced; c) Deformation of the momentum distribution of the electrons in the region of defect. The energy spectrum of electrons is also becomes softer, and the average energy of the electrons (on which positrons annihilate) is less. The experimentally were measured spectra of photons in the zone of annihilation and were calculated the distribution of defects in depth for a number of metals.
7. International Conference on Positron Annihilation (6th) held at the University of Texas at Arlington, April 3-7, 1982. Program and Collected Abstracts.
DTIC Science & Technology
1983-02-23
PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERSThe University of Texas at Arlington It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEq...Reception 3:00 - 4:00 p.m. Hosted by Dr. Wendell H. Nedderman, President of The University of Texas at Arlington. Coaches leave for Fort Worth at 4:00 p.m. 4...State Lifetimes A.P. MILLS, JR. P-127 Electron and Positron Work Functions of Cr(lO0) R.J. WILSON and A.P. MILLS, JR. P-127A A Method for Calculating
8. Free volume of an epoxy resin and its relation to structural relaxation: Evidence from positron lifetime and pressure-volume-temperature experiments
Dlubek, Günter; Hassan, E. M.; Krause-Rehberg, Reinhard; Pionteck, Jürgen
2006-03-01
The microstructure of the free volume and its temperature dependence in the epoxy resin diglycidyl ether of bisphenol-A (DGEBA) have been examined using positron annihilation lifetime spectroscopy (PALS, 80-350K , 10-5Pa ) and pressure-volume-temperature (PVT, 293-470K , 0.1-200MPa ) experiments. Employing the Simha-Somcynsky lattice-hole theory (S-S eos), the excess (hole) free volume fraction h and the specific free and occupied volumes, Vf=hV and Vocc=(1-h)V , were estimated. From the PALS spectra analyzed with the new routine LT9.0 the hole size distribution, its mean, ⟨vh⟩ , and mean dispersion, σh , were calculated. ⟨vh⟩ varies from 35to130Å3 . From a comparison of ⟨vh⟩ with V and Vf , the specific hole number Nh' was estimated to be independent of the temperature [Nh(300K)=Nh'/V=0.65nm-3] . From comparison with reported dielectric and viscosity measurements, we found that the structural relaxation slows down faster than the shrinkage of the hole free volume Vf would predict on the basis of the free volume theory. Our results indicate that the structural relaxation in DGEBA operates via the free-volume mechanism only when liquidlike clusters of cells of the S-S lattice appear which contain a local free volume of ˜1.5 or more empty S-S cells. The same conclusion follows from the pressure dependency of the structural relaxation and Vf . It is shown that PALS mirrors thermal volume fluctuations on a subnanometer scale via the dispersion in the ortho-positronium lifetimes. Using a fluctuation approach, the temperature dependency of the characteristic length of dynamic heterogeneity, ξ , is estimated to vary from ξ=1.9nm at Tg to 1.0nm at T/Tg>1.2 . A model was proposed which relates the spatial structure of the free volume as concluded from PALS to the known mobility pattern of the dynamic glass transition at low (cooperative α -relaxation) and high ( a -relaxation) temperatures. We discuss possible reasons for the differences between the
9. Improved generalized gradient approximation for positron states in solids
Kuriplach, Jan; Barbiellini, Bernardo
2014-04-01
Several first-principles calculations of positron-annihilation characteristics in solids have added gradient corrections to the local-density approximation within the theory by Arponen and Pajanne [Ann. Phys. (NY) 121, 343 (1979), 10.1016/0003-4916(79)90101-5] since this theory systematically overestimates the annihilation rates. As a further remedy, we propose to use gradient corrections for other local-density approximation schemes based on perturbed hypernetted chain and on quantum Monte Carlo results. Our calculations for various metals and semiconductors show that the proposed schemes generally improve the positron lifetimes when they are confronted with experiment. We also compare the resulting positron affinities in solids with data from slow-positron measurements.
10. Bulk defect analysis with a high-energy positron beam
SciTech Connect
Hartley, J. H.; Howell, R. H.; Sterne, P. A.
1998-09-23
A program using a positron beam to probe defects in bulk materials has been developed at Lawrence Livermore National Laboratory. Positron annihilation lifetime spectroscopy (PALS) provides non-destructive analysis of average defect size and concentration. A 3 MeV positron beam is supplied by Sodium-22 at the terminal of a Pelletron accelerator. The high-energy beam allows large (greater than or equal to 1 cm2) engineering samples to be measured in air or even sealed in an independent environment. A description of the beam-PALS system will be presented along with a summary of recent measuremen
11. Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints
Ho, K. F.; Beling, C. D.; Fung, S.; Cheng, Vincent K. W.; Ng, Michael K.; Yip, A. M.
2003-11-01
A generalized least-square method with Tikonov-Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy (CDBS) spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization parameters for different simulated experimental conditions. Good retrieval of the underlying positron-electron momentum distributions in the low momentum region is demonstrated. The algorithm has been successfully used to deconvolute experimental CDBS data from aluminum.
12. To the problem of positron states in metal-insulator nanosandwiches
Babich, A. V.; Vakula, P. V.; Pogosov, V. V.
2015-01-01
The potential profiles, wave functions, energies of surface subbands, and lifetimes of positrons in aluminum nanofilms bordering insulators (solid inert gases and SiO2) have been calculated self-consistently in the previously proposed models. The size effects and the influence of the effective masses of electrons and positrons on the energy and annihilation characteristics in systems with double potential wells formed by image potentials have been investigated. The possibility of localizing a positronium atom in nanosandwiches has been discussed.
13. Positron Annihilation Spectroscopy and Small Angle Neutron Scattering Characterization of the Effect of Mn on the Nanostructural Features formed in Irradiated Fe-Cu-Mn Alloys
SciTech Connect
Glade, S C; Wirth, B D; Asoka-Kumar, P; Odette, G R; Sterne, P A; Howell, R H
2003-02-27
The size, number density and composition of the nanometer defects responsible for the hardening and embrittlement in irradiated Fe-0.9wt.% Cu and Fe-0.9wt.% Cu-1.0wt% Mn model reactor pressure vessel alloys were measured using small angle neutron scattering and positron annihilation spectroscopy. These alloys were irradiated at 290 C to relatively low neutron fluences (E > 1 MeV, 6.0 x 10{sup 20} to 4.0 x 10{sup 21} n/m{sup 2}) in order to study the effect of manganese on the nucleation and growth of copper rich precipitates and secondary defect features. Copper rich precipitates were present in both alloys following irradiation. The Fe-Cu-Mn alloy had smaller precipitates and a larger number density of precipitates, suggesting Mn segregation at the iron matrix-precipitate interface which reduces the interfacial energy and in turn the driving force for coarsening. Mn also retards the precipitation kinetics and inhibits large vacancy cluster formation, suggesting a strong Mn-vacancy interaction which reduces radiation enhanced diffusion.
14. Correlation of polycrystalline Cu(In,Ga)Se{sub 2} device efficiency with homojunction depth and interfacial structure: X-ray photoemission and positron annihilation spectroscopic characterization
SciTech Connect
Nelson, A.J.; Sobol, P.E.; Gabor, A.M.; Contreras, M.A.; Asoka-Kumar, P.; Lynn, K.G.
1994-06-01
Angled-resolved high resolution photoemission measurements on valence band electronic structure and Cu 2p, In 3d, Ga 2p, and Se 3d core lines were used to evaluate surface and near-surface chemistry of CuInSe{sub 2} and Cu(In,Ga)Se{sub 2} device grade thin films. XPS compositional depth profiles were also acquired from the near-surface region, and bonding of the Cu, In, Ga, and Se was determined as a function of depth. A Cu-poor region was found, indicating CuIn{sub 5}Se{sub 8} or a CuIn{sub 3}Se{sub 5}-In{sub 2}Se{sub 3} mixture. Correlation between the depth of the Cu-poor region/bulk interface and device efficiency showed that the depth was 115 {angstrom} for a 16.4% CIGS device, 240 {angstrom} for a 15.0% CIGS, and 300 {angstrom} for 14.0% CIGS, with similar trends for CIS films. The surface region is n-type, the bulk is p-type, with a 0.5 eV valence band offset. Depth of homojunction may be the determining factor in device performance. Positron annihilation spectroscopy gave similarly illuminating results.
15. Matrix Isolation Spectroscopy Applied to Positron Moderatioin in Cryogenic Solids
DTIC Science & Technology
2011-07-01
nanoseconds. Positrons that reach a free surface of the moderator before annihilating with an electron may escape into vacuum where they can be...0324. 3 • The positron (e+) is the antiparticle to the electron (e-). • Positrons are stable, but annihilate with electrons to produce γ-rays...Current Positron Applications • 2-γ decay exploited in Positron Emission Tomography (PET) scanners. • Positrons localize & annihilate preferentially at
16. Ionization levels of As vacancies in as-grown GaAs studied by positron-lifetime spectroscopy
SciTech Connect
Saarinen, K.; Hautojaervi, P.; Lanki, P. ); Corbel, C. )
1991-11-15
The properties of the native monovacancy defects are systematically investigated by positron-lifetime measurements in {ital n}-type GaAs with carrier concentrations of {ital n}=10{sup 15--}10{sup 18} cm{sup {minus}3}. The native defects present two ionization levels at {ital E}{sub {ital C}}{minus}30 meV and {ital E}{sub {ital C}}{minus}140 meV. The first corresponds to a charge transition 1{minus}{r arrow}0 and the second to 0{r arrow}1+. The transitions are attributed to ionizations of As vacancy, which may be isolated or part of a complex. In a simple identification of the defect with {ital V}{sub As}, the ionization level at {ital E}{sub {ital C}}{minus}30 meV is attributed to the transition {ital V}{sub As}{sup {minus}}{r arrow}{ital V}{sub As}{sup 0} and the ionization level at {ital E}{sub {ital C}}{minus}140 meV to the transition {ital V}{sub As}{sup 0}{r arrow}{ital V}{sub As}{sup +}. The results show further that the configuration of {ital V}{sub As}{sup {minus}} is strongly relaxed inwards compared to the structure of {ital V}{sub As}{sup 0}.
17. Simulations of <1 0 0> edge and 1/2<1 1 1> screw dislocations in α-iron and tungsten and positron lifetime calculations
Staikov, P.; Djourelov, N.
2013-03-01
Dislocations in BCC metals are of crucial importance for understanding behavior of fusion materials. In this study model positron lifetime quantum-mechanical calculations have been carried out in the two-component density functional theory (DFT) in local density approximation (LDA) for perfect iron and tungsten lattices, lattices with <1 0 0> edge and 1/2<1 1 1> screw dislocations and several cases in which dislocations interact with a vacancy, bi-vacancy and vacancies containing hydrogen or helium atoms. The core structures of the dislocations have been obtained by MD-simulations using Mendelev and Ackland potentials for iron and Finnis-Sinclair potential for tungsten. The calculated values for iron are 153 ps for edge dislocation and 124 ps for screw dislocation, while for tungsten are 161 and 130 ps, respectively. We report new results for screw dislocation showing that minor dilation of the lattice volume associated with second-order elasticity theory influences the calculated positron lifetime.
18. Positron accumulation effect in particles embedded in a low-density matrix
SciTech Connect
Dryzek, Jerzy; Siemek, Krzysztof
2015-02-07
Systematic studies of the so-called positron accumulation effect for samples with particles embedded in a matrix are reported. This effect is related to energetic positrons which penetrate inhomogeneous medium. Due to differences in the linear absorption coefficient, different amounts of positrons are accumulated and annihilate in the identical volume of both materials. Positron lifetime spectroscopy and Doppler broadening of the annihilation line using Na-22 positrons were applied to the studies of the epoxy resin samples with embedded micro-sized particles of transition metals, i.e., Ni, Sn, Mo, W, and nonmetal particles, i.e., Si and NaF. The significant difference between the determined fraction of positrons annihilating in the particles and the particle volume fraction indicates the positron accumulation effect. The simple phenomenological model and Monte Carlo simulations are able to describe the main features of the obtained dependencies. The aluminum alloy with embedded Sn nanoparticles is also considered for demonstration differences between the accumulation and another related effect, i.e., the positron affinity.
19. Positron accumulation effect in particles embedded in a low-density matrix
Dryzek, Jerzy; Siemek, Krzysztof
2015-02-01
Systematic studies of the so-called positron accumulation effect for samples with particles embedded in a matrix are reported. This effect is related to energetic positrons which penetrate inhomogeneous medium. Due to differences in the linear absorption coefficient, different amounts of positrons are accumulated and annihilate in the identical volume of both materials. Positron lifetime spectroscopy and Doppler broadening of the annihilation line using Na-22 positrons were applied to the studies of the epoxy resin samples with embedded micro-sized particles of transition metals, i.e., Ni, Sn, Mo, W, and nonmetal particles, i.e., Si and NaF. The significant difference between the determined fraction of positrons annihilating in the particles and the particle volume fraction indicates the positron accumulation effect. The simple phenomenological model and Monte Carlo simulations are able to describe the main features of the obtained dependencies. The aluminum alloy with embedded Sn nanoparticles is also considered for demonstration differences between the accumulation and another related effect, i.e., the positron affinity.
20. Comparison of three-jet and radiative two-jet events in electron-positron annihilation at 29 GeV
SciTech Connect
Sheldon, P.D.
1986-11-01
By comparing 3-jet (e/sup +/e/sup -/ ..-->.. q anti q g) and radiative 2-jet (e/sup +/e/sup -/ ..-->.. q anti q ..gamma..) events from electron-positron annihilation, we have studied the local and global effects of the presence of a hard bremsstrahlung gluon in hadronic events. Detector and event selection efficiencies and biases affect these two kinds of events almost equally because they have very similar kinematics and topologies. Accurate comparisons of q anti q g and q anti q ..gamma.. events can therefore be made. Globally, we observe a depletion of hadrons in q anti q g events relative to q anti q ..gamma.. events on the opposite side of the event plane from the gluon, in the angular region between the q and anti q jets. This depletion is shown to be in agreement with the predictions of Quantum Chromodynamics (QCD). The existence of this effect demonstrates that the presence of a gluon significantly alters the color forces and hence the fragmentation process in hadronic events. We also use these q anti q ..gamma.. and q anti q g events to compare low energy (4.5 GeV) gluon and quark jets. Our data indicate that gluon jets have softer x/sub p/ distributions than quark jets, while the transverse momentum distributions of these two types of jets are identical within our errors. Although we are unable to determine if the multiplicities of gluon (n/sub /) and quark (n/sub q/) jets are different, the ratio n/sub g//n/sub q/ = 9/4 predicted asymptotically in QCD would not be consistent with our data.
1. SMM observations of gamma-ray transients. 3: A search for a broadened, redshifted positron annihilation line from the direction of the Galactic center
NASA Technical Reports Server (NTRS)
Harris, Michael J.; Share, Gerald H.; Leising, Mark D.
1994-01-01
We have searched for 1980-1988 Solar Maximum Mission gamma-ray spectrometer data for transient emission on timescales from hours to approximately 12 days of broad gamma-ray lines at energies approximately 400 keV, which were reported by the High Energy Astronomy Observatory (HEAO) 1 and SIGMA experiments from two sources lying toward the Galactic center. The lines have been interpreted as the product of the annihilation of positrons in pair plasmas surrounding the black hole candidate 1E 1740.7-2942 and the X-ray binary 1H 1822-371. Our results from a combined exposure of approximately 1.5 x 10(exp 7)s provide no convincing evidence for transient emission of this line on any timescale between approximately 9 hr and approximately 1 yr. Our 3 sigma upper limits on the line flux during approximately 12 day intervals are characteristically 4.8 x 10(exp -3) photon/sq cm/s, while for approximately 1 day intervals our 3 sigma upper limits are characteristically 4.9 x 10(exp -3) photon/sq cm/s. These results imply a duty cycle of less than 1.3% for the transient line measured from 1H 1822-371 during a approximately 3 week interval in 1977 by HEAO 1, and a duty cycle of less than or = 0.8% for the transient line detected in 1990 and 1992 from 1E 1740.7-2942 on approximately 1 day timescales by SIGMA.
2. Defect evolution and its impact on the ferromagnetism of Cu-doped ZnO nanocrystals upon thermal treatment: A positron annihilation study
Chen, Zhi-Yuan; Chen, Yuqian; Zhang, Q. K.; Qi, N.; Chen, Z. Q.; Wang, S. J.; Li, P. H.; Mascher, P.
2017-01-01
CuO/ZnO nanocomposites with 4 at. % CuO were annealed in air at various temperatures between 100 and 1200 °C to produce Cu-doped ZnO nanocrystals. X-ray diffraction shows that a CuO phase can be observed in the CuO/ZnO nanocomposites annealed at different temperatures, and the Cu-doped ZnO nanocrystals are identified to be of wurtzite structure. The main peak (101) appears at slightly lower diffraction angles with increasing annealing temperature from 400 up to 1200 °C, which confirms the successful doping of Cu into the ZnO lattice above 400 °C. Scanning electron microscopy indicates that most particles in the CuO/ZnO nanocomposites are isolated when annealing at 100-400 °C, but these particles have a tendency to form clusters or aggregates as the annealing temperature increases from 700 to 1000 °C. Positron annihilation measurements reveal a large number of vacancy defects in the interface region of the nanocomposites, and they are gradually recovered with increasing annealing temperature up to 1000 °C. Room-temperature ferromagnetism can be observed in the CuO/ZnO nanocomposites, and the magnetization decreases continuously with increasing annealing temperature. However, there may be several different origins of ferromagnetism in the CuO/ZnO nanocomposites. At low annealing temperatures, the ferromagnetism originates from the CuO nanograins, and the ferromagnetism of CuO nanograins decreases with an increase in the grain size after subsequent higher temperature annealing, which leads to the weakening of ferromagnetism in the CuO/ZnO nanocomposites. After annealing from 400 to 1000 °C, the ferromagnetism gradually vanishes. The ferromagnetism is probably induced by Cu substitution but is mediated by vacancy defects in the CuO/ZnO nanocomposites. The disappearance of ferromagnetism coincides well with the recovery of vacancy defects. It can be inferred that the ferromagnetism is mediated by vacancy defects that are distributed in the interface region.
3. Annihilation in Gases and Galaxies
NASA Technical Reports Server (NTRS)
Drachman, Richard J. (Editor)
1990-01-01
This publication contains most of the papers, both invited and contributed, that were presented at the Workshop of Annihilation in Gases and Galaxies. This was the fifth in a biennial series associated with the International Conference on the Physics of Electronic and Atomic Collisions. Subjects covered included the scattering and annihilation of positrons and positronium atoms in various media, including those of astrophysical interest. In addition, the topics of antimatter and dark matter were covered.
4. First-cycle defect evolution of Li1-xNi1/3Mn1/3Co1/3O2 lithium ion battery electrodes investigated by positron annihilation spectroscopy
Seidlmayer, Stefan; Buchberger, Irmgard; Reiner, Markus; Gigl, Thomas; Gilles, Ralph; Gasteiger, Hubert A.; Hugenschmidt, Christoph
2016-12-01
In this study the structure and evolution of vacancy type defects in lithium ion batteries are investigated in respect of crystallographic properties. The relation between positron annihilation and electronic structure is discussed in terms of structural dynamics during the lithiation process. Samples of Li1-xNi1/3Mn1/3Co1/3O2 (NMC-111) electrodes with decreasing lithium content (x = 0-0.7) covering the whole range of state of charge were electrochemically prepared for the non-destructive analysis using positron coincidence Doppler broadening spectroscopy (CDBS). The positron measurements allowed us to observe the evolution of the defect structure caused by the delithiation process in the NMC-111 electrodes. The combination of CDBS with X-ray diffraction for the characterization of the lattice structures enabled the analysis of the well-known kinetic-hindrance-effect in the first charge-discharge cycle and possible implications of vacancy ordering. In particular, CDBS revealed the highest degree of relithiation after discharge to 3.0 V at 55 °C. For the first time, we report on the successful application of CDBS on NMC-111 electrodes yielding new insights in the important role of defects caused by the delithiation process and the kinetic hindrance effect.
5. Enhanced positron trapping by Ag nanoclusters at low temperatures: A challenge of positron sensitivity to quantum dots
Zou, B.; Qi, N.; Liu, Z. W.; Chen, Z. Q.; Liu, H. Q.; Yi, D. Q.; Tang, Z.
2017-03-01
Microstructure evolution of three Al-Ag alloys with different Ag contents (1 wt. % Ag, 5 wt. % Ag, and 15 wt. % Ag) was studied by positron annihilation spectroscopy during the aging process. In situ measurements of the positron lifetime and Doppler broadening of annihilation radiation indicate the fast formation of Ag-rich clusters during natural aging of the alloys. The formation of Ag-rich clusters was further confirmed by coincidence Doppler broadening measurements. The Ag signal reflected by the Coincidence Doppler broadening spectrum increases with increasing Ag content and is further enhanced after subsequent artificial aging at 140 °C. This might be due to the increase in the size of Ag clusters. The temperature dependence of the Doppler broadening spectra between 10 K and 290 K was measured for the Al-Ag alloys after natural and artificial aging. Detrapping of positrons from Ag clusters with increasing temperature was observed for all the three Al-Ag alloys after natural aging and for the Al-1 wt. % Ag after artificial aging. This indicates that Ag clusters act as shallow positron trapping centers. The thermal detrapping of positrons becomes ambiguous with increasing Ag content in the alloy and is nearly invisible in the artificially aged Al-5 wt. % Ag and Al-15 wt. % Ag. The positron binding energy of the Ag cluster is roughly estimated to be about 18.8 meV and 50 meV in the Al-1 wt. % Ag sample after natural aging and artificial aging at 140 °C, respectively, which suggests that the confinement of positrons in the quantum-dot like state depends on the size or chemical composition of clusters. Theoretical calculations confirm positron trapping by Ag nanoclusters, and the confinement of positrons is enhanced with increasing Ag cluster size.
6. Correlation between ferromagnetism and the concentration of interfacial defects in multiferroic Bi7Fe2.75Co0.25Ti3O21 studied by positron annihilation
Ge, W. N.; Li, X. N.; Xu, J. P.; Huang, S. J.; Liu, J. D.; Zhu, Z.; Fu, Z. P.; Lu, Y. L.; Ye, B. J.
2017-03-01
This paper investigated the effect of the annealing temperature on the interfacial defects and the magnetization of a single-phase multiferroic Bi7Fe2.75Co0.25Ti3O21. With the increase of annealing temperature, the average thickness of the nonaplates increased from 80 to 180 nm. But the magnetic property measurement shows that the saturation magnetization gradually decreases with the increase of the annealing temperature correspondingly. Positron annihilation measurements reveal that the interfacial defects disappear obviously when the annealing temperature increased, which is found to agree well with the variation of saturation magnetization. The results suggest that with the higher concentration of interfacial defects may bring about higher saturation magnetization for the Aurivillius phase material, opening a window to improve the magnetic performance through controlling the concentration of interfacial defects.
7. Four-dimensional positron age-momentum correlation
Ackermann, Ulrich; Löwe, Benjamin; Dickmann, Marcel; Mitteneder, Johannes; Sperr, Peter; Egger, Werner; Reiner, Markus; Dollinger, Günther
2016-11-01
We have performed first four-dimensional age-momentum correlation (4D-AMOC) measurements at a pulsed high intensity positron micro beam and determined the absolute value of the three-dimensional momentum of the electrons annihilating with the positrons in coincidence with the positron age in the sample material. We operated two position sensitive detectors in coincidence to measure the annihilation radiation: a pixelated HPGe-detector and a microchannel plate image intensifier with a CeBr3 scintillator pixel array. The transversal momentum resolution of the 4D-AMOC setup was measured to be about 17 × 10-3 {m}0c (FWHM) and was circa 3.5 times larger than the longitudinal momentum resolution. The total time resolution was 540 ps (FWHM). We measured two samples: a gold foil and a carbon tape at a positron implantation energy of 2 keV. For each sample discrete electron momentum states and their respective positron lifetimes were extracted.
8. Cold Positrons from Decaying Dark Matter
SciTech Connect
Boubekeur, Lotfi; Dodelson, Scott; Vives, Oscar
2012-11-01
Many models of dark matter contain more than one new particle beyond those in the Standard Model. Often heavier particles decay into the lightest dark matter particle as the Universe evolves. Here we explore the possibilities that arise if one of the products in a (Heavy Particle) $\\rightarrow$ (Dark Matter) decay is a positron, and the lifetime is shorter than the age of the Universe. The positrons cool down by scattering off the cosmic microwave background and eventually annihilate when they fall into Galactic potential wells. The resulting 511 keV flux not only places constraints on this class of models but might even be consistent with that observed by the INTEGRAL satellite.
9. Positron studies of metal-oxide-semiconductor structures
SciTech Connect
Au, H.L.; Asoka-Kumar, P.; Nielsen, B.; Lynn, K.G. )
1993-03-15
Positron annihilation spectroscopy provides a new probe to study the properties of interface traps in metal-oxide semiconductors (MOS). Using positrons, we have examined the behavior of the interface traps as a function of gate bias. We propose a simple model to explain the positron annihilation spectra from the interface region of a MOS capacitor.
10. Nuclear Instruments and Methods in Physics Research. Section B; Microstructural Characterization of Semi-Interpenetrating Polymer Networks by Positron Lifetime Spectroscopy
NASA Technical Reports Server (NTRS)
Singh, Jag J.; Pater, Ruth H.; Eftekhari, Abe
1998-01-01
Thermoset and thermoplastic polyimides have complementary physical/mechanical properties. Whereas thermoset polyimides are brittle and generally easier to process, thermoplastic polyimides are tough but harder to process. It is expected that a combination of these two types of polyimides may help produce polymers more suitable for aerospace applications. Semi-Interpenetrating Polymer Networks (S-IPNs) of thermoset LaRC(Trademark)-RP46 and thermoplastic LARC(Trademark)-IA polyimides were prepared in weight percent ratios ranging from 100:0 to 0: 100. Positron lifetime measurements were made in these samples to correlate their free volume features with physical/mechanical properties. As expected, positronium atoms are not formed in these samples. The second life time component has been used to infer the positron trap dimensions. The "free volume" goes through a minimum at about 50:50 ratio, suggesting that S-IPN samples are not merely solid solutions of the two polymers. These data and related structural properties of the S-IPN samples have been discussed in this paper.
11. Positron-electron autocorrelation function study of E-center in silicon
Ho, K. F.; Ching, H. M.; Beling, C. D.; Fung, S.; Ng, K. P.; Biasini, M.; Ferro, G.; Gong, M.
2003-11-01
Two-dimensional angular correlation of annihilation radiation (2D-ACAR) spectra have been taken for 1019cm-3 phosphorus-doped Si in the as-grown state after having been subjected to 1.8 MeV electron fluences of 1×1018 and 2×1018 cm-2. Positron annihilation lifetime spectroscopy confirms, in accordance with previous works, that positrons are saturation trapping into (VSi:P) pair defect (E-center) monovacancy sites in the electron irradiated samples. In the as-grown case, the positron-electron autocorrelation functions along the [111] and [1-10] directions, obtained through Fourier transformation of the 2D-ACAR data, reveal zero-crossings that deviate only slightly from the lattice points, in a manner consistent with positron-electron correlation effects. Conversely, in the spectra of the irradiated samples, the zero-crossing points are observed to move outward further by between 0.15 and 0.50 Å. This displacement is associated with positron annihilation with electrons in localized orbitals at the defect site. An attempt is made to extract just the component of the defect's positron-electron autocorrelation function that relates to the localized defect orbitals. In doing this features are found that correspond to the expected atomic positions at the vacancy defect site suggesting that this real-space function may provide a convenient means for obtaining a mapping of localized orbitals. The observed approximate separability of positron and electron wave-function autocorrelates leads to an estimate of 0.22 eV for the positron binding energy to the E-center.
12. Present and future experiments using bright low-energy positron beams
Hugenschmidt, Christoph
2017-01-01
Bright slow positron beams enable not only experiments with drastically reduced measurement time and improved signal-to-noise ratio but also the realization of novel experimental techniques. In solid state physics and materials science positron beams are usually applied for the depth dependent analysis of vacancy-like defects and their chemical surrounding using positron lifetime and (coincident) Doppler broadening spectroscopy. For surface studies, annihilation induced Auger-electron spectroscopy allows the analysis of the elemental composition in the topmost atomic layer, and the atomic positions at the surface can be determined by positron diffraction with outstanding accuracy. In fundamental research low-energy positron beams are used for the production of e.g. cold positronium or positronium negative ions. All the aforementioned experiments benefit from the high intensity of present positron beam facilities. In this paper, we scrutinize the technical constraints limiting the achievable positron intensity and the available kinetic energy at the sample position. Current efforts and future developments towards the generation of high intensity spin-polarized slow positron beams paving the way for new positron experiments are discussed.
13. Positron annihilation study of Sr Doping in La{sub 2-x}Sr{sub x}CuO{sub 4}
SciTech Connect
Sterne, P.A. |; Howell, R.H.; Fluss, M.J.; Kaiser, J.H.; Kitazawa, K.; Kojima, H.
1993-04-22
We present a combined experimental and threshold study of effects of Sr doping on electronic structure of La{sub 2-x}Sr{sub x}CuO{sub 4}. Electron-positron momentum distributions have been measured to high statistical precision (> 4 {times} 10{sup 8} counts) at room temperature for samples with Sr concentrations of x = 0.0, 0.1, 0.13 and 0.2. Analysis of all four spectra reveal strong features due to electron-positron wavefunction overlap, in quantitative agreement with theoretical calculations. The Sr doped samples show discontinuities consistent with presence of a Fermi surface. The form and position of these features are in general agreement with the predictions of band theory. Correspondence between theory and experiment, as well as some differences, are revealed by a detailed study of the changes in electron-position momentum density with increasing Sr doping.
14. Implications of the first AMS-02 measurement for dark matter annihilation and decay
SciTech Connect
Jin, Hong-Bo; Wu, Yue-Liang; Zhou, Yu-Feng E-mail: [email protected]
2013-11-01
In light of the first measurement of the positron fraction by the AMS-02 experiment, we perform a detailed global analysis on the interpretation of the latest data of PAMELA, Fermi-LAT, and AMS-02 in terms of dark matter (DM) annihilation and decay in various propagation models. The allowed regions for the DM particle mass and annihilation cross section or decay life-time are obtained for channels with leptonic final states: 2e, 2μ, 2τ, 4e, 4μ and 4τ. We show that for the conventional astrophysical background the AMS-02 positron fraction data alone favour a DM particle mass ∼ 500(800) GeV if DM particles annihilate dominantly into 2μ(4μ) final states, which is significantly lower than that favoured by the Fermi-LAT data of the total flux of electrons and positrons. The allowed regions by the two experiments do not overlap at a high confidence level (99.99999%C.L.). We consider a number of propagation models with different halo height Z{sub h}, diffusion parameters D{sub 0} and δ{sub 1/2}, and power indices of primary nucleon sources γ{sub p1/p2}. The normalization and the slope of the electron background are also allowed to vary. We find that the tension between the two experiments can be only slightly reduced in the propagation model with large Z{sub h} and D{sub 0}. The consistency of fit is improved for annihilation channels with 2τ and 4τ final states which favour TeV scale DM particle with large cross sections above ∼ 10{sup −23} cm{sup 3}s{sup −1}. In all the considered leptonic channels, the current data favour the scenario of DM annihilation over DM decay. In the decay scenario, the charge asymmetric DM decay is slightly favoured.
15. High-field penning-malmberg trap: confinement properties and use in positron accumulation
SciTech Connect
Hartley, J.H.
1997-09-01
This dissertation reports on the development of the 60 kG cryogenic positron trap at Lawrence Livermore National Laboratory, and compares the traps confinement properties with other nonneutral plasma devices. The device is designed for the accumulation of up to 2{times}10{sup 9} positrons from a linear-accelerator source. This positron plasma could then be used in Bhabha scattering experiments. Initial efforts at time-of-flight accumulation of positrons from the accelerator show rapid ({approximately}100 ms) deconfinement, inconsistent with the long electron lifetimes. Several possible deconfinement mechanisms have been explored, including annihilation on residual gas, injection heating, rf noise from the accelerator, magnet field curvature, and stray fields. Detailed studies of electron confinement demonstrate that the empirical scaling law used to design the trap cannot be extrapolated into the parameter regime of this device. Several possible methods for overcoming these limitations are presented.
16. Portable Positron Measurement System (PPMS)
SciTech Connect
2011-01-01
Portable Positron Measurement System (PPMS) is an automated, non-destructive inspection system based on positron annihilation, which characterizes a material's in situatomic-level properties during the manufacturing processes of formation, solidification, and heat treatment. Simultaneous manufacturing and quality monitoring now are possible. Learn more about the lab's project on our facebook site http://www.facebook.com/idahonationallaboratory.
17. Portable Positron Measurement System (PPMS)
ScienceCinema
None
2016-07-12
Portable Positron Measurement System (PPMS) is an automated, non-destructive inspection system based on positron annihilation, which characterizes a material's in situatomic-level properties during the manufacturing processes of formation, solidification, and heat treatment. Simultaneous manufacturing and quality monitoring now are possible. Learn more about the lab's project on our facebook site http://www.facebook.com/idahonationallaboratory.
18. Precise Determination of the Strong Coupling Constant at NNLO in QCD from the Three-Jet Rate in Electron-Positron Annihilation at LEP
SciTech Connect
Dissertori, G.; Gehrmann-DeRidder, A.; Gehrmann, T.; Glover, E. W. N.; Heinrich, G.; Stenzel, H.
2010-02-19
We present the first determination of the strong coupling constant from the three-jet rate in e{sup +}e{sup -} annihilation at LEP, based on a next-to-next-to-leading-order (NNLO) perturbative QCD prediction. More precisely, we extract {alpha}{sub s}(M{sub Z}) by fitting perturbative QCD predictions at O({alpha}{sub s}{sup 3}) to data from the ALEPH experiment at LEP. Over a large range of the jet-resolution parameter y{sub cut}, this observable is characterized by small nonperturbative corrections and an excellent stability under renormalization scale variation. We find {alpha}{sub s}(M{sub Z})=0.1175+-0.0020(expt)+-0.0015(theor), which is more accurate than the values of {alpha}{sub s}(M{sub Z}) from e{sup +}e{sup -} event-shape data currently used in the world average.
19. Investigating the binding properties of porous drug delivery systems using nuclear sensors (radiotracers) and positron annihilation lifetime spectroscopy--predicting conditions for optimum performance.
PubMed
Mume, Eskender; Lynch, Daniel E; Uedono, Akira; Smith, Suzanne V
2011-06-21
Understanding how the size, charge and number of available pores in porous material influences the uptake and release properties is important for optimising their design and ultimately their application. Unfortunately there are no standard methods for screening porous materials in solution and therefore formulations must be developed for each encapsulated agent. This study investigates the potential of a library of radiotracers (nuclear sensors) for assessing the binding properties of hollow silica shell materials. Uptake and release of Cu(2+) and Co(2+) and their respective complexes with polyazacarboxylate macrocycles (dota and teta) and a series of hexa aza cages (diamsar, sarar and bis-(p-aminobenzyl)-diamsar) from the hollow silica shells was monitored using their radioisotopic analogues. Coordination chemistry of the metal (M) species, subtle alterations in the molecular architecture of ligands (Ligand) and their resultant complexes (M-Ligand) were found to significantly influence their uptake over pH 3 to 9 at room temperature. Positively charged species were selectively and rapidly (within 10 min) absorbed at pH 7 to 9. Negatively charged species were preferentially absorbed at low pH (3 to 5). Rates of release varied for each nuclear sensor, and time to establish equilibrium varied from minutes to days. The subtle changes in design of the nuclear sensors proved to be a valuable tool for determining the binding properties of porous materials. The data support the development of a library of nuclear sensors for screening porous materials for use in optimising the design of porous materials and the potential of nuclear sensors for high through-put screening of materials.
20. Microwave irradiation induced modifications on the interfaces in SAN/EVA/PVC and PVAc/BPA/PVP ternary polymer blends: Positron lifetime study
Dinesh, Meghala; Chikkakuntappa, Ranganathaiah
2013-09-01
Ternary polymer blends of poly(styrene-co-acrylonitrile)/poly(ethylene-co-vinylacetate)/poly(vinyl chloride) (SAN/EVA/PVC) and poly(vinyl acetate)/bisphenol A/polyvinylpyrrolidone (PVAc/BPA/PVP) with different compositions have been prepared by solvent casting method and characterized by positron lifetime spectroscopy and differential scanning calorimetry DSC. Phase modifications have been induced by irradiating the blends with microwave radiation. These changes have been monitored by measuring the free-volume content in the blends. The results clearly show improved interactions between the constituent polymers of the blends upon microwave irradiation. However, the free-volume data and DSC measurements are found to be inadequate to reveal the changes at the interfaces and the interfaces determine the final properties of the blend. For this we have used hydrodynamic interaction (αij) approach developed by us to measure strength of hydrodynamic interaction at the interfaces. These results show that microwave irradiation stabilizes the interfaces if the blend contains strong polar groups. SAN/EVA/PVC blend shows an increased effective hydrodynamic interaction from -3.18 to -4.85 at composition 50/35/15 upon microwave irradiation and PVAc/BPA/PVP blend shows an increased effective hydrodynamic interaction from -3.81 to -7.57 at composition 20/50/30 after irradiation.
1. Photoluminescence and positron annihilation spectroscopy of MeV Si{sup +} ion-irradiated Si{sub y}O{sub 1-y}:Er (y{approx_equal}1/3) thin films
SciTech Connect
Blakie, D. E.; Zalloum, O. H. Y.; Wojcik, J.; Irving, E. A.; Knights, A. P.; Mascher, P.; Simpson, P. J.
2009-03-01
Amorphous erbium-doped silicon oxide (Si{sub y}O{sub 1-y}:Er, y{>=}1/3) thin films are currently under investigation as a luminescent material system for complementary metal-oxide semiconductor compatible light emitters. We have grown films with y{approx_equal}1/3 and investigated their properties using both positron annihilation and photoluminescence (PL) spectroscopies. Films were characterized ''as deposited,'' following irradiation with 1 MeV Si{sup +} ions and after isochronal annealing. The PL yield from both Er{sup 3+} ions and sensitizing defects is reduced by irradiation, depending strongly on the irradiation fluence and reaching saturation at {approx}4x10{sup 13} Si{sup +}/cm{sup 2}. Higher implantation fluences result in an open-volume defect structure in the film that persists after annealing. This annealing behavior is similar to that of an unrecoverable quenching effect on Er{sup 3+}-related PL near 1540 nm, and we suggest that these open-volume defects may cause a decoupling of the Er{sup 3+} ions from sensitizing oxide point defects that form as a result of the film deposition process.
2. Defect-induced magnetism in liquid sodium-exposed stainless steel as studied by Mössbauer and positron annihilation spectroscopic techniques
Panda, Alaka; Herojit Singh, L.; Govindaraj, R.; Abhaya, S.; Yadav, R. Kumar; Rajagopalan, S.; Venugopal Rao, G.; Ragunathan, V.; Amarendra, G.
2017-03-01
Detailed Mössbauer studies carried out in liquid sodium (Na)-exposed austenitic stainless steel (SS-316) show that there is a partial formation of ferromagnetically (FM)-ordered ferritic zones in the paramagnetic austenitic matrix. Results of low energy positron beam-based Doppler broadening studies imply the occurrence of vacancy kind of defects in the liquid Na-exposed SS-316. Correlating these results, the partial occurrence of FM-ordered zones in the liquid Na-exposed SS-316 is understood to be due to open volume defects, predominantly that of Ni vacancies occurring at the surface and upto a certain depth of liquid Na-exposed stainless steel. These results are elucidated in terms of hyperfine parameters associated with ferritic zones.
3. Positron program at the Idaho Accelerator Center
SciTech Connect
Stancari, Giulio
2009-09-02
Positron physics is an important part of the research activities at the Idaho Accelerator Center (IAC). With positron annihilation spectroscopy, maps of nanodefects in materials have been obtained. For this purpose, positrons are generated by radioactive decay, photoactivation, or pair production. Preliminary tests of positron sources in the MeV range based on electron linacs have also been carried out at the IAC, and an expansion of this program is planned. A similar positron beam at Jefferson Lab would greatly improve our knowledge of the inner structure of the proton. In this paper, research with positrons at the IAC is reviewed. After a description of the Center's facilities, results from positron annihilation spectroscopy are discussed, together with future plans for testing a prototype positron source for CEBAF.
4. High current pulsed positron microprobe
SciTech Connect
Howell, R.H.; Stoeffl, W.; Kumar, A.; Sterne, P.A.; Cowan, T.E.; Hartley, J.
1997-05-01
We are developing a low energy, microscopically focused, pulsed positron beam for defect analysis by positron lifetime spectroscopy to provide a new defect analysis capability at the 10{sup 10} e{sup +}s{sup -l} beam at the Lawrence Livermore National Laboratory electron linac. When completed, the pulsed positron microprobe will enable defect specific, 3-dimensional maps of defect concentrations with sub-micron resolution of defect location. By coupling these data with first principles calculations of defect specific positron lifetimes and positron implantation profiles we will both map the identity and concentration of defect distributions.
5. The slowing down times of positrons emitted from selected β+ isotopes into metals
Dryzek, Jerzy; Horodek, Paweł; Siemek, Krzysztof
2012-11-01
We report the GEANT4 Monte Carlo simulations and the approximated calculations of the slowing down time (SDT) for positrons emitted from three β+ isotopes, i.e., 22Na, 68Ge/68Ga and 48V. The first two isotopes are commonly used in the positron annihilation spectroscopy. The results revealed that the SDT exhibits the nonsymmetrical distribution and its average value depends on the end point energy of the isotope, the density and atomic number of the implanted material. For metals the average SDT varies from 0.4 ps to a few ps. We argue that this can affect the analysis of the measured positron lifetime and should be considered in theoretical calculations. The SDT in selected gases was simulated as well and in this case its average values are about four orders higher than in metals.
6. High intensity positron program at LLNL
SciTech Connect
Asoka-Kumar, P.; Howell, R.H.; Stoeffl, W.
1998-09-23
Lawrence Livermore National Laboratory (LLNL) is the home of the world's highest current beam of keV positrons. The potential for establishing a national center for materials analysis using positron annihilation techniques around this capability is being actively pursued. The high LLNL beam current will enable investigations in several new areas. We are developing a positron microprobe that will produce a pulsed, focused positron beam for 3-dimensional scans of defect size and concentration with submicron resolution. Below we summarize the important design features of this microprobe. Several experimental end stations will be available that can utilize the high current beam with a time distribution determined by the electron linac pulse structure, quasi-continuous, or bunched at 20 MHz, and can operate in an electrostatic or (and) magnetostatic environment. Some of the planned early experiments are: two-dimensional angular correlation of annihilation radiation of thin films and buried interfaces, positron diffraction holography, positron induced desorption, and positron induced Auger spectra.
7. Positron microprobe at LLNL
SciTech Connect
Asoka, P; Howell, R; Stoeffl, W
1998-11-01
The electron linac based positron source at Lawrence Livermore National Laboratory (LLNL) provides the world's highest current beam of keV positrons. We are building a positron microprobe that will produce a pulsed, focused positron beam for 3-dimensional scans of defect size and concentration with sub-micron resolution. The widely spaced and intense positron packets from the tungsten moderator at the end of the 100 MeV LLNL linac are captured and trapped in a magnetic bottle. The positrons are then released in 1 ns bunches at a 20 MHz repetition rate. With a three-stage re-moderation we will compress the cm-sized original beam to a 1 micro-meter diameter final spot on the target. The buncher will compress the arrival time of positrons on the target to less than 100 ps. A detector array with up to 60 BaF2 crystals in paired coincidence will measure the annihilation radiation with high efficiency and low background. The energy of the positrons can be varied from less than 1 keV up to 50 keV.
8. Positrons in surface physics
Hugenschmidt, Christoph
2016-12-01
Within the last decade powerful methods have been developed to study surfaces using bright low-energy positron beams. These novel analysis tools exploit the unique properties of positron interaction with surfaces, which comprise the absence of exchange interaction, repulsive crystal potential and positron trapping in delocalized surface states at low energies. By applying reflection high-energy positron diffraction (RHEPD) one can benefit from the phenomenon of total reflection below a critical angle that is not present in electron surface diffraction. Therefore, RHEPD allows the determination of the atom positions of (reconstructed) surfaces with outstanding accuracy. The main advantages of positron annihilation induced Auger-electron spectroscopy (PAES) are the missing secondary electron background in the energy region of Auger-transitions and its topmost layer sensitivity for elemental analysis. In order to enable the investigation of the electron polarization at surfaces low-energy spin-polarized positrons are used to probe the outermost electrons of the surface. Furthermore, in fundamental research the preparation of well defined surfaces tailored for the production of bound leptonic systems plays an outstanding role. In this report, it is envisaged to cover both the fundamental aspects of positron surface interaction and the present status of surface studies using modern positron beam techniques.
9. Positron emission tomography wrist detector
DOEpatents
Schlyer, David J.; O'Connor, Paul; Woody, Craig; Junnarkar, Sachin Shrirang; Radeka, Veljko; Vaska, Paul; Pratte, Jean-Francois
2006-08-15
A method of serially transferring annihilation information in a compact positron emission tomography (PET) scanner includes generating a time signal representing a time-of-occurrence of an annihilation event, generating an address signal representing a channel detecting the annihilation event, and generating a channel signal including the time and address signals. The method also includes generating a composite signal including the channel signal and another similarly generated channel signal concerning another annihilation event. An apparatus that serially transfers annihilation information includes a time signal generator, address signal generator, channel signal generator, and composite signal generator. The time signal is asynchronous and the address signal is synchronous to a clock signal. A PET scanner includes a scintillation array, detection array, front-end array, and a serial encoder. The serial encoders include the time signal generator, address signal generator, channel signal generator, and composite signal generator.
10. Applicability of the MCPNX particle transport code for determination of the source correction effect in positron lifetime measurements on thin polymer films
SciTech Connect
J.M. Urban-Klaehn
2007-09-01
The method presented herein uses the MCNPX Monte Carlo particle transport code to track individual positrons and other particles through geometry that accounts for the detectors, backing foils, samples and sources with their actual sizes, positions and material characteristics. Polymer material, polydimethylsiloxane (PDMS), with different thickness of films served as samples. The excellent agreement between the experimental results and the MCNPX simulation of source correction effects for varied positron sources and different film thicknesses validates the applicability of the MCNPX code.
11. The intense slow positron beam facility at the PULSTAR reactor and applications in nano-materials study
SciTech Connect
Liu, Ming; Moxom, Jeremy; Hawari, Ayman I.; Gidley, David W.
2013-04-19
An intense slow positron beam has been established at the PULSTAR nuclear research reactor of North Carolina State University. The slow positrons are generated by pair production in a tungsten moderator from gammarays produced in the reactor core and by neutron capture reactions in cadmium. The moderated positrons are electrostatically extracted and magnetically guided out of the region near the core. Subsequently, the positrons are used in two spectrometers that are capable of performing positron annihilation lifetime spectroscopy (PALS) and positron Doppler broadening spectroscopy (DBS) to probe the defect and free volume properties of materials. One of the spectrometers (e{sup +}-PALS) utilizes an rf buncher to produce a pulsed beam and has a timing resolution of 277 ps. The second spectrometer (Ps-PALS) uses a secondary electron timing technique and is dedicated to positronium lifetime measurements with an approximately 1 ns timing resolution. PALS measurements have been conducted in the e{sup +}-PALS spectrometer on a series of nano-materials including organic photovoltaic thin films, membranes for filtration, and polymeric fibers. These studies have resulted in understanding some critical issues related to the development of the examined nano-materials.
12. Positron confinement in embedded lithium nanoclusters
van Huis, M. A.; van Veen, A.; Schut, H.; Falub, C. V.; Eijt, S. W.; Mijnarends, P. E.; Kuriplach, J.
2002-02-01
Quantum confinement of positrons in nanoclusters offers the opportunity to obtain detailed information on the electronic structure of nanoclusters by application of positron annihilation spectroscopy techniques. In this work, positron confinement is investigated in lithium nanoclusters embedded in monocrystalline MgO. These nanoclusters were created by means of ion implantation and subsequent annealing. It was found from the results of Doppler broadening positron beam analysis that approximately 92% of the implanted positrons annihilate in lithium nanoclusters rather than in the embedding MgO, while the local fraction of lithium at the implantation depth is only 1.3 at. %. The results of two-dimensional angular correlation of annihilation radiation confirm the presence of crystalline bulk lithium. The confinement of positrons is ascribed to the difference in positron affinity between lithium and MgO. The nanocluster acts as a potential well for positrons, where the depth of the potential well is equal to the difference in the positron affinities of lithium and MgO. These affinities were calculated using the linear muffin-tin orbital atomic sphere approximation method. This yields a positronic potential step at the MgO||Li interface of 1.8 eV using the generalized gradient approximation and 2.8 eV using the insulator model.
13. Descriptions of positron defect analysis capabilities
SciTech Connect
Howell, R.H.
1994-10-01
A series of descriptive papers and graphics appropriate for distribution to potential collaborators has been assembled. These describe the capabilities for defect analysis using positron annihilation spectroscopy. The application of positrons to problems in the polymer and semiconductor industries is addressed.
14. The multilayer Fe/Hf studied with slow positron beam
Murashige, Y.; Tashiro, M.; Nakajyo, T.; Koizumi, T.; Kanazawa, I.; Komori, F.; Ito, Y.
1997-04-01
The positron annihilation parameter versus the incident positron energy is measured in the thin Fe films and the Fe/Hf bilayer on silica substrate, by means of the variable energetic slow-positron beam technique. We have analyzed the change in open-volume spaces and vacancy-type defects among the Fe microcrystals in these thin films with the deposition temperature.
15. Magnetic Enhancements to Dark Matter Annihilation
Gardner, William G.; Tinsley, Todd
2017-01-01
The rate of dark matter annihilation should be greatest where the dark matter density is maximal. This is typically in the gravity wells of large stars where it also happens to be true that magnetic fields can be very large. In this poster we present an examination of how these intense magnetic fields can alter the cross section for dark matter annihilation into electron-positron pairs. We work within the framework of the minimally supersymmetric extension to the Standard Model (MSSM), and we choose its lightest neutralino as our dark matter candidate. Within this theory, dark matter can annihilate into many different final-state particles through several channels. We restrict our analysis to an electron-positron pair final state because of the low mass and reasonable detection signature. Since strong magnetic fields change how momentum is conserved for charged particles, this calculation investigates the relationship between the annihilation cross section and the electron's and positron's landau level. This is work is supported by NASA/Arkansas Space Grant Consortium and the Hendrix College Odyssey Program.
16. What is the fate of runaway positrons in tokamaks?
DOE PAGES
Liu, Jian; Qin, Hong; Fisch, Nathaniel J.; ...
2014-06-19
In this study, massive runaway positrons are generated by runaway electrons in tokamaks. The fate of these positrons encodes valuable information about the runaway dynamics. The phase space dynamics of a runaway position is investigated using a Lagrangian that incorporates the tokamak geometry, loop voltage, radiation and collisional effects. It is found numerically that runaway positrons will drift out of the plasma to annihilate on the first wall, with an in-plasma annihilation possibility less than 0.1%. The dynamics of runaway positrons provides signatures that can be observed as diagnostic tools.
17. Unthermalized positrons in gamma ray burst sources
NASA Technical Reports Server (NTRS)
Tkaczyk, W.; Karakula, S.
1992-01-01
The spectra of the broadening 0.511 MeV annihilation line produced by high temperatures was calculated in the case of unthermalized plasma; i.e., T sub e(+) is not = T sub e(-). The flattening in the spectrum of the annihilation lines for large differences of electron and positron temperatures is a strong indication that the observed features of the hard tailed spectrum of the gamma bursts can be well described by annihilation of unthermalized positrons. It is proposed that the charge separation occurring in Eddington limited accretion onto a neutron star or the one photon pair production in strong magnetic fields as a mechanism for the production of unthermalized positrons in the sources of gamma bursts. From the best fit of experimental spectra by the model, the parameters of sources for which the regions with different plasma temperatures can exist is evaluated.
18. Annihilation physics of exotic galactic dark matter particles
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1990-01-01
Various theoretical arguments make exotic heavy neutral weakly interacting fermions, particularly those predicted by supersymmetry theory, attractive candidates for making up the large amount of unseen gravitating mass in galactic halos. Such particles can annihilate with each other, producing secondary particles of cosmic-ray energies, among which are antiprotons, positrons, neutrinos, and gamma-rays. Spectra and fluxes of these annihilation products can be calculated, partly by making use of positron electron collider data and quantum chromodynamic models of particle production derived therefrom. These spectra may provide detectable signatures of exotic particle remnants of the big bang.
19. Resolvability of positron decay channels
SciTech Connect
Fluss, M.J.; Howell, R.H.; Rosenberg, I.J.; Meyer, P.
1985-03-07
Many data analysis treatments of positron experiments attempt to resolve two or more positron decay or exist channels which may be open simultaneously. Examples of the need to employ such treatments of the experimental results can be found in the resolution of the constituents of a defect ensemble, or in the analysis of the complex spectra which arise from the interaction of slow positrons at or near the surfaces of solids. Experimental one- and two-dimensional angular correlation of annihilation radiation experiments in Al single crystals have shown that two defect species (mono- and divacancies) can be resolved under suitable conditions. Recent experiments at LLNL indicate that there are a variety of complex exit channels open to positrons interacting at surfaces, and ultimely these decay channels must also be suitably resolved from one another. 6 refs., 4 figs.
20. Studies of Oxidation of the Cu(100) Surface Using Low Energy Positrons
SciTech Connect
Fazleev, N. G.; Maddox, W. B.; Nadesalingam, M.; Rajeshwar, K.; Weiss, A. H.
2009-03-10
Changes in the surface of an oxidized Cu(100) single crystal resulting from vacuum annealing have been investigated using positron annihilation induced Auger electron spectroscopy (PAES). PAES measurements show a large increase in the intensity of the positron annihilation induced Cu M{sub 2,3}VV Auger peak as the sample is subjected to a series of isochronal anneals in vacuum up to annealing temperature 300 deg. C. The intensity then decreases monotonically as the annealing temperature is increased to {approx}600 deg. C. Experimental PAES results are analyzed by performing calculations of positron surface states and annihilation probabilities of surface-trapped positrons with relevant core electrons taking into account the charge redistribution at the surface, surface reconstructions, and electron-positron correlations effects. Possible explanation for the observed behavior of the intensity of positron annihilation induced Cu M{sub 2,3}VV Auger peak with changes of the annealing temperature is proposed.
1. Mesopore quality determines the lifetime of hierarchically structured zeolite catalysts
Milina, Maria; Mitchell, Sharon; Crivelli, Paolo; Cooke, David; Pérez-Ramírez, Javier
2014-05-01
Deactivation due to coking limits the lifetime of zeolite catalysts in the production of chemicals and fuels. Superior performance can be achieved through hierarchically structuring the zeolite porosity, yet no relation has been established between the mesopore architecture and the catalyst lifetime. Here we introduce a top-down demetallation strategy to locate mesopores in different regions of MFI-type crystals with identical bulk porous and acidic properties. In contrast, well-established bottom-up strategies as carbon templating and seed silanization fail to yield materials with matching characteristics. Advanced characterization tools capable of accurately discriminating the mesopore size, distribution and connectivity are applied to corroborate the concept of mesopore quality. Positron annihilation lifetime spectroscopy proves powerful to quantify the global connectivity of the intracrystalline pore network, which, as demonstrated in the conversions of methanol or of propanal to hydrocarbons, is closely linked to the lifetime of zeolite catalysts. The findings emphasize the need to aptly tailor hierarchical materials for maximal catalytic advantage.
2. Vacancy defects in thin-film La{sub 0.5}Sr{sub 0.5}CoO{sub 3{minus}{delta}} observed by positron annihilation
SciTech Connect
Keeble, D.J.; Krishnan, A.; Friessnegg, T.; Nielsen, B.; Madhukar, S.; Aggarwal, S.; Ramesh, R.; Poindexter, E.H.
1998-07-01
Vacancy-related defects in laser ablated thin films of the conducting metal{endash}oxide La{sub 0.5}Sr{sub 0.5}CoO{sub 3{minus}{delta}} were detected using a variable-energy positron beam. The nonstoichiometry, {delta}, was altered by varying the oxygen partial pressure within the deposition chamber present during cooling. Conductivity measurements confirmed the change in oxygen content. Increased positron trapping at vacancy defects was observed with increasing nonstoichiometry. It is proposed that vacancy clusters were present in the film cooled in 10{sup {minus}5}thinspTorr oxygen. {copyright} {ital 1998 American Institute of Physics.}
3. ZnO Luminescence and scintillation studied via photoexcitation, X-ray excitation, and gamma-induced positron spectroscopy
Ji, J.; Colosimo, A. M.; Anwand, W.; Boatner, L. A.; Wagner, A.; Stepanov, P. S.; Trinh, T. T.; Liedke, M. O.; Krause-Rehberg, R.; Cowan, T. E.; Selim, F. A.
2016-08-01
The luminescence and scintillation properties of ZnO single crystals were studied by photoluminescence and X-ray-induced luminescence (XRIL) techniques. XRIL allowed a direct comparison to be made between the near-band emission (NBE) and trap emissions providing insight into the carrier recombination efficiency in the ZnO crystals. It also provided bulk luminescence measurements that were not affected by surface states. The origin of a green emission, the dominant trap emission in ZnO, was then investigated by gamma-induced positron spectroscopy (GIPS) - a unique defect spectroscopy method that enables positron lifetime measurements to be made for a sample without contributions from positron annihilation in the source materials. The measurements showed a single positron decay curve with a 175 ps lifetime component that was attributed to Zn vacancies passivated by hydrogen. Both oxygen vacancies and hydrogen-decorated Zn vacancies were suggested to contribute to the green emission. By combining scintillation measurements with XRIL, the fast scintillation in ZnO crystals was found to be strongly correlated with the ratio between the defect luminescence and NBE. This study reports the first application of GIPS to semiconductors, and it reveals the great benefits of the XRIL technique for the study of emission and scintillation properties of materials.
4. ZnO Luminescence and scintillation studied via photoexcitation, X-ray excitation, and gamma-induced positron spectroscopy
PubMed Central
Ji, J.; Colosimo, A. M.; Anwand, W.; Boatner, L. A.; Wagner, A.; Stepanov, P. S.; Trinh, T. T.; Liedke, M. O.; Krause-Rehberg, R.; Cowan, T. E.; Selim, F. A.
2016-01-01
The luminescence and scintillation properties of ZnO single crystals were studied by photoluminescence and X-ray-induced luminescence (XRIL) techniques. XRIL allowed a direct comparison to be made between the near-band emission (NBE) and trap emissions providing insight into the carrier recombination efficiency in the ZnO crystals. It also provided bulk luminescence measurements that were not affected by surface states. The origin of a green emission, the dominant trap emission in ZnO, was then investigated by gamma-induced positron spectroscopy (GIPS) - a unique defect spectroscopy method that enables positron lifetime measurements to be made for a sample without contributions from positron annihilation in the source materials. The measurements showed a single positron decay curve with a 175 ps lifetime component that was attributed to Zn vacancies passivated by hydrogen. Both oxygen vacancies and hydrogen-decorated Zn vacancies were suggested to contribute to the green emission. By combining scintillation measurements with XRIL, the fast scintillation in ZnO crystals was found to be strongly correlated with the ratio between the defect luminescence and NBE. This study reports the first application of GIPS to semiconductors, and it reveals the great benefits of the XRIL technique for the study of emission and scintillation properties of materials. PMID:27550235
5. ZnO Luminescence and scintillation studied via photoexcitation, X-ray excitation, and gamma-induced positron spectroscopy.
PubMed
Ji, J; Colosimo, A M; Anwand, W; Boatner, L A; Wagner, A; Stepanov, P S; Trinh, T T; Liedke, M O; Krause-Rehberg, R; Cowan, T E; Selim, F A
2016-08-23
The luminescence and scintillation properties of ZnO single crystals were studied by photoluminescence and X-ray-induced luminescence (XRIL) techniques. XRIL allowed a direct comparison to be made between the near-band emission (NBE) and trap emissions providing insight into the carrier recombination efficiency in the ZnO crystals. It also provided bulk luminescence measurements that were not affected by surface states. The origin of a green emission, the dominant trap emission in ZnO, was then investigated by gamma-induced positron spectroscopy (GIPS) - a unique defect spectroscopy method that enables positron lifetime measurements to be made for a sample without contributions from positron annihilation in the source materials. The measurements showed a single positron decay curve with a 175 ps lifetime component that was attributed to Zn vacancies passivated by hydrogen. Both oxygen vacancies and hydrogen-decorated Zn vacancies were suggested to contribute to the green emission. By combining scintillation measurements with XRIL, the fast scintillation in ZnO crystals was found to be strongly correlated with the ratio between the defect luminescence and NBE. This study reports the first application of GIPS to semiconductors, and it reveals the great benefits of the XRIL technique for the study of emission and scintillation properties of materials.
6. Positron microscopy
SciTech Connect
Hulett, L.D. Jr.; Xu, J.
1995-02-01
The negative work function property that some materials have for positrons make possible the development of positron reemission microscopy (PRM). Because of the low energies with which the positrons are emitted, some unique applications, such as the imaging of defects, can be made. The history of the concept of PRM, and its present state of development will be reviewed. The potential of positron microprobe techniques will be discussed also.
7. Recent Developments in Positron Emission Tomography (PET) Instrumentation
DOE R&D Accomplishments Database
Derenzo, S. E.; Budinger, T. F.
1986-04-01
This paper presents recent detector developments and perspectives for positron emission tomography (PET) instrumentation used for medical research, as well as the physical processes in positron annihilation, photon scattering and detection, tomograph design considerations, and the potentials for new advances in detectors.
8. Recent developments in positron emission tomography (PET) instrumentation
SciTech Connect
Derenzo, S.E.; Budinger, T.F.
1986-04-01
This paper presents recent detector developments and perspectives for positron emission tomography (PET) instrumentation used for medical research, as well as the physical processes in positron annihilation, photon scattering and detection, tomograph design considerations, and the potentials for new advances in detectors. 117 refs., 4 figs., 4 tabs.
9. Measuring positron-atom binding energies through laser-assisted photorecombination
Surko, C. M.; Danielson, J. R.; Gribakin, G. F.; Continetti, R. E.
2012-06-01
Described here is a proposed experiment to use laser-assisted photorecombination of positrons from a trap-based beam and metal atoms in the gas phase to measure positron-atom binding energies. Signal rates are estimated, based in part upon experience studying resonant annihilation spectra using a trap-based positron beam.
10. Positron trapping at grain boundaries
SciTech Connect
Dupasquier, A. ); Romero, R.; Somoza, A. )
1993-10-01
The standard positron trapping model has often been applied, as a simple approximation, to the interpretation of positron lifetime spectra in situations of diffusion-controlled trapping. This paper shows that this approximation is not sufficiently accurate, and presents a model based on the correct solution of the diffusion equation, in the version appropriate for studying positron trapping at grain boundaries. The model is used for the analysis of new experimental data on positron lifetime spectra in a fine-grained Al-Ca-Zn alloy. Previous results on similar systems are also discussed and reinterpreted. The analysis yields effective diffusion coefficients not far from the values known for the base metals of the alloys.
11. Radiative proton-antiproton annihilation to a lepton pair
SciTech Connect
Ahmadov, A. I.; Bytev, V. V.; Kuraev, E. A.; Tomasi-Gustafsson, E.
2010-11-01
The annihilation of proton and antiproton to an electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.
12. Positrons in the Galaxy: Their Births, Marriages and Deaths
NASA Technical Reports Server (NTRS)
Skinner, Gerald K.
2010-01-01
High energy (approximately GeV) positrons are seen within cosmic rays and observation of a narrow line at 511 keV shows that positrons are annihilating in the galaxy after slowing down to approximately keV energies or less. Our state of knowledge of the origin of these positrons, of the formation of positronium 'atoms', and of the circumstances of their annihilation or escape from the galaxy are reviewed and the question of whether the two phenomena are linked is discussed.
13. Positron moderation and detection for positronic atoms
An apparatus is under development for H--+* production, atoms consisting of a positron bound in a Rydberg state to an H-- ion. High energy e+ from radioactive N2211a are slowed (moderated) to eV energies in solid neon and captured in a Penning trap. The procedure to deposit the neon is optimized, resulting in a 1.5% efficiency for moderating high energy e +. Neutral H--+* atoms with ˜100 eV will be produced from these trapped e+ and exit the trap, hitting a metal surface where the e+ annihilates. Back-to-back annihilation gamma photons (Egamma ≈ 0.511 MeV) detected in coincidence, at the expected energy are the fingerprint for H--+* production. A N2211a test source mocks H--+* experiments with ˜2.7% of the e+ emitting disintegrations detected. This high efficiency, with a background rate of ˜2.8 events/hour is achieved by surrounding the detectors with lead and cosmic ray detectors.
14. A General Quantum Mechanical Method to Predict Positron Spectroscopy
DTIC Science & Technology
2007-06-01
70 6.2.3 Positronic Systems for Modeling and Experiment 71 Appendix A. Electron-Positron Annihilation Observables from NEO-HF and NEO-MP2...spectroscopy (PAS) experiments are widely used to study materials defects, including point defects in semiconductors and voids in composite materials...addition to traditional PAS techniques, experiments involving VFRs are also discussed. In Section 2.2, methods for modeling positron interaction with
15. 2D ACAR momentum density study of the nature of the positron surface state on Al(100)
SciTech Connect
Berko, S.; Canter, K.F.; Lynn, K.G.; Mills, A.P.; Roellig, L.O.; West, R.N.
1985-01-01
The two-dimensional angular correlation of the 2..gamma.. annihilation radiation (2D ACAR) has been measured from an Al(100) surface bombarded by 200-eV positrons. After removing the contribution of fast para-positronium annihilation, the spectrum from positrons annihilating at the surface exhibits a nearly isotropic conical shape with a (7.1 +- 0.5) mrad FWHM. 5 refs., 6 figs.
16. The Buffer-Gas Positron Accumulator and Resonances in Positron-Molecule Interactions
NASA Technical Reports Server (NTRS)
Surko, C.M.
2007-01-01
This is a personal account of the development of our buffer-gas positron trap and the new generation of cold beams that these traps enabled. Dick Drachman provided much appreciated advice to us from the time we started the project. The physics underlying trap operation is related to resonances (or apparent resonances) in positron-molecule interactions. Amusingly, experiments enabled by the trap allowed us to understand these processes. The positron-resonance "box score" to date is one resounding "yes," namely vibrational Feshbach resonances in positron annihilation on hydrocarbons; a "probably" for positron-impact electronic excitation of CO and NZ;an d a "maybe" for vibrational excitation of selected molecules. Two of these processes enabled the efficient operation of the trap, and one almost killed it in infancy. We conclude with a brief overview of further applications of the trapping technology discussed here, such as "massive" positron storage and beams with meV energy resolution.
17. Positron Spectroscopy Investigation of Normal Brain Section and Brain Section with Glioma Derived from a Rat Glioma Model
Yang, SH.; Ballmann, C.; Quarles, C. A.
2009-03-01
18. Positron Spectroscopy Investigation of Normal Brain Section and Brain Section with Glioma Derived from a Rat Glioma Model
SciTech Connect
Yang, SH.; Ballmann, C.; Quarles, C. A.
2009-03-10
19. Nuclear annihilation by antinucleons
DOE PAGES
Lee, Teck-Ghee; Wong, Cheuk-Yin
2016-01-25
We examine the momentum dependence ofmore » $$\\bar{p}$$p and $$\\bar{n}$$p annihilation cross sections by considering the transmission through a nuclear potential and the $$\\bar {p}$$p Coulomb interaction. Compared to the $$\\bar{n}$$p annihilation cross section, the $$\\bar{p}$$p annihilation cross section is significantly enhanced by the Coulomb interaction for projectile momenta below plab < 500 MeV/c, and the two annihilation cross sections approach the Pomeranchuk's equality limit [JETP 30, 423 (1956)] at plab ~500 MeV/c. Using these elementary cross sections as the basic input data, the extended Glauber model is employed to evaluate the annihilation cross sections for $$\\bar{n}$$ and $$\\bar{p}$$ interaction with nuclei and the results compare well with experimental data.« less
20. Nuclear annihilation by antinucleons
SciTech Connect
Lee, Teck-Ghee; Wong, Cheuk-Yin
2016-01-25
We examine the momentum dependence of $\\bar{p}$p and $\\bar{n}$p annihilation cross sections by considering the transmission through a nuclear potential and the $\\bar {p}$p Coulomb interaction. Compared to the $\\bar{n}$p annihilation cross section, the $\\bar{p}$p annihilation cross section is significantly enhanced by the Coulomb interaction for projectile momenta below plab < 500 MeV/c, and the two annihilation cross sections approach the Pomeranchuk's equality limit [JETP 30, 423 (1956)] at plab ~500 MeV/c. Using these elementary cross sections as the basic input data, the extended Glauber model is employed to evaluate the annihilation cross sections for $\\bar{n}$ and $\\bar{p}$ interaction with nuclei and the results compare well with experimental data.
1. Sgr A* as Source of the Positrons Observed in the Galactic Center Region
Jean, Pierre; Guessoum, Nidhal; Ferrière, Katia
2017-01-01
We explore the possibility that a substantial fraction of the positrons observed to annihilate in the central region of our Galaxy come from the supermassive black hole Sgr A* that lies at the center. This idea was proposed by several authors, but the propagation of the emitted positrons into the bulge and beyond remained a serious problem for models of the origin of GC positrons. We assume models of positron production with different energies. The propagation of positrons from their production site is followed in detail with Monte-Carlo simulations, taking into account the physical conditions of the propagation regions as well as various physical interactions. Using the known physics of positron annihilation in astrophysical environments, we calculate the properties of the annihilation emission (time evolution and spatial distribution) for the different models under consideration. We present the results of these simulations and the conclusions/constraints that can be inferred from them.
2. Gamma-Ray background spectrum and annihilation rate in the baryon-symmetric big-bang cosmology
NASA Technical Reports Server (NTRS)
Puget, J. L.
1973-01-01
An attempt was made to extract experimental data on baryon symmetry by observing annihilation products. Specifically, gamma rays and neutrons with long mean free paths were analyzed. Data cover absorption cross sections and radiation background of the 0.511 MeV gamma rays from positron annihilations and the 70 MeV gamma rays from neutral pion decay.
3. The Positron as a Probe for Studying Bulk and Defect Properties in Semiconductors
Dlubek, G.; Brümmer, O.
Positron lifetime measurements are used to study various doped and undoped III-V compound semiconductors like GaAs, GaP, InAs and InP. In some as-grown crystals native vacancies (V, V) or their complexes with dopants (TeAsV, VPZnInV) are detected with maximum concentrations of a few 1018 cm-3. In undoped GaAs neutral As vacancies V are identified, the concentration of which varies locally. The vacancies have their origin in deviations from the stoichiometrie composition of the compound. They disappear at 500°C. At this temperature defects created by irradiation with fast neutrons anneal also out. The relation between the bulk positron lifetime and the density and polarization of valence electrons is analyzed. Further, the potential of the positron annihilation method in identifying and characterizing vacancy-type defects in semiconductors is discussed.Translated AbstractDas Positron als Sonde zur Untersuchung der Volumen- und Fehlstelleneigenschaften in HalbleiternPositronenlebensdauermessungen werden angewandt, um verschiedene dotierte und undotierte AIIIBV-Verbindungshalbleiter, wie GaAs, GaP, InAs und InP, zu untersuchen. In einigen Kristallen werden Leerstellen (V, V) oder ihre Komplexe mit Dotierungen (TeAsV, VPZnInV) mit maximalen Konzentrationen von einigen 1018 cm-3 nachgewiesen. In undotierten GaAs werden neutrale As-Leerstellen V identifiziert, deren Konzentration lokal variiert. Die Leerstellen haben ihren Ursprung in Abweichungen von der stöchiometrischen Zusammensetzung der Verbindung. Sie verschwinden bei 500°C. Bei dieser Temperatur heilen auch Defekte aus, welche durch Bestrahlung mit schnellen Neutronen erzeugt wurden. Die Beziehung zwischen der Positronenlebensdauer im Kristall und der Dichte und Polarisierung der Valenzelektronen wird analysiert. Weiterhin wird das Potential der Methode der Positronenannihilation zur Identifizierung und Charakterisierung leerstellenartiger Defekte in Halbleitern diskutiert.
4. Dark matter annihilation and the PAMELA, FERMI, and ATIC anomalies
SciTech Connect
El Zant, A. A.; Okada, H.; Khalil, S.
2010-06-15
If dark matter annihilation accounts for the tantalizing excess of cosmic ray electron/positrons, as reported by the PAMELA, ATIC, HESS, and FERMI observatories, then the implied annihilation cross section must be relatively large. This results, in the context of standard cosmological models, in very small relic dark matter abundances that are incompatible with astrophysical observations. We explore possible resolutions to this apparent conflict in terms of nonstandard cosmological scenarios; plausibly allowing for large cross sections, while maintaining relic abundances in accord with current observations.
5. Positron-molecule bound states and positive ion production
NASA Technical Reports Server (NTRS)
Leventhal, M.; Passner, A.; Surko, C. M.
1990-01-01
The interaction was studied of low energy positrons with large molecules such as alkanes. These data provide evidencce for the existence of long lived resonances and bound states of positrons with neutral molecules. The formation process and the nature of these resonances are discussed. The positive ions produced when a positron annihilates with an electron in one of these resonances were observed and this positive ion formation process is discussed. A review is presented of the current state of the understanding of these positron-molecule resonances and the resulting positive ion formation. A number of outstanding issues in this area is also discussed.
6. Evidence of the participation of electronic excited states in the mechanism of positronium formation in substitutional Tb(1-x)Eu(x)(dpm)3 solid solutions studied by optical and positron annihilation spectroscopies.
PubMed
Fulgêncio, F; de Oliveira, F C; Windmöller, D; Brito, H F; Malta, O L; de Sá, G F; Magalhães, W F; Machado, J C
2012-07-28
Positronium formation in the bimary molecular solid solutions Tb(1-x)Eu(x) (dpm)(3) (dpm = dipivaloylmethanate) has been investigated. A strong linear correlation between the (5)D(4) Tb(iii) energy level excited state lifetime and the positronium formation probability has been observed. This correlation indicates that the ligand-to-metal charge transfer LMCT states act in both luminescence quenching and positronium formation inhibition, as previously proposed. A kinetic mechanism is proposed to explain this correlation and shows that excited electronic states have a very important role in the positronium formation mechanism.
7. Neutron-irradiated model alloys and pressure-vessel steels studied using positron spectroscopy
Cumblidge, Stephen Eric
8. Positron kinetics in an idealized PET environment
Robson, R. E.; Brunger, M. J.; Buckman, S. J.; Garcia, G.; Petrović, Z. Lj.; White, R. D.
2015-08-01
The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the ‘gas-phase’ assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.
9. On the localization of positrons in metal vacancies
Babich, A. V.; Pogosov, V. V.; Reva, V. I.
2015-11-01
The probability of localization of positrons in single vacancies of Al, Cu, and Zn as a function of temperature has been calculated. Vacancy has been simulated by a cavity with a radius of the Wigner-Seitz cell in the stabilized jellium model. A formula for the rate of trapping of a positron by a vacancy as a function of the positron energy has been obtained using the "golden" rule for transitions under the assumption that the positron energy is spent on excitation of electron-hole pairs. The temperature dependence of the localization rate has been calculated for thermalized positrons. It has been found that, in the vicinity of the triple point, the localization rate is close in order of magnitude to the annihilation rate. Based on the results reported in our previous publications devoted to the evaluation of the influence of vacancies on the work function of free positrons, it has been assumed that, near the surface of the metal, there are vacancies charged by positrons. In the approximation of a two-dimensional superlattice, the near-surface vacancy barrier has been estimated. The experimentally revealed shift of the energy distribution of re-emitted positrons has been assumed to be caused by the reflection of low-energy positrons from the vacancy barrier back into the bulk of the metal where they annihilate.
10. Electroweak fragmentation functions for dark matter annihilation
SciTech Connect
Cavasonza, Leila Ali; Krämer, Michael; Pellen, Mathieu
2015-02-18
Electroweak corrections can play a crucial role in dark matter annihilation. The emission of gauge bosons, in particular, leads to a secondary flux consisting of all Standard Model particles, and may be described by electroweak fragmentation functions. To assess the quality of the fragmentation function approximation to electroweak radiation in dark matter annihilation, we have calculated the flux of secondary particles from gauge-boson emission in models with Majorana fermion and vector dark matter, respectively. For both models, we have compared cross sections and energy spectra of positrons and antiprotons after propagation through the galactic halo in the fragmentation function approximation and in the full calculation. Fragmentation functions fail to describe the particle fluxes in the case of Majorana fermion annihilation into light fermions: the helicity suppression of the lowest-order cross section in such models cannot be lifted by the leading logarithmic contributions included in the fragmentation function approach. However, for other classes of models like vector dark matter, where the lowest-order cross section is not suppressed, electroweak fragmentation functions provide a simple, model-independent and accurate description of secondary particle fluxes.
11. Directional Dependence for Dark Matter Annihilation in Extreme Astrophysical Environments
2017-01-01
This research explores the directional dependence that extreme magnetic fields have on the annihilation of dark matter into electron-positron pairs. We take the neutralino of the Minimally Supersymmetric Standard Model (MSSM) as our dark matter candidate and assume magnetic field strengths on the order of the critical field (Bc 1013 G). This is characteristic of extreme astrophysical environments in which dark matter may accumulate. We will present the results for the annihilation cross section at varying incoming particle direction. In addition, we will present how these results differ with neutralino mass and energy, as well as with the magnetic field strength. Our goal is to demonstrate the ways that the direction of the magnetic field affects the states of the final electron and positron. This work is supported by NASA/Arkansas Space Grant Consortium and the Hendrix Odyssey Program.
12. Positron emission tomography within a magnetic field using photomultiplier tubes and lightguides.
PubMed
Christensen, N L; Hammer, B E; Heil, B G; Fetterly, K
1995-04-01
The spatial resolution of positron emission tomography (PET) improves when positron annihilation takes place in a strong magnetic field. In a magnetic field, the Lorentz force restricts positron range perpendicular to the field. Since positron annihilation occurs closer to its point of origin, the positron annihilation point spread function decreases. This was verified experimentally by measuring the spread function of positron annihilation from a 500 mm 68Ge bead imbedded in tissue-equivalent wax. At 5 T the spread function full width at half maximum (FWHM) and the full width at tenth maximum (FWTM) decrease by a factor of 1.42 and 2.09, respectively. Two NaI(Tl) scintillation crystals that interface to a pair of photomultiplier tubes (PMTS) through long lightguides detect positron annihilation at zero field and 5.0 T. Photomultiplier tubes, inoperable in strong magnetic fields, are functional if lightguides bring the photons produced by scintillators within the field to a minimal magnetic field. These tests also demonstrate techniques necessary for combining magnetic resonance imaging (MRI) and PET into one scanner.
13. Electron capture from solids by positrons
SciTech Connect
Howell, R.
1987-08-01
The capture of electrons in solids is modified from that in gasses by several factors. The most important is the collective interaction of the electrons which results in a density of electron states in the solid in wide bands. Also the high density of electrons in many solids gives a high frequency of interaction as compared to gasses, and quickly destroys any electron-positron states in the metal matrix. Consequently, most positrons implanted in a metal will rapidly thermalize, and unless they reach the surface will annihilate with an electron in an uncorrelated state. Positronium formation from positrons scattered at a metal surface is analogous to ion neutralization however, most of the positronium comes from positrons passing through the surface from the bulk. The dominant motivation for studying positronium formation has been the hope that the distribution of the electrons at the surface would be obtained through the annihilation properties of positrons trapped at the surface or through analysis of the energy and angular distributions of the positronium emitted into the vacuum. These distributions have been measured and are included in this paper. 17 refs.
14. A method to detect positron anisotropies with Pamela data
Panico, B.; Adriani, O.; Barbarino, G. C.; Bazilevskaya, G. A.; Bellotti, R.; Boezio, M.; Bogomolov, E. A.; Bongi, M.; Bonvicini, V.; Bottai, S.; Bruno, A.; Cafagna, F.; Campana, D.; Carbone, R.; Carlson, P.; Casolino, M.; Castellini, G.; De Donato, C.; De Santis, C.; De Simone, N.; Di Felice, V.; Formato, V.; Galper, A. M.; Giaccari, U.; Karelin, A. V.; Koldashov, S. V.; Koldobskiy, S.; Krutkov, S. Y.; Kvashnin, A. N.; Leonov, A.; Malakhov, V.; Marcelli, L.; Martucci, M.; Mayorov, A. G.; Menn, W.; Merge, M.; Mikhailov, V. V.; Mocchiutti, E.; Monaco, A.; Mori, N.; Munini, R.; Osteria, G.; Palma, F.; Papini, P.; Pearce, M.; Picozza, P.; Pizzolotto, C.; Ricci, M.; Ricciarini, S. B.; Sarkar, R.; Scotti, V.; Simon, M.; Sparvoli, R.; Spillantini, P.; Stozhkov, Y. I.; Vacchi, A.; Vannuccini, E.; Vasilyev, G. I.; Voronov, S. A.; Yurkin, Y. T.; Zampa, G.; Zampa, N.; Zverev, V. G.
2014-11-01
The PAMELA experiment is collecting data since 2006; its results indicate the presence of a large flux of positron with respect to electrons in the CR spectrum above 10 GeV. This excess might also be originated in objects such as pulsars and microquasars or through dark matter annihilation. Here the electrons and positrons events collected by PAMELA have been analized searching for anisotropies. The analysis is performed at different angular scales and results will be presented at the conference.
15. Positron Physics
NASA Technical Reports Server (NTRS)
Drachman, Richard J.
2003-01-01
I will give a review of the history of low-energy positron physics, experimental and theoretical, concentrating on the type of work pioneered by John Humberston and the positronics group at University College. This subject became a legitimate subfield of atomic physics under the enthusiastic direction of the late Sir Harrie Massey, and it attracted a diverse following throughout the world. At first purely theoretical, the subject has now expanded to include high brightness beams of low-energy positrons, positronium beams, and, lately, experiments involving anti-hydrogen atoms. The theory requires a certain type of persistence in its practitioners, as well as an eagerness to try new mathematical and numerical techniques. I will conclude with a short summary of some of the most interesting recent advances.
16. PhytoBeta imager: a positron imager for plant biology
SciTech Connect
Weisenberger, Andrew G; Lee, Seungjoon; McKisson, John; McKisson, J E; Xi, Wenze; Zorn, Carl; Reid, Chantal D; Howell, Calvin R; Crowell, Alexander S; Cumberbatch, Laurie; Fallin, Brent; Stolin, Alexander; Smith, Mark F
2012-06-01
Several positron emitting radioisotopes such as 11C and 13N can be used in plant biology research. The 11CO2 tracer is used to facilitate plant biology research toward optimization of plant productivity, biofuel development and carbon sequestration in biomass. Positron emission tomography (PET) imaging has been used to study carbon transport in live plants using 11CO2. Because plants typically have very thin leaves, little medium is present for the emitted positrons to undergo an annihilation event. The emitted positrons from 11C (maximum energy 960 keV) could require up to approximately 4 mm of water equivalent material for positron annihilation. Thus many of the positrons do not annihilate inside the leaf, resulting in limited sensitivity for PET imaging. To address this problem we have developed a compact beta-positive, beta-minus particle imager (PhytoBeta imager) for 11CO2 leaf imaging. The detector is based on a Hamamatsu H8500 position sensitive photomultiplier tube optically coupled via optical grease to a 0.5 mm thick Eljen EJ-212 plastic scintillator. The detector is equipped with a flexible arm to allow its placement and orientation over or under the leaf to be studied while maintaining the leaf's original orientation. To test the utility of the system the detector was used to measure carbon translocation in a leaf of the spicebush (Lindera benzoin) under two transient light conditions.
17. CALET's sensitivity to Dark Matter annihilation in the galactic halo
SciTech Connect
Motz, H.; Asaoka, Y.; Torii, S.; Bhattacharyya, S. E-mail: [email protected] E-mail: [email protected]
2015-12-01
CALET (Calorimetric Electron Telescope), installed on the ISS in August 2015, directly measures the electron+positron cosmic rays flux up to 20 TeV. With its proton rejection capability of 1 : 10{sup 5} and an aperture of 1200 cm{sup 2·} sr, it will provide good statistics even well above one TeV, while also featuring an energy resolution of 2%, which allows it to detect fine structures in the spectrum. Such structures may originate from Dark Matter annihilation or decay, making indirect Dark Matter search one of CALET's main science objectives among others such as identification of signatures from nearby supernova remnants, study of the heavy nuclei spectra and gamma astronomy. The latest results from AMS-02 on positron fraction and total electron+positron flux can be fitted with a parametrization including a single pulsar as an extra power law source with exponential cut-off, which emits an equal amount of electrons and positrons. This single pulsar scenario for the positron excess is extrapolated into the TeV region and the expected CALET data for this case are simulated. Based on this prediction for CALET data, the sensitivity of CALET to Dark Matter annihilation in the galactic halo has been calculated. It is shown that CALET could significantly improve the limits compared to current data, especially for those Dark Matter candidates that feature a large fraction of annihilation directly into e{sup +} + e{sup −}, such as the LKP (Lightest Kaluza-Klein particle)
18. First platinum moderated positron beam based on neutron capture
Hugenschmidt, C.; Kögel, G.; Repper, R.; Schreckenbach, K.; Sperr, P.; Triftshäuser, W.
2002-12-01
A positron beam based on absorption of high energy prompt γ-rays from thermal neutron capture in 113Cd was installed at a neutron guide of the high flux reactor at the ILL in Grenoble. Measurements were performed for various source geometries, dependent on converter mass, moderator surface and extraction voltages. The results lead to an optimised design of the in-pile positron source which will be implemented at the Munich research reactor FRM-II. The positron source consists of platinum foils acting as γ-e +e --converter and positron moderator. Due to the negative positron work function moderation in heated platinum leads to emission of monoenergetic positrons. The positron work function of polycrystalline platinum was determined to 1.95(5) eV. After acceleration to several keV by four electrical lenses the beam was magnetically guided in a solenoid field of 7.5 mT leading to a NaI-detector in order to detect the 511 keV γ-radiation of the annihilating positrons. The positron beam with a diameter of less than 20 mm yielded an intensity of 3.1×10 4 moderated positrons per second. The total moderation efficiency of the positron source was about ɛ=1.06(16)×10 -4. Within the first 20 h of operation a degradation of the moderation efficiency of 30% was observed. An annealing procedure at 873 K in air recovers the platinum moderator.
19. Development of a method to study positron diffusion in metals by the observation of positronium negative ions
Suzuki, Takuji; Terabe, Hiroki; Iida, Shimpei; Yamashita, Takashi; Nagashima, Yasuyuki
2014-09-01
We have developed a new method to study positron diffusion in metals. In this method, we observe positronium negative ions emitted from the sample surfaces after coating with alkali-metals to evaluate the yields of the positrons which return to the surfaces. γ-rays from the ions accelerated using an electric field are clearly distinguished from those emitted from pair-annihilation of positrons in the bulk or on the surface and self-annihilation of emitted positronium atoms. Reliable studies on positron diffusion in metals have been enabled by this method.
20. Apparatus for the analysis of surfaces in gas environments using Positron Spectroscopy
Satyal, Suman; Lim, Lawrence; Joglekar, Prasad; Kalaskar, Sushant; Shastry, Karthik; Weiss, Alexander
2011-03-01
Positron spectroscopy performed with low energy beams can provide highly surface specific information due to the trapping of positrons in an image potential surface state at the time of annihilation. Here we present design details of a new positron beam system for the analysis of surfaces gas environments. The new system will employ differential pumping to transport the positrons most of the way from the source to the sample under high vacuum. The positrons will then be transported through a thin gas layer surrounding the sample. The positrons will be implanted into the sample at energies less than ~ 10 keV ensuring that a large fraction will diffuse back to the surface before annihilation. The Elemental content of the surface interacting with the gas environment will then be determined from the Doppler broadened gamma spectra. Welch Y1100, NSF DMR 0907679.
1. Positron and positronium interactions with Cu
SciTech Connect
Bromley, M.W.J.; Mitroy, J.
2002-12-01
The configuration-interaction (CI) method is used to investigate the interactions of positrons and positronium with copper at low energies. The calculations were performed within the framework of the fixed-core approximation with semiempirical polarization potentials used to model dynamical interactions between the active particles and the (1s-3d) core. Initially, calculations upon the e{sup +}Li system were used to refine the numerical procedures and highlighted the extreme difficulties of using an orthodox CI calculation to describe the e{sup +} Li system. The positron binding energy of e{sup +}Cu derived from a CI calculation which included electron and positron orbitals with l{<=}18 was 0.005 12 hartree while the spin-averaged annihilation rate was 0.507x10{sup 9} s{sup -1}. The configuration basis used for the bound-state calculation was also used as a part of the trial wave function for a Kohn variational calculation of positron-copper scattering. The positron-copper system has a scattering length of about 13.1a{sub 0} and the annihilation parameter Z{sub eff} at threshold was 72.9. The dipole polarizability of the neutral copper ground state was computed and found to be 41.6a{sub 0}{sup 3}. The structure of CuPs was also studied with the CI method and it was found to have a binding energy of 0.0143 hartree and an annihilation rate of {approx}2x10{sup 9} s{sup -1}.
2. Solving the charging effect in insulating materials probed by a variable monoenergy slow positron beam.
PubMed
Hung, Wei-Song; De Guzman, Manuel; An, Quanfu; Lee, Kueir-Rarn; Jean, Yan-Ching; Lai, Juin-Yih
2011-03-15
A variable monoenergy slow positron beam (VMSPB) operating at a high vacuum on insulating materials encounters a problem of significant surface charging effect with time. As a result, positronium formation is inhibited, and the positron annihilation radiation counting rate is reduced; these consequently distorted the experimental positron annihilation and results. To solve such problems, a technique of depositing an ultrathin layer of sputtering noble metals on insulators is developed. We report a successful method of sputtering a few atomic layers of platinum (∼1 nm) on a polyamide membrane to completely remove the charging effect for VMSPB applications in insulators.
3. Characterization of Porous Structures in Advanced Low-k Films with Thin TaN Layers Using Monoenergetic Positron Beams
Uedono, Akira; Verdonck, Patrick; Delabie, Annelies; Swerts, Johan; Witters, Thomas; Conard, Thierry; Baklanov, Mikhail R.; Van Elshocht, Sven; Oshima, Nagayasu; Suzuki, Ryoichi
2013-10-01
Pore sizes and their depth distributions in advanced low-k (ALK) films fabricated using plasma-enhanced chemical vapor deposition were determined using monoenergetic positron beams. The measurement of the energy distributions of annihilation γ-rays and the positron lifetime spectra of the ALK films before and after thin TaN atomic layer deposition showed that Ta atoms diffused into the films. As a result, mean pore size decreased, with the number of larger pores decreasing preferentially. From the measurements of the electron momentum distribution, we found that almost all the inner walls of pores were covered by Ta for the ALK film without pretreatment before TaN deposition. The penetration of Ta into the film, however, was suppressed by plasma treatment using an Ar/N2 or Ar/H2 gas mixture, where the Ar/N2-plasma treatment more effectively blocked Ta diffusion than the Ar/H2-plasma treatment. Through this work, we have demonstrated that monoenergetic positron beams are a powerful tool for characterizing capped porous films and the trapping of metallic atoms by pores.
4. Advances in defect characterizations of semiconductors using positrons
SciTech Connect
Lynn, K.G.; Asoka-Kumar, P.
1996-12-31
Positron Annihilation Spectroscopy (PAS) is a sensitive probe for studying the electronic structure of defects in solids. The authors summarize recent developments in defect characterization of semiconductors using depth-resolved PAS. The progress achieved in extending the capabilities of the PAS method is also described.
5. Models of pair annihilation in 1E 1740.7-2942 and the HEAO 1 A-4 annihilation source
NASA Technical Reports Server (NTRS)
Maciolek-Niedzwiecki, Andrzej; Zdziarski, Andrzej
1994-01-01
We study possible models of two Galactic sources of transient pair annihilation radiation, 1E 1740.7-2942 and a source observed by High Energy Astronomy Observatory (HEAO) 1 A-4. We fit the observed spectral features by thermal annihilation spectra and find that the redshifts obtained by us are much larger than those obtained from fitting Caussian lines centered on 511 keV. This effect, which is due to the net blueshift (with respect to 511 keV) of the annihilation spectrum due to the thermal energies of pairs, puts strong constraints on models of sources. We consider those constraints first without considering the mechanism of positron production. From the shape of the observed spectra, we are able to rule out both spherical clouds and layers above cold matter as possible source geometries. The observed spectra are compatible with two source geometries: (1) a nearly face-on disk in the Kerr metric and (2) a jet close to a black hole. We consider, then, the origin of the pairs. Theories of both thermal and nonthermal pair equilibria predict that photon-pair production is unable to produce annihilation features that contain as much as half of the bolometric luminosity, which is observed. A possible solution to this problem is obscuration of a nonthermal source (in which pairs are produced by photon-photon collisions) and an outflow of pairs to an unobscured region. This makes annihilation in a jet the most likely model of the considered sources.
6. Resonances in Positron-molecule Interactions
Surko, C. M.
2006-05-01
The development of cold, trap-based beams has enabled high-resolution, energy-resolved studies of positron scattering and annihilation processes [1]. This talk focuses on three topics in this area. For hydrocarbon molecules such as alkanes (CnH2n+2), giant enhancements in annihilation rates are observed due to vibrational Feshbach resonances. The dependence of the rates on positron energy provides evidence that positrons bind to these molecules and a measure of the binding energies [1]. Recent results include evidence for a second, positronically excited'' bound state and new data for the methane series, CH3X, where X is a halogen. Other resonance-like features'' are sharp increases in the near-threshold electronic excitation cross sections for CO and N2 [2], and in the vibrational excitation cross sections for CO, CO2 and CH4 [3, 4]. Outstanding questions and the relationship of these observations to available theoretical predictions will be discussed.1. C. M. Surko, G. F. Gribakin, and S. J. Buckman, J. Phys. B 38, R57 (2005).2. J. P. Marler and C. M. Surko, Phys. Rev. A 72, 062713 (2005).3. J. P. Marler and C. M. Surko, Phys. Rev. A 72, 062702 (2005).4. J. P. Marler, G. F. Gribakin and C. M. Surko, Nuclear Instrum. and Meth. B, in press (2006).
7. Positron production using a 1.7 MV pelletron accelerator
SciTech Connect
Alcantara, K. F.; Santos, A. C. F.; Crivelli, P.
2013-04-19
We report the foremost phase of a fourth generation positron source, being constructed at the Federal University of Rio de Janeiro. Positron yields are reported by making use of the {sup 19}F(p,{alpha}e{sup +}e{sup -}){sup 16}O reaction, where the fluorine target is in the form of a CaF{sub 2} pellet. Positron production has been observed by detecting 511 keV annihilation gamma rays emerging from the irradiated CaF{sub 2} target.
8. Annealing properties of open volumes in HfSiO{sub x} and HfAlO{sub x} gate dielectrics studied using monoenergetic positron beams
SciTech Connect
Uedono, A.; Ikeuchi, K.; Yamabe, K.; Ohdaira, T.; Muramatsu, M.; Suzuki, R.; Hamid, A. S.; Chikyow, T.; Torii, K.; Yamada, K.
2005-07-15
Thin Hf{sub 0.6}Si{sub 0.4}O{sub x} and Hf{sub 0.3}Al{sub 0.7}O{sub x} films fabricated by metal-organic chemical-vapor deposition and atomic-layer-deposition techniques were characterized using monoenergetic positron beams. Measurements of the Doppler broadening spectra of annihilation radiation and the lifetime spectra of positions indicated that positrons annihilated from the trapped state by open volumes that exist intrinsically in amorphous structures of the films. For HfSiO{sub x}, the mean size of the open volumes and their size distribution decreased with increasing postdeposition annealing (PDA) temperature. For HfAlO{sub x}, although the overall behavior of the open volumes in response to annealing was similar to that for HfSiO{sub x}, PDA caused a separation of the mean size of the open volumes. When this separation occurred, the value of the line-shape parameter S increased, suggesting an oxygen deficiency in the amorphous matrix. This fragmentation of the amorphous matrix can be suppressed by decreasing the annealing time.
9. Study of SiO[sub 2]-Si and metal-oxide-semiconductor structures using positrons
SciTech Connect
Leung, T.C.; Asoka-Kumar, P.; Nielsen, B.; Lynn, K.G. )
1993-01-01
Studies of SiO[sub 2]-Si and metal-oxide-semiconductor (MOS) structures using positrons are summarized and a concise picture of the present understanding of positrons in these systems is provided. Positron annihilation line-shape [ital S] data are presented as a function of the positron incident energy, gate voltage, and annealing, and are described with a diffusion-annihilation equation for positrons. The data are compared with electrical measurements. Distinct annihilation characteristics were observed at the SiO[sub 2]-Si interface and have been studied as a function of bias voltage and annealing conditions. The shift of the centroid (peak) of [gamma]-ray energy distributions in the depletion region of the MOS structures was studied as a function of positron energy and gate voltage, and the shifts are explained by the corresponding variations in the strength of the electric field and thickness of the depletion layer. The potential role of the positron annihilation technique as a noncontact, nondestructive, and depth-sensitive characterization tool for the technologically important, deeply buried interface is shown.
10. Antiproton annihilations in nuclei
SciTech Connect
McGaughey, P.L.; Bol, K.D.; Clover, M.R.; DeVries, R.M.; DiGiacomo, N.J.; Kapustinsky, J.S.; Smith, G.R.; Sunier, J.W.; Sondheim, W.E.; Yariv, Y.
1985-01-01
Recent results from LEAR experiment PS187 are presented. Preliminary data for the inclusive production of ..pi../sup +/, K/sup +/, and p from the annihilation of 180 MeV antiprotpns in /sup 28/Si and /sup 238/U are compared with predictions of intranuclear cascade calculations. Proton and pion production data are well reproduced by the calculations, but kaon yields at low momenta appear to be strongly suppressed in the experimental data. 8 refs., 5 figs.
11. Theoretical calculation of positron affinities of solute clusters in aluminum alloys
Mizuno, Masataka; Araki, Hideki; Shirai, Yasuharu
2016-01-01
We have performed theoretical calculations of positron states for solute clusters in aluminum alloys to estimate the positron affinity of solute clusters. Positron states of solute clusters in aluminum alloys were calculated under the electronic structures obtained by first- principles molecular orbital calculations using Al158-X13 clusters. We defined the positron affinity of the solute clusters by the difference in the lowest potential sensed by positrons between the solute clusters and Al bulk. With increasing atomic number of 3d metals, the annihilation fraction of the solute clusters rapidly increases at Mn and shows a maximum at Ni. A similar trend is observed for 4d metals. The localization of positron at the solute clusters mainly arises from charge transfer from Al matrix to solute clusters. The positron affinity defined in this work well represents the localization of positron at the solute clusters in aluminum alloys.
12. Compact Beta Particle/Positron Imager for Plant Biology
SciTech Connect
Weisenberger, Andrew; Lee, Seung Joon; McKisson, John; Xi, Wenze; Zorn, Carl; Stolin, Alexander; Majewski, Stan; Majewski, Stanislaw; Howell, Calvin; Crowell, Alec; Smith, Mark
2011-06-01
The 11CO2 tracer is used to facilitate plant biology research towards optimization of plant productivity, biofuel development and carbon sequestration in biomass. Positron emission tomography (PET) imaging has been used to study carbon transport in live plants using 11CO2. Plants typically have very thin leaves resulting in little medium for the emitted positrons to undergo an annihilation event. For the emitted positron from 11C decay approximately 1mm of water equivalent material is needed for positron annihilation. Thus most of the positrons do not annihilate inside the leaf, resulting in limited sensitivity for PET imaging. To address this problem we have developed a compact beta-positive beta-minus particle (BPBM) imager for 11CO2 leaf imaging. The detector is based on a Hamamatsu H8500 position sensitive photomultiplier tube optically coupled via optical grease and a 3mm thick glass plate to a 0.5mm thick Eljin EJ-212 plastic scintillator. The detector is equipped with a flexible arm to allow its placement and orientation on the leaf of the plant of interest while maintaining the leaf's original orientation. We are planning to utilize the imaging device at the Duke University Phytotron to investigate dynamic carbon transport differences between invasive and native species.
13. Vacancy-type defects induced by grinding of Si wafers studied by monoenergetic positron beams
SciTech Connect
Uedono, Akira; Yoshihara, Nakaaki; Mizushima, Yoriko; Kim, Youngsuk; Nakamura, Tomoji; Ohba, Takayuki; Oshima, Nagayasu; Suzuki, Ryoichi
2014-10-07
Vacancy-type defects introduced by the grinding of Czochralski-grown Si wafers were studied using monoenergetic positron beams. Measurements of Doppler broadening spectra of the annihilation radiation and the lifetime spectra of positrons showed that vacancy-type defects were introduced in the surface region (<98 nm), and the major defect species were identified as (i) relatively small vacancies incorporated in dislocations and (ii) large vacancy clusters. Annealing experiments showed that the defect concentration decreased with increasing annealing temperature in the range between 100 and 500°C. After 600–700°C annealing, the defect-rich region expanded up to about 170 nm, which was attributed to rearrangements of dislocation networks, and a resultant emission of point defects toward the inside of the sample. Above 800°C, the stability limit of those vacancies was reached and they started to disappear. After the vacancies were annealed out (900°C), oxygen-related defects were the major point defects and they were located at <25 nm.
14. Quark flavor identification in electron-positron annihilation
SciTech Connect
Kaye, H.S.
1983-09-01
The theoretical issues relevant to inclusive muon analysis, the MAC detector and its data flow structure, the identification of muons in hadronic events and the measurement of their momenta, and the selection of events so as to minimize background are described. Experimental results are presented describing the fragmentation of heavy quarks into hadrons, the semimuonic branching fractions of the heavy quarks, the asymmetry in the angular distribution of the heavy quarks, and the invariant mass and charged multiplicity of heavy quark jets. In addition, lower limits are set on the masses of certain proposed particles that are expected to decay semileptonically. Finally, events containing two muons are analyzed in order to investigate the possibility of mixing in the B-B system and whether the b might form its own SU(2) singlet.
15. Three Dimensional Positron Annihilation Momentum Spectroscopy of Lithium Tetraborate Crystals
DTIC Science & Technology
2013-03-21
defect analysis and will complement other characterization methods such as X-ray fluorescence (XRF), cathodoluminescence, thermoluminescence , and...candidate for high-sensitivity thermoluminescence dosimetry applications. Figure 5 shows a diagram of the basic structural component of the crystal
16. Analytical positron range modelling in heterogeneous media for PET Monte Carlo simulation.
PubMed
Lehnert, Wencke; Gregoire, Marie-Claude; Reilhac, Anthonin; Meikle, Steven R
2011-06-07
Monte Carlo simulation codes that model positron interactions along their tortuous path are expected to be accurate but are usually slow. A simpler and potentially faster approach is to model positron range from analytical annihilation density distributions. The aims of this paper were to efficiently implement and validate such a method, with the addition of medium heterogeneity representing a further challenge. The analytical positron range model was evaluated by comparing annihilation density distributions with those produced by the Monte Carlo simulator GATE and by quantitatively analysing the final reconstructed images of Monte Carlo simulated data. In addition, the influence of positronium formation on positron range and hence on the performance of Monte Carlo simulation was investigated. The results demonstrate that 1D annihilation density distributions for different isotope-media combinations can be fitted with Gaussian functions and hence be described by simple look-up-tables of fitting coefficients. Together with the method developed for simulating positron range in heterogeneous media, this allows for efficient modelling of positron range in Monte Carlo simulation. The level of agreement of the analytical model with GATE depends somewhat on the simulated scanner and the particular research task, but appears to be suitable for lower energy positron emitters, such as (18)F or (11)C. No reliable conclusion about the influence of positronium formation on positron range and simulation accuracy could be drawn.
17. Some Annihilating Particle Systems.
Balding, David
Available from UMI in association with The British Library. Requires signed TDF. Systems of annihilating and coalescing particles on both infinite and periodic one-dimensional state spaces are studied. These systems have various applications in the physical sciences, in particular they are useful as simple models of diffusion-limited reactions. A unified approach to computing properties of the systems using duality methods is presented and it is shown that many results in the scientific literature, derived using diverse techniques, are readily obtained in this general framework. The transition distributions of the processes with arbitrary initial configurations are characterized in terms of two-particle annihilation processes. Further, a concise expression for the distribution of the cardinality of the processes with finite initial configurations is given and particular cases of interest from the applications perspective are described in detail. Asymptotic site occupancies, previously known for certain classes of initial configurations, are derived for all spatially stationary configurations. The asymptotic spatial structure is described for many cases by showing convergence to point processes whose properties are given.
18. Eternal annihilations: New constraints on long-lived particles from big-bang nucleosynthesis
Frieman, Joshua A.; Kolb, Edward W.; Turner, Michael S.
1990-05-01
In the early Universe, the relative abundance of a massive weakly interacting particle species freezes out'' when the annihilation rate becomes less than the expansion rate. Although ineffective in reducing the total number of the species, occasional annihilations still occur after freeze-out. The residual annihilations of massive particles (10 MeV<~mX<~1 GeV) after primordial nucleosynthesis can strongly alter the light-element abundances through photodissociation. For particles with typical weak-interaction cross sections and lifetimes τX>~5×106 sec, we find that the mass range mX<~1 GeV is ruled out, independent of how they subsequently decay.
19. Compact conscious animal positron emission tomography scanner
DOEpatents
Schyler, David J.; O'Connor, Paul; Woody, Craig; Junnarkar, Sachin Shrirang; Radeka, Veljko; Vaska, Paul; Pratte, Jean-Francois; Volkow, Nora
2006-10-24
A method of serially transferring annihilation information in a compact positron emission tomography (PET) scanner includes generating a time signal for an event, generating an address signal representing a detecting channel, generating a detector channel signal including the time and address signals, and generating a composite signal including the channel signal and similarly generated signals. The composite signal includes events from detectors in a block and is serially output. An apparatus that serially transfers annihilation information from a block includes time signal generators for detectors in a block and an address and channel signal generator. The PET scanner includes a ring tomograph that mounts onto a portion of an animal, which includes opposing block pairs. Each of the blocks in a block pair includes a scintillator layer, detection array, front-end array, and a serial encoder. The serial encoder includes time signal generators and an address signal and channel signal generator.
20. Positrons and Antiprotons in Galactic Cosmic Rays
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https://www.coursehero.com/file/71478352/%D8%AD%D8%B3%D8%A7%D8%A8-%D8%A7%D9%84%D8%AA%D9%83%D8%A7%D9%85%D9%84-%D8%A7%D9%84%D8%BA%D8%A7%D9%85%D8%AF%D9%8Apdf/
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# u062du0633u0627u0628...
• 207
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This preview shows page 1 out of 207 pages.
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https://brilliant.org/problems/all-even-2/
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# All Even
If $$\dfrac{n}{2}$$ is an even number, then $$n(n^{2}-1)$$ must be divisible by which of the following numbers?
×
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https://hiof.brage.unit.no/hiof-xmlui/browse?value=Kvaal,%20Knut&type=author
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Viser treff 1-1 av 1
• Evaluating Flood Exposure for Properties in Urban Areas Using a Multivariate Modelling Technique
(Journal article; Peer reviewed, 2017)
Urban flooding caused by heavy rainfall is expected to increase in the future. The main purpose of this study was to investigate the variables characterizing the placement of a house, which seem to have an impact when it ...
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http://mathhelpforum.com/advanced-algebra/138212-homomorphism-a4.html
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# Math Help - homomorphism from A4
1. ## homomorphism from A4
Show that
(1) there is no homomorphism from A4 onto a group of order 2, 4, or 6
(2) there is a homomorphism from A4 onto a group of order 3.
Can anyone please give me some hints ?
2. Let's see some work for the first one.
Originally Posted by xmcestmoi
(2) there is a homomorphism from A4 onto a group of order 3.
Can anyone please give me some hints ?
How much do you know about $A_4$? A (moderately) common fact is that $A_4$ has only one subgroup of order four (namely $\{e, (12)(34), (13)(24), (14)(23)\}=N$). But, it is fairly easy to prove that since $N$ is the only subgroup of order four and conjugation by any element of that subgroup (i.e. $gNg^{-1}$) is another subgroup of order four that $N$ must be invariant under conjugation. Thus, $N\unlhd A_4$. So, the canonical homomorphism is $\theta:G\to G/N$ given by $g\mapsto gN$. This is a surjective homomorphism and $|G/N|=[G:N]=\frac{12}{4}=3$
3. Thank you !!
4. Now I'm curious. How do you know there's no homorphism onto groups with order 4 or 6?
|
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|
https://www.physicsforums.com/threads/at-what-point-would-we-stop-seeing-a-star.869378/
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# At what point would we stop seeing a star?
• B
• Thread starter thetexan
• Start date
• #1
250
8
The universe is expanding and at some point faster than light so once it reaches that point we wont see the light from those stars. I forget what this point is called.
If someone happened to be watching a star as it crossed that point would we see it simply blink out or close to that or would it kind of fade away to blackness. It seems to me that there should be a precise point where the speed of light is reached and one mile an hour faster than that would stop us from seeing it.
Of course since the star is huge the light from the leading edge of the star would be the first to go out then it would progress to the trailing edge so maybe it would not quite be a blink but close to it.
Am I thinking right?
tex
## Answers and Replies
• #2
George Jones
Staff Emeritus
Science Advisor
Gold Member
7,413
1,054
The universe is expanding and at some point faster than light so once it reaches that point we wont see the light from those stars. I forget what this point is called.
Care is needed with respect to the definition of "speed" in a cosmological setting.
this isn't true. It is true that recession speeds of galaxies that we now see will eventually exceed c, but it is not true that we loose sight of a galaxy once its recession speed exceeds c. If we see a galaxy now, then we will (in principle) always see the galaxy, even when its recession speed exceeds c.
Suppose we now see galaxy A. Assume that at time t in the future, A's recession speed is greater than c, and that at this time someone in galaxy A fires a laser pulse directly at us. Even though the pulse is fired directly at us, the proper distance between us and the pulse will initially increase. After a while, however, the pulse will "turn around", and the proper distance between us and the pulse will decrease, and the pulse will reach us, i.e., we still see galaxy A.
This can happen because the Hubble constant decreases with time (more on this near the end of this post) in the standard cosmological model for our universe. Consider the following diagram:
Code:
O B A C
* * * *
* * * *
O B A C
The bottom row of asterisks represents the positions in space (proper distances) of us (O) and galaxies B, A, and C, all at the same instant of cosmic time, $t_e$. The top row of asterisks represents the positions in space of us (O) and galaxies B, A, and C, all at some later instant of cosmic time, $t$. Notice that space has "expanded" between times $t_e$ and $t$.
Suppose that at time $t_e$: 1) galaxy A has recession speed (from us) greater than c; 2) galaxy A fires a laser pulse directed at us. Also suppose that at time $t$, galaxy B receives this laser pulse. In other words, the pulse was emitted from A in the bottom row and received by B in the top row. Because A's recession speed at time $t_e$ is greater than c, the pulse fired towards us has actually moved away from us between times $t_e$ and $t$.
Now, suppose that the distance from us to galaxy B at time $t$ is the same as the distance to galaxy C at time $t_e$. Even though the distances are the same, the recession speed of B at time $t$ is less than than the recession speed of C at time $t_e$ because:
1) recession speed equals the Hubble constant multiplied by distance;
2) the value of the Hubble constant decreases between times $t_e$ and $t$.
Since A's recession speed at time $t_e$ is greater than c, and galaxy C is farther than A, galaxy C's recession speed at time $t_e$ also is greater than c. If, however, the Hubble constant decreases enough between times $t_e$ and $t$, then B's recession speed at time $t$ can be less than c. If this is the case, then at time $t$ (and spatial position B), the pulse is moving towards us, i.e., the pulse "turned around" at some time between times $t_e$ and $t$.
If the value of the Hubble constant changes with time, what does the "constant" part of "Hubble constant" mean? It means constant in space. At time $t_e$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. At time $t$, galaxies O, B, A, and C all perceive the same value for the Hubble constant. But these two values are different.
Probably some of my explanation is unclear. If so, please ask more questions.
• #3
727
168
Since the speed of recession is approaching the speed of light the star would be red-shifting. The horizon of the Universe behave very much like a black hole event horizon, the star would appear frozen at the horizon and red shift out of existence.
• #4
Jorrie
Science Advisor
Gold Member
1,132
106
Since the speed of recession is approaching the speed of light the star would be red-shifting. The horizon of the Universe behave very much like a black hole event horizon, the star would appear frozen at the horizon and red shift out of existence.
This is not quite correct. The distance to the cosmological horizon D_Hor is larger than the Hubble radius R, where the recession rate equals c.
They only approach each other in the far future, when H becomes constant. Distant stars were always moving through the Hubble radius and we will see them farther and farther away, just red-shifting out of detectability, but never "frozen" at the horizon.
#### Attachments
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• #5
Jorrie
Science Advisor
Gold Member
1,132
106
does there come a point when matter becomes to dense that light cant reflect through it? pluto reflecting through over 3billion miles of matter,
What do you mean by "light reflect through it"? And what matter are you referring to?
• #6
3,379
944
If someone happened to be watching a star as it crossed that point would we see it simply blink out or close to that or would it kind of fade away to blackness.
Your second idea is right.
It will be seen to red shift increasingly until it become indistinguishable from background noise.
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http://mathematica.stackexchange.com/questions/54891/get-part-of-lousy-data
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# Get part of lousy data
I want to get part of large data. some part of this data is as follows:
data = {{"(100)", -0.033716509, -0.19824611,
"(101)", -0.026845098, -0.18296293,
"(102)", -0.021913837, -0.17231199}, {"(103)", -0.015043555,
-0.16745934, "(104)", -0.0076064845, -0.16494502,
"(105)", -1.1449175*^-15, -0.16417456}, {"(106)",
0.0076064845, -0.16494502, "(107)", 0.015043555, -0.16745934,
"(108)", 0.021913837, -0.17231199}, {"(109)",
0.026845098, -0.18296293, "(110)", 0.033716509, -0.19824611,
"(111)", -0.054776429, -0.23685639}, {"(112)", -0.042058374,
-0.20053958, "(113)", -0.029721072, -0.19132756,
"(114)", -0.019094091, -0.18620841}, {"(115)", -0.0093881514,
-0.18374386, "(116)", -1.4016566*^-15, -0.18296576, "(117)",
0.0093881514, -0.18374386}, {"(118)",
0.019094091, -0.18620841, "(119)", 0.029721072, -0.19132756,
"(120)", 0.042058374, -0.20053958}, {"(121)",
0.054776429, -0.23685639, "("}, {}, {"ELE", "CENTROID",
"CARTESIAN", "STRESSES", "PRIN", "STRESSES", "PRIN", "STRAINS",
"PRINCIPAL", "STRAINS", "YM"}};
I want to get the elements starting from "(111)" to {}. I prefer not to use Flatten simply because I want the output to match the elements levels (but if Flatten is need that is ok). the lists between "(111)" to {} is a variable and can be more or less. what is the best pattern that can take the elements from "(111)" to {}?
Note: This set of data is repeated multiple times in the large data list and I want them all.
Many thanks.
-
Interesting problem given the need to preserve structure. The first idea that comes to mind:
pull[data_, s_, f_] := data /. {___, {___, s, a___}, b___, f, ___} :> {{s, a}, b, f}
Test:
pull[data, "(111)", {}]
{{"(111)", -0.0547764, -0.236856}, {"(112)", -0.0420584, -0.20054,
"(113)", -0.0297211, -0.191328,
"(114)", -0.0190941, -0.186208}, {"(115)", -0.00938815, -0.183744,
"(116)", -1.40166*10^-15, -0.182966, "(117)", 0.00938815, -0.183744}, {"(118)",
0.0190941, -0.186208, "(119)", 0.0297211, -0.191328, "(120)",
0.0420584, -0.20054}, {"(121)", 0.0547764, -0.236856, "("}, {}}
From your updated question I think you will want:
pullAll[data_, s_, f_] :=
Cases[data, {___, {___, s, a___}, b___, f, ___} :> {{s, a}, b, f}, {0, -3}]
The levelspec {0, -3} will cover everything from the entire expression (as used here) to the deepest level at which it is possible for the pattern to match. If you can narrow the range further it will likely improve performance.
-
+1 for this one :) – Mike Honeychurch Jul 15 '14 at 9:38
Thanks, @Mike ! :D – Mr.Wizard Jul 15 '14 at 9:39
+1 from me also :) – Algohi Jul 15 '14 at 9:39
@Mr.Wizard can this answer be used in large data where same data above is repeated (the only difference is the numbers not the strings)? I am thinking to use this pattern with Cases. – Algohi Jul 15 '14 at 9:52
@Algohi The only way to know is to try it an see. :^) It should work if the data has the same structure, assuming I understand it. What do you mean about using the pattern with Cases? – Mr.Wizard Jul 15 '14 at 9:54
PullAll[data_, s_] :=
DeleteDuplicates@Cases[data, {___, s, a__} :> {s, a}]~Join~
Most@DeleteCases[data, {a_ /; ToExpression@a < ToExpression@s, __}];
PullAll[data, "(116)"]
{{"(116)", -1.40166*10^-15, -0.182966, "(117)", 0.00938815, -0.183744}, {"(118)", 0.0190941, -0.186208, "(119)", 0.0297211, -0.191328, "(120)", 0.0420584, -0.20054}, {"(121)", 0.0547764, -0.236856, "("}, {}}
-
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https://astronomy.stackexchange.com/questions/38785/why-both-sunrise-and-sunset-use-the-position-of-the-suns-upper-limb
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Why both sunrise and sunset use the position of the sun's upper limb?
It is my understanding, that astronomical moments of both rise and set use the relative position of background object's upper limb to the foreground object's horizon.
When were these definitions formulated?
Is this done purely because sunrise and sunset are the main examples of such events and it is easier for the naked eye to tell when sun is completely below horizon?
Wouldn't this offset the symmetry of rotations (since the "day" is always longer than the "night" by the duration it takes the background object to move fully below the foreground horizon)?
• I would guess that then the upper limb disappears the light simply disappears even if visibility is poor. If you want to determine when the lower limb touches, it requires much better imaging perhaps. e.g. 01:30 here: youtu.be/lwus2nqU0SY Compare to the funny business at the bottom of the moon making it difficult to determine when it last touches the horizon here youtu.be/LEH0WmCZTAo
– uhoh
Sep 9 '20 at 4:44
• Ya, that might in fact be right and my guess is wrong!
– uhoh
Sep 9 '20 at 7:06
When were these definitions formulated?
Multiple religions have rather strict requirements based on sunrise / sunset, for example, when one must start or can stop fasting, or when exactly to sacrifice a lamb (or a human in some religions). The definition has very deep roots.
Is this done purely because sunrise and sunset are the main examples of such events and it is easier for the naked eye to tell when sun is completely below horizon?
Yes.
Wouldn't this offset the symmetry of rotations (since the "day" is always longer than the "night" by the duration it takes the background object to move fully below the foreground horizon)?
Daytime is not longer than nighttime in the middle of winter, in places that do have winter. The definition of sunrise and sunset does make daytime be a bit longer than nighttime on the equinoxes.
Suppose sunrise was instead defined as the time at which the entire Sun first appears above the horizon and sunset was instead defined as the time at which the first bit of the Sun drops below the horizon. Even with these extreme definitions, daytime would still last longer than nighttime on the equinoxes thanks to atmospheric refraction.
• The skew towards longer day than night at equinoxes is also - and even more - by the effect of refraction, that is the sun is physically already below the horizon but the atmosphere still bends the sun rays towards the observer. This effect is around arc minutes, thus bigger than the sun's diameter. Sep 9 '20 at 10:20
• @planetmaker - That is exactly what the last paragraph in the answer addresses. Sep 9 '20 at 18:49
• timeanddate.com/astronomy/refraction.html has a nice picture showing the apparent sun and astronomical sun, and states that the difference may be "several minutes". It would be nice to have some kind of typical value or range here. Sep 10 '20 at 23:00
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https://www.andrewheiss.com/blog/2021/12/18/bayesian-propensity-scores-weights/
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# How to use Bayesian propensity scores and inverse probability weights
For mathematical and philosophical reasons, propensity scores and inverse probability weights don’t work in Bayesian inference. But never fear! There’s still a way to do it!
r
tidyverse
regression
statistics
data visualization
causal inference
do calculus
DAGs
bayes
brms
stan
Author
Published
Saturday, December 18, 2021
This post combines two of my long-standing interests: causal inference and Bayesian statistics. I’ve been teaching a course on program evaluation and causal inference for a couple years now and it has become one of my favorite classes ever. It has reshaped how I do my research, and I’ve been trying to carefully incorporate causal approaches in my different project—as evidenced by an ever-growing series of blog posts here about different issues I run into and figure out (like this and this and this and this.)
Additionally, ever since stumbling on this blog post as a PhD student back in 2016 following the invention of rstanarm and brms, both of which make it easy to use Stan with R, I’ve been as Bayesian as possible in all my research. I find Bayesian approaches to inference way more intuitive than frequentist null hypothesis significance testing. My work with Bayesian approaches has also led to a bunch of blog posts here (like this and this and this).
However, the combination of these two interests is a little fraught. In one of my projects, I’m using marginal structural models and inverse probability weights to account for confounding and make causal claims. I also want to do this Bayesianly so that I can work with posterior distributions and use Bayesian inference rather than null hypotheses and significance. But using inverse probability weights and Bayesian methods simultaneously seems to be impossible! Robins, Hernán, and Wasserman (2015) even have an article where they explicitly say that “Bayesian inference must ignore the propensity score,” effectively making it impossible to use things like inverse probability weights Bayesianly. Oh no!
I recently came across a new article that gives me hope though! There’s a group of epidemiologists and biostatisticians who have been working on finding ways to use a Bayesian approach to propensity scores and weights (Saarela et al. (2015); Zigler (2016); Liao and Zigler (2020), among others), and Liao and Zigler (2020) provide a useful (and understandable!) approach for doing it. This post is my attempt at translating Liao and Zigler’s paper from conceptual math and MCMCPack-based R code into tidyverse, brms, and Stan-based code. Here we go!
## Who this post is for
Here’s what I assume you know:
• You’re familiar with R and the tidyverse (particularly dplyr and ggplot2).
• You’re familiar with brms for running Bayesian regression models. See the vignettes here, examples like this, or resources like these for an introduction.
• You know a little about DAGs and causal model-based approaches to causal inference, and you’ve heard about statistical adjustment to isolate causal effects (i.e. “closing backdoors in a DAG”)
## General approach to inverse probability weighting
I won’t go into the details of how inverse probability weighting works here. For more details, check out this fully worked out example or this chapter, which has references to lots of other more detailed resources. Instead, I’ll provide a super short abbreviated overview of how inverse probability weights are used for causal inference and why and how we can use them.
When trying to make causal inferences with observational data, there is inevitably confounding—people self-select into (or out of) treatment conditions because of a host of external factors. We can adjust for these confounding factors with lots of different methods. Quasi-experimental approaches like difference-in-differences, regression discontinuity, and instrumental variables let us use specific (and often weird) situations to adjust for confounding and make comparable treatment and control groups. Alternatively, we can use model-based inference using DAGs and do-calculus, identifying which variables open up backdoor pathways between treatment and outcome, and statistically adjusting for those variables to isolate the treatment → outcome pathway.
One way to adjust for confounders is to use inverse probability weighting. In short, here’s how it works for a binary (0/1) treatment:
1. Create a model that predicts treatment (often called a treatment model or design stage). Use confounders (identified with a DAG) as the covariates. Use whatever modeling approach you want here—logistic regression, random forests, fancy machine learning things, etc.
2. Use the results of the treatment model to calculate propensity scores.
3. Convert those propensity scores into inverse probability of treatment weights (IPTW) using this formula:
$\frac{\text{Treatment}}{\text{Propensity}} + \frac{1 - \text{Treatment}}{1 - \text{Propensity}}$
4. Create a model that estimates the effect of treatment on outcome, weighted by the IPTWs (often called an outcome model or analysis stage). The coefficient for the treatment variable is the average treatment effect (ATE).
### Basic frequentist example
Throughout this post, we’ll use some simulated data for a fake hypothetical social program that distributes mosquito nets in order to reduce malaria risk. I created this data for my course on program evaluation and causal inference and use it for teaching adjustment with inverse probability weighting.
library(tidyverse)
library(brms)
library(broom)
library(broom.mixed)
library(ggdag)
library(MetBrewer)
set.seed(3273) # From random.org
# Use the delightful Isfahan1 palette from the MetBrewer package
isfahan <- MetBrewer::met.brewer("Isfahan1")
# Custom ggplot theme to make pretty plots
# Get Archivo Narrow at https://fonts.google.com/specimen/Archivo+Narrow
theme_nice <- function() {
theme_minimal(base_family = "Archivo Narrow") +
theme(panel.grid.minor = element_blank(),
plot.background = element_rect(fill = "white", color = NA),
plot.title = element_text(face = "bold"),
axis.title = element_text(face = "bold"),
strip.text = element_text(face = "bold", size = rel(0.8), hjust = 0),
strip.background = element_rect(fill = "grey80", color = NA),
legend.title = element_text(face = "bold"))
}
# Use this theme on all plots
theme_set(
theme_nice()
)
# Make all labels use Archivo by default
update_geom_defaults("label",
list(family = "Archivo Narrow",
fontface = "bold"))
nets <- read_csv("https://evalf21.classes.andrewheiss.com/data/mosquito_nets.csv")
I normally use a more complicated DAG with other nodes that don’t need to be adjusted for, but for the sake of simplicity here, this DAG only includes the confounders. The relationship between net usage (measured as a 0/1 binary variable where 1 = person used a net) and malaria risk (measured on a scale of 0-100, with higher values representing higher risk) is confounded by monthly income (in USD), health (measured on a scale of 0-100, with higher values representing better health), and nighttime temperatures at the person’s home (measured in Celsius).
mosquito_dag <- dagify(
malaria_risk ~ net + income + health + temperature,
net ~ income + health + temperature,
health ~ income,
exposure = "net",
outcome = "malaria_risk",
coords = list(x = c(malaria_risk = 7, net = 3, income = 4, health = 5, temperature = 6),
y = c(malaria_risk = 2, net = 2, income = 3, health = 1, temperature = 3)),
labels = c(malaria_risk = "Risk of malaria", net = "Mosquito net", income = "Income",
health = "Health", temperature = "Nighttime temperatures",
resistance = "Insecticide resistance")
)
# Turn DAG into a tidy data frame for plotting
mosquito_dag_tidy <- mosquito_dag %>%
tidy_dagitty() %>%
node_status() # Add column for exposure/outcome/latent
status_colors <- c(exposure = isfahan[2], outcome = isfahan[7], latent = "grey50")
# Fancier graph
ggplot(mosquito_dag_tidy, aes(x = x, y = y, xend = xend, yend = yend)) +
geom_dag_edges() +
geom_dag_point(aes(color = status)) +
geom_label(aes(label = label, fill = status),
color = "white", fontface = "bold", nudge_y = -0.3) +
scale_color_manual(values = status_colors, na.value = "grey20") +
scale_fill_manual(values = status_colors, na.value = "grey20") +
guides(color = "none", fill = "none") +
theme_dag()
Following the logic of do-calculus, we need to adjust for three of these nodes in order to isolate the pathway between net usage and malaria risk:
library(dagitty)
## { health, income, temperature }
We can adjust for these variables using inverse probability weighting. We’ll first make a treatment model (or “design stage” in the world of biostats) that uses these confounders to predict net use, then we’ll create propensity scores and inverse probability treatment weights, and then we’ll use those weights in an outcome model (or “analysis stage” in the world of biostats) to calculate the average treatment effect (ATE) of net usage.
I built in a 10 point decrease in malaria risk due to nets (hooray for fake data!), so let’s see if we can recover that treatment effect:
# Step 1: Create model that predicts treatment status using confounders
model_treatment_freq <- glm(net ~ income + temperature + health,
data = nets,
# Step 2: Use the treatment model to calculate propensity scores, and
# Step 3: Use the propensity scores to calculate inverse probability of treatment weights
nets_with_weights <- augment(model_treatment_freq, nets,
type.predict = "response") %>%
rename(propensity = .fitted) %>%
mutate(iptw = (net_num / propensity) + ((1 - net_num) / (1 - propensity)))
# Step 4: Use the IPTWs in a model that estimates the effect of treatment on outcome
model_outcome_freq <- lm(malaria_risk ~ net,
data = nets_with_weights,
weights = iptw)
# Coefficient for net should be -10ish
tidy(model_outcome_freq)
## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 39.7 0.468 84.7 0
## 2 netTRUE -10.1 0.658 -15.4 3.21e-50
It worked! After going through this two-step process of (1) creating propensity scores and weights, and (2) using those weights to estimate the actual effect, we successfully closed the backdoor pathways that confounded the relationship between net use and malaria risk, ending up with an unbiased ATE. Neato.
### Pseudo-populations
Before looking at how to do this analysis Bayesianly, it’s helpful to understand what these weights are actually doing behind the scenes. The point of these IPTWs is to create pseudo-populations of treated and untreated observations that are comparable across all the different levels of confounders. They’re essentially a way to let us fake treatment and control groups so that we can interpret the results of outcome models causally.
Visualizing the propensity scores for treated and untreated people can help show what’s going on. Here are the distributions of propensity scores for these two groups: the treated group is in the top half in brown; the untreated group is in the bottom half in turquoise. (Thanks to Lucy D’Agostino McGowan for this really neat way of looking at weight distributions!)
ggplot() +
geom_histogram(data = filter(nets_with_weights, net_num == 1),
bins = 50, aes(x = propensity),
fill = isfahan[2]) +
geom_histogram(data = filter(nets_with_weights, net_num == 0),
bins = 50, aes(x = propensity, y = -..count..),
fill = isfahan[6]) +
geom_hline(yintercept = 0) +
annotate(geom = "label", x = 0.1, y = 20, label = "Treated",
fill = isfahan[2], color = "white", hjust = 0) +
annotate(geom = "label", x = 0.1, y = -20, label = "Untreated",
fill = isfahan[6], color = "white", hjust = 0) +
scale_y_continuous(label = abs) +
coord_cartesian(xlim = c(0.1, 0.8), ylim = c(-80, 100)) +
labs(x = "Propensity", y = "Count")
## Warning: The dot-dot notation (..count..) was deprecated in ggplot2 3.4.0.
## ℹ Please use after_stat(count) instead.
We can learn a few different things from this plot. Fewer people received the treatment than didn’t—there are more people in the untreated part of the graph. We can confirm this really quick:
nets %>% count(net)
## # A tibble: 2 × 2
## net n
## <lgl> <int>
## 1 FALSE 1071
## 2 TRUE 681
Yep. There are ≈400 more net-non-users than net-users.
We can also see that those who did not receive treatment tend to have a lower probability of doing so—the bulk of the untreated distribution is clustered in the low end of propensity scores. This makes sense! If people have a low chance of using a mosquito net, there should be fewer people ultimately using a bed net.
But these two groups—treated and untreated—aren’t exactly comparable at this point. There are confounding factors that make people who didn’t use nets less likely to use them. To make causal inferences about the effect of nets, we’d need to look at a “treatment” and a “control” group with similar characteristics and with similar probabilities of using nets.
To get around this, we can create two pseudo-populations of treated and untreated people. We can give less statistical importance (or weight) to those who had a low probability of being treated and who subsequently weren’t treated (since there are a ton of those people) and more statistical weight to those who had a high probability of being treated but weren’t. Similarly, we can give more weight to treated people who had a low probability of being treated (that’s surprising!) and less weight to treated people who had a high probability of being treated (that’s not surprising!). If we scale each person by their weight, given the confounders of income, temperature, and health, we can create comparable treated and untreated populations:
ggplot() +
geom_histogram(data = filter(nets_with_weights, net_num == 1),
bins = 50, aes(x = propensity, weight = iptw),
fill = colorspace::lighten(isfahan[2], 0.35)) +
geom_histogram(data = filter(nets_with_weights, net_num == 0),
bins = 50, aes(x = propensity, weight = iptw, y = -..count..),
fill = colorspace::lighten(isfahan[6], 0.35)) +
geom_histogram(data = filter(nets_with_weights, net_num == 1),
bins = 50, aes(x = propensity),
fill = isfahan[2]) +
geom_histogram(data = filter(nets_with_weights, net_num == 0),
bins = 50, aes(x = propensity, y = -..count..),
fill = isfahan[6]) +
annotate(geom = "label", x = 0.8, y = 70, label = "Treated (actual)",
fill = isfahan[2], color = "white", hjust = 1) +
annotate(geom = "label", x = 0.8, y = 90, label = "Treated (IPTW pseudo-population)",
fill = colorspace::lighten(isfahan[2], 0.35), color = "white", hjust = 1) +
annotate(geom = "label", x = 0.8, y = -60, label = "Untreated (actual)",
fill = isfahan[6], color = "white", hjust = 1) +
annotate(geom = "label", x = 0.8, y = -80, label = "Untreated (IPTW pseudo-population)",
fill = colorspace::lighten(isfahan[6], 0.35), color = "white", hjust = 1) +
geom_hline(yintercept = 0, color = "white", size = 0.25) +
scale_y_continuous(label = abs) +
coord_cartesian(xlim = c(0.1, 0.8), ylim = c(-80, 100)) +
labs(x = "Propensity", y = "Count")
## Warning: Using size aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use linewidth instead.
This plot shows the original distributions for treated and untreated propensities in darker colors and overlays the weighted/adjusted propensities in lighter colors. These pseudo-populations mirror each other pretty well now! These two rescaled and reweighted groups are now much more equally sized and comparable: the low-propensity net users have a much higher weight, while high-propensity non-net users also get more weight.
## Bayesian inverse probability weighting
### Why even do this Bayesianly?
We successfully found the causal effect of -10 malaria risk points using regular frequentist regression, so why am I trying to make life more complex and do this with Bayesian methods instead? Mostly because I’m not a fan of null hypothesis signficance testing (NHST), or the whole process of proposing a null hypothesis, generating a statistical test, finding a p-value, and seeing if the test/p-value/confidence interval provides enough evidence to reject the null hypothesis. With frequentist statistics we test for the probability of the data given a null hypothesis, or $$P(\text{data} \mid H_0)$$, while with Bayesian statistics, we get to test for the probability of a hypothesis given the data, or $$P(H \mid \text{data})$$.
Testing a hypothesis directly with Bayesian inference is a lot more intuitive, with Bayesian credible intervals and inferential approaches like measuring the probability that a parameter is greater/less than 0 (i.e. probability of direction), or measuring the proportion of a posterior that falls within a null region of practical equivalence, or ROPE. See this page for an overview of all these methods and a comparison with frequentism, and check out this amazing (and free!) textbook on Bayesianism in general.
Plus, the amazing brms package lets us make all sorts of powerful and complex models with multilevel nested intercepts and slopes and fancy families like beta, zero-inflated beta, hurdled lognormal, and so on.
### Fundamental problem with Bayesian propensity scores
However, there are serious mathematical and philosophical issues with using propensity scores (and IPTWs) in Bayesian models. Put simply, IPTWs aren’t actually part of the model! They’re a neat way to scale and shift the population into comparable pseudo-populations, but they’re not part of the data-generating process for any element of a Bayesian model.
Here’s how Robins, Hernán, and Wasserman (2015), Zigler (2016), and Liao and Zigler (2020) explain it (but substantially simplified to the point of being a little bit wrong, but acceptably wrong). We can more formally define the average treatment effect (ATE) of mosquito nets on malaria risk using this estimand:
$\Delta_{\text{ATE}} = E[ \overbrace{E \left( Y_i \mid T_i = 1, X_i \right)}^{\substack{\text{Average outcome } Y \text{ when} \\ \text{treated, given confounders }X}} - \overbrace{E \left( Y_i \mid T_i = 0, X_i \right)}^{\substack{\text{Average outcome } Y \text{ when} \\ \text{not treated, given confounders }X}} ]$
There are three moving parts in the equation for the ATE here: the treatment effect is a function of the outcome $$Y$$ (malaria risk), the treatment $$T$$ (nets), and all other covariates $$X$$ (health, income, temperatures). In order to calculate this ATE, we need to create some sort of function that incorporates all three, or something like this that calculates $$\Delta$$ given $$T$$, $$X$$, and $$Y$$:
$f(\Delta \mid \boldsymbol{T}, \boldsymbol{X}, \boldsymbol{Y})$
This works well with Bayesian methods. We don’t know what $$\Delta$$ is, so we can use Bayes’ theorem to estimate it given our existing data for $$T$$, $$X$$, and $$Y$$. To quote from Liao and Zigler (2020),
[T]raditional Bayeisan inference for $$\Delta$$ would follow from specification of a likelihood for $$(\boldsymbol{T}, \boldsymbol{X}, \boldsymbol{Y})$$ conditional on unknown parameters, $$\theta$$, a prior distribution for $$\theta$$, and some function relating the data and $$\theta$$ to the quantity $$\Delta$$.
Note that the equation below is slightly wrong—ordinarily in Bayesian modeling we’re interested in estimating an unknown $$\theta$$ parameter, so if we wanted to be super official we’d need to create “some function relating the data and $$\theta$$ to the quantity $$\Delta$$”, but for the sake of simplicity and intuition we’ll skip that part and pretend that $$\Delta$$ is the output of the model:
$\overbrace{P[\Delta \mid (\boldsymbol{T}, \boldsymbol{X}, \boldsymbol{Y})]}^{\substack{\text{Posterior estimate} \\ \text{of } \Delta \text{, given data}}} \propto \overbrace{P[(\boldsymbol{T}, \boldsymbol{X}, \boldsymbol{Y}) \mid \Delta]}^{\substack{\text{Likelihood for existing} \\ \text{data, given unknown }\Delta}} \times \overbrace{P[\Delta]}^{\substack{\text{Prior} \\ \text{for }\Delta}}$
But guess what’s missing entirely from this equation?! Our weights! Propensity scores and inverse probability weights have no place in this kind of Bayesian estimation. They would theoretically show up in the likelihood part of the Bayesian equation, but in practice, weights aren’t part of the data-generating process and thus aren’t actually part of the likelihood. This is the key problem with Bayesian weights: these weights are not part of the model for calculating the ATE ($$f(\Delta \mid \boldsymbol{T}, \boldsymbol{X}, \boldsymbol{Y})$$). We can’t set a prior on the weight parameter—there isn’t even a weight parameter to work with in the likelihood. In order to be a true Bayesian, we can’t use propensity scores and weighting. This is the argument that Robins, Hernán, and Wasserman (2015) make: because propensity scores (and thus weights) aren’t part of the likelihood, we can’t do anything Bayesian with them.
And that’s disappointing because Bayesian inference is great! I find it far more intuitive (and fun) to make inferences with posterior distributions rather than work with null hypothesis significance testing.
## Things I don’t know yet but want to know!
So, thanks to Liao and Zigler (2020), we have a fully Bayesian treatment/design model and we can incorporate the uncertainty from that model’s propensity scores and weights into the outcome/analysis model. That’s so neat!
However, in their paper Liao and Zigler use a frequentist outcome model, like we just did here. While combining the ATEs from 2,000 different frequentist OLS-based models feels quasi-Bayesian, I don’t know if we can legally talk about these results Bayesianly. Can we pretend that this distribution of ATEs is similar to a posterior distribution and use Bayesian inference rather than null hypothesis significance testing, or do we still need to talk about null hypotheses? These 2,000 models are essentially a mathematical transformation of the posterior, so maybe it’s legal? But the Bayesian model is for predicting treatment, not the outcome, so maybe it’s not legal? idk. (Turns out the answer is no—there’s no uncertainty in the outcome model here, since all the uncertainty comes from the treatment model. Ah! Well. Nevertheless.)
We could technically run a Bayesian outcome model with brm(), but we’d have to run it 2,000 times—one model per set of weights—and that would take literally forever and might melt my computer. There could be a way to only run a single outcome model once and use one set of weights for each of the iterations (i.e. use the first column of propensity scores for the first iteration of the outcome model, the second for the second, and so on), but that goes beyond my skills with brms. (UPDATE: Thanks to Jordan Nafa, this is actually possible! See here!)
## References
Liao, Shirley X., and Corwin M. Zigler. 2020. “Uncertainty in the Design Stage of Two-Stage Bayesian Propensity Score Analysis.” Statistics in Medicine 39 (17): 2265–90. https://doi.org/10.1002/sim.8486.
Robins, James M., Miguel A. Hernán, and Larry Wasserman. 2015. “On Bayesian Estimation of Marginal Structural Models.” Biometrics 71 (2): 296–99. https://doi.org/10.1111/biom.12273.
Rubin, Donald B. 1987. Multiple Imputation for Nonresponse in Surveys. New York: John Wiley & Sons. https://doi.org/10.1002/9780470316696.
Saarela, Olli, David A. Stephens, Erica E. M. Moodie, and Marina B. Klein. 2015. “On Bayesian Estimation of Marginal Structural Models.” Biometrics 71 (2): 279–88. https://doi.org/10.1111/biom.12269.
Zigler, Corwin Matthew. 2016. “The Central Role of Bayes’ Theorem for Joint Estimation of Causal Effects and Propensity Scores.” The American Statistician 70 (1): 47–54. https://doi.org/10.1080/00031305.2015.1111260.
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|
http://mathhelpforum.com/algebra/43220-summer-school.html
|
# Math Help - Summer School
1. ## Summer School
Okay, So I'm in an accelerated Algebra II course for this summer and things just seem to be moving so fast, at first nothing made sense, now I'm beginning to understand certain things but even after reading through purple math and several other sites, I still can't make sense of certain problems. We have a test everyday and since I didn't understand anything the first few days (last week was the first week) My average is now a 68 . However On Friday last week I think I did a little better on the test and today I felt confident as well, but knowing myself I still probably only scored in the 80s.
Now that I'm done ranting...
I'm probable going to post questions in this thread everyday if you don't mind giving me advice I would GREATLY appreciate it.
So for starters, what to do with expressions like this:
3*√x^10 (in case my notation is bad: the cubed root of x to the tenth power)
Next:
Tonight my HW included (and the test tommorrow will include):
-Extracting square roots:
x^2 - 6x +2 =0
I understand how to get to here:
x^2 -6x +9 = 7
but do not understand getting here:
(x-3)^2 = 7
from this step on however I can solve these.
-Complex numbers:
-adding and subtracting is simple enough, just treat "i" like a variable
-Multiplication also doesn't seem that scary if I just remember to take any "i" to the power of 2 and change it to a negative one(i^2=-1).
-division isn't so bad either, just multiply the by the conjugate base.
the problem is with things like this:
3i * (4+5i)^2 = 3i(16+10i+25i^2) =48i+30i^2+75i^3
(4-5i)^2 (4+5i)^2 (1?)
where do I go from here? what exactly happens to the denominator? will it always cancel completely (did it even do that here?)?
And Lastly...
Polynomial equations
???????????
that means like any type of polynomial, solving for x! Some of them I can do, but there are so many different types!
First of all I have no clue what to do when you have a fractional exponent:
4x^3/2 - 8 = 0
the book adds 8 then divides by 4, I'm good up to here:
x^3/2= 2
But what did they do to get the 3/2 onto the two like this:
x=2^2/3
Next up are equations with radicals:
I guess I'm really okay with these, it's just sometimes they pop up in equations and I get confused, I'll list a bunch of equations that confuse me at the end of this (long) post.
WORD PROBLEMS:
A college charters a bus for $1700. 6 more students join and the cost per student drops$7.50. How many students were in original group.
►how to set up and explanation, please!
Complex interest:
deposit of2500, matures to 3052.49 after five years. interest is compounded monthly. how to solve for interest, since its part fraction which is part of a quantity being squared, I get confused.
These are all the types of problems, but there are some specific ones which I can't seem to solve:
36) (3+√-5)(7-√10)
16) 36t^4 + 29t^2-7 =0
36) x + (√31-9x) =5
44) 4√x-3 - √6x-17 =3
52) 4x^2(x-1)^1/3 + 6x(x-1)^4/3
2. Originally Posted by keybowvio
...
So for starters, what to do with expressions like this:
3*√x^10 (in case my notation is bad: the cubed root of x to the tenth power)
You can change this term into: $\sqrt[3]{x^{10}} = \left(x^{10} \right)^{\frac13} = x^{\frac{10}3}$
Next:
...
I understand how to get to here:
x^2 -6x +9 = 7
but do not understand getting here:
(x-3)^2 = 7
from this step on however I can solve these.
You are supposed to know
$(a+b)^2 = a^2+2ab+b^2$ ....... and
$(a-b)^2 = a^2-2ab+b^2$
That means if you have a sum like the RHS of the formulae which represent a complete square you can write it as a square.
the problem is with things like this:
3i * (4+5i)^2 = 3i(16+10i+25i^2) =48i+30i^2+75i^3
(4-5i)^2 (4+5i)^2 (1?)
where do I go from here? what exactly happens to the denominator? will it always cancel completely (did it even do that here?)?
Unfortunately the problem is nearly unreadable ...
Maybe you are asked to simplify
$\frac{3i}{4-5i} = \frac{3i}{4-5i} \cdot \frac{4+5i}{4+5i} = \frac{12i+15i^2}{16-25i^2}=\frac{12i-15}{41}$
And Lastly...
Polynomial equations
...
First of all I have no clue what to do when you have a fractional exponent:
4x^3/2 - 8 = 0
the book adds 8 then divides by 4, I'm good up to here:
x^3/2= 2
But what did they do to get the 3/2 onto the two like this:
x=2^2/3
You have to transform the equation until you have only the unknown to the power of something. Then you want to get the unknown to the power of one. Use the property:
$\left(x^a\right)^{\frac1a} = x^{\frac aa} = x^1 = x$
$\left(x^{\frac32}\right)^{\frac23}= 2^{\frac23}$
$x^1 = \sqrt[3]{4}$
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http://www.ck12.org/physical-science/Deposition-in-Physical-Science/lessonplanx/Changing-State%3A-Freezing/r1/
|
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Deposition
Describes the process where a gas changes directly to a solid without going through the liquid state.
Estimated2 minsto complete
%
Progress
Practice Deposition
MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated2 minsto complete
%
Changing State: Freezing
Gives several experiments and lessons to help students understand freezing.
Open the resource in a new window.
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https://www.therightgate.com/line-integration-electromagnetics/
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Line Integration in Electromagnetics | Definition and Significance
# What is Line Integration in Electromagnetics?
Almost all the Science Pupil are well aware of the term Integration. It is a common term in Mathematics. It also plays a very important role in the theory of Electromagnetics. In this article, I am going to discuss the formal meaning of integration and specifically what is Line Integration and its significance in the Electromagnetics.
In Mathematics, formally the Integration gives the area under the curve. Consider the integration shown in the figure below.
The differential or infinitesimal length is “dx” and corresponding to this small length an infinitesimal rectangular strip is shown. The area of this strip can be considered as multiplication of the value of f(x) at that x and length dx. In the process of integration, we add all such infinitesimal strips from A to B to give the area under the curve.
In Electromagnetics, we deal with various vector fields like Electric field, Magnetic field etc. Consider any such vector field E as shown in the following figure. Say, a line or vector AB is present within that field.
If we want the product of the length of the vector and component of the field along this vector (line) at every point of line then we write the integration as follows: –
This integration is termed as a line integration.
## The significance of Line Integration in Electromagnetics
The formula for work in Electromagnetics is based on the concept of line integration. Say we are moving a charge in the electric field, then work done is calculated by
Basically, the line integration is required when we want to calculate the component or value of any vector field along the given vector path as in Ampere’s law.
## Different types of Differential lengths
In Electromagnetics we deal with Cartesian Coordinate System, Cylindrical Coordinate System, and Spherical Coordinate System. So the infinitesimal length “dl” should be defined in each of the coordinate systems. As we deal with vectors and vector fields in Electromagnetics, “dl” consists of infinitesimal change along each axis of the respective coordinate system.
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http://mathhelpforum.com/pre-calculus/110639-solving-trig-equation.html
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# Math Help - Solving a trig equation?
1. ## Solving a trig equation?
I need to solve the following trig expression:
4cos4θ=0 (reads four cosine four theta)
Its the formula of a graph but i need to find the zeros or the points that it passes through the pole (its a polar graph)
Would i use the double angle formula or find when cos=0 and multiply the period by 4? Im confused
2. I think you are making this more difficult than it really is....
4cos4θ=0
the four is insignificant (because 0/4 is still 0). so now we have:
cos4θ=0.
I think the 4 is confusing you so let x=4θ so now we have:
cosx=0
and the solutions to that is when x=pi/2 or 3pi/2
now substitute 4θ in for x and you have
4θ=pi/2 and 4θ=3pi/2
so dividing by four yields:
θ=pi/8 and θ=3pi/8
Hope that helped!!
3. Also what domain are you looking for solutions in?
The previous post gives the solutions on $x \in \left[0,\frac{\pi}{2}\right]$
You can find all solutions as $x = \frac{(2n+1)\pi}{8}, n\in \mathbb{Z}$
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https://mathhelpboards.com/threads/sequence-with-recursive-definition.2367/
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# sequence with recursive definition?
#### skatenerd
##### Active member
Oct 3, 2012
114
Sorry to spam my problems all over this forum but series have me struggling somewhat. Last problem on my homework is the sequence an defined recursively by:
a1=1
and
an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$
First part was the only part i know how to do. it was to find an for n=1 through 5.
However this next part has me stumped. Assume that:
The limit as n approaches infinity = alpha > 0
Obtain the value alpha by taking the limit of both sides of (1) [(1) is the info given in the beginning].
Now I can already tell this limit is going to $$\sqrt{2}$$ because it is kind of hinted to in the later parts of this problem. However I am kind of confused as to how to approach doing this limit of both sides of an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$ . How would I evaluate this limit when the right side of the equation is in terms of an?
#### MarkFL
Staff member
Feb 24, 2012
13,775
One way (though not as directed by the problem) to demonstrate the sequence converges to $\displaystyle \sqrt{2}$ is to observe that if we begin with the function:
$\displaystyle f(x)=x^2-2=0$
which we know has the positive root $\displaystyle \sqrt{2}$ and apply Newton's method:
$\displaystyle f'(x)=2x$
$\displaystyle x_{n+1}=x_n-\frac{x_n^2-2}{2x_n}$
$\displaystyle x_{n+1}=\frac{2x_n^2-x_n^2+2}{2x_n}$
$\displaystyle x_{n+1}=\frac{x_n^2+2}{2x_n}$
$\displaystyle x_{n+1}=\frac{x_n}{2}+\frac{1}{x_n}$
For any positive initial value, the series will converge to the positive root of the defining function.
#### CaptainBlack
##### Well-known member
Jan 26, 2012
890
Sorry to spam my problems all over this forum but series have me struggling somewhat. Last problem on my homework is the sequence an defined recursively by:
a1=1
and
an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$
First part was the only part i know how to do. it was to find an for n=1 through 5.
However this next part has me stumped. Assume that:
The limit as n approaches infinity = alpha > 0
Obtain the value alpha by taking the limit of both sides of (1) [(1) is the info given in the beginning].
Now I can already tell this limit is going to $$\sqrt{2}$$ because it is kind of hinted to in the later parts of this problem. However I am kind of confused as to how to approach doing this limit of both sides of an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$ . How would I evaluate this limit when the right side of the equation is in terms of an?
If the limit $$\alpha$$ exists and is non-zero then:
$\alpha=(\alpha/2) + (1/\alpha)$
(arrived at by taking limits of both sides of the recursion relation)
CB
#### skatenerd
##### Active member
Oct 3, 2012
114
Oh man thank you to you both. To CaptainBlack, I guess I didn't realize that seeing that if limit of n approaching infinity of an = alpha, then so will the this limit of an+1. Makes sense now! Thanks again.
#### chisigma
##### Well-known member
Feb 13, 2012
1,704
Sorry to spam my problems all over this forum but series have me struggling somewhat. Last problem on my homework is the sequence an defined recursively by:
a1=1
and
an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$
First part was the only part i know how to do. it was to find an for n=1 through 5.
However this next part has me stumped. Assume that:
The limit as n approaches infinity = alpha > 0
Obtain the value alpha by taking the limit of both sides of (1) [(1) is the info given in the beginning].
Now I can already tell this limit is going to $$\sqrt{2}$$ because it is kind of hinted to in the later parts of this problem. However I am kind of confused as to how to approach doing this limit of both sides of an+1= $$\frac{a_n}{2}$$ + $$\frac{1}{a_n}$$ . How would I evaluate this limit when the right side of the equation is in terms of an?
The solving procedure for this type of problems is illustrated in...
http://www.mathhelpboards.com/f15/difference-equation-tutorial-draft-part-i-426/
The difference equation can be written as...
$\displaystyle \Delta_{n}= a_{n+1}-a_{n}= \frac{1}{a_{n}}- \frac{a_{n}}{2} = f(a_{n})$ (1)
The function f(x) has two 'attractive fixed points' in $x=\pm \sqrt{2}$ and, because for both the fixed points the theorem 4.2 is satisfied, roughly specking any initial value >0 will generate a sequence which tends to $+\sqrt{2}$ and any initial value <0 will generate a sequence which tends to $-\sqrt{2}$. An important detail in the case $a_{0}>0$ is that the sequence for any n>0 is decreasing...
Kind regards
$\chi$ $\sigma$
#### skatenerd
##### Active member
Oct 3, 2012
114
My teacher went over this problem recently and showed that it was a funny way of doing a proof of The Newtonian Method. Seeing as it was something we had never learned about before, I guess it was just a little something our teacher threw in to see if we could teach ourselves a concept on our own.
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http://physics.stackexchange.com/users/12549/josh314
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# josh314
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Theoretical physicist turned programmer.
4 Flow of momentum is pressure 3 Gauge fixing and equations of motion 2 Differences between the gravitational constants $G$ and $g$? 2 Does an oscillating electrical monopole radiate? 1 Charged Black holes - What is the Interest in those?
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https://www.physicsforums.com/threads/integration-by-parts-and-substitution-help.295186/
|
# Integration by parts and substitution help
• Start date
• #1
1
0
Integration by parts and substitution help!!
∫0
-1 e ^√x+1
## The Attempt at a Solution
• #2
HallsofIvy
Homework Helper
41,833
964
I'm sorry, but I simply cannot figure out what that integral is intended to be.
Is that $$\int_{-1}^0 e^{\sqrt{x+1}} dx$$ or $$\int_{-1}^0 e^{\sqrt{x}+ 1} dx$$ or $$\int_{-1}^0 e^{\sqrt{x}}+ 1 dx$$?
If it is the first, take $u= \sqrt{x+1}= (x+1)^{1/2}$ so that $du= (1/2)(x+1)^{-1/2}dx$ so that $(x+1)^{1/2}du= u du= dx$. When x= -1, u= 0, when x= 0, u= 1 The integral becomes
$$\int_0^1 ue^{u}du$$
and can be done by "integration by parts".
If the second, write it as $$e\int_{-1}^0 e^{\sqrt{x}}dx$$ and let $u= \sqrt{x}$.
If the third, write it as $$\int_{-1}^0 e^{\sqrt{x}}dx+ \int_{-1}^0 dx$$.
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https://smac-group.github.io/ds/rmarkdown.html
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# Chapter 2 RMarkdown
RMarkdown is a framework that provides a literate programming format for data science. It can be used to save and execute R code within RStudio and also as a simple formatting syntax for authoring HTML, PDF, ODT, RTF, and MS Word documents as well as seamless transitions between available formats. The name “markdown” is an intentional contrast to other “markup” languages–e.g., hypertext markup language (HTML)–which require syntax that can be quite difficult to decipher for the uninitiated. One aim of the markdown paradigm is a syntax that is as human-readable as possible. “RMarkdown” is an implementation of the “markdown” language designed to accommodate embedded R code.
### What is literate programming ?
Literate programming is the notion for programmers of adding narrative context with code to produce documentation for the program simultaneously. Consequently, it is possible to read through the code with explanations so that any viewer can follow through the presentation. RMarkdown offers a simple tool that allows to create reports or presentation slides in a reproducible manner with collateral advantages such as avoiding repetitive tasks by, for example, changing all figures when data are updated.
### What is reproducible research ?
Reproducible research or reproducible analysis is the notion that an experiment’s whole process, including collecting data, performing analysis and producing output, can be reproduced the same way by someone else. Building non-reproducible experiments has been a problem both in research and in the industry, and having such an issue highly decreases the credibility of the authors’ findings and, potentially, the authors themselves. In essence, allowing for reproducible research implies that anyone could run the code (knit the document, etc.) and obtain the same exact results as the original research and RMarkdown is commonly used to address this issue.
Below is a short video showing a basic overview of RMarkdown.
We have created a framework application that you can use to test out different RMarkdown functions. Simply run the following code within the introDS package by using either
# RMarkdown Web
introDS::runShiny('rmd')
# RMarkdown Mobile
introDS::runShiny('rmd_mini')
## Warning: package 'shiny' was built under R version 3.6.2
## PhantomJS not found. You can install it with webshot::install_phantomjs(). If it is installed, please make sure the phantomjs executable can be found via the PATH variable.
Shiny applications not supported in static R Markdown documents
Then a shiny app window will pop out for you to access the application like the following:
As you can see, the toolbar on the left hand side allows you to try different RMarkdown functions. On the right hand side, Raw code shows the original R code that generates the output, Compiled html shows the compiled output based on the Raw code, and BibTex file shows the formatting lists of references.
For example, let’s try to compile some R code within RMarkdown. Click on the Code in the toolbar for some example code:
Then when we click on the Compiled html, we can see the following output:
You can also try multiple functions at the same time. For example, let’s click both Code and Emoji in the toolbar, we can see the following R code used:
The above code generates the following output:
Now you are ready to experiment different RMarkdown functions and test the corresponding outputs! 😉
## 2.1 Create an R Markdown file in RStudio
Within RStudio, click FileNew FileR Markdown. Give the file a title and the author (your name) and select the default output, HTML. We can change this later so don’t worry about it for the moment.
An RMarkdown is a plain text file that contains three different aspects:
• Text
• Code Chunks
YAML stands for YAML Ain’t Markup Language and is used to specify document configurations and properties such as name, date, output format, etc. The (optional) YAML header is surrounded before and after by “—” on a dedicated line.
You can also include additional formatting options such as a table of contents or even a custom CSS style template which can be used to further enhance the presentation. For the purpose of this book, the default options should be sufficient. Below is an example knit output of the above RMarkdown file.
The default output above is an html_document format but this format can be modified using, for example, pdf_document to output a pdf. However, the pdf format requires additional installation and configuration of a TeX distribution such as MikTeX. Once available, the user can also include raw LaTeX and even define LaTeX macros in the RMarkdown document if necessary (we’ll discuss more about LaTeX further on).
### 2.2.1 Subsections
To make your sections numbered as sections and subsections, make sure you specify number_sections: yes as part of the YAML Metadata as shown below.
## 2.3 Text
Due to its literate nature, text will be an essential part in explaining your analysis. With RMarkdown, we can specify custom text formatting with emphases such as italics, bold, or code style. To understand how to format text, our previous sentence would be typed out as follows in RMarkdown:
With RMarkdown, we can specify custom text formatting with emphases such as *italics*, **bold**, or code style
As seen above, headers are preceded by a #. A single # produces the largest heading text while, to produce smaller headings, you simply need to add more #s! Heading level also impacts section and subsection nesting in documents and tables of contents, as well as slide breaks in presentation formats.
### 2.3.2 Lists
Lists can be extremely convenient to make text more readable or to take course notes during class. RMarkdown allows to create different list structures as shown in the code below:
* You can create bullet points by using symbols such as *, +, or -.
+ simply add an indent or four preceding spaces to indent a list.
+ You can manipulate the number of spaces or indents to your liking.
- Like this.
* Here we go back to the first indent.
1. To make the list ordered, use numbers.
1. We can use one again to continue our ordered list.
2. Or we can add the next consecutive number.
which delivers the following list structure:
• You can create bullet points by using symbols such as *, +, or -.
• simply add an indent or four preceding spaces to indent a list.
• You can manipulate the number of spaces or indents to your liking.
• Like this.
• Here we go back to the first indent.
1. To make the list ordered, use numbers.
2. We can use one again to continue our ordered list.
3. Or we can add the next consecutive number.
### 2.3.4 Blockquotes
Use the > character in front of a line, just like in email to produce blockquotes which styles the text in a way to use if we quote a person, a song or another entity.
“To grow taller, you should shave your head. Remember to bring the towels!”
Justin Lee
### 2.3.5 Pictures
which will produce:
Otherwise, to add a picture without any captions, follow the syntax below:
which delivers:
### 2.3.6 LaTeX
LaTeX is a document preparation system that uses plain text as opposed to formatted text that is used for applications such as Microsoft Word. It is widely used in academia as a standard for the publication of scientific documents. It has control over large documents containing sectioning, cross-references, tables and figures.
#### 2.3.6.1 LaTeX in RMarkdown
Unlike a highly formatted word processor, we cannot produce equations by clicking on symbols. As data scientists there is often the need to explain distributions and equations that are behind the methods we present. Within the text section of an RMarkdown document you can include LaTeX format text to output different forms of text, mainly equations and mathematical expressions.
Inline mathematical expressions can be added using the syntax: $math expression$. For example, if we want to write “where $$\alpha$$ is in degrees” we would write:
"where $\alpha$ is in degrees".
Using a slightly different syntax (i.e. $$math expression$$) we can obtain centered mathematical expressions. For example, the binomial probability distribution in LaTeX is written as
$$f(y|N,p) = \frac{N!}{y!(N-y)!}\cdot p^y \cdot (1-p)^{N-y} = {{N}\choose{y}} \cdot p^y \cdot (1-p)^{N-y}$$
which is output as:
$f(y|N,p) = \frac{N!}{y!(N-y)!}\cdot p^y \cdot (1-p)^{N-y} = {{N}\choose{y}} \cdot p^y \cdot (1-p)^{N-y}$
An introduction to the LaTeX format can be found here if you want to learn more about the basics. An alternative can be to insert custom LaTeX formulas using a graphical interface such as codecogs.
### 2.3.7 Cross-referencing Sections
You can also use the same syntax \@ref(label) to reference sections, where label is the section identifier (ID). By default, Pandoc will generate IDs for all section headers, e.g., # Hello World will have an ID hello-world. To call header hello-world as a header, we type \@ref(hello-world) to cross-reference the section. In order to avoid forgetting to update the reference label after you change the section header, you may also manually assign an ID to a section header by appending {#id} to it.
### 2.3.8 Citations and Bibliography
Citations and bibliographies can automatically be generated with RMarkdown. In order to use this feature we first need to create a “BibTex” database which is a simple plain text file (with the extension “.bib”) where each reference you would like to cite is entered in a specific manner.
To illustrate how this is done, let us take the example of a recent paper where two researchers from Oxford University investigated the connection between the taste of food and various features of cutlery such as weight and color (calling this phenomenon the “taste of cutlery”). The BibTeX “entry” for this paper is given below:
@article{harrar2013taste,
title={The taste of cutlery: how the taste of food is affected by the weight, size,
shape, and colour of the cutlery used to eat it},
author={Harrar, Vanessa and Spence, Charles},
journal={Flavour},
volume={2},
number={1},
pages={21},
year={2013},
publisher={BioMed Central}
}
This may look like a complicated format to save a reference but there is an easy way to obtain this format without having to manually fill in the different slots. To do so, go online and search for “Google Scholar” which is a search engine specifically dedicated to academic or other types of publications. In the latter search engine you can insert keywords or the title and/or authors of the publication you are interested in and find it in the list of results. In our example we search for “The taste of cutlery” and the publication we are interested in is the first in the results list.
Below every publication in the list there is a set of options among which the one we are interested in is the “Cite” option that should open a window in which a series of reference options are available. Aside from different reference formats that can be copied and pasted into your document, at the bottom of the window you can find another set of options (with related links) that refer to different bibliography managers.
For “.bib” files we are interested in the “BibTeX” option and by clicking on it we will be taken to another tab in which the format of the reference we want is provided. All that needs to be done at this point is to copy this format (that we saw earlier in this section) and paste in the “.bib” file you created and save the changes.
However, your RMarkdown document does not know about the existence of this bibliography file and therefore we need to insert this information in the YAML metadata at the start of our document. To do so, let us suppose that you named this file “biblio.bib” (saved in the same location as your RMarkdown document). All that needs to be done is to add another line in the YAML metadata with bibliography: biblio.bib and your RMarkdown will now be able to recognize the references within your “.bib” file.
There are also a series of other options that can be specified for the bibliography such as its format or the way references can be used within the text (see links at the end of this section).
Once the “.bib” file has been created and has been linked to your RMarkdown document through the details in the YAML metadata, you can now start using the references you have collected in the “.bib” file. To insert these references within your document at any point of your text you need to use the name that starts the reference field in your “.bib” file and place it immediately after the @ symbol (without spaces). So, for example, say that we wanted to cite the publication on the “taste of cutlery”: in your RMarkdown all you have to do is to type @harrar2013taste at the point where you want this citation in the text and you will obtain: Harrar and Spence (2013). Moreover, it is often useful to put a citation in braces and for example if you want to obtain (see e.g. Harrar and Spence 2013) you can simply write [see e.g. @harrar2013taste].
The user can also change the name that is used to call the desired reference as long as the same name is used to cite it in the RMarkdown document and that this name is not the same as another reference.
The references in the “.bib” file will not appear in the references that are output from the RMarkdown compiling procedure unless they are specifically used within the RMarkdown document.
Additional information on BibTeX and reference in RMarkdown can be found in the links below:
### 2.3.9 Tables
For simple tables, we can be manually insert values as such follows:
+---------------+---------------+--------------------+
| Fruit | Price | Advantages |
+===============+===============+====================+
| *Bananas* | $1.34 | - built-in wrapper | | | | - bright color | +---------------+---------------+--------------------+ | Oranges |$2.10 | - cures scurvy |
| | | - **tasty** |
+---------------+---------------+--------------------+
to produce:
Bananas $1.34 • built-in wrapper • bright color Oranges$2.10
• cures scurvy
• tasty
As an alternative we can use the simple graphical user interface online. For more extensive tables, we create dataframe objects and project them using knitr::kable() which we will explain later on this book.
There are many more elements to creating a useful report using RMarkdown, and we encourage you to use the RMarkdown Cheatsheet as a reference.
## 2.4 Code Chunks
Code chunks are those parts of the RMarkdown document where it is possible to embed R code within your output. To insert these chunks within your RMarkdown file you can use the following shortcuts:
• the keyboard shortcut Ctrl + Alt + I (OS X: Cmd + Option + I)
• the Add Chunk command in the editor toolbar
• by typing the chunk delimiters {* and **.
The following example highlights the code chunks in the example RMarkdown document we saw at the start of this chapter:
### 2.4.1 Code Chunk Options
A variety of options can be specified to manage the code chunks contained in the document. For example, as can be seen in the third code chunk in the example above, we specify an argument that reads echo = FALSE which is a parameter that was added to the code chunk to prevent printing the R code that generated the plot. This is a useful way to embed figures. More options can be found from the RMarkdown Cheatsheet and Yihui’s notes on knitr options. Here are some explanations of the most commonly used chunk options taken from these references:
• eval: (TRUE; logical) whether to evaluate the code chunk;
• echo: (TRUE; logical or numeric) whether to include R source code in the output file;
• warning: (TRUE; logical) whether to preserve warnings (produced by warning()) in the output like we run R code in a terminal (if FALSE, all warnings will be printed in the console instead of the output document);
• cache: (FALSE; logical) whether to “cache” a code chunk. This option is particularly important in practice and is discussed in more details in Section 2.4.4.
Plot figure options:
• fig.path: (‘figure/’; character) prefix to be used for figure filenames (fig.path and chunk labels are concatenated to make filenames);
• fig.show: (‘asis’; character) how to show/arrange the plots;
• fig.width, fig.height: (both are 7; numeric) width and height of the plot, to be used in the graphics device (in inches) and have to be numeric;
• fig.align: (‘default’; character) alignment of figures in the output document (possible values are left, right and center;
• fig.cap: (NULL; character) figure caption to be used in a figure environment.
Adding comments to describe the code is extremely useful (if not essential) during every coding and programming process. It helps you take notes and remember what is going on and why you made use of these functions, as well as helping others understand your code. Forgetting to comment or document your code often becomes a larger problem in the future when, among numerous lines of code, you have forgotten the reason for using certain functions or algorithms.
“Don’t document bad code – rewrite it.” The Elements of Programming Style, Kernighan & Plauger
# Comment your code by preceding text with a #
# Keep it brief but comprehensible, so you can return to it
### 2.4.3 In-line R
The variables we store in an RMarkdown document will stay within the environment they were created in. This means that we can call and manipulate them anywhere within the document. For example, supposing we have a variable called x to which we assign a specific value, then in RMarkdown we can reference this variable by using r x: this will affix the value of the variable directly in a sentence. Here is a practical example:
a <- 2
where we have stored the value 2 in a variable called a. We can use the value of a as follows:
The value of $a$ is r a.
This translates in R Markdown to “The value of $$a$$ is 2.”
### 2.4.4 Cache
Depending on the complexity of calculations in your embedded R code, it may be convenient to avoid re-running the computations (which could be lengthy) each time you knit the document together. For this purpose, it possible to specify an additional argument for your embedded R code which is the cache argument. By default this argument is assigned the value FALSE and therefore the R code is run every time your document is compiled. However, if you specify this argument as cache = TRUE, then the code is only run the first time the document is compiled while the following times it simply stores and presents the results of the computations when the document was first compiled.
Below is a short video introducing caching in R Markdown.
The RMarkdown file used for this particular example can be found here: caching.Rmd.
Let us consider an example where we want to embed an R code with a very simple operation such as assigning the value of 2 to an object that we call a (that we saw earlier). This is clearly not the best example since this operation runs extremely quickly and there is no visible loss in document compilation time. However, we will use it just to highlight how the cache argument works. Therefore, if we want to avoid running this operation each time the document is compiled, then we just embed our R code as follows:
a <- 2
which would be written in RMarkdown as:
{r computeA, cache = TRUE}
a <- 2
You will notice that we called this chunk of embedded R code computeA and the reason for this will become apparent further on. Once we have done this we can compile the document that will run this operation and store its result. Now, if we compile the document again (independently from whether we made changes to the rest of the document or not) this operation will not be run and the result of the previous (first) compiling will be presented. However, if changes are made to the R code which has been “cached”, then the code will be run again and this time its new result will be stored for all the following compilings until it is changed again.
This argument can therefore be very useful when computationally intensive R code is embedded within your document. Nevertheless it can suffer from a drawback which consists in dependencies of your “cached” R code with other chunks within the document. In this case, the other chunks of R code can be modified thereby outputting different results but these will not be considered by your “cached” R code. As an example, suppose we have another chunk of R code that we can “cache” and that takes the value of a from the previous chunk:
(d <- 2*a)
## [1] 4
which would be written in RMarkdown as:
{r, cache = TRUE}
(d <- 2*a)
In this case, the output of this chunk will be ## 4 since a <- 2 (from the previous chunk). What happens however if we modify the value of a in the previous chunk? In this case, the previous chunk will be recomputed but the value of d (in the following chunk) will not be updated since it has stored the value of 4 and it is not recomputed since this chunk has not been modified. To avoid this, a solution is to specify the chunks of code that the “cached” code depends on. This is why we initially gave a name to the first chunk of code (“computeA”) so as to refer to it in following chunks of “cached” code that depend on it. To refer to this code you need to use the option dependson as follows:
(d <- 2*a)
## [1] 4
which we would write as:
{r, cache = TRUE, dependson = "computeA"}
(d <- 2*a)
In this manner, if the value of a changes in the first chunk, the value of d will also change but will be stored until either the computeA chunk or the latter chunk is modified.
## 2.5 Render Output
After you are done, run RMarkdown::render() or click the Knit button at the top of the RStudio scripts pane to save the output in your working directory.
The use of RMarkdown makes it possible to generate any file format such as HTML, pdf and Word processor formats using pandoc. Pandoc is a free software that understands and converts useful markdown syntax, such as the code mentioned above, into a readable and clean format.
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https://alphons.io/3004/what-is-the-chemical-formula-of-water/
|
👋 Hello! I'm Alphonsio the robot. Ask me a question, I'll try to answer.
# What is the chemical formula of water?
The chemical formula of water is H2O.
More
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http://sekiheki.pv.land.to/toriisin.html
|
### HƍZEkZEOdHƛ{ZݍZOW
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|
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https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/946
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## Structural relaxation and magnetic anisotropies in Co/Cu(001) films
• The magnetic anisotropy of Co/Cu~001! films has been investigated by the magneto-optical Kerr effect, both in the pseudomorphic growth regime and above the critical thickness where strain relaxation sets in. A clear correlation between the onset of strain relaxation as measured by means of reflection high-energy electron diffraction and changes of the magnetic anisotropy has been found.
$Rev: 13581$
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http://physics.stackexchange.com/users/8774/clevy
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# clevy
less info
reputation
6
bio website location age member for 2 years, 6 months seen Mar 14 at 4:33 profile views 10
I am currently majoring in physics/astrophysics at Berkeley. I will probably primarily inhabit the mathematica/latex/physics/Apple exchanges, however I am also into photography should they make an exchange for that.
# 1 Question
21 What is the mass density distribution of an electron?
# 108 Reputation
+105 What is the mass density distribution of an electron?
This user has not answered any questions
# 3 Tags
0 electrons 0 particle-physics 0 black-holes
# 8 Accounts
Physics 108 rep 6 Mathematics 38 rep 5 Stack Overflow 6 rep 3 Meta Stack Exchange 1 rep TeX - LaTeX 1 rep 1
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https://www.physicsforums.com/threads/taking-courses-at-university-a-few-questions.418534/
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# Schools Taking courses at university-a few questions
1. Jul 26, 2010
### kramer733
So i was wondering about taking a course in university or two. If you take only 1 course in university, do you still have to pay tuition? Because honestly 5 grand for 1 course along with the textbook(s) that entail with the class seems like alot. Is there any way to get aroudn this?
2. Jul 26, 2010
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https://www.rieselprime.de/z/index.php?title=Leonhard_Euler&direction=prev&oldid=1466
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# Leonhard Euler
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Introduction
Leonhard Euler (April 15, 1707, Basel – September 18, 1783, St. Petersburg) was undoubtedly the most prolific of famous mathematicians. Born in Switzerland but most closely associated with the Berlin of Frederick the Great and the St. Petersburg of Catherine the Great. His career covered a highly productive period in mathematics when the newly discovered calculus was being extended in all directions at once, and he made significant contributions to all areas of mathematics. More than any other individual, Euler was responsible for the notation of modern mathematics, including $\large \pi$,$\large e$ and $\large i$, the summation notation $\sum$ and the standard function notation $f(x)$, and was in fact the first to use the term 'function' in this context. He is the only mathematician to have two numbers named after him.
In the 17th century, the age of Fermat and Mersenne, there was a distinct lack of interest in providing logical proofs of the discoveries that were made. In an increasingly mechanised and industrial world, results were judged by their practical application and methods did not necessarily meet the ancient Greek ideal of proof exemplified by Euclid. Then, along came Euler, who provided explanations for many of the discoveries made by earlier mathematicians but which they had failed to account for. Euler's methods would play a significant role in opening up new windows onto our understanding, not just of the primes, but in many other areas of mathematics as well.
## Youth and Education
Leonhard Euler was the son of a Lutheran minister, Paul Euler, who had studied theology at Basel University and attended lectures given by Jacob Bernoulli, the founder of a whole dynasty of mathematician sons. In fact, Paul Euler had lived in the Bernoulli house while an undergraduate in Basel, and this association with a great mathematical family was to influence not just his life, but also that of his as yet unborn son. Leaving university, Paul Euler married Margaret Brucker, the daughter of another Lutheran minister and they made their home in Basel where, on 15th April 1707 Leonhard Euler was born.
When Leonhard was one year old the family moved to Riehen, not far from Basel, and this is where he was brought up. He was sent to school in Basel and lived with his maternal grandmother. His interest in mathematics already sparked by his father's teaching, Leonhard studied the subject in his own time, and it is quite possible that his father was unaware of this interest when in 1720 he sent his son to Basel University. The idea was that he would first receive a general education before moving on to the study of theology in preparation for joining his father in the church.
Leonhard quickly made contact with Johann Bernoulli, who had succeeded his father as professor of mathematics, and was given permission to visit him each Sunday afternoon for mathematical studies. In 1723 Euler completed the general education, obtaining a Master's degree in philosophy with a treatise in which he contrasted the philosophical ideas of Newton and Descartes. In the autumn of that year he continued to follow his father's wishes and commenced his study of theology. But he could not find the same enthusiasm for it that he found in mathematics, and with some help and encouragement from Johann Bernoulli, he obtained his father's permission to change from theology to mathematics.
Euler completed his studies in 1726 and the following year submitted an entry for the Grand Prix of the Paris Academy, which that year was for the best arrangement of masts on a ship. The Grand Prix went to Bouguer, an expert on ship design, but Euler's entry won him second prize and confirmed his entry into the world of mathematics. The mid-eighteenth century was a time of court patronage. Rulers throughout Europe were keenly aware of the potential for scientific and mathematical skills to boost their countries military and industrial worth, and surrounded themselves with intellectuals as a mark of their standing and enlightenment. It was therefore, somewhat fortuitous that in July 1726 Nicholas Bernoulli died in St. Petersburg creating a vacancy at the St. Petersburg Academy of Sciences. No doubt some family strings were pulled somewhere and Euler was offered the post. This was not, however, Euler's first choice. He applied for the chair in Physics at Basel University, and as part of his submission wrote a paper on acoustics that went on to become a classic in its field. The final decision was made by the drawing of lots, and with lady luck against him, on 5th April 1727 - just 10 days before his 20th birthday - Leonhard Euler left Basel for St. Petersburg.
## St. Petersburg, the first time
It took six weeks to complete the journey, taking a boat down the Rhine, crossing Germany in coaches and then another boat from Lubeck saw him arrive on 17th May in the sophisticated milieu of an intellectual academy just two years after it had been founded by Catherine I, the wife of Peter the Great. Already at the academy were the geometer Jakob Hermann, a distant relative who also hailed from Basel; Daniel Bernoulli, another of the vast Bernoulli clan whose interest lay in applied mathematics; Christian Goldbach, he of the Goldbach Conjecture; F. C. Maier working in trigonometry and the astronomer and geographer J. N. De-Lisle.
Euler served as a medical lieutenant in the Russian navy for the first three years, becoming Professor of Physics at the Academy in 1730. This allowed him to give up his naval post and he moved to St. Petersburg where he lived with Daniel Bernoulli, who held the senior chair in mathematics. Bernoulli left St. Petersburg to return to Basel in 1733 and Euler was appointed to replace him, boosting his finances sufficiently for him to marry, on 17th January 1734, Katharina Gsell, the daughter of a painter from St. Petersburg. They had thirteen children together although only five survived their infancy. In later life, Euler often claimed that he made many of his most important discoveries with a baby on his knee and several children playing round his feet.
The year after marrying, Euler's health problems began. In 1735 he had a severe fever, which he kept secret from friends and relatives in Basel. In his autobiographical writing Euler said that his eye problems began in 1738 with eyestrain caused by his cartographic work. At least one author, however, has argued that the fever was a symptom of the eyestrain, and another claimed that the eye problem was caused by the severity of the climate. What is certain is that by 1756 he was almost blind in one eye - the famous portrait of him by Emanuel Handmann clearly shows his right eye to be almost closed. Whether this was caused by or merely exacerbated by either cartographic work or the climate is pure conjecture but neither of these would have helped an already weakened eye. Soon after 1766 he suffered an unknown illness and became totally blind. There were a few days respite in 1771 when an operation to remove a cataract appeared to be successful, but it was not to be and Euler was totally blind for the rest of his life.
After taking up his post as professor of physics at the St. Petersburg Academy he carried out state projects in cartography, magnetism, fire engines and shipbuilding. At the same time the outline of his approach to mathematical research becomes apparent. He saw studies of number theory as being vital to the foundations of calculus, and that special functions and differential equations were essential to the solution of the more concrete problems of rational mechanics. In 1736 he published his first book, Mechanica, which for the first time translated Newtonian dynamics into the language of Mathematical Analysis.
## Berlin Interlude
By 1740, Euler's reputation had spread throughout Europe, not least by having twice won the Grand Prix of the Paris Academy, in 1738 and 1740, though on both occasions he shared the prize with others. This brought an invitation from Frederick the Great for him to go to Berlin to help found the planned Berlin Academy of Science. This proved an irresistible opportunity and Euler left St. Petersburg in June 1741 arriving in Berlin on 25th July. Soon after his arrival he wrote to a friend, "... the king calls me his professor, and I think I am the happiest man in the world.". His happiness was to last for 25 years.
Maupertuis was the president of the Berlin Academy and Euler was appointed Director of Mathematics. His work, however, covered much more than mathematics including supervising the observatory, the botanical gardens and the publication of calendars and maps. He sat on the committee for the academy library, did work for the government on lotteries, pensions and artillery, and supervised works on the plumbing system at Sans Souci, the royal summer palace. In 1749 he was charged by the king with a project to correct the flow of the Finow Canal.
Through all this he kept up a steady stream of mathematical work, writing books on the calculus of variations, on ballistics and artillery and on the calculation of planetary orbits. He also wrote over 350 other mathematical papers and articles during this period including an early example of popular mathematics, Letters to a Princess of Germany, published in three volumes between 1768 and 1772, and which remained a standard treatise on the subject for half a century. The princess of the title is popularly assumed to have been the Princess of Anhault-Dessau to whom Euler gave lessons on physics and mathematics.
In 1748 he published in two parts his Introduction to Infinite Analysis, which was intended to serve as an introduction to pure analytical mathematics. The first part contains the bulk of the subject matter found in modern textbooks under algebra, the theory of equations and trigonometry. In the algebra he paid particular attention to the expansion of various functions in series and to the summation of a given series. He explicitly stated that a series cannot be safely employed unless it is convergent. In the trigonometry he expanded on the idea of F. C. Maier (1727) and Johann Bernoulli (1734) that the subject was a branch of analysis and not simply an appendage of astronomy or geometry. He also introduced the trigonometric functions and showed that the trigonometric functions and exponential functions were connected.
The second part of the Infinite Analysis is on analytical geometry. Euler commenced this part by dividing curves into algebraic and transcendental curves, and established a variety of propositions that are true for all algebraic curves. He then applied these to the general equation of the second degree in two dimensions, showed that it represents the various conic sections, and deduced most of their properties from the general equation. He also considered the classification of cubic, quartic and other algebraic curves. He next discussed the question of surfaces represented by the general equation of the second degree in three dimensions, and how they may be discriminated one from the other: some of these surfaces had not been previously investigated. In the course of this analysis he laid down the rules for the transformation of co-ordinates in space. This was also the earliest attempt to bring the curvature of surfaces within mathematics, and the first complete discussion of tortuous curves.
The use of a single symbol to denote the number 3.14159... appears to have been introduced about the beginning of the eighteenth century. W. Jones in 1706 represented it by $\pi$ a symbol that had been used by Oughtred in 1647, and by Barrow a few years later, to denote the circumference of a circle. Johann Bernoulli represented the number by c. Euler in 1734 denoted it by p, and in a letter of 1736 (in which he first stated the closed form of the sum of the reciprocals of the squares of the integers) he used the letter c. Christian Goldbach in 1742 used $\pi$ and following the publication of Euler's Analysis in 1748 the symbol has been universally accepted.
In 1759 Maupertuis died and Euler assumed the role but not the title of President of the Academy. By 1763 Euler was no longer the king's favourite and the title of President was offered instead to d'Alembert, with whom Euler had argued over scientific matters. However, d'Alembert refused to move to Berlin and the king retained overall control of the academy. Disturbed by the king's interference, in 1766 Euler decided to return to St. Petersburg where, unbelievably, they had kept his post open for him for 25 years.
## Back to St. Petersburg
From this point in his life, when he was 59 years of age, he produced almost half his prolific output even though as previously noted he was totally blind for the rest of his life. On returning to St. Petersburg in 1766, Euler's son, Johann Albrecht Euler, was appointed to the chair of physics at the St. Petersburg Academy - becoming secretary of the academy in 1769 - and he also doubled as an unofficial assistant with practical aspects of his father's work. Euler also had two assistants appointed by the academy, W. L. Krafft and A. J. Lexell. In 1772 these were joined by Euler's grandson-in-law, Nicholas Fuss who was a young mathematician recently graduated from Basel University. These assistants were more than just secretaries taking dictation from their blind master. He discussed with them the outline of his work, explained his ideas and they were expected to calculate any tables and compile examples. Notwithstanding this help his output was more than prolific. To again quote Fuss from his eulogy, -He would give up his food before work, and now work became a perpetual habit-.
The academy of St. Petersburg was still bringing out un-published works by Euler 50 years after his death, and his complete works runs to over 80 volumes. It has been estimated that simply to write out Euler's life work by hand would take 50 years of eight-hour days, which leaves very little time for thinking, for conjecturing, or for playing with grandchildren.
On the morning of 18 September 1783 Euler gave a mathematics lesson to one of his grandchildren. After lunch he spent a couple of hours calculating the motion of balloons, then spent some time discussing with his assistants the orbit of the newly discovered planet Uranus. Around 5 O'clock, while seated in the garden playing with a grandson he suffered a brain haemorrhage and around 11 O'clock that night he died. He was survived by his second wife, Salome Abigail Gsell, the sister-in-law of his first wife who died in a fire in 1771, by three of his thirteen children and by twenty-six grandchildren.
## Mathematics
The basic language of mathematics, its symbols and notation owes so much to Euler; $\large e$ for the base of natural logarithms in 1727, f(x) for functions in 1734, $\sum$ for summation and as previously mentioned $\large\pi$ for the ratio of the circumference of a circle to its diameter in 1755, $\large i$ for the $\large\sqrt{-1}$ in 1777, the notation for finite differences $\large\delta y$ and $\large\delta^2 y$ and many more.
He was the first to consider $\large \cos$ and $\large \sin$ as functions rather than as chords as all those since Ptolemy had done. He made fundamental contributions to number theory, calculus and geometry, and combined Newton's fluxions with Liebniz's differential calculus to almost single-handed create modern mathematical analysis.
Note: I have not finished this, I just wanted you to know I had not forgotten about it.
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https://blog.jverkamp.com/2012/03/27/wombat-ide---busy-day-for-small-changes/
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# Wombat IDE - Busy day for small changes
Bug fixes:
• Issue 138: Automatically create a backup file (with a ~ suffix) on save and an option to disable it. There have been a few issues with Wombat crashing that I haven’t managed to track down, this should help people recover from those. (They’re rare; as in 2 cases reported among over 150 students for several months, so this shouldn’t happen to the majority of users).
• The mnemonic in the recent documents menu has been tweaked to be ascending and 1 based rather than descending and 0 based.
• Fixed an issue where occasionally hitting enter in the REPL wouldn’t run the current code based on incorrect bracket matching.
• list->image and image->list are not properly highlighted as keywords.
Other enhancements:
• Licenses have been added to all source code. The project itself is licensed under the GPL v3 (it has to be because of the InfoNode code; that’s a topic for another time), but the source code itself has been released under the 3-clause BSD license.
• Issue 86: I finally got line numbers along the left side working; see below for a screen shot. At some point, I managed to fix the line sizing issues that I was having, although I don’t recall exactly when.
• Issue 129: Added a new syntax definition file rather than storing the syntax in the Java Preferences with the rest of the options. This will make automatically updating it much easier.
Example of the new line numbers:
You shouldn’t have to do anything other than let Wombat update to get the new version. If you have at least 2.86.4, you already have it. If you don’t already have Wombat, you can download the launcher here.
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https://in.mathworks.com/help/signal/ref/lp2lp.html
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lp2lp
Change cutoff frequency for lowpass analog filter
Syntax
``[bt,at] = lp2lp(b,a,Wo)``
``[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo)``
Description
example
````[bt,at] = lp2lp(b,a,Wo)` transforms an analog lowpass filter prototype given by polynomial coefficients (specified by row vectors `b` and `a`) into a lowpass filter with cutoff angular frequency `Wo`. The input system must be an analog filter prototype.```
````[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo)` converts the continuous-time state-space lowpass filter prototype (specified by matrices `A`, `B`, `C`, and `D`) to a lowpass filter with cutoff angular frequency `Wo`. The input system must be an analog filter prototype.```
Examples
collapse all
Design an 8th-order Chebyshev Type I analog lowpass filter prototype with 3 dB of ripple in the passband.
`[z,p,k] = cheb1ap(8,3);`
Convert the prototype to transfer function form and display its magnitude and frequency responses.
```[b,a] = zp2tf(z,p,k); freqs(b,a)```
Transform the prototype to a lowpass filter with a cutoff frequency of 30 Hz. Specify the cutoff frequency in rad/s. Display the magnitude and frequency responses of the transformed filter.
```Wo = 2*pi*30; [bt,at] = lp2lp(b,a,Wo); freqs(bt,at)```
Input Arguments
collapse all
Prototype numerator and denominator coefficients, specified as row vectors. `b` and `a` specify the coefficients of the numerator and denominator of the prototype in descending powers of s:
`$\frac{B\left(s\right)}{A\left(s\right)}=\frac{b\left(1\right){s}^{n}+\cdots +b\left(n\right)s+b\left(n+1\right)}{a\left(1\right){s}^{m}+\cdots +a\left(m\right)s+a\left(m+1\right)}$`
Data Types: `single` | `double`
Prototype state-space representation, specified as matrices. The state-space matrices relate the state vector x, the input u, and the output y through
`$\begin{array}{l}\stackrel{˙}{x}=Ax+Bu\\ y=Cx+Du\end{array}$`
Data Types: `single` | `double`
Cutoff angular frequency, specified as a scalar. Express `Wo` in units of rad/s.
Data Types: `single` | `double`
Output Arguments
collapse all
Transformed numerator and denominator coefficients, returned as row vectors.
Transformed state-space representation, returned as matrices.
Algorithms
`lp2lp` transforms an analog lowpass filter prototype with a cutoff angular frequency of 1 rad/s into a lowpass filter with any specified cutoff angular frequency. The transformation is one step in the digital filter design process for the `butter`, `cheby1`, `cheby2`, and `ellip` functions.
`lp2lp` is a highly accurate state-space formulation of the classic analog filter frequency transformation. If a lowpass filter has cutoff angular frequency ω0, the standard s-domain transformation is
`$s=p/{\omega }_{0}$`
The state-space version of this transformation is
`$At={\omega }_{0}\cdot A$`
`$Bt={\omega }_{0}\cdot B$`
`$Ct=C$`
`$Dt=D$`
The `lp2lp` function can perform the transformation on two different linear system representations: transfer function form and state-space form. See `lp2bp` for a derivation of the bandpass version of this transformation.
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http://mathoverflow.net/questions/125988/questions-of-localization-of-topos
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# questions of localization of topos
Let $T$ be a topos, and $F \in T$, $T/F$ a localization of $T$. So we have a natural morphism $i: T/F \longrightarrow T$.
My questions are:
1.What are the definitions of $i_{\ast}$ and $i^{\ast}$ without using site ?
2.Dose there exist a site $S$ such that $Sh(S) \cong T$ and there is an $U \in S$ which $U^{\sim} \cong F$ ?
-
Hello !
$i^*$ is the functor which send an object $X \in T$ to $X \times F$ with the natural projection as map into $F$.
$i_*$ is a little harder to describe, if $p: Y \rightarrow F$ is an object of $T/F$, then $i\_*(Y)$ is the sub-object of $[F,Y]$ (the internal hom object) which corresponds to map $f$ from $F$ to $Y$ such that $p \circ f =Id\_F$ this can be express as an equaliser or with internal language as you prefers)
You also have a $i\_!$ functor (left adjoint to $i^*$ ) which is just the forget functor who send $p:Y \rightarrow F$ to $Y$.
You can chose any generating family $B$ of $T$ (for example the image by the yoneda embeddings of a site of definition of $T$) add $F$ to this familly, the familly $B'$ you obtain seen as a full subcategory of $T$ and endowed with the canonical topology of $T$ is (by the Grothendieck comparison lemma) a site of definition of $T$, and you simply choose $U$ to be $F$.
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https://www.comsol.fr/blogs/3-approaches-to-modeling-moving-loads-and-constraints-in-comsol/?setlang=1
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## 3 Approaches to Modeling Moving Loads and Constraints in COMSOL®
##### Walter Frei October 22, 2018
One of the core strengths of the COMSOL Multiphysics® software is the ability to easily define loads and constraints that move over time. There are actually several different ways in which this can be done, all within the core functionality of the software. In today’s blog post, we will guide you through three of these approaches.
### The Example: Laser Heating of a Flat Plate
Let’s consider the case of a flat plate of material that is being heated by a laser heat source. The plate is centered at the origin, as shown in the figure below, and we want to heat its surface at varying locations over time. Suppose that the laser (or the workpiece) is mounted on a stage that provides positional control of the focus point. Let’s also assume that there are some optics that shape the beam profile of the laser, so the heat source is spread over a small area around the focus.
Schematic of a laser heat source traversing over a workpiece.
Now, let’s look at several different ways in which we can define the moving focus point to follow a known tool path.
### Method 1: Using Variables
The simplest approach is to use a set of variables to define the position of the focus and distribution of the heat load over time. Let’s say that we want to have a 1-kW total heat load moving in a 40-cm radius circular path every 10 s. Furthermore, the heat load has a Gaussian intensity distribution with a 5-cm waist radius. We can define this information using variables, as shown in the screenshot below.
The first four definitions, Rb, P0, Rp, and T0, are actually just constants. If we would like to alter any of these definitions via a parametric sweep later on, we could also define them as Global Parameters. For now, it is simplest to just show them all in one place.
The next two variables, x_focus and y_focus, are not constant: They vary as a function of time, the built-in variable t. We can see that these variables describe a point moving on a circular path about the origin as:
Rp*cos(2*pi*t/T0)
Rp*sin(2*pi*t/T0)
The next variable, R, is a function of time and space. It makes use of the coordinate variables x and y, as well as x_focus and y_focus, which we just saw are functions of time. So at each instant in time and at every point in space, this variable tells us the distance (in the xy-plane) from the laser focal point.
The last variable, HeatFlux, is a function of R and the constants. It defines a Gaussian intensity profile about the focal point such that the total heat flux equals the defined power. It is this variable, HeatFlux, that we enter as a boundary condition, as shown in the screenshot below.
This prescribed heat flux expression then gives the heating profile path visualized below.
A circular heating profile set up via the Variables node.
### Method 2: Using Interpolation Functions
So far, this isn’t very complicated; just a few expressions. But we can replace the simple expressions for x_focus and y_focus with something more general. COMSOL Multiphysics provides a variety of built-in functions in the software. For our discussion here, the most useful is the Interpolation function, which lets us read in data from a text file. Let’s suppose we have a text file containing rows of data of time and the x– and y-locations of the laser focus at that time. A sample of such a file is shown below:
Such data can be read in to the Interpolation function using the settings shown below. Note that there is just a single argument here, time, and the two columns of data after that represent the x-focus and y-focus, respectively, in units of centimeters. Between the specified points in time, we want the laser to move linearly. We specify the function names as x_f and y_f, respectively, and make sure to set the arguments correctly.
We can then just alter our previous expressions for the focus to be x_focus = x_f(t) and y_focus = y_f(t) and get the moving load pictured below.
A heating profile read in from a text file.
We can see that this Interpolation function quickly lets us read in some very complicated profile patterns, we just need a way to generate these profiles and the text files. For example, the text file format used here is not too different from the G-code format, so if you have a heating path defined in such a format, it can be pretty simple to convert it to a COMSOL®-friendly input. On the other hand, maybe we would like to import a profile created in the ubiquitous 2D DXF file format. Let’s look at that next…
### Method 3: Using Paths Imported from CAD Geometries
Suppose we want the load to move along a path we read in from an external file, as shown in the image below. We would like the laser to move smoothly along this path from one end to the other. Now, we need to do a bit more work.
The S-shaped profile of the laser path is read in from a DXF file as a geometry.
The file that we’ve read in doesn’t have any information about time within it: It is just a path that we expect the laser to follow at a constant speed. Now, each edge of this imported path (and there may be thousands of edges) does have parameters s1 and s2 that vary linearly along the length, but if there are many edges, we probably wouldn’t want to work with these parameters. So instead, how do we compute where the laser is at every point in time along the entire set of lines? One way in which we can do this is by introducing another partial differential equation (PDE) to solve, along the desired set of lines. The PDE we want to solve is:
\nabla_t \cdot \left( c \nabla_t u \right) = 0
where \nabla_t refers to the tangential direction to the curve.
This PDE, along with the boundary conditions of u = 0 at one end of the path and u = 1 at the other end, will give us a field along the path that varies linearly from 0 to 1, which will be proportional to the total arc length of all of the edges. We can set this up using the Coefficient Form Edge PDE interface, as shown in the screenshots below. All coefficient terms other than the Diffusion Coefficient, c, are set to zero.
Left: Settings of the Coefficient Form Edge PDE interface needed to compute the path. Right: The diffusion coefficient term, c, is a constant; all other coefficients are set to zero.
Then, two Dirichlet boundary conditions set the field, u, at either ends, and we solve this PDE in a stationary step, prior to solving the heat transfer problem but still within the same study.
Two Dirichlet boundary conditions are used at the start and end of the profile path to constrain the field.
Next, we introduce a single minimum component coupling operator into the model, with the source selected as the edges to follow. This minimum operator is used to define the focal point coordinates, e.g.:
x_focus = minop1(abs(u-t/T0),x)
y_focus = minop1(abs(u-t/T0),y)
Note that the minimum operator is given two arguments. When we call the operator with two arguments, it will return the value of the second argument where the first argument is at a minimum. Thus, at each time, t, it will return the x– and y-locations of a point on the edge that is t/T0 fraction of the way from one end to the other.
Left: The minimum operator is defined over the path that the heat source follows. Right: The laser heat source following the path defined by an imported DXF file.
And what if we would like the laser to traverse different parts of the path at different speeds? We would just need to adjust the coefficient, c, along those sets of edges. Suppose we want the laser to move three times faster along the curved boundaries than along the straight lines: just make c three times larger. Note that the absolute value doesn’t matter, it is just the ratio of the coefficient magnitudes that matters. The one drawback to this approach arises when the path crosses itself. In that situation, you would need to subdivide the path into two, or more, groups of paths; solve a PDE on each; and do a bit more bookkeeping for the variables.
### Closing Remarks on Modeling Moving Loads and Constraints
In this blog post, we have looked at three different approaches of modeling a moving load. To try them yourself, click the button below to head to the Application Gallery. There, you can download the MPH-files for the models featured above (must have a COMSOL Access account and valid software license).
Several other examples within the Application Gallery also make use of these techniques, including:
Although in this blog post we only considered loads, note that we can also apply these techniques to constraints, as described in How to Make Boundary Conditions Conditional in Your Simulation.
Do you have further questions about using COMSOL Multiphysics for your modeling applications? Please let us know!
#### Post Tags
Technical Content
1. Elif Demirbas January 21, 2019 6:50 pm
Hi Walter,
I have a question related to laser power. In most of the laser heating tutorials, laser power is constant. Is it possible to define a varying laser power over time, for example like a gaussian function? And use this laser power function to heat the wafer. In the original laser heating wafer tutorial, the expression for the heat flux is p_laser[1/W]*gp1(x-wv1(t))*gp1(y) under the Analytic section. I tried replacing the p_laser with a gaussian function with an argument t, “gp2(t)*gp1(x-wv1(t))*gp1(y)”, however when I plot it, it plots over x and y only. How can I include the time dependency to the laser power?
Any information is much appreciated.
Thanks,
Elif
2. Walter Frei January 22, 2019 8:45 am
Hello Elif,
Yes, you can modify the power function to vary with time, just introduce a function that varies over time as well. See also: https://www.comsol.com/support/knowledgebase/1245/
|
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|
https://www.particleincell.com/2013/cubic-line-intersection/?replytocom=82661
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Computing Intersections Between a Cubic Bezier Curve and a Line
Posted on August 10th, 2013
Previous Article :: Next Article
Introduction
Last week I was running a Starfish simulation of a molecular transport through a vent. Starfish was designed to support both linear and cubic spline representation of surfaces. But while testing the code by tracing particles, I noticed that the particle hits with curved surfaces were not being computed correctly. Digging deeper I found the issue: I never implemented the algorithm for finding intersection between a cubic and a line! Instead, the code was using the line-line intersection by connecting the two end points of the curve. Oops!
Before continuing, let me just say that I am really starting to enjoy algorithm development using interactive HTML technologies! In the past, I would write the code in Java or C++ and have it output the splines and intersection points to a file which I would subsequently visualize using some plotting program. Or using Matlab, I could do the plotting right from the program. But I would still be confined to testing just a single case. With HTML, we can do something much better: we can interactively manipulate the curves and see the algorithm respond in real time!
Demo
You can try this out in the demo above. If everything loaded fine, you should see a blue cubic Bezier curve and a red line. You will also see two white circles, these are the two control points $$\mathbf{P}_1$$ and $$\mathbf{P}_2$$ defining the cubic. As you change the curves by dragging the large circles, you should see a small black dot track the intersection point. You will see additional points appear if you orient the curve such that there are multiple intersections. This is shown below in Figure 1.
Math Background
So how does this code work? The visualization is similar to the article on smooth splines through prescribed points. This mathematical algorithm is based on this answer. One way to represent an infinitely-long line is as follows
$$\displaystyle \frac{(x-x_1)}{(x_2-x_1)} = \frac{(y-y_1)}{(y_2-y_1)}$$
which can be rewritten as
$$x(y_2-y_1) + y(x_1-x_2) + x_1(y_1-y_2)+y_1(x_2-x_1)=0$$
or
$$Ax + By + C = 0 \qquad (1)$$
We next constrain the $$(x,y)$$ pairs to those located on the cubic curve. A cubic Bezier curve is given by
$$\mathbf{r}(t)=(1-t)^3\mathbf{P}_0 + 3(1-t)^2t\mathbf{P}_1 + 3(1-t)t^2\mathbf{P}_2 + t^3\mathbf{P}_3, \quad t\in [0,1]$$
where $$\mathbf{r}(t)$$ is the position vector. If we substitute these $$(x,y)$$ components into equation (1), we obtain a cubic equation in $$t$$. Finding the intersection points is then a “simple” matter of finding the roots of the cubic equation.
Cubic Roots
One way to find a single root is using Newton’s method. Unfortunately, a cubic can have up to 3 roots. This is because, as shown in Figure 1, a line can intersect a cubic spline in up to 3 locations. Since we are using this algorithm for particle tracing, we are interested in the first intersection along the line. There is no guarantee that the Newton’s method will converge to this root. As such, we need to find all existing roots and sort them. Finding additional roots with Newton’s method is possible but not trivial. Third-order polynomials also have an analytical solution for their roots. But unlike the well known quadratic formula, there are multiple equations for cubic roots. In the end, I ended up using algorithm from Stephen Schmitt’s site:
/*based on http://mysite.verizon.net/res148h4j/javascript/script_exact_cubic.html#the%20source%20code*/
function cubicRoots(P)
{
var a=P[0];
var b=P[1];
var c=P[2];
var d=P[3];
var A=b/a;
var B=c/a;
var C=d/a;
var Q, R, D, S, T, Im;
var Q = (3*B - Math.pow(A, 2))/9;
var R = (9*A*B - 27*C - 2*Math.pow(A, 3))/54;
var D = Math.pow(Q, 3) + Math.pow(R, 2); // polynomial discriminant
var t=Array();
if (D >= 0) // complex or duplicate roots
{
var S = sgn(R + Math.sqrt(D))*Math.pow(Math.abs(R + Math.sqrt(D)),(1/3));
var T = sgn(R - Math.sqrt(D))*Math.pow(Math.abs(R - Math.sqrt(D)),(1/3));
t[0] = -A/3 + (S + T); // real root
t[1] = -A/3 - (S + T)/2; // real part of complex root
t[2] = -A/3 - (S + T)/2; // real part of complex root
Im = Math.abs(Math.sqrt(3)*(S - T)/2); // complex part of root pair
if (Im!=0)
{
t[1]=-1;
t[2]=-1;
}
}
else // distinct real roots
{
var th = Math.acos(R/Math.sqrt(-Math.pow(Q, 3)));
t[0] = 2*Math.sqrt(-Q)*Math.cos(th/3) - A/3;
t[1] = 2*Math.sqrt(-Q)*Math.cos((th + 2*Math.PI)/3) - A/3;
t[2] = 2*Math.sqrt(-Q)*Math.cos((th + 4*Math.PI)/3) - A/3;
Im = 0.0;
}
/*discard out of spec roots*/
for (var i=0;i<3;i++)
if (t[i]<0 || t[i]>1.0) t[i]=-1;
/*sort but place -1 at the end*/
t=sortSpecial(t);
console.log(t[0]+" "+t[1]+" "+t[2]);
return t;
}
This algorithm returns an array of parametric intersection locations along the cubic, with -1 indicating an out-of-bounds intersection (before or after the end point or in the imaginary plane). We also need to verify that the intersections are within the limits of the linear segment. This is done by the following code:
/*computes intersection between a cubic spline and a line segment*/
function computeIntersections(px,py,lx,ly)
{
var X=Array();
var A=ly[1]-ly[0]; //A=y2-y1
var B=lx[0]-lx[1]; //B=x1-x2
var C=lx[0]*(ly[0]-ly[1]) +
ly[0]*(lx[1]-lx[0]); //C=x1*(y1-y2)+y1*(x2-x1)
var bx = bezierCoeffs(px[0],px[1],px[2],px[3]);
var by = bezierCoeffs(py[0],py[1],py[2],py[3]);
var P = Array();
P[0] = A*bx[0]+B*by[0]; /*t^3*/
P[1] = A*bx[1]+B*by[1]; /*t^2*/
P[2] = A*bx[2]+B*by[2]; /*t*/
P[3] = A*bx[3]+B*by[3] + C; /*1*/
var r=cubicRoots(P);
/*verify the roots are in bounds of the linear segment*/
for (var i=0;i<3;i++)
{
t=r[i];
X[0]=bx[0]*t*t*t+bx[1]*t*t+bx[2]*t+bx[3];
X[1]=by[0]*t*t*t+by[1]*t*t+by[2]*t+by[3];
/*above is intersection point assuming infinitely long line segment,
make sure we are also in bounds of the line*/
var s;
if ((lx[1]-lx[0])!=0) /*if not vertical line*/
s=(X[0]-lx[0])/(lx[1]-lx[0]);
else
s=(X[1]-ly[0])/(ly[1]-ly[0]);
/*in bounds?*/
if (t<0 || t>1.0 || s<0 || s>1.0)
{
X[0]=-100; /*move off screen*/
X[1]=-100;
}
/*move intersection point*/
I[i].setAttributeNS(null,"cx",X[0]);
I[i].setAttributeNS(null,"cy",X[1]);
}
}
As you can see, we are always plotting 3 intersection locations, but the out-of-bounds intersections are moved off screen to location (-100,-100). The above code also does not sort the intersections along the line, but this change is ease to implement by storing the s parametric positions in array.
Source Code
And that’s it. You can download the code by right clicking and selecting “save as” on this link: cubic-line.svg
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24 comments to “Computing Intersections Between a Cubic Bezier Curve and a Line”
1. Oli
January 13, 2014 at 8:40 pm
Hello,
first I want to say that I really like the blog and topics discussed here. I remember finding the Boris-push post years ago and it helped my a lot at that time.
But on the topic: How do you check if particles are inside your domain? In my problems I just have an arbitrary shaped boundary. I classify each cell as either inside, outside or boundary cell. For the boundary cells I use a (kind of reduced) point-in-polygon check. But how would one do it for cubic splines? Just always calculate if there is an intersection point?
I hope you can clear things up like in the past :).
Cheers
Oli
• August 28, 2014 at 4:43 pm
Hey Oli,
as a quick rejection of collision with bezier, you can check for collision with the hull created by the control points of the bezier. If it doesn’t collide with the hull, it can’t collide with the curve.
from wikipedia:
Bézier curves are widely used in computer graphics to model smooth curves. As the curve is completely contained in the convex hull of its control points, the points can be graphically displayed and used to manipulate the curve intuitively
2. August 12, 2014 at 10:47 am
Hi there,
I guess you may feel interested about my research on curve-to-curve intersection too, https://sites.google.com/site/curvesintersection/
Enjoy my show! Cheers,
Hunt Chang
• August 14, 2014 at 6:08 am
Thanks for sharing!
3. November 18, 2015 at 1:23 am
Hey! Just wanted to say this was incredibly helpful to me in a project I’m working on. Thanks a lot!
• November 18, 2015 at 4:01 pm
Thanks and glad to hear that!
4. esseci
March 11, 2016 at 4:48 am
Your code saved really a lot of time!
Many thanks!!
5. Luca
June 14, 2016 at 11:55 am
Thanks for sharing this, it really helped!
6. Ben
January 18, 2017 at 1:38 am
It’s good to use generic line equation.
7. Joshua Pilkington
May 23, 2017 at 10:47 pm
Thanks for the helpful code!
I did find one issue where the calculated coefficients could end up having zero values for either or both of the cube or square with certain configurations (e.g. for A*x^3 + B*x^2 + C*x + D, A and/or B could end up being zero). This causes a divide-by-zero error when attempting to calculate the cubic roots (resulting in the line segment going through the bezier curve but NOT showing an intersection point). I simply added quadratic and linear cases to handle such scenarios.
Here is a scenario that causes the zero coefficients:
/*create control points for the cubic*/
P[0] = createMarkerV(100,50,"blue");
P[1] = createMarkerK(200,250);
P[2] = createMarkerK(300,250);
P[3] = createMarkerV(400,450,"blue");
/*create control points for the line*/
P[4] = createMarkerV(200,50,"red");
P[5] = createMarkerV(200,350,"red");
You can see it happen as you move one of the line segment endpoints around from being vertical to non-vertical.
To fix the issue, I added this to the cubicRoots function:
if( P[0] == 0 )
{
if( P[1] == 0 )
{
console.log("Linear formula detected");
var t = Array();
t[0] = -1 * ( P[3] / P[2] );
t[1] = -1;
t[2] = -1;
/*discard out of spec roots*/
for (var i=0;i<1;i++)
if (t[i]1.0) t[i]=-1;
/*sort but place -1 at the end*/
t=sortSpecial(t);
console.log(t[0]);
return t;
}
var DQ = Math.pow(P[2], 2) + 4*P[1]*P[3]; // quadratic discriminant
if( DQ >= 0 )
{
DQ = Math.sqrt(DQ);
var t = Array();
t[0] = -1 * ( ( DQ + P[2] ) / ( 2 * P[1] ) );
t[1] = ( ( DQ - P[2] ) / ( 2 * P[1] ) );
t[2] = -1;
/*discard out of spec roots*/
for (var i=0;i<2;i++)
if (t[i]1.0) t[i]=-1;
/*sort but place -1 at the end*/
t=sortSpecial(t);
console.log(t[0]+" "+t[1]);
return t;
}
}
Again, awesome code!
• NounoursPanda
May 2, 2018 at 10:52 am
Hey man, thank a lot for this improvement ! But I found a syntax error. Here is the final code I think :
function cubicRoots(P)
{
if( P[0] == 0 )
{
if( P[1] == 0 )
{
console.log(“Linear formula detected”);
var t = Array();
t[0] = -1 * ( P[3] / P[2] );
t[1] = -1;
t[2] = -1;
/*discard out of spec roots*/
for (var i=0;i<1;i++)
if (t[i]1.0) t[i]=-1;
/*sort but place -1 at the end*/
t=sortSpecial(t);
console.log(t[0]);
return t;
}
var DQ = Math.pow(P[2], 2) – 4*P[1]*P[3]; // quadratic discriminant
if( DQ >= 0 )
{
DQ = Math.sqrt(DQ);
var t = Array();
t[0] = -1 * ( ( DQ + P[2] ) / ( 2 * P[1] ) );
t[1] = ( ( DQ – P[2] ) / ( 2 * P[1] ) );
t[2] = -1;
/*discard out of spec roots*/
for (var i=0;i<2;i++)
if (t[i]1.0) t[i]=-1;
/*sort but place -1 at the end*/
t=sortSpecial(t);
console.log(t[0]+” “+t[1]);
return t;
}
}
• NounoursPanda
May 2, 2018 at 10:56 am
well…
I understand now why there was an syntax error. This appear when we copy past in this comment section the code near “/*discard out of spec roots*/”
You just need to copy the original post for this part, don’t copy past the code I sent.
• Mark
December 20, 2019 at 1:46 am
Should be: if (t[i]<0 || t[i]>1.0) t[i]=-1;
When typing the symbols for less-than (<) and greater-than (>), the browser will first try to interpret them as HTML tags. Only when it fails to do so will it display them as symbols.
• May 19, 2018 at 5:54 pm
Thanks!
8. Joshua Pilkington
May 23, 2017 at 10:57 pm
By the way,
var DQ = Math.pow(P[2], 2) + 4*P[1]*P[3]; // quadratic discriminant
should have been
var DQ = Math.pow(P[2], 2) - 4*P[1]*P[3]; // quadratic discriminant
I accidentally used a ‘+’ in the place of a ‘-‘.
9. shengpei zheng
July 4, 2017 at 4:48 pm
Thank u a lot.it’s interesting.
10. Matt H.
January 18, 2018 at 6:20 pm
This is a GREAT demo. Any updates to this? It is very useful sample. I’m working with it trying to make it work for multiple lines but still allowing for multiple intersections per line, and I have also run into the issue Joshua ran into. If you have any updates or info to share that would be very appreciated.
• January 18, 2018 at 6:34 pm
I wasn’t really planning on making any updates to this, but I guess I should implement Joshua’s fixes. One of these days. I can help you with your code offline (email me directly) if needed. Truly, I am quite surprised by how much interest this article generated. This is really an off-shoot of my main work (plasma modeling) but it seems this is the most interesting article on the entire blog!
• Jesse
July 19, 2018 at 5:02 pm
That’s definitely because bezier curves are more widespread than plasma modeling
11. Sergiy
March 13, 2018 at 12:37 am
Hi,
Thanx for your code, it works perfectly.
However, it seems I cannot find the explanation for that part of code:
var P = Array();
P[0] = A*bx[0]+B*by[0]; /*t^3*/
P[1] = A*bx[1]+B*by[1]; /*t^2*/
P[2] = A*bx[2]+B*by[2]; /*t*/
P[3] = A*bx[3]+B*by[3] + C; /*1*/
What does it do, what math is behind it?
It looks like this is the key to the whole thing of plugging two equations together and it’s not explained or I could not comprehend it.
Regards, Sergiy
• March 14, 2018 at 10:53 am
Hi Sergiy,
I probably should have included more of the intermediate math. Basically, we have the equation Ax+By+C=0. We can however rewrite both x and y as functions of t. This will then give you A*x(t) + B*y(t) + C = 0, which is now an equation in only a single unknown (t) that we can find root(s) for. A Bezier curve can be converted to form x = bx[0]*t^3 + bx[1]*t^2 + bx[2]*t + bx[3] (ignore the coefficient ordering, in hindsight they should be numbered in reverse). Similar equation exists for y. You can plug these into the A*x(t) + B*y(t) + C = 0 equation. You will then obtain the following equation (A*bx[0]+B*by[0])*t^3 + (A*bx[1]+B*by[1])*t^2 + (A*bx[2]+B*by[2])*t + (A*bx[3]+B*by[3]+C) = 0, or P0*t^3 + P1*t^2 + P2*t + P3 = 0.
12. NounoursPanda
May 2, 2018 at 10:50 am
Hello, thank’s a lot, this was very helpful for a project !!!!
13. March 3, 2019 at 7:35 pm
Thanks for this – very useful! I was able to translate this into NodeBox 3 (a visual language).
One problem. I found erratic behavior in some cases which turned out to be rounding errors when some of the intermediate values became extremely large or small. This happened in some cases when control point values had repeating decimals (e.g. 133.3333333333)
I was able to solve this by rounding the X and Y values of the initial four bezier points to two digits of precision (e.g. 133.33333333333 becomes 133.33). This made no visible impact on the lines, curves, or intersection points and solved the problem.
14. Ben Zamos
June 20, 2019 at 1:39 pm
Hi! How would I use this method in a C++ program?
|
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|
http://rockandcode.ga/linux/troubleshooting/Start-Conky-on-X-Login/
|
# Starting Conky with X Login
Conky is a great Linux tool for system monitoring. It’s quite handy to have this “widget” start when you login to your system.
Typically you do this trhrough having something like the following in ~/.xinitrc.
exec ~/.fehbg &
exec ~/scripts/conky_start.sh &
exec /usr/bin/dwm
Nothing special there, just make sure ~/scripts/conky_start.sh is executable. Lately something’s been acting up where I have to manually execute ~/scripts/conky_start.sh after loging in. I recall having had this issue before and the solution being quite simple. Fortunately some wuick Googleing reminded me to put a delay (via sleep) on the execution of the conky command in ~/scripts/conky_start.sh like so:
#!/bin/sh
sleep 3 &&
conky
The crux being that if conky starts before dwm is up and running, it’s going, but you can’t see it “under” dwm.
|
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|
https://oxfordre.com/politics/display/10.1093/acrefore/9780190228637.001.0001/acrefore-9780190228637-e-969;jsessionid=B99F16037A7FFB7FEF02917740B094E2?rskey=oZE9cR&result=1
|
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date: 06 February 2023
# The Search for Real-World Media Effects on Political Decision Making
• Thomas J. LeeperThomas J. LeeperDepartment of Methodology, London School of Economics and Political Science
### Summary
Empirical media effects research involves associating two things: measures of media content or experience and measures of audience outcomes. Any quantitative evidence of correlation between media supply and audience response—combined with assumptions about temporal ordering and an absence of spuriousness—is taken as evidence of media effects. This seemingly straightforward exercise is burdened by three challenges: the measurement of the outcomes, the measurement of the media and individuals’ exposure to it, and the tools and techniques for associating the two.
While measuring the outcomes potentially affected by media is in many ways trivial (surveys, election outcomes, and online behavior provide numerous measurement devices), the other two aspects of studying the effects of media present nearly insurmountable difficulties short of ambitious experimentation. Rather than find solutions to these challenges, much of collective body of media effects research has focused on the effort to develop and apply survey-based measures of individual media exposure to use as the empirical basis for studying media effects. This effort to use survey-based media exposure measures to generate causal insight has ultimately distracted from the design of both causally credible methods and thicker descriptive research on the content and experience of media. Outside the laboratory, we understand media effects too little despite this considerable effort to measure exposure through survey questionnaires.
The canonical approach for assessing such effects: namely, using survey questions about individual media experiences to measure the putatively causal variable and correlating those measures with other measured outcomes suffers from substantial limitations. Experimental—and sometimes quasi-experimental—methods provide definitely superior causal inference about media effects and a uniquely fruitful path forward for insight into media and their effects. Simultaneous to this, however, thicker forms of description than what is available from close-ended survey questions holds promise to give richer understanding of changing media landscape and changing audience experiences. Better causal inference and better description are co-equal paths forward in the search for real-world media effects.
### Subjects
• Political Behavior
• Political Communication
• Public Opinion
• Qualitative Political Methodology
• Quantitative Political Methodology
### Introduction
The study of media effects entails the empirical association of two things: measures of media content or experience and measures of audience outcomes. Any quantitative evidence of correlation between the two—in tandem with assumptions about causal ordering and an absence of spuriousness—constitutes evidence of media effects. Social scientists are particularly interested in any such effects on the public’s perceptions of the social and political world, their knowledge or lack thereof about the same, their preferences over goods, candidates, or issues, and finally their behavior. The search for media effects takes many forms and this article focuses on the search for those effects outside the confines of experimental laboratories, in the buzzing, blooming confusion of everyday life.
At stake in the search are three challenges: the measurement of the outcomes, the measurement of the media and individuals’ exposure to it, and the tools and techniques for associating the two. While measuring the outcomes potentially affected by media exposure is in many ways trivial (surveys, election outcomes, and online behavior provide numerous measurement devices), the latter two aspects of studying media effects present nearly insurmountable empirical difficulties short of ambitious experimental design. Despite these challenges, media effects research has been preoccupied for much of its history by an effort to develop and apply survey-based measures of individual media exposure that serve as the empirical basis for studying media effects. Despite Prior’s (2013) call to arms that “developing better measures of media exposure is a pressing goal” (p. 621), the effort to do so has been a largely failed exercise that has left social scientists with little credible insight into media effects outside laboratory settings—precisely those locations where such effects matter the most. The effort to use survey-based measures to generate causal insight into media effects has ultimately distracted from the design of both causally credible methods such as field experiments and thicker descriptive research on the content and experience of media. Outside the laboratory, we understand media effects too little despite considerable time and effort.
Laboratory experiments have demonstrated causal possibilities, but can generalize weakly given the self-selected nature of media experiences (Arceneaux & Johnson, 2012; Gaines & Kuklinski, 2011; Leeper, 2017) and the arbitrary selection of treatments, outcomes, and samples in much experimental work (Druckman & Leeper, 2012b). Field experimental studies therefore present the best path forward for insights into media effects outside such settings because of their causal credibility and the advantage of true experiments—relative to so-called natural experiments (Sekhon & Titiunik, 2012)—at offering insight into anything beyond quirks of causality. But just as field experiments present an ideal path for obtaining credible and realistic insights into media effects, thick descriptive methods spanning the qualitative–quantitative divide present promising opportunities for studying media content and media experiences that are likely to generate far more useful insights than thin-descriptive survey measures of media exposure. Like the seminal use of in-depth interviews by Graber (1988), methods that go beyond “mere exposure” are vital for understanding the complexities of media experiences that might be the basis for “media effects.”
This article provides a discussion of the concept of “media effects” and the evidentiary standards necessary to establish that media have a causal effect on politically relevant outcomes. This includes the substantial limitations in the canonical approach for assessing such effects: namely, using survey questions about individual media experiences to measure the putatively causal variable and correlating those measures with other measured outcomes. Instead, experimental—and sometimes quasi-experimental—methods provide definitely superior causal inference about media effects. The article concludes with a discussion of how these methods—and others—might be fruitfully deployed moving forward.
### What Are Media Effects and How Would We Know Them When We See Them?
Like any causal relationship, there are two ways to frame the question of media effects: either as a “backward causal question” emphasizing the role media variables—relative to many others—might play in the production of observed outcomes or as a “forward causal question” emphasizing how outcomes might differ across counterfactual values of media variables (Gelman & Imbens, 2013).1 The backward-looking approach takes outcomes as phenomena to be explained and seeks out explanations for what might have caused them, ultimately attempting to assess the absolute or relative size of the media contribution to those outcomes. These outcomes might be macro level, like election outcomes or public discourse, or they might be micro-level outcomes, like individual beliefs, opinions, affect, cognition, physiology, or behaviors (Potter, 2011). To be less abstract, why did individuals vote for Donald Trump in the 2016 U.S. presidential election? Why did Britain vote Leave in the 2016 referendum on European Union membership? “Media,” however defined and conceptualized, might be sought out as one among many possible causes of these outcomes. Media variables typically take the form of metrics of media content or metrics of individuals’ exposure to, attention to, or reception of said content.
The forward-looking approach instead takes media or a feature thereof to be a well-defined and perhaps manipulable variable that generates different outcomes across counterfactual values of the variable (Holland, 1986; Rubin, 1978). The outcomes of interest are the same, but the forward-looking approach attempts to reduce “media” as a concept to an isolatable event, experience, or exposure and assess how realized outcomes compare to counterfactual outcomes where media were different. For example, if the Hillary Clinton campaign had spent more on television advertising in swing states in the 2016 presidential election, would vote shares have been different? If media had covered the Leave campaign’s “£350 million per week for the NHS” claim differently, would vote intentions in the 2016 referendum have been different?
The phenomena and the causal relationships are the same, but the backward and forward framings of media effects steer attention to specific kinds of questions and specific kinds of research designs. In the backward-looking framing, research in search of media effects substantiates effects when variation in outcomes across variations in media variables persists once other explanations for that outcome variation have been considered and controlled for. In the forward-looking framing, research in search of media effects substantiates effects when variation in outcomes manifests in response to a real or approximate manipulation of a media variable. Backward causal questions are exploratory; forward causal questions are experiment-like. Whereas forward-looking questions generate a definitive statement about the direction(s) and size(s) of media influence on outcomes of interest, backward-looking questions lead only to further questions or new hypotheses.
Humans tend to think about causal effects—including those of media—in backward-looking terms, so we naturally gravitate toward trying to answer those questions directly. But as Gelman and Imbens (2013) argue, these questions never lead to clear answers because they ultimately generate correlational evidence influenced by unobserved or unobservable additional factors. In the words of Hovland (1959): “while the conceptualization of the survey researcher is often very valuable, his [sic] correlational research design leaves much to be desired” (p. 15). Instead, to understand media effects researchers need to transform backward-looking questions into forward-looking questions or treat the answers to backward-looking questions as exploratory steps that lead toward new forward-looking questions. A backward-looking question at best generates hypotheses about possible causes but does not rule out causes or definitively clarify the magnitude of causal effects because there can always be some other set of unobserved factors that explain away any observed patterns or mask causality under apparent non-correlation. The researcher must identify and measure not just the media variable but all other potential causes.2
Despite the difficulty of answering backward-looking causal questions about media effects, researchers continue to search for explanations of outcomes by associating those outcomes with measures of media variables controlling for a subset of other observable, measurable phenomena. Such analysis is facilitated by the frequent inclusion of coarse, unreliable, and error-prone survey-based measures of media exposure in nearly all election surveys and many public opinion polls. Despite the general, philosophical challenges to backward causal inference, much research continues to proceed from an assumption that not only is backward-looking causal inference possible but also that survey-based measures have any utility at all in causal inference. In an infamous example, Bartels (1993) regresses various election-related, individual-level political outcomes on two American National Election Studies items measuring television viewing and daily newspaper readership, controlling for party identification, age, education, and race. The results suggest larger than anticipated effects due to corrections for measurement error in the media measures providing an apparently substantial corrective to a field the author terms “one of the most notable embarrassments of modern social science” (p. 267).
### Design Trumps Analysis in Studying Media Effects
A causal effect (of media) for an individual is conventionally understood as a difference between two or more potential outcomes that this individual might have expressed had they been exposed to varying values of a media variable (see Gerber & Green, 2012; Holland, 1986; Rosenbaum & Rubin, 1983). To take a canonical example, an individual’s opinion on whether to tolerate a rally by a hate group might be affected by different media portrayals of the issue (“framing”), such as coverage that emphasizes free speech considerations versus coverage that emphasizes public safety considerations (Nelson, Clawson, & Oxley, 1997). The individual-level causal effect, TE, is defined as the difference in the individual’s, i, potential opinion, Yit, when they are exposed to one or the other framing at a given point in time, t:
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Defined in this way, these two media experiences constitute the complete set of possible media experiences available at time t.3 Because individuals can only experience one of these forms of media content, the individual-level media effect is unobservable due to the fundamental problem of causal inference (Holland, 1986).4 We can never know how media affect an individual without insight into unobservable counterfactuals where their contemporaneous media experiences are different.5
Causal inference, however, often proceeds from the idea that while individual-level effects are not observable, an average treatment effect across a population (or sample thereof) is observable and provides useful insight into the central tendency of the individual-level effect distribution. Because of the following equality:
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we can reach inferences about the average effect of the free speech framing (relative to public safety framing) by comparing average outcomes among individuals exposed to each type of content, provided we are willing to assume that these individuals receive content independent of the values they would take for YFree Speech and YPublic Safety. In an experimental setting we can assume this independence by design because physical randomization of individuals to experiences operates without regard for each individual’s schedule of potential outcomes. In all other (observational) research designs, we must arrive upon that independence only conditionally by mathematically conditioning on factors that are theorized to influence both individuals’ exposure to particular media at a particular point in time and their potential outcomes. Fully identifying and measuring these other factors is daunting.
This essential difference between how we draw causal inferences in experimental and observational research—in the former case by design and in the latter case only by careful and complete measurement of confounding factors—highlights why experimental studies are seen to provide a “gold standard.” However, this particularly favorable standing among alternative research designs is not absolute. Indeed, experiments taking place in laboratory settings—including some of the earliest experimental research in media effects by Iyengar and Kinder (1987)—are seen as particularly limited in value. Yet as Hovland (1959) argued decades ago, integrating observational (survey) and (laboratory) experimental methods “will require on the part of the experimentalist an awareness of the narrowness of the laboratory in interpreting the larger and more comprehensive effects of communication. It will require on the part of the survey researcher a greater awareness of the limitations of the correlational method as a basis for establishing causal relationships” (p. 14). Experimental designs for studying media effects provide the possibility of clear inference about average media effects, but they do not necessarily do so in a way that is consistently useful, and the reliance upon experimental manipulation limits the degree to which experimentation explains mediatized phenomena. Operating outside the laboratory and beyond the scope of survey-based measures of media exposure is likely to be particularly fruitful and is the focus of this article.
Strictly speaking, experiments (be they in a laboratory, survey, or field setting) provide insights into causal possibilities. Media effects experiments test whether a particular media variation can cause an outcome, within the implicit constraints of the sample, setting, and treatment used in the experiment (see Shadish, Cook, & Campbell, 2001, esp. ch. 13). Evidence that a given experience is, on average, effectual in a particular time and place for a particular set of individuals does not mean that the same results would be obtained elsewhere. Experimental evidence of media effects must always be read as “media can cause,” not “media do cause.” But experiments are also limited by the prospective, forward-looking nature of the research design. Short of massive-scale, field-based interventions into everyday life, experiments also cannot generate inferences of the form “media did cause.” For example, Feezell (2017) demonstrates that social media can serve an agenda-setting function but not that they have in any particular instance outside the experimental context. Druckman, Levendusky, and McLain (2018) show that mediatized messages can further spread through interpersonal discussions but not that they have in any particular instance outside the experimental context. Searles, Fowler, Ridout, Strach, and Zuber (2017) show that male and female voices can be differentially effective in campaign advertising but not that they are in any particular instance outside the experimental context. Extrapolation beyond the experimental setting, sample, treatment, and outcome measures requires assumptions about or an explicit model for the transportability of the causal effects. This means experiments are typically powerless on their own to provide retrospective or historical insight and thus powerless to answer the kinds of backward-looking causal questions that social scientists frequently gravitate toward.
This is particularly worth in-depth consideration given that media experiences, the effects of which researchers might desire to know, are not commonly randomly assigned (Arceneaux & Johnson, 2012; Bennett & Iyengar, 2008; Hovland, 1959; Leeper, 2017), nor do they consist of strictly captive exposure to forced stimuli (Druckman, Fein, & Leeper, 2012). Media content and audience exposure to that content are anything but random.6 Experiments thus provide “gold standard” causal insight into experiences, but only to the extent that the variation introduced by experimental control resembles the real-world variation in media experiences that researchers might desire to understand and that such experiences are prone to be easily randomized.
On face value, then, observational methods of obtaining causal inference about media effects would seem to have some advantages over these narrow experimental approaches. For example, observational methods would allow a greater flexibility over the sample of individuals, settings, causes, and outcomes being studied given that the experiment-eligible populations of individuals, settings, causes, and outcomes are a nonrepresentative subset of this hyperpopulation of interest. Similarly, observational methods may be deployed in service to retrospective questions that are impossible for prospective experimental techniques to answer. And observational methods rely upon naturalistic—rather than researcher-forced—variation in media experiences, minimizing concerns about the artifice of the experimental experience. But these apparent superiorities of observational approaches are frequently illusory. Single-study characteristics that imply generalizability, such as representative sampling of causes, outcomes, settings, and units, are only useful for learning about media effects to the extent those ostensibly more “general” research designs also offer causal identification. Frequently, they do not. Thus the oft-mentioned trade-off is not between internal validity and external validity but between clear identification of a possible causal effect and an alternative design that does not offer clarity about either internal or external validity.
An increasingly popular middle ground between experimental media effects research and observational media effects research are so-called quasi-experiments or natural experiments (Shadish, Cook, & Campbell, 2001). Unlike experiments, quasi-experiments do not involve the active intervention of the researcher but instead analysis of variation in outcomes across random or as-if-random interventions generated by other forces (such as temporal and geographical discontinuities, the random spread of technologies, weather patterns or geological factors, or lotteries administered for other purposes). Such designs might attempt to understand the direct effect of a randomized media phenomenon or to use randomization-like variation in something else to instrument for media coverage, access, or exposure. For example, researchers have studied how electoral outcomes vary geographically across areas affected early or late by the nonrandom but also not wholly systematic rollout of cable television, broadband Internet (Lelkes, Sood, & Iyengar, 2015) or Fox News (Clinton & Enamorado, 2014; DellaVigna & Kaplan, 2007). Other quasi-experimental approaches to media effects use discontinuities in radio or television signal strength in Russia (Enikolopov, Petrova, & Zhuravskaya, 2011) or Silvio Berlusconi’s Mediaset network in Italy (Durante, Pinotti, & Tesei, 2013), arbitrary channel positioning of Fox News across U.S. cable providers (Martin & Yurukoglu, 2017), or the unintentional overlap of U.S. competitive-state media markets into neighboring noncompetitive districts (Huber & Arceneaux, 2007; Krasno & Green, 2008). A recent study of climate change messages took advantage of the existence of two cable TV systems in the same market, showing ads on one but not the other, then measuring attitudes toward global warming among subscribers of each system (Romero-Canyas et al., 2018).
Relying on strong assumptions about the randomness of these “natural” interventions, quasi-experiments provide an observational research design that generates more credible causal inference than traditional correlational designs given that areas affected and unaffected by such interventions are considered to be similar with the intervention occurring as-if-random (for methodological discussion, see Keele & Titiunik, 2014; Sovey & Green, 2011). The advantage of quasi-experiments over researcher-administered experiments is the ability to gain retrospective and historical insight into outcomes that might have been impacted by quasi-experimental intervention (see, for example, Voigtlaender & Voth, 2014). Even more so than experiments, however, they have a narrowness of scope—and thus a severe inferential localness—due to the rarity of naturally occurring randomization. True lotteries occur (e.g., with the Vietnam War draft lottery; Angrist, 1990; Erikson & Stoker, 2011), but most quasi-experiments leverage a strong assumption of randomness applied to a one-off media occurrence. Rather than being a middle ground between poorly identified observational methods and well-identified experimental methods, quasi-experiments, in the rare instances in which they occur, carry the strengths and limitations of both approaches in that they serve as very useful by providing a retrospective approach to answering a forward-looking causal question but may tend to cumulate poorly given the typical impossibility of replicating a given nonexperimental intervention. But as we have seen, all causally oriented research suffers from some degree of localness.
Despite the promise, quasi-experiments provide useful but ultimately narrow historical insight into media effects. Experimental methods offer a superior alternative given the inherent repeatability of interventions (although not necessarily the settings in which they are randomized). Whereas both experiments and quasi-experiments offer a precise definition of a cause and precise statement of effects, observational methods for measuring media effects suffer from the lack of such precision because—despite decades of scholarly effort—we often cannot effectively conceptualize let alone measure variations in individual media experiences. If we do not know how to ensure that two media experiences differ in one and only one way, observational research leaves us with a “bundles of sticks” problem (Sen & Wasow, 2016) where we attribute differences in outcomes to “media” (vaguely defined and coarsely measured) without any clear insight into what part of “media” is producing effects. Observational methods for obtaining causal inference only achieve credibility when we can define, measure, and control for all other differences in experiences; this is something we cannot do. In essence, we learn nothing.
### Measuring Media and Media Exposure
Such pessimism about observational approaches is warranted. While much social science research would seem to imply that researchers believe it is possible to measure media exposure using surveys, this is simply not the case. Though numerous scholars have advocated for improved measures of media exposure and attempted to expose the deficiencies or advantages of particular approaches (Althaus & Tewksbury, 2007; Bartels, 1993; Chaffee & Schleuder, 1986; de Vreese & Boomgaarden, 2006; Dilliplane, 2011; Dilliplane, Goldman, & Mutz, 2013; Eveland, Hayes, Shah, & Kwak, 2005; Eveland, Hutchens, & Shen, 2009; Eveland & Scheufele, 2000; Eveland, Seo, & Marton, 2002; Freedman & Goldstein, 1999; Garrett, Carnahan, & Lynch, 2013; Goldman, Mutz, & Dilliplane, 2013; Guess, 2014; Jerit et al., 2016; Price & Zaller, 1993; Prior, 2003, 2009a, 2009b, 2013; Slater, Goodall, & Hayes, 2009; Tewksbury, Althaus, & Hibbing, 2011), this collective effort at obtaining complete measures of media exposure is fundamentally flawed. This goes beyond the use of such measures in causal inference.
Consider, for example, a few common ways of measuring media exposure using survey self-reports. We might ask individuals to report whether they have been exposed to (or attentive to) a particular source, a particular medium, or a particular event. Alternatively, we might ask for a ranking of the degree of attention to certain sources (like CNN or Fox News) or news content (e.g., about a particular piece of legislation or world event). Alternatively, we might ask for degree of attentiveness or ratings of intensity of use of various media (like television or Internet news). Alternatively, we might ask for time-based or frequency-based measures that count the number of days, hours, or minutes spent with media. All these approaches might vary in their source specificity from an abstract medium (e.g., television and newspapers) to specific sources (e.g., World News Tonight on ABC) and vary in their content specificity from abstract topics (e.g., news about politics and international affairs) to specific facts (e.g., news of Donald Trump’s alleged affair with pornographic actress Stormy Daniels during the pregnancy of his third wife, Melania Trump). And each can vary in the granularity of time used to measure such exposure or to rank exposure to media alternatives: we might ask about typical behavior, behavior the previous week, behavior that day, or even hours, minutes, or seconds of time use. These measures tell us what people believe their media experiences are, but only coarsely and with substantial error. The public substantially overreport media attention for a variety of reasons (Prior, 2013), and efforts at improved measures (like those just alluded to) have not produced any degree of consensus on how to improve media use measures.
The challenges discussed in the literature are quite superficial, however. These tend to include measurement error, overreporting, lack of over-time reliability, and social desirability biases. But if one wants to understand media effects apart from understanding media use, then a larger epistemological issue is whether it makes sense to talk about effects of ill-defined causes. If we imbue an error-prone, biased survey-based measure of media attention with causal meaning, what kinds of claims can we generate? Consider, for example, a claim by Kull, Ramsay, and Lewis (2003) in their study of misperceptions related to the Iraq War that in a regression analysis of misperceptions controlling for demographics, “the respondent’s primary source of news is still a strong and significant factor; indeed, it was one of the most powerful factors predicting misperception” (p. 587). In other words, Fox News had the effect of leading the public to be misinformed about the Iraq War. Setting aside the low credibility of causal ordering in this design, what does the “Fox News effect” mean here?7
Rubin (1990) describes how causal inference in the potential outcomes framework requires a stable unit treatment value assumption (SUTVA). While most research focuses on the noninterference part of this assumption, SUTVA also requires that there is only version or form of the treatment (see Sinclair, 2012). This treatment homogeneity is perhaps the most overlooked assumption of causal inference. If a person is characterized as having an identical value of treatment (e.g., FoxViewer = 1) then the assumption is that this person’s treatment is the same as another person coded the same way. Fox News is Fox News. But is it? There is reason to be skeptical. When someone broadly reports that she views Fox News, that measure says little about what stimuli—that is, what causes—that person actually encountered during such viewing. Two people reporting viewing Fox News report only “nominally identical” experiences that might in practice vary systematically (Rubin, 1990, p. 475). Did they see a particular claim about the Iraq War? Did they see particular on-screen visuals? Did they hear particular arguments about the war? These are components of media that laboratory-based media effects research typical finds to be causally relevant. The self-reported exposure to Fox News does not tell us any of this without assumptions about what that viewership entailed (e.g., in terms of timing and duration) and assumptions about what content that time-specific viewership offered (in terms of information, arguments, issue emphasis, visuals, etc.). Without these assumptions that experiences are homogeneous (even if viewing Fox News means different things to different people), it is impossible to draw out causal insight from such self-reported exposure. If we want to understand the causal influence of media, we have to understand particularistic media experiences, exposure, or nonexposure, which would generate counterfactual outcomes. Exposure self-reports gloss over this in hopes that a time- or source-based measure proxies for particularistic exposure, yet these measures—despite decades of effort—continue to be coarse, unreliable, and frequently invalid and they regularly become out of date as media landscapes change. Goldman et al. (2013) argue that despite difficulty of measuring exposure per se and responding to such over-time changes, “measurement consists of the best one can do at any given point in history; we must make do with what is on offer” (p. 651). But there is simply no reason to settle when the entire enterprise is flawed per se.
### The Challenges of Measuring Particularistic Media Experiences
Ultimately, what we mean by “media” and “media exposure” and what we can learn about the effects thereof are therefore tied up with the measures we can use to summarize the high dimensionality of “media” as a concept. Experimental and quasi-experimental approaches to studying media effects avoid these challenges by defining media effects narrowly and studying the effects of isolatable experiences. Media effects in an observational approach, however, typically define effects more broadly in terms of outcome variation across degrees, amounts, or types of content exposure. This canonical approach poses two insurmountable problems. First, media experiences are infinitely complex and the effort to measure those experiences reduces that complexity in seemingly useful but ultimately futile ways. Our sense of what variation there is in media experience is thus entirely defined by the granularity of our measurement devices. Finer granularity, rather than assuring depth of understanding, simply reveals the further complexity of these more granular slices of media experiences. As new measures identify and attempt to resolve the deficiencies of previous approaches, researchers typically reveal not merely weaknesses in measures—like coarseness—but also inadequate conceptualization—like low dimensionality—of media experiences in a way that continuously expands the relevant set of complexities that must thereafter be measured. Media effects cannot progress if effects are defined in terms of such complex bundles of causes. Second, though this ever-expanding complexity of conceptualization and measurement might be downplayed in order to obtain partial understandings of media experiences, the complexity and constantly emerging new forms of complexity reveal that media diets involve noncomparable experiences across modes, geographies, time periods, and persons that ultimately limit the extent to which particular simplifications of media complexity that are acceptable in one context can be considered acceptable elsewhere. These problems can be termed, respectively, the “complexity problem” and the “incommensurability problem” in media measurement.
First, to assess media effects, media as a cause must be reducible to a well-defined set of counterfactual experiences that can be measured with minimal bias and maximal precision. But media experiences are not so easily summarized unless experimental methods are deployed. Take, for instance, the hate rally framing example. In that design, media experience is defined narrowly as a single exposure to a single, well-defined message mutually exclusive of exposure to another well-defined message, all else constant. While the broader media landscape is complicated by numerous mediums, numerous sources therein, and an overwhelming abundance of content, “media” becomes narrowly defined so that its effect(s) can be identified. The value of the forward-looking style of causal inference should be immediately obvious because randomization of these alternative experiences and measurement of any relevant outcomes give immediate and uncomplicated insight into the possible effect(s) of this message. Identifying that effect using observational data is far more challenging. What counts as exposure? Does it have to happen on a particular medium or channel? For how long? How often? How would we know if a given individual saw the message? Would we ask that person? What if the individual has forgotten? It might require a measure of time-specific exposure, plus content analysis of all possible channels or sources through which the information might have been transmitted. What is the universe of such sources? How would we find and categorize them all? Could we track the individual’s behavior online using a browser plug-in? What if the individual opts out? Could we use Nielsen boxes? Yes, if the individual is already impaneled? Even then, how do we know that person was actually attentive? What about radio exposure, or second-hand exposure via social media or interpersonal discussions? Does that count? If it does, how would we know if it occurred? As media landscapes grow more diverse and more numerous, the complexity becomes overwhelming. Like a fractal diagram, the closer we look, the more there is to see. Whatever ruler we hold up to the world reveals that a more precise ruler might grant superior precision and an ultimately substantively distinct insight. And the answers to these questions about the seemingly infinite complexity of the media landscape only address the challenge of scoring individuals on whether or not they were exposed to a message; we haven’t even thought about outcome measurement yet, or holding all else constant.
Researchers have acknowledged this complexity and responded to it by generating measures that respond to previously ignored sources of complexity. As cable and satellite television emerged in the United States, surveys increasingly measured respondents’ access to, subscription to, and use of these sources. Similarly as media landscapes diversified from the 1990s onward and as the Internet emerged as a key source of information, survey-based measures of media exposure were similarly updated to measure these new sources of landscape complexity. At the same time, the coarseness of self-reported exposure measures also generated innovation in techniques aimed at better capturing complexity, like Nielsen boxes that record television viewing, radio listening devices, media journaling, and passive tracking of web usage. Yet all the research deploying these more granular measures of media exposure reveal that survey-based measures of media exposure gloss over immense variation in individual media experiences facilitated by the fractionalized and segmented media landscape of the 21st century. That Internet users vary in their exposure to political content all the way from zero news stories per campaign to dozens reflects that whatever simplifying value is afforded by coarse, survey-based measures inhibits the use of such measures for meaningful causal inferences. When we attempt to understand the causal effect of broadly defined “media” and measure the putatively causal factor using traditionally coarse measures, we lose insight into precisely the causally interesting within-medium variation. Immense, increasing, and fractal complexity means that “media” defined according to broad notions of “exposure” is an ill-conceived foundation for generating causal inference.
This complexity understandably leads to the kinds of oversimplifications that characterize the survey-based, observational media effects literature. Relying on time use measures and coarse summaries of viewership reduces that complexity to continuous measures of time and artificially discrete measures of audience segmentation. As such, it becomes possible to quantitatively process measures of multiple media. Newspaper readership, television viewing, and radio listening, treated as measures of time, can simply be summed. Membership in distinct audiences can be handled with Boolean algebra to reduce complexity further into categories like “online news user” or “like-minded news viewer.” The audience for Fox in 1998 can be compared to the audience for Fox in 2018. Broadsheet readers in Norway can be compared to broadsheet readers in the United States.
This leads to the second insurmountable challenge. By reducing the complexity of the source experiences, comparability is seemingly simple. But media experiences across sources, mediums, times, and geographies are fundamentally incommensurable. Reading the New York Times on September 10, 2001, is different from reading the New York Times on September 12, 2001. While the editorial line, overall ideology, and issue coverage might typically be stable day to day, the content is ultimately different. If we define media effects as differences in potential outcomes in response to well-defined differences in media experiences, then any effect of the New York Times today is definitionally distinct from any effect of the New York Times tomorrow. The treatment is heterogeneous, but we can pretend that it is not because the label for the two treatments is a constant, a result of vagueness rather than comparability. This false equivalence becomes even more obvious when we compare media experiences at the level of medium or the level of time units. An hour of television news may have once meant a relatively homogeneous experience, but that is no longer the case in any locale with more than one dominant news source. An hour of Internet use might have once conveyed a certain kind of experience, but commensurability across people in a specific context is diminished in even a modestly complex media landscape, let alone comparability across time and/or geography. Even comparisons of equivalent time usage of an identical media service, like Netflix or Twitter or Google News, suffer the same problem as interfaces are localized and algorithmically personalized. An hour of this and an hour of that is apples and oranges.
We cannot define, let alone speak of, the so-called effect of such experiences because they are not in fact a singular media experience. The issue is massive variation in the content to which individuals might be exposed if they spend a similar amount of time on even quite similar media outlets.8 Ultimately we cannot learn about the effects of media unless we can precisely define what we mean by a particular media experience and have measurement tools capable of accurately and precisely measuring whether a given individual had that experience. A possible response is that combinations of survey-based measures of media exposure in tandem with content analysis of media sources might allow for a reduction of complexity by tracing similar experiences across the apparent complexity of sources and exposure patterns. While sidestepping issues of incommensurability by focusing in on a single dimension or feature of media, such approaches multiply rather than reduce apparent complexity by requiring not only precise and unbiased measures of exposure but also precise and unbiased measures of content. It may be that such a mixed-method approach will facilitate observational causal inference because this at least reduces complexity and steers researchers toward definition and measurement of a singular, potentially causal media experience, but more work is needed in this area.
### Distinguishing Research Goals to Open Multiple Paths Forward
A pessimist might read this whole line of argument as a strong case against studying media and media effects at all. The intention, however, is quite different. Rather than abandoning the research goals of understanding the role of media in society and politics and rather than abandoning observational methods entirely, social scientists must instead come to terms with the reality that multiple goals of research—and thus plural methods for obtaining those distinct goals—are coeval. The goal of obtaining causal inference is something best left to the methods most capable of credibly achieving it.9 Observational approaches are, by default, inappropriate tools for studying media effects without strong, typically insatiable assumptions. Yet experiments are also limited to providing prospective insight into narrow causal possibilities. Experiments are thus typically deployed inappropriately if in service to any other research goal. And these other research goals are just as, if not more, important. Take, for instance, the goal of obtaining thorough descriptive insights into the abundant content of the ever-expanding media landscape and fine-grained characterizations of the media diets of human populations. This goal is best tackled with methods suited to the purpose. Experimental techniques are not the suitable methods.
Narrowly defining media effects research as an enterprise of causal inference, as is done here, is meant to highlight that one tool should be primarily deployed in service to that goal. Other closely aligned goals are well served by alternative approaches. This ideal might be challenging as the social sciences have hit a distinctly confirmatory moment in the history of methodology. The “credibility revolution” has meant that observational methods have almost disappeared from policy evaluation and political economy research in high-profile journals; the fields of political communication and public opinion, which were already heavily experimental, appear to have become even more so. Experiments are no mere fad and the push for trial-like preregistration of analysis plans has pushed the social sciences into even more confirmatory ways of thinking about research methods and the goals of research. Even as qualitative methods have been prominently showcased in recent high-profile work on political behavior and political communication (e.g., Cramer, 2016; Nielsen, 2012), exploratory, inductive, and thick-descriptive research goals seem to have fallen out of favor in prominent disciplinary outlets. The dominance of the experimental approach has been good for confirmatory research, but it has diverted attention from the multiple, equally valid objectives of social science—that is, to describe and to explain.
As the complexity of media increases and the rate of change therein accelerates, such thin description leaves ever-greater portions of the political and social world hidden from scholarly attention. Without thick and thorough understanding of this complexity, the hypotheses tested by identification-oriented research will constitute a smaller and smaller portion of the interesting variation in media experiences. What can be done to provide more depth? Both quantitative and qualitative methods are the answer. Computational methods to gather and characterize especially online media content offer the prospect of characterizing media at a scale previously unimaginable, as well as assessing the diversity of media content across times, platforms, geographies, and individuals. Web-tracking methods offer the possibility of studying media exposure with a very high degree of granularity that might be able to meaningfully separate exposure from attention and quantify depth of engagement with particular sources, articles, or issues. Ethnographic, qualitative interviewing, and diary methods offer a quite distinct form of thick description. Just as the production of media has rapidly evolved and changed, necessitating sophisticated approaches to map and characterize the media landscape, the consumption of media necessitates in-depth insight into how citizens feel and think about media. A compelling example of this can be found in the use of in-depth interviews (Toff & Nielsen, 2018) to understand how the seemingly inattentive segments of society understand their own learning processes. Cramer and Toff (2017) use similar methods to demonstrate that what the public considers to be politically consequential knowledge often differs from the type that is measured on political surveys. This form of evidence gathering provides highly useful hypothesis generation. Although these kinds of inductive, qualitative methods—like their massive-scale quantitative analogues—will not credibly identify media effects, that is not their ambition. This kind of thick description and exploration is needed more than ever.
Thus the effort here to make a strong case for limiting the study of media effects to experimental approaches must be read as part of a larger advocacy for a more pluralistic social science that is diverse not only in its methods but also in its questions. This idea that different methods suit different goals is familiar, but appeals to mixed methods are typically made with an implicit or explicit goal of triangulation: that is, arriving upon similar answers from different methods (for some discussion, see Seawright, 2016). As comparative studies of observational and experimental methods quite consistently show, different methods applied even to identical research questions tend to diverge somewhat in their conclusions (Arceneaux, Gerber, & Green, 2006; LaLonde, 1986). Triangulation is a flawed way forward. Mixing methods to arrive at different answers to different questions, by contrast, will provide a richness of understanding of media and its effects that no method alone and no method deployed in service to triangulation can provide. Rather than debating whether different methods can triangulate on causal inferences (thus implicitly limiting research attention to confirmatory research), a more fruitful path is discriminating about methods while retaining plurality with respect to research questions.
### Conclusion
This article has discussed what media effects are and how they might be studied outside a laboratory-experimental setting, focusing on two major challenges posed by the study of “real-world” media effects—the challenging of operationalizing media and the difficulty of credibly claiming linkages between media and outcomes of interest. Even so, experimental and quasi-experimental research designs have been effectively used to draw causal inferences about media effects. While the article might suggest a degree of fatalism about the media effects literature, all hope is not lost. Indeed, if readers take away one message from this article it should be that the question of media effects is too important to be lost in dead ends. Greater reliance on survey and laboratory experiments can be used to understand the mechanisms of media influence, heterogeneity in media effects, and the variety of possible effects media may have. Similarly, field experimental and quasi-experimental designs can be used to understand the direction and magnitude of media influence in real-world settings. Ultimately, though, we do not need survey-based measures of media exposure to understand media effects, so we should spend much less time, effort, and resources improving them. The opportunity cost is too great and there is too much that we do not yet know.
Yet this is not to diminish observational research in service to closely aligned but qualitatively distinct research objectives. More than ever, exploratory, observational research is needed for its own sake, to serve the distinct goals of describing media and media experiences and generating theoretical insights that might be tested experimentally. Understanding media through these tools must be a complement to credible methods for obtaining the distinct goal of causal inference. Computational methods, in particular, offer the prospect of systematically characterizing textual media content at a scale previously unimaginable. Digital trace data provided by social media application programming interfaces and web-tracking software promises to provide insight into individual-level online experiences that can hardly be understood using aggregated user counts or web traffic statistics or the kinds of survey self-reports that have dominated media research (Barberá, Jost, Nagler, Tucker, & Bonneau, 2015; Lazer & Radford, 2017; Menchen-Trevino & Karr, 2012). At the same time, ethnographic approaches and interview-based methods seem capable of exposing how people think and talk about their experiences of media using language and concepts that cannot necessarily be captured by closed-ended time use questions on survey questionnaires. Discourse analytic and content analysis methods can serve to critique understandings of and interpretations of media content. These objectives are well served by methods other than experimentation.
But an even more difficult conclusion than this relates to what can be learned from experimental methods. While observational methods, by definition, cannot generally provide insight into the causal effects of media and, furthermore, experimental techniques are uniquely capable in this respect, the reality is that experimental methods are also deficient. They can only provide insight into causal possibilities and only demonstrate or explain phenomena to the extent that they entail experiences, treatments, outcomes, and participants reflective of those of broad interest. They might generalize, but it is hard to know how far without extensive, multistudy programs of research. In the end, an individual experiment—regardless of the size and scope of the intervention or the number of participants involved—is never going to be able to comprehensively and generalizably describe the effects of media. But that is an unobtainable ideal that no single instance of any method can obtain. We should learn what we can from experiments—namely, about the possible effects of media—and similarly learn what we can from observational methods—namely, about patterns of media content and experience, all of this while acknowledging the fundamental limits to what is knowable and acknowledging that any understanding of media or its effects is prone to be immediately out of date.
### Acknowledgments
This article benefited from discussion and feedback from participants at the University of Southern California in November 2017.
#### References
• Albertson, B. L., & Lawrence, A. (2009). After the credits roll: The long-term effects of educational television on public knowledge and attitudes. American Politics Research, 37(2), 275–300.
• Althaus, S. L., & Tewksbury, D. (2007). Toward a new generation of media use measures for the ANES report to the Board of Overseers (Technical report). American National Election Studies Board of Governors.
• Angrist, J. D. (1990). Lifetime earnings and the Vietnam draft lottery: Evidence from Social Security administrative records. American Economic Review, 80(3), 313–336.
• Arceneaux, K., Gerber, A. S., & Green, D. P. (2006). Comparing experimental and matching methods using a large-scale field experiment on voter mobilization. Political Analysis, 14(1), 37–62.
• Arceneaux, K., & Johnson, M. (2012). Changing minds or changing channels? Media effects in the era of viewer choice. Chicago, IL: University of Chicago Press.
• Barberá, P., Jost, J. T., Nagler, J., Tucker, J. A., & Bonneau, R. (2015). Tweeting from left to right: Is online political communication more than an echo chamber? Psychological Science, 26(10), 1531–1542.
• Bartels, L. M. (1993). Messages received: The political impact of media exposure. American Political Science Review, 87(2), 267–285.
• Bennett, W. L., & Iyengar, S. (2008). A new era of minimal effects? The changing foundations of political communication. Journal of Communication, 58, 707–731.
• Berelson, B. R., Lazarsfeld, P. F., & McPhee, W. N. (1954). Voting: A study of opinion formation in a presidential campaign. Chicago, IL: University of Chicago Press.
• Cantril, H. (1940). Gauging public opinion. Princeton, NJ: Princeton University Press.
• Chaffee, S. H., & Schleuder, J. (1986). Measurement and effects of attention to media news. Human Communication Research, 13(1), 76–107.
• Clinton, J. D., & Enamorado, T. (2014). The national news media’s effect on Congress: How Fox News affected elites in Congress. Journal of Politics, 76(4), 928–943.
• Cramer, K. J. (2016). Politics of resentment. Chicago, IL: University of Chicago Press.
• Cramer, K. J., & Toff, B. J. (2017). The fact of experience: Rethinking political knowledge and civic competence. Perspectives on Politics, 15(3), 754–770.
• DellaVigna, S., & Kaplan, E. (2007). The Fox News effect: Media bias and voting. Quarterly Journal of Economics, 122(3), 1187–1234.
• Dilliplane, S. (2011). All the news you want to hear: The impact of partisan news exposure on political participation. Public Opinion Quarterly, 75(2), 287–316.
• Dilliplane, S., Goldman, S. K., & Mutz, D. C. (2013). Televised exposure to politics: New measures for a fragmented media environment. American Journal of Political Science, 57(1), 236–248.
• Druckman, J. N., Fein, J., & Leeper, T. J. (2012). A source of bias in public opinion stability. American Political Science Review, 106(2), 430–454.
• Druckman, J. N., & Leeper, T. J. (2012a). Is public opinion stable? Resolving the micro/macro disconnect in studies of public opinion. Daedalus, 141(4), 50–68.
• Druckman, J. N., & Leeper, T. J. (2012b). Learning more from political communication experiments: Pretreatment and its effects. American Journal of Political Science, 56(4), 875–896.
• Druckman, J. N., Levendusky, M. S., & McLain, A. (2018). No need to watch: How the effects of partisan media can spread via interpersonal discussions. American Journal of Political Science, 61(1), 99–112.
• Durante, R., Pinotti, P., & Tesei, A. (2013). Voting alone? The political and cultural consequences of commercial TV. Paolo Baffi Centre Research Paper No. 2013-137.
• Enikolopov, R., Petrova, M., & Zhuravskaya, E. (2011). Media and political persuasion: Evidence from Russia. American Economic Review, 101(7), 3253–3285.
• Erikson, R. S., & Stoker, L. (2011). Caught in the draft: The effects of Vietnam draft lottery status on political attitudes. American Political Science Review, 105(2), 1–17.
• Eveland, W. P., Hayes, A. F., Shah, D. V., & Kwak, N. (2005). Understanding the relationship between communication and political knowledge: A model comparison approach using panel data. Political Communication, 22(4), 423–446.
• Eveland, W. P., Hutchens, M. J., & Shen, F. (2009). Exposure, attention, or “use” of news? Assessing aspects of the reliability and validity of a central concept in political communication research. Communication Methods and Measures, 3(4), 223–244.
• Eveland, W. P., & Scheufele, D. A. (2000). Connecting news media use with gaps in knowledge and participation. Political Communication, 17(3), 215–237.
• Eveland, W. P., Seo, M., & Marton, K. (2002). Learning from the news in campaign 2000: An experimental comparison of TV news, newspapers, and online news. Media Psychology, 4(4), 353–378.
• Feezell, J. T. 2017. Agenda setting through social media: The importance of incidental news exposure and social filtering in the digital era. Political Research Quarterly, 71(2), 482–494.
• Freedman, P., & Goldstein, K. (1999). Measuring media exposure and the effects of negative campaign ads. American Journal of Political Science, 43(4), 1189–1208.
• Fridkin, K. L., Kenney, P. J., Gershon, S. A., Shafer, K., & Woodall, G. S. (2007). Capturing the power of a campaign event: The 2004 presidential debate in Tempe. Journal of Politics, 69(3), 770–785.
• Gaines, B. J., & Kuklinski, J. H. (2011). Experimental estimation of heterogeneous treatment effects related to self-selection. American Journal of Political Science, 55(3), 724–736.
• Garrett, R. K., Carnahan, D., & Lynch, E. K. (2013). A turn toward avoidance? Selective exposure to online political information, 2004–2008. Political Behavior, 35(1), 113–134.
• Gelman, A., & Imbens. G. W. (2013). Why ask why? Forward causal inference and reverse causal questions. NBER Working Paper 19614.
• Gerber, A. S., Gimpel, J. G., Green, D. P., & Shaw, D. R. (2011). How large and long-lasting are the persuasive effects of televised campaign ads? Results from a large scale randomized experiment. American Political Science Review, 105(1), 135–150.
• Gerber, A. S., & Green, D. P. (2012). Field experiments: Design, analysis, and interpretation. New York: W. W. Norton.
• Goldman, S. K., Mutz, D. C., & Dilliplane, S. (2013). All virtue is relative: A response to prior. Political Communication, 30(4), 635–653.
• Graber, D. A. (1988). Processing the news: How people tame the information tide. New York, NY: Guilford Press.
• Guess, A. M. (2014). Measure for measure: An experimental test of online political media exposure. Political Analysis, 23(1), 59–75.
• Hayes, D., & Turgeon, M. (2009). A matter of distinction: Candidate polarization and information processing in election campaigns. American Politics Research, 38(1), 165–192.
• Holland, P. W. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81(396), 945–960.
• Hovland, C. I. (1959). Reconciling conflicting results derived from experimental and survey studies of attitude change. American Psychologist, 14(1), 8–17.
• Huber, G. A., & Arceneaux, K. (2007). Identifying the persuasive effects of presidential advertising. American Journal of Political Science, 51(4), 957–977.
• Iyengar, S., & Kinder, D. R. (1987). News that matters: Television and American opinion. Chicago, IL: University of Chicago Press.
• Jerit, J., Barabas, J., Pollock, W., Banducci, S., Stevens, D., & Schoonvelde, M. (2016). Manipulated vs. measured: Using an experimental benchmark to investigate the performance of self-reported media exposure. Communication Methods and Measures, 10(2–3), 99–114.
• Katz, E., & Lazarsfeld, P. F. (2005). Personal influence: The part played by people in the flow of mass communication. Brunswick, NJ: Transaction. (Original work published 1960)
• Keele, L. J., & Titiunik, R. (2014). Geographic boundaries as regression discontinuities. Political Analysis, 23(1), 127–155.
• King, G., Schneer, B., & White, W. (2017). How the news media activate public expression and influence national agendas. Science, 358(6364), 776–780.
• Krasno, J. S., & Green, D. P. (2008). Do televised presidential ads increase voter turnout? Evidence from a natural experiment. Journal of Politics, 70(1), 245–261.
• Kull, S., Ramsay, C., & Lewis, E. (2003). Misperceptions, the media, and the Iraq war. Political Science Quarterly, 118(4), 569–598.
• LaLonde, R. J. (1986). Evaluating the econometric evaluations of training programs with experimental data. American Economic Review, 76(4), 604–620.
• Lazarsfeld, P. F. (1940a). “Panel” studies. Public Opinion Quarterly, 4(1), 122–128.
• Lazarsfeld, P. F. (1940b). Radio and the printed page. New York, NY: Duell, Sloan & Pierce.
• Lazarsfeld, P. F., & Fiske, M. (1938). The “panel” as a new tool for measuring opinion. Public Opinion Quarterly, 2(4), 596–612.
• Lazer, D., & Radford, J. (2017). Data ex machina: Introduction to big data. Annual Review of Sociology, 43(1), 19–39.
• Leeper, T. J. (2017). How does treatment self-selection affect inferences about political communication? Journal of Experimental Political Science, 4(1), 21–33.
• Lelkes, Y., Sood, G., & Iyengar, S. (2015). The hostile audience: The effect of access to broadband Internet on partisan affect. Unpublished manuscript, University of Amsterdam.
• Lerner, D. (1958). The passing of traditional society: Modernizing the Middle East. Glencoe, IL: Free Press of Glencoe.
• Martin, G. J., & Yurukoglu, A. (2017). Bias in cable news: Persuasion and polarization. American Economic Review, 107(9), 2565–2599.
• Menchen-Trevino, E., & Karr, C. (2012). Researching real-world web use with Roxy: Collecting observational web data with informed consent. Journal of Information Technology & Politics, 9(3), 254–268.
• Morgan, S. L., & Winship, C. (2015). Counterfactuals and causal inference: Methods and principles for social research (2nd ed.). New York, NY: Cambridge University Press.
• Nelson, T. E., Clawson, R. A., & Oxley, Z. M. (1997). Media framing of a civil liberties conflict and its effect on tolerance. American Political Science Review, 91(3), 567–583.
• Nielsen, R. K. (2012). Ground wars: Personalized communication in political campaigns. Princeton, NJ: Princeton University Press.
• Paluck, E. Levy, Lagunes, P., Green, D. P., Vavreck, L., Peer, L., & Gomila, R. (2015). Does product placement change television viewers’ social behavior? PLOS ONE, 10(9), e0138610.
• Panagopoulos, C., & Green, D. P. (2008). Field experiments testing the impact of radio advertisements on electoral competition. American Journal of Political Science, 52(1), 156–168.
• Potter, W. J. (2011). Conceptualizing mass media effect. Journal of Communication, 61(5), 896–915.
• Price, V., & Zaller, J. (1993). Who gets the news? Alternative measures of news reception and their implications for research. Public Opinion Quarterly, 57(2), 133–164.
• Prior, M. (2003). Any good news in soft news? The impact of soft news preference on political knowledge. Political Communication, 20(2), 149–171.
• Prior, M. (2007). Post-broadcast democracy: How media choice increases inequality in political involvement and polarizes elections. New York, NY: Cambridge University Press.
• Prior, M. (2009a). The immensely inflated news audience: Assessing bias in self-reported news exposure. Public Opinion Quarterly, 73(1), 130–143.
• Prior, M. (2009b). Improving media effects research through better measurement of news exposure. Journal of Politics, 71(3), 893–908.
• Prior, M. (2013). The challenge of measuring media exposure: Reply to Dilliplane, Goldman, and Mutz. Political Communication, 30(4), 620–634.
• Romero-Canyas, R., Larson-Konar, D., Redlawsk, D. P., Borie-Holtz, D., Gaby, K., Langer, S., & Schneider, B. (2018). Bringing the heat home: Television spots about local impacts reduce global warming denialism. Environmental Communication, 5(3), 1–21.
• Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55.
• Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. Annals of Statistics, 6(1), 34–58.
• Rubin, D. B. (1990). Comment: Neyman (1923) and causal inference in experiments and observational studies. Statistical Science, 5(4), 472–480.
• Searles, K., Fowler, E. F., Ridout, T. N., Strach, P., & Zuber, K. (2017). The effects of men’s and women’s voices in political advertising. Journal of Political Marketing, 1–29.
• Seawright, J. (2016). Multi-method social science: Combining qualitative and quantitative tools. Cambridge, UK: Cambridge University Press.
• Sekhon, J. S., & Titiunik, R. (2012). When natural experiments are neither natural nor experiments. American Political Science Review, 106(1), 1–23.
• Sen, M., & Wasow, O. (2016). Race as a bundle of sticks: Designs that estimate effects of seemingly immutable characteristics. Annual Review of Political Science, 19(1), 499–522.
• Shadish, W. R., Cook, T. D., & Campbell, D. T. (2001). Experimental and quasi-experimental designs for generalized causal inference. Boston, MA: Houghton Mifflin.
• Sinclair, B. (2012). The social citizen: Peer networks and political behavior. Chicago, IL: University of Chicago Press.
• Slater, M. D., Goodall, C. E., & Hayes, A. F. (2009). Self-reported news attention does assess differential processing of media content: An experiment on risk perceptions utilizing a random sample of U.S. local crime and accident news. Journal of Communication, 59(1), 117–134.
• Slothuus, R. (2015). Assessing the influence of political parties on public opinion: The challenge from pretreatment effects. Political Communication, 33(2), 1–26.
• Sovey, A. J., & Green, D. P. (2011). Instrumental variables estimation in political science: A readers’ guide. American Journal of Political Science, 55(1), 188–200.
• Tewksbury, D., Althaus, S. L., & Hibbing, M. V. (2011). Estimating self-reported news exposure across and within typical days: Should surveys use more refined measures? Communication Methods and Measures, 5(4), 311–328.
• Toff, B., & Nielsen, R. K. (2018). “I just Google it”: Folk theories of distributed discovery. Journal of Communication, 68(3), 636–657.
• Voigtlaender, N., & Voth, H.-J. (2014). Highway to Hitler. NBER Working Paper 20150. doi:10.3386/w20150
• de Vreese, C. H., & Boomgaarden, H. G. (2006). Media message flows and interpersonal communication: The conditional nature of effects on public opinion. Communication Research, 33(1), 19–37.
### Notes
• 1. The study of media can also view media as an outcome to be explained—either at the macro level from a supply-side perspective or at the micro level in terms of determinants of individual-level demand or exposure—but I set aside these questions for the purposes of this article.
• 2. A critique sometimes raised at this point is that even though observational methods risk being subject to unobserved confounding, they at least provide “externally valid” or “generalizable” insights. This is, however, a canard. Unless an observational method satisfies assumptions that enable causal inference, any supposed “effect” that is identified (e.g., via a regression coefficient) is not generalizable because it is not a valid causal effect estimate to begin with (Morgan & Winship, 2015).
• 3. Traditional potential outcomes notation typically omits time subscripts, which can be incorrectly interpreted to mean that within-person, over-time variations in a cause provide direct insight into causal effects. That can be true, but only under a strong assumption that potential outcomes are independent of earlier potential outcomes (in other words, that treatments are noncumulative). In light of strong evidence of pretreatment dynamics (Druckman & Leeper, 2012a; Slothuus, 2015), it is not generally appropriate to make that assumption.
• 4. We might define x differently, allowing for a variety of other experiences such as non-exposure or exposure to varying mixes of public safety and free speech content, but effects would be defined similarly: The causal effect of any particular kind of coverage would be a difference in individual potential outcomes relative to some specified alternative.
• 5. This is a strict definition of “media effect.” Researchers might also be interested in various descriptives such as individuals’ interpretations of media, reflections upon media expressed in lay causal language, or subjective perceptions of first- or third-person media effects, but we should not consider those subjective interpretations to be media effect in a strict sense.
• 6. Of course, some media content is actually random. But short of published evaluations of these tests (e.g., Gerber, Gimpel, Green, & Shaw, 2011; King, Schneer, & White, 2017; Paluck et al., 2015; Panagopoulos & Green, 2008), it would be hard to know what is random and what is not.
• 7. There is no reason to believe, without further assumptions, that individuals attentive to different news sources had similar levels of misperceptions in the absence of any news exposure. Self-selection into media and effects of media are empirically indistinguishable in cross-sectional, observational research.
• 8. While researchers have classically distinguished mere exposure from more in-depth attention or reception of content, media effects can occur in the absence of more in-depth engagement and processing of content. What matters then is not what citizens can recall about their experience but the content of those experiences per se. Media effects are defined by stimuli or inputs, not recollection thereof.
• 9. Recognizing, of course, that what is considered the most credible method will no doubt change in the future.
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http://mathhelpforum.com/statistics/189658-find-number-different-order-triples.html
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# Thread: find the number of different order triples
1. ## find the number of different order triples
Find the number of different order triples (a,b,c) s.t a+b+c=12 if
a) a,b,c must be nonegetive integers
b) a,b,c must be positive integers
is this permatutaion or combination? Suppose there is 12 choices for a , then b will be depend on a, and c will depend on both a and b
2. ## Re: find the number of different order triples
Hello, wopashui!
Believe it or not this is a Combination problem.
But you'll have see the explanation.
Find the number of different ordered triples $(a,b,c)$
such that $a+b+c\,=\,12$ if:
. . a) $a,b,c$ must be nonnegetive integers.
Place 12 objects in a row, inserting a space before, after and between them.
. . $\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;* \;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_$
Place two "dividers" in any of the 13 spaces.
So that: . $*\;*\;*\;*\;*\,|\,*\;*\;*\;*\,|\,*\;*\;\:*$ .represents: $5 + 4 + 3$
. . and: . $*\;*\;*\;*\,||\,*\;*\;*\;*\;*\;*\;*\;\,*$ .represents: $4 + 0 + 8$
If the dividers are placed in two different spaces, there are: . $_{13}C_2 = 78$ ways.
If the dividers are placed in the same space, there are: $13$ ways.
Hence, there are: . $78 + 13 \,=\,91$ ways to place the dividers.
Therefore, there are $91$ triples of nonnegative integers whose sum is 12.
b) $a,b,c$ must be positive integers.
Place 12 objects in a row, inserting a space between them.
. . $*\;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;* \;\_\;*\;\_\;*\;\_\;*\;\_\;*\;\_\;*$
Choose 2 of the 11 spaces and insert "dividers".
So that: . $*\;*\;*\;*\;*\,|\,*\;*\;*\;*\,|\,*\;*\;\:*$ .represents: $5 + 4 + 3$
. . and: . $*\;*\;*\;*\,|\,*\;*\;*\;*\;*\;*\;*\,|\,*$ .represents: $4 + 7 + 1$
The dividers are placed in two different spaces.
. . There are: . $_{11}C_2 = 55$ ways.
Therefore, there are $55$ ordered triples of positive integers whose sum is 12.
3. ## Re: find the number of different order triples
thanks alot, but i dun understand why is the second part only has 11C2, not 13C2?
4. ## Re: find the number of different order triples
anyone can explain?
5. ## Re: find the number of different order triples
Originally Posted by wopashui
Find the number of different order triples (a,b,c) s.t a+b+c=12 if
b) a,b,c must be positive integers
Originally Posted by wopashui
thanks alot, but i dun understand why is the second part only has 11C2, not 13C2?
Think of the 12 as being twelve 1's. Lets make the variables positive by putting a 1 is each to begin with. Now that leaves us with nine 1's to distribute: $\binom{9+3-1}{9}$.
6. ## Re: find the number of different order triples
thx,, so the first part would be 12+3-1 C 14, which is 91
7. ## Re: find the number of different order triples
Originally Posted by wopashui
thx,, so the first part would be 12+3-1 C 14, which is 91
@wopashui,
You have absolutely no idea about any of this.
You are either playing us for fools or you just don't get it.
I am done with you in any case.
Good luck.
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https://www.esaral.com/q/find-the-value-50719
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Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!
# Find the value
Question:
Let $A=\{1,2,3), B=\{4,5,6,7)$ and let $f=\{(1,4),(2,5),(3,6)\}$ be a function from $A$ to $B .$ State whether $f$ is one-one.
Solution:
To state: Whether f is one-one
Given: $f=\{(1,4),(2,5),(3,6)\}$
Here the function is defined from $A \rightarrow B$
For a function to be one-one if the images of distinct elements of $A$ under $f$ are distinct i.e. 1,2 and 3 must have a distinct image.
From $f=\{(1,4),(2,5),(3,6)\}$ we can see that 1,2 and 3 have distinct image.
Therefore $\mathrm{f}$ is one-one
Ans) $f$ is one-one
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https://www.hardinscientific.com/blogs/news/if-the-strong-nuclear-force-is-stronger-than-electrostatic-repulsion-why-dont-nuclei-collapse-into-a-point
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# If the strong nuclear force is stronger than electrostatic repulsion, why don't nuclei collapse into a point?
Today in class we were discussing the strong nuclear force, and our teacher was explaining about how the strong nuclear force counteracts the repulsion force between protons in a nucleus. When asked about the relative strength of the two forces in question, she said that "The strong nuclear force is the strongest force of nature, and is infinitely stronger than the repulsion force between the protons". Now, if that were true, how would the atom remain in equilibrium, because if I'm correct, Equilibrium is achieved when the net force on a body is zero. However, in this situation, that doesn't seem to be the case. Could someone elaborate on this apparent contradiction? $\begingroup$ I would strongly disagree with that statement (bad puns are great). Obviously the strong force is not infinitely times greater than the repulsion force. In order for that to be true, there would either have to be zero force repelling the protons or infinite strong force holding them together. I'm afraid neither is the case. Even a cursory search on wikipedia should tell you that the strong force is only 137 times greater than the EM force. Go back to your prof and tell her you disagree $\endgroup$ – Jim Jul 26 '16 at 13:11 $\begingroup$ The origin of the strong force is the fact that the electromagnetic theory as it is known now demands the nucleus to fall apart. It isn't the case, so something had to be invented. $\endgroup$ – bright magus Jul 26 '16 at 13:12 $\begingroup$ Are you sure that your teacher said 'strong force isinfinitely stronger than repulsive force between protons? Is she said that, then its wrong. $\endgroup$ – AMS Jul 26 '16 at 13:16 $\begingroup$ @Jim That is a pretty weak argument.The gravity of this question makes me wonder about how strongly you are trying to, em, help, given the bad pun in your answer.Together, unified, we can do better; we can lift up a standard of high quality comments, break the confinement of off topic comments, be grander than ourselves, stop stringing people along, and model better behavior.In theory, QED, but more importantly: OP, does simply pointing out that the ratio isn't actually infinite sufficient to answer your question, or are you wondering how the protons don't collide? $\endgroup$ – Yakk Jul 26 '16 at 15:29 $\begingroup$ @Yakk I sentence you to walk the Planck. $\endgroup$ – Don Branson Jul 26 '16 at 15:41 First, the strong force acts on scales where our classical idea of forces as something that obeys Newton's laws breaks down anyway. The proper description of the strong force is as a quantum field theory. On the level of quarks, this is a theory of gluons, but on scales of the nucleus, only a "residual strong force", the nuclear force remains, which can be thought of as being effectively mediated by pions. Now, a force mediated by pions is very different from one mediated by photons, for the simple reason that pions are massive. Massive forces do not, in their classical limit, follow a pure inverse square law, but yield the more general Yukawa potential, which goes as $\propto \frac{\mathrm{e}^{-mr}}{r^2}$ where $m$ is the mass of the mediating particle. That is, massive forces fall off far faster than electromagnetism. So this makes it already difficult to tell what the "strength" of a force exactly is - it depends on the scale you are looking at, as Wikipedia's table for the strengths of the fundamental forces rightly acknowledges. However, in no sense is the strong force "infinitely stronger" than the electromagnetic force - it is simply much stronger than it, sufficient to keep nuclei together against electromagnetic repulsion. Now, the person who said that it is "infinitely stronger" might have had something different in mind which is not actually related to the strength of the force but to its fundamentally quantum mechanical nature: Confinement, the phenomenon that particles charged under the fundamental (not the residual) strong force cannot freely exist in nature. When you try - electromagnetically or otherwise - to separate two quarks bound by the strong force, then you will never get two free quarks. The force between these two quarks stays constant with increasing distance, it does not obey an inverse square law at all, and in particular the energy to being on of the two quarks to infinity is not finite. At some point, when you have invested enough energy, there will be a spontaneous creation of a new quark-antiquark pair and you will end up with two bound quark systems, but no free quark. In this sense, one might say that the strong force is "infinitely stronger", but crucially this is not the aspect of the strong force that keeps nuclei together; the theory of pions shows no confinement. $\begingroup$ The equilibrium question: shouldn't mentioning exclusion pressure be part of an answer? $\endgroup$ – Yakk Jul 26 '16 at 15:15 $\begingroup$ @Yakk Yes, if one wanted to do a full account of all the forces at work, exclusion would add to the electromagnetic repulsion. But the question appeared to me to be about a misconception that the strong force is "infinitely strong" - I presume OP has no problem with accepting that finitely strong forces (no matter whether there are two, three, four, or even more at work) can achieve equilibrium. $\endgroup$ – ACuriousMind♦ Jul 26 '16 at 15:23 $\begingroup$ Nice answer, I just would like to point out that it is not the force between two quarks that grows linearly with distance. It is the energy of the pair. $\endgroup$ – Diracology Jul 26 '16 at 15:59 $\begingroup$ @Diracology: Ahh, right. The force is constant, I guess. $\endgroup$ – ACuriousMind♦ Jul 26 '16 at 16:01 $\begingroup$ This is still a bit short of the posed question, though. (i) The strong force doesn't need to be infinitely stronger than electromagnetic repulsion, it just needs to be stronger at all positions, and (ii) Yukawa potentials die off past a certain point, but the question concerns what happens in the $r\to0$ limit, and there the Yukawa potential is essentially equivalent to a Coulombic force. When two protons approach, at some point the strong attraction turns off and they must begin to repel past an equilibrium position - that's what the question is asking for. $\endgroup$ – Emilio Pisanty Jul 27 '16 at 0:56 Your existing answer talks about quark confinement, but stable nuclei can't really be described using quark and gluon degrees of freedom.Also your existing answer doesn't answer your title question: why don't nuclei collapse to a point? To first approximation, nuclei do collapse into a point.The diameter of a nucleus is typically about $10^{-5}$ the diameter of an atom, which means the nucleus occupies something like $10^{-15}$ of the atomic volume.If your atom were the size of a house, the nucleus, to scale, would be the size of a grain of salt (and yet containing 99.95% of the atom's mass). In nuclear physics it makes more sense to talk about energy than it does to talk about force.The two concepts are closely related.Two protons separated by a distance $r$ have an "electrical" interaction energy $$U_E = +\alpha\frac{\hbar c}{r}.$$ Here $\hbar c = 200\rm\,MeV\,fm$ relates distance and energy. The fine structure constant, $\alpha \approx 0.0073 \approx 1/137$, represents the strength of the electrical interaction. The positive sign, and the $r$ on the bottom, mean that bringing two protons closer together stores energy in the electric field between them. If you find yourself with two protons at rest some distance apart, they'll tend to evolve to reduce the energy stored in the electric field by moving yet further apart; this is the sense in which the electric interaction is repulsive. The electric field isn't the only place where interacting protons can store energy.There is also the pion field, whose interaction energy is given by a Yukawa potential, $$U_\pi = -\alpha_\pi \frac{\hbar c}r \times e^{-m_\pi r}.$$ This is mostly the same as the electrical potential, but the differences are important: The sign is negative: protons liberate energy from the pion field by approaching each other, so the force is attractive. There's a different coupling constant, $\alpha_\pi$.If I'm converting units correctly, the pion coupling constant is something like $\alpha_\pi\sim100$: the energy associated with the "pion exchange" interaction may be as much as ten thousand times stronger than the energy associated with a "photon exchange" interaction. Critically, there's an exponential factor that depends on the mass of the pion, $m_\pi$.To be proper this should have some factors of $\hbar$ and $c$ to make the argument of the exponential dimensionless; alternatively we can be cleverer about units and not have any distracting cruft.This means there is a length scale $r_0 \propto 1/m_\pi$ beyond which the pion interaction totally dies away, but for very short distances the interaction looks like electricity with a different coupling constant. These differences address a little of your confusion. The strong interaction is much stronger than electromagnetism, but not infinitely stronger.But your title question still remains: why doesn't the nucleus collapse exactly to a point?That's because we still haven't exhausted the forest of different ways that two protons can store energy.The next two that are important are the rho and omega fields, \begin{align} U_\rho &= +\alpha_\rho \frac{\hbar c}r \times e^{-m_\rho r}, \\ U_\omega &= +\alpha_\omega \frac{\hbar c}r \times e^{-m_\omega r}. \end{align} Like the pion field, these meson interactions "turn off" when the nuclei separate from each other, but the distances are shorter than for the pion because the masses are larger.So the interaction between two protons has at least three different regions: Here's a plot using the potentials we've discussed so far: This simple model reproduces several real features of real nuclei: In uniform nuclear matter, nucleons are separated by about 1.2 fm. The energy required to remove one nucleon from a nucleus is typically about 10 MeV. In very heavy nuclei, the length scale for nuclear attraction is shorter than the diameter of the nucleus; such nuclei are unstable. You can't tell from this plot, but the total interaction energy becomes positive --- that is, electrostatic repulsion wins out over strong attraction --- at a separation of about 12.5 fm. Uranium-235, famously unstable, has diameter 14 fm. Uranium is unstable because protons at one end of the nucleus are repelled by, rather than attracted to, protons at the other end of the nucleus. So let me get this correct. Gravity is what binds things together but the strong force is the glue holding everything in place!! Hmm something not right here. The universeis made of 99.9% plasma. And electromagnetism rules our reality. Why concentrate on the front force at scales of Planck length which have no importance on our reality whatsoever.
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http://www.cs.columbia.edu/~rocco/papers/stoc03ptfdb.html
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New Degree Bounds for Polynomial Threshold Functions.
R. O'Donnell and R. Servedio.
Combinatorica 30(3), 2010, pp. 327-358.
Preliminary version in 35th Annual Symposium on Theory of Computing (STOC), 2003, pp. 325-334.
Abstract:
We give new upper and lower bounds on the degree of real multivariate polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of {\em superconstant} depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved {\em constructively}; we give explicit dual solutions to the necessary linear programs.
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https://space.stackexchange.com/tags/performance/hot
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# Tag Info
111
Because linear increases in delta-v require exponential increases in mass, small changes to the assumptions you make about fuel tank structural mass and engine thrust-to-weight ratio start to make very large changes in the final size of the rocket. For example, if you're getting off a 3.6g planet with a 7-stage rocket, the difference between 88% fuel ...
26
First, let us look at the rocket equation: $$\Delta v=\ln \left(\frac{m_0}{m_f}\right)v_e$$ That tells how much a rocket can change its velocity (the $\Delta v$). The requirements for reaching a higher velocity for a minimal orbit would increase on your heavier Earth. (For constant density it is proportional to the radius.) How can we increase the $\Delta ... 19 A few different factors contribute to the Raptor's higher thrust: The specific impulse -- force delivered per mass of propellant consumed -- of methane-LOX combustion is generally higher than kerosene-LOX, because the exhaust is composed of simpler and lighter molecules; The Raptor uses the staged combustion cycle, where the hot partially-combusted gases ... 14 First, let's get terminology straight: "Tilt maneuver", or "Gravity turn", sometimes also called "Pitch maneuver". It was called "Roll Program" in case of Space Shuttles, because it was connected with a roll, necessary for technical reasons but not contributing to flight efficiency directly. All rockets (and all flying bodies on Earth for that matter) are ... 13 The delta-v needed from low Earth orbit to a Hohmann transfer orbit with a periapse inside the Sun is actually "just" 21,300 m/s. But there is a better option. A bi-elliptic transfer to just hit a central body is better when the ratio between the orbital radius and the radius of the central body is larger than 4.82. The orbital radius of the Earth divided ... 13 According to Wikipedia, HIBEX employed a star-grain "composite modified double-base propellant", known as FDN-80, created from the mixing of ammonium perchlorate, aluminum, and double-base smokeless powder, with zirconium staples "randomly dispersed" throughout the matrix. APCP (ammonium perchlorate composite propellant) is occasionally ... 12 Launchers generally start at full throttle, so for the most part their immediate performance off the pad is determined solely by the type of launcher and mass of payload. Falcon 9's initial acceleration is quite modest, about 1.5 m/s2 vertically (thrust to weight ratio about 1.15, cancelling and exceeding 9.8m/s2 of surface gravity). Shuttle's initial TWR ... 11 This depends on what "better" is. But let us talk about fluorine. The main point of using it is that turning your hydrogen into$HF$gives more energy than getting$H_2O$for pure hydrogen, that gives a small improvement of$I_{sp}$. However, for fuels containing carbon, like JP1, (or perhaps RP-1 or JP4. JP1 has some unfortunate properties for rocket ... 9 I can answer the second question — engines are by and large fuel specific. There's plenty of complicated stuff that goes on in the combustion and the transition to supersonic flow that means you can't just exchange one fuel for another and expect it to be high-performing. As far as I know, there are no pre-existing methalox-burning engines that SpaceX ... 9 One thing mentioned was that it allowed the vehicle to lift more mass. All things being equal, I fail to see how tilt can increase the ability to increase the potential energy of the payload. All things weren't equal. The Shuttle was not an axially symmetric vehicle. The Shuttle roll program was performed starting about ten seconds after launch and lasted ... 9 There is likely minimal effect. At rocket speeds, there is very little effect of shear stress, the only significant effect is particles hitting the leading surface of the rocket. Also due to how fast hey are going, the effect of the rocket of "pushing air out of the way" does not have time to get far ahead of the rocket, and this drops further behind as ... 7 Almost all the launch vehicles lift off vertically and are designed to reach orbital speed, altitude and orientation as the upper stage completes its injection burn. Consider a launch vehicle lifting off vertically- The vehicle accelerates to overcome two forces- earth's gravity and the atmospheric drag. Image from rocketmime.com If the launch vehicle goes ... 7 note: I've accepted an answer 2.5 years ago. This paper was published recently so I thought I would add this supplemental answer since it may be an interesting reference for future readers. The Space.com article No Way Out? Aliens on 'Super-Earth' Planets May Be Trapped by Gravity links to Michael Hippke's ArXiv preprint Spaceflight from Super-Earths is ... 6 I'd assumed that Isp expresses the axial component of the velocity, so even if there is some transverse flow in the expanding exhaust, that wouldn't have to be accounted for beyond Isp, but is there something else? To be pedantic, Isp is specific impulse, or more fully "mass specific impulse": the impulse delivered per unit of mass flow. Impulse is force ... 6 The final stage of a rocket has to lift not just the payload but also itself. So lets look not at the payload mass alone but at the total mass lifted to the final orbit. According to http://www.spaceflightinsider.com/hangar/falcon/ the empty mass of the second stage is 3,900 kg. Lets add that the numbers in the table. If we add the mass of the final stage ... 6 All else being equal (e.g. propellant choice), higher-energy trajectories favor a rocket with more stages. One thought experiment that can help you understand this is to consider two missions launched on identical rockets, the first to LEO and the second to an interplanetary trajectory. Both missions have payloads sized to "max out" the capacity of the ... 6 This response addresses just the last part of your question "what sort of$I_\text{sp}$and thrust might it have", and does so in the sense of an ideal resistojet. I hope this isn't too basic an approach but its worth stepping through it to develop a more intuitive view of the very high level physics. There are similar equations in the link you gave though, ... 6 There were several factors in the launch date The late John F. Kennedy had promised to go to the moon within the decade. This was a secondary concern, but an important one nevertheless The failure of the Soviet N1 rocket on July 3, 1969. The Soviet program was desperately trying to keep up with the American program. NASA feared the Soviets would overtake ... 6 "Yes", but that would sort of be silly and it would highly depend on where you live, since it may be illegal in your country to mix your own rocket propellant. HIBEX used what is essentially a precursor to modern APCP (Ammonium Perchlorate Composite Propellant), which is widely used in amateur rocketry and commercially available. Its propellant ... 5 Borrowing from Wikipedia's article on modern ICBMs: One particular weapon developed by the Soviet Union (Fractional Orbital Bombardment System) had a partial orbital trajectory, and unlike most ICBMs its target could not be deduced from its orbital flight path. It was decommissioned in compliance with arms control agreements, which address the maximum ... 5 Not a planetological exposition in sight so, I'll add my two cents to this rather theoretical discussion. Amongst exoplanetologists, the consensus has emerged that 1.6 Earth radii and 5 Earth masses is likely to be the upper limit to rocky planets¹. Simulations have shown that above these figures, the bodies develop increasingly Mini-Neptune² like ... 5 The Ariane 5 user manual has the following data: Using a storable propellant upper stage, through a delayed ignition of this upper stage, Ariane 5, in the A5G version, has demonstrated its ability to carry a satellite weighing 3065 kg, leading to a total required performance of 3190 kg, towards the following earth escape orbit: - infinite velocity V∞ =... 5 The paper does not describe how the calculations for the tether are done, but I can make a guess. We take a small piece of the tether with mass$\delta m$and length$\delta r$, at distance$r$from the center. The tether is spinning at an angular rate$\omega$, and has an ultimate tensile strength$\sigma_\text{max}$and density$\rho$. The area$A$is a ... 5 They aren't launched slower but they are launched in different trajectories. This can be to control abort conditions and G-Loads. The most efficient launch is to get as high as possible before going for speed. The STS however was shallower to allow for the abort modes and control the forces. The best example I can think of at the moment is the man rating ... 5 Hall effect thrusters do not use strong magnetic fields and radio frequency power to heat electrons to high energy for ionization of the gas. Instead they rely on a DC current of electrons accelerated to a few hundred volts flowing through the gas volume for ionization. Since Krypton has a higher ionization potential than Xenon (roughly 14.0 versus 12.1 eV), ... 5 The season when the Saturn V launches doesn't matter, especially in Florida where the temperature remains relatively warm year round. The Saturn V was engineered to be very resilient and to withstand almost every weather condition. You can see the launch commit criteria of modern rockets here. As Uwe said, there have been Apollo missions launched in the ... 4 Besides pure oxygen, several other oxidizers in theory have better performance with hydrocarbon fuels, but none of them are used because of stability, toxicity and price issues. But let mention some of them: Ozone O3. It's allotrope of oxygen with enthalpy of formation 142,67 KJ/mol (2.97MJ/kg) which can bust combustion energy up to 30% depending on fuel ... 4 Not sure you'll get much useful data, but here's a useful datum point: Bloodhound SSC - the worlds fastest car is expected to reach 1000mph in 55 seconds from rest (42 seconds would be a perfect run, but 55 is the expected run), with a peak acceleration of 2g. 0 - 300mph (Point a) using the EJ-200 jet engine (generating around 0.5g), where the rocket will ... 4 Ignoring the complicated separation issue, there is a simple relation to calculate the effect on thrust based on mismatch of the exit plane pressure and ambient pressure, namely: $$F = q V_e + (P_e-P_a) A_e$$ Where$P_e$is the exit plane pressure,$P_a$is ambient pressure, and$A_e$is the exit plane area.$qV_e\$ without the correction term gives the ...
4
According to this article, in an overexpanded nozzle, the loss of efficiency is caused by the "pinching" of the exhaust plume by the ambient air pressure. In grossly overexpanded nozzles, there's another, more serious problem, where the exhaust flow separates from one side of the nozzle, adhering to the opposite side, which causes very uneven heating and ...
Only top voted, non community-wiki answers of a minimum length are eligible
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https://testbook.com/question-answer/abc-is-an-equilateral-triangle-the-side-bc-is-tri--607d0cfbda8b9d849be08dfd
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# ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3 BD. What is the ratio of AD2 to AB2?
This question was previously asked in
CDS Maths Previous Paper 10 (Held On: 8 Nov 2020) - 10
View all CDS Papers >
1. 7 ∶ 9
2. 1 ∶ 3
3. 5 ∶ 7
4. 1 ∶ 2
Option 1 : 7 ∶ 9
## Detailed Solution
Given:
In equilateral Δ ABC, BC is trisected at D such that BC = 3 × BD.
Calculation:
Observe the diagram given below carefully,
According to the question,
BC = 3 × BD
⇒ BD = BC/3
Also, We know that,
BE = BC/2 ----(∵ AE is the median of the Δ ABC which bisects BC)
Now,
In Δ AEB,
DE = BE - BD
⇒ (BC/2) - (BC/3)
⇒ (3 × BC - 2 × BC)/6
⇒ BC/6
Now, Applying Pythagoras Theorem in Δ ADE,
(AD)2 = (AE)2 + (DE)2 ----(i)
Again, Applying Pythagoras Theorem in Δ ABE,
(AB)2 = (AE)2 + (BE)2 ----(ii)
Subtracting equation (i) from equation (ii),
(AB)2 - (AD)2 = {(AE)2 - (AE)2} + {(BE)2 - (DE)2}
⇒ (AB)2 - (AD)2 = 0 + {(BC/2)2 - (BC/6)2}
⇒ (AB)2 - (AD)2 = {(BC)2/4} - {(BC)2/36}
⇒ (AB)2 - (AD)2 = (8/36) × (BC)2
⇒ (AB)2 - (AD)= (2/9) × (AB)2 ----(∵ AB = BC = CA, as Δ ABC is an equilateral triangle)
⇒ (AD)2 = (AB)2 - {(2/9) × (AB)2}
⇒ (AD)2 = (7/9) × (AB)2
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http://link.springer.com/journal/220
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# Communications in Mathematical Physics
ISSN: 0010-3616 (Print) 1432-0916 (Online)
## Description
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
331 Volumes 1,068 Issues 9,114 Articles available from 1965 - 2014
## Latest Articles
1. OriginalPaper
### Generalized Kähler Geometry
(October 2014)
2. OriginalPaper
### Hausdorff and Packing Spectra, Large Deviations, and Free Energy for Branching Random Walks in $${\mathbb{R}^d}$$ R d
(October 2014)
3. OriginalPaper
### The Scaling Limit of Polymer Pinning Dynamics and a One Dimensional Stefan Freezing Problem
(October 2014)
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http://www.numdam.org/item/AIHPC_2010__27_1_351_0/
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Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, p. 351-376
We consider the nonlinear Klein–Gordon equations coupled with the Born–Infeld theory under the electrostatic solitary wave ansatz. The existence of the least-action solitary waves is proved in both bounded smooth domain case and ${ℝ}^{3}$ case. In particular, for bounded smooth domain case, we study the asymptotic behaviors and profiles of the positive least-action solitary waves with respect to the frequency parameter ω. We show that when κ and ω are suitably large, the least-action solitary waves admit only one local maximum point. When $\omega \to \infty$, the point-condensation phenomenon occurs if we consider the normalized least-action solitary waves.
@article{AIHPC_2010__27_1_351_0,
author = {Yu, Yong},
title = {Solitary waves for nonlinear Klein--Gordon equations coupled with Born--Infeld theory},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {1},
year = {2010},
pages = {351-376},
doi = {10.1016/j.anihpc.2009.11.001},
zbl = {1184.35286},
mrnumber = {2580514},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_1_351_0}
}
Yu, Yong. Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, pp. 351-376. doi : 10.1016/j.anihpc.2009.11.001. http://www.numdam.org/item/AIHPC_2010__27_1_351_0/
[1] J.C. Brunelli, Dispersionless limit of integrable models, Brazilian J. Physics 30 no. 2 (June 2000), 455-468
[2] Max Born, Modified field equations with a finite radius of the electron, Nature 132 (1933), 282 | Zbl 0007.23402
[3] Max Born, On the quantum theory of the electromagnetic field, Proc. Roy. Soc. A 143 (1934), 410-437 | Zbl 0008.13803
[4] V. Benci, D. Fortunato, Solitary waves of the nonlinear Klein–Gordon equation coupled with the Maxwell equations, Rev. Math. Phys. 14 no. 4 (2002), 409-420 | MR 1901222 | Zbl 1037.35075
[5] V. Benci, D. Fortunato, Solitary waves in the nonlinear wave equation and in gauge theories, Fixed Point Theory Appl. 1 (2007), 61-86 | MR 2282344 | Zbl 1122.35121
[6] V. Benci, D. Fortunato, Solitary waves in classical field theory, V. Benci, A. Masiello (ed.), Nonlinear Analysis and Applications to Physical Sciences, Springer, Milano (2004), 1-50 | MR 2085829 | Zbl 06143112
[7] V. Benci, D. Fortunato, On the existence of infinitely many geodesics on space–time manifolds, Adv. in Math. 105 (1994), 1-25 | MR 1275190 | Zbl 0808.58016
[8] M. Born, L. Infeld, Foundation of the new field theory, Nature 132 (1933), 1004 | Zbl 0008.18405
[9] M. Born, L. Infeld, Foundation of the new field theory, Proc. Roy. Soc. A 144 (1934), 425-451 | Zbl 0008.42203
[10] V. Benci, P.H. Rabinowitz, Critical points theorems for indefinite functionals, Invent. Math. 52 (1979), 241-273 | MR 537061 | Zbl 0465.49006
[11] D. Cassani, Existence and non-existence of solitary waves for the critical Klein–Gordon equation coupled with Maxwell's equations, Nonlinear Anal. 58 (2004), 733-747 | MR 2085333 | Zbl 1057.35041
[12] Teresa D'Aprile, Dimitri Mugnai, Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations, Proc. Roy. Soc. Edinburgh Sect. A 134 no. 5 (2004), 893-906 | MR 2099569 | Zbl 1064.35182
[13] Pietro D'Avenia, Lorenzo Pisani, Nonlinear Klein–Gordon equations coupled with Born–Infeld type equations, Elect. J. Diff. Eqns. 26 (2002), 1-13 | MR 1884995 | Zbl 0993.35083
[14] H. Egnell, Asymptotic results for finite energy solutions of semilinear elliptic equations, J. Differential Equations 98 (1992), 34-56 | MR 1168970 | Zbl 0778.35009
[15] M. Esteban, P.L. Lions, Existence and non-existence results for semilinear elliptic problems in unbounded domanis, Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 1-14 | MR 688279 | Zbl 0506.35035
[16] M. Esteban, E. Séré, Stationary states of the nonlinear Dirac equation: A variational approach, Comm. Math. Phys. 171 (1995), 323-350 | MR 1344729 | Zbl 0843.35114
[17] D. Fortunato, L. Orsina, L. Pisani, Born–Infeld type equations for electrostatic fields, J. of Math. Phys. 43 no. 11 (2002), 5698-5706 | MR 1936545 | Zbl 1060.78004
[18] G.W. Gibbons, Born–Infeld particles and Dirichlet p-branes, Nucl. Phys. B 514 (1998), 603 | MR 1619525 | Zbl 0917.53032
[19] B. Gidas, W.-M. Ni, L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in ${R}^{n}$, Adv. in Math. 7A no. Suppl. Stud. (1981), 369-402 | MR 634248
[20] D. Gilbarg, Neil S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer (2001) | MR 1814364 | Zbl 1042.35002
[21] M.K. Kwong, Uniqueness of positive solutions of $\Delta u-u+{u}^{p}=0$ in ${R}^{n}$, Arch. Rational Mech. Anal. 105 (1989), 243-266 | MR 969899 | Zbl 0676.35032
[22] E. Long, Existence and stability of solitary waves in non-linear Klein–Gordon–Maxwell equations, Rev. Math. Phys. 18 (2006), 747-779 | MR 2267114 | Zbl 1169.78003
[23] C.-S. Lin, W.-M. Ni, I. Takagi, Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations 72 (1988), 1-27 | MR 929196 | Zbl 0676.35030
[24] F. Lin, Y. Yang, Gauged harmonic maps, Born–Infeld electromagnetism, and magnetic vortices, CPAM 56 (2003), 1631-1665 | MR 1995872 | Zbl 1141.58304
[25] D. Mugnai, Coupled Klein–Gordon and Born–Infeld type equations: Looking for solitary waves, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004), 1519-1528 | MR 2066416 | Zbl 1078.35100
[26] W.-M. Ni, J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, CPAM XLVIII (1995), 731-768 | MR 1342381 | Zbl 0838.35009
[27] N. Ogawa, Chaplygin Gas and Brane, Proceedings of the 8th International Conference on Geometry Integrability & Quantization (June 2007), 279-291 | MR 2341210
[28] R.S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19-30 | MR 547524 | Zbl 0417.58007
[29] J. Polchinski, TASI lectures on D-branes, arXiv:hep-th/9611050 R. Argurio, Brane physics in M-theory, hep-th/9807171 K.G. Savvidy, Born–Infeld action in string theory, hep-th/9906075
[30] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Reg. Conf. Ser. Math. vol. 65 (1986) | MR 845785
[31] M. Struwe, Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, 3rd edition
[32] N. Seilberg, E. Witten, String theory and noncommutative geometry, JHEP 9909 (1999), 032 | MR 1720697
[33] W.-M. Ni, I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, CPAM 44 (1991), 819-851 | MR 1115095 | Zbl 0754.35042
[34] Y. Yang, Classical solutions in the Born–Infeld theory, Proceedings: Mathematical, Physical and Engineering Sciences 456 no. 1995 (2000), 615-640 | MR 1808753 | Zbl 1122.78301
[35] X.-P. Zhu, Multiple entire solutions of a semilinear elliptic equation, Nonlinear Anal. 12 (1988), 1297-1316 | MR 969507 | Zbl 0671.35023
[36] Z. Zhang, K. Li, Spike-layered solutions of singularly perturbed quasilinear Dirichlet problems, J. Math. Anal. Appl. 283 (2003), 667-680 | MR 1991834 | Zbl 1073.35017
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http://math.stackexchange.com/users/29733/eliya-gwetta
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# eliya gwetta
less info
reputation
4
bio website location Chicago, IL age member for 1 year, 10 months seen Dec 11 '13 at 16:44 profile views 18
3 Question regarding Nested Interval Theorem 1 Existence of the empty set in the standard d-metric topology on a set $X$. 1 Reference request on analysis in $\mathbb{R}$ 1 Is this a valid proof of $f(S \cap T) \subseteq f(S) \cap f(T)$?
# 65 Reputation
+10 Reference request on analysis in $\mathbb{R}$ +10 Existence of the empty set in the standard d-metric topology on a set $X$. +10 Is this a valid proof of $f(S \cap T) \subseteq f(S) \cap f(T)$? +10 Question regarding Nested Interval Theorem
# 0 Questions
This user has not asked any questions
# 8 Tags
4 real-analysis × 2 1 functions 3 analysis 1 elementary-set-theory 3 sequences-and-series 1 general-topology 1 discrete-mathematics 1 homework
# 4 Accounts
Mathematics 65 rep 4 TeX - LaTeX 53 rep 5 Stack Overflow 1 rep MathOverflow 1 rep
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http://lambda-the-ultimate.org/node/4997
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## Parser error handling without exceptions
In brief
------
I'm porting an existing compiler/interpreter framework to Swift, from a more imperative code base. It currently exists in JavaScript (feh), Dart, and Objective-C. It has more-or-less the same (recursive descent) structure in all three languages; in particular, I use exceptions to immediately bail when I encounter a syntax error.
My proximal question is: how can I structure an exception-free parser to conveniently handle syntax errors? My more global question is: how do people do that in an idiomatically functional way?
Remarks
-------
Just about every line of parser code can (transitively) result in a syntax error. For example, to parse the language construct "split x into y" I write (roughly):
acceptToken(split) // Could fail if split is misspelled
source = expression() // Could fail if expression is faulty or missing
acceptToken(into) // Could fail
dest = expression() // Could fail
acceptToken(newline) // Could fail
return new JoinNode(source, dest)
It is convenient to expect that any of these calls will throw an exception, in particular that lines subsequent to the failure will not execute. Repeated wrapping and testing each line is just the sort of thing exceptions are supposed to save us from. (Although I agree the details of handling exceptions — rolling back the program state — are almost impossible to get right.)
What I am looking for is a design architecture that will let me continue exploit the isomorphism between the grammar and the code structure: one term in the grammar maps to one line of parser code. Not one line of parser code, wrapped in conditional tests, with each line testing the success/failure of its predecessor.
There have been some suggestions in this thread:
that involve optional types and comparisons to languages like Rust and Scala, but I did not see usable ideas from actual compiler writers. Suggestions or pointers/references welcome.
## Comment viewing options
### Parser combinators
Look into parser combinators, such as Haskell's Parsec package or Text.ReadP. These could express your current program almost exactly.
### Backtracking
In order to express the rules separately (using combinators or whatever) backtracking is the critical mechanism. Without backtracking you have to accept symbol at a time and know which alternatives are available at each step. The data structure would look like a regular tree for this (branching at the choice points) rather than a table of separate rules.
### Swift "has" exceptions
It just forces you to note them at the type level. The trivial case is Optional, which enforces handling of null pointer exceptions. There aren't traditional exception handling with try-blocks and what not, but pattern matching on an algebraic data type (enumerations in Swift) are equivalent. Another example would be NaNs and Infinities... these are exceptional values of floats, but they don't "raise" exceptions. Any function that takes in a float is expected to handle these values appropriately, along with all other values of floats. With algebraic data types, the compiler can actually enforce that each case is considered. Some IDEs attempt to warn you when you aren't handling exceptions raised in some exceptional languages, but I've not seen one that was correct all the time, nor do these languages have compile-time static analysis enforcing exception handling at all points. Perhaps there's something to be said along the lines of 'all languages with exceptions are dynamically typed', but I'm not willing to go that far.
Initially I was worried that Swift left out exceptions because Go has done alright without exceptions, but Go's syntax for error handling is rather obtuse. Upon realizing that Swift left out exceptions more because of Haskell's head [], I was much less disappointed in Swift.
### unwinding
Thanks kms, I did notice that there is a notion of exceptional behavior in Swift. What I am looking for is exception-style flow control, in particular the unwinding of deeply-nested, possibly recursive, activation record stacks. As Keean pointed out in the original Swift thread, this is very helpful in writing a parser where *every* line of code can (transitively) discover a syntax error, and must therefore somehow be prepared to alter flow control. Wrapping a method (and implicitly-transitively all its called methods) in a try block says "Every line of this block has an automatic test-and-break added to it."
I see that optional types and monads can achieve similar flow control and will try to wrap my imperative head around it.
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https://socratic.org/questions/how-do-you-use-the-quadratic-formula-to-find-both-solutions-to-the-quadratic-equ-3
|
Algebra
Topics
# How do you use the quadratic formula to find both solutions to the quadratic equation (2y - 3) (y + 1) = 5?
Jul 6, 2015
Multiply out and rearrange into the form $a {y}^{2} + b y + c = 0$ then use the quadratic formula to find:
$y = \frac{1 \pm \sqrt{65}}{4}$
#### Explanation:
$5 = \left(2 y - 3\right) \left(y + 1\right) = 2 {y}^{2} - y - 3$
Subtract $5$ from both sides to get:
$2 {y}^{2} - y - 8 = 0$
This is of the form $a {y}^{2} + b y + c = 0$
with $a = 2$, $b = - 1$ and $c = - 8$
This has solutions given by the quadratic formula:
$y = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$= \frac{1 \pm \sqrt{{\left(- 1\right)}^{2} - \left(4 \times 2 \times - 8\right)}}{2 \cdot 2}$
$= \frac{1 \pm \sqrt{65}}{4}$
##### Impact of this question
98 views around the world
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https://www.physicsforums.com/threads/future-pointing-and-past-pointing-time-like-vectors.850151/
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# Future-pointing and past-pointing time-like vectors
1. Dec 30, 2015
### spaghetti3451
1. The problem statement, all variables and given/known data
I need to prove the following:
a) If $P^{a}$ and $Q^{a}$ are time-like and $P^{a}Q_{a}>0$, then either both are future-pointing or both are past-pointing.
b) If $U^{a}$, $V^{a}$ and $W^{a}$ are time-like with $U^{a}V_{a}>0$ and $U^{a}W_{a}>0$, then $V^{a}W_{a}>0$.
2. Relevant equations
Using the 'mostly minus' convention, $A^a$ is time-like, null and space-like if $A^{a}A_{a}$ is $>0,=0,<0$ respectively.
A time-orientation is chosen by taking at will some time-like vector, say $U^{a} = (1,0,0,0)$, and designating it to be future-pointing. Any other time-like or null vector $V^{a}$ such that $g_{ab}U^{a}V^{b}>0$ is also future-pointing, whereas if $g_{ab}U^{a}V^{b}<0$, then $V^{a}$ is past-pointing.
3. The attempt at a solution
a) If $P^{a}$ is time-like future-pointing and $P^{a}Q_{a}>0$, then (by definition) $Q^{a}$ is also future-pointing.
Simialarly, for $P^{a}$ past-pointing.
b) If $U^{a}$ is time-like future-pointing and $U^{a}V_{a}>0$, then (by definition) $V^{a}$ is also future-pointing.
If $U^{a}$ is time-like future-pointing and $U^{a}W_{a}>0$, then (by definition) $W^{a}$ is also future-pointing.
Since both $V^{a}$ and $W^{a}$ are future-pointing, $V^{a}W_{a}>0$.
Similar argument for $U^{a}$ past-pointing.
Are my proofs sound?
2. Dec 30, 2015
### Staff: Mentor
Where is the definition for that?
Not by definition, but via (a).
(b) is fine once you fix (a).
Schwarz Inequality is your friend (from today!)
3. Dec 30, 2015
### spaghetti3451
I can see that the following theorem is useful:
For $U^{a}$ and $V^{a}$ timelike and $U^{0}, V^{0} >0$, we have that $U^{a}V_{a}>0$.
How do I relate the fact that $U^{0}, V^{0} >0$ with future-pointing and past-pointing vectors?
Last edited: Dec 30, 2015
4. Dec 30, 2015
### Staff: Mentor
That you can get from the definition now, if you evaluate the sums there explicitely.
5. Jan 1, 2016
### spaghetti3451
Alright, here's my proof.
We are given that $P^{a}$ and $Q^{a}$ are timelike and that $P^{a}Q_{a}>0$.
If $P^{a}$ is timelike, then $P^{a}P_{a}>0 \implies (P^{0})^{2}>(\vec{P})^{2}$. Similarly, for $Q^{a}$.
Therefore, $(P^{0})^{2}(Q^{0})^{2}>(\vec{P})^{2}(\vec{Q})^{2}$.
So, by the Cauchy-Schwarz inequality, $(P^{0}Q^{0})^{2}>(\vec{P}\cdot{\vec{Q}})^{2}$, which implies that either $P^{0}Q^{0}>\vec{P}\cdot{\vec{Q}}$, where the RHS is positive or $P^{0}Q^{0}<\vec{P}\cdot{\vec{Q}}$, where the RHS is negative.
On the other hand, if $P^{a}Q_{a}>0$, then $P^{0}Q^{0}>\vec{P}\cdot{\vec{Q}}$. Therefore, $P^{0}Q^{0}>0$.
So, either both $P^{0}$ and $Q^{0}$ are positive and hence future-pointing, or both $P^{0}$ and $Q^{0}$ are negative and hence past-pointing.
Is my proof correct?
6. Jan 1, 2016
### Staff: Mentor
Correct.
You can add a 1-line proof that future-pointing <=> P0>0.
7. Jan 1, 2016
### spaghetti3451
Isn't it a convention that a four-vector $P^{0}$ is future pointing iff $P^{0}>0$?
8. Jan 1, 2016
### Staff: Mentor
The definition you have in post 1 expresses it in a slightly different way, although you get this result by evaluating the sums there.
9. Jan 1, 2016
### spaghetti3451
So, you mean that a four-vector $P^{0}$ being future pointing iff $P^{0}>0$ is not a convention?
10. Jan 1, 2016
### spaghetti3451
The definition says that we choose an arbitrary time-like vector $P^{a}=(1,0,0,0)$ with $P^{0}>0$ and designate it to be future-pointing. Then, if $g_{ab}P^{a}Q_{a}>0$ for some time-like vector $Q^{a}$, then $Q^{a}$ is also future-pointing.
What strikes me is that the definition arbitrarily assigns a time-like vector $P^{a}$ with $P^{0}>0$ as being future-pointing. That's why I ask if it's a convention that a time-like vector $P^{a}$ with $P^{0}>0$ is called future-pointing.
And if so, I don't see why we need to use the $g_{ab}P^{a}Q_{a}>0$ to evaluate sums.
Last edited: Jan 1, 2016
11. Jan 1, 2016
### Staff: Mentor
It is an arbitrary convention, right - you could also assign positive time-components to past-pointing and negative ones to future-pointing. Would be odd, but it would lead to consistent physics as well.
You need to use it because you are given this definition of future-pointing.
12. Jan 1, 2016
### spaghetti3451
Ah! I see.
So, it is indeed an arbitrary definition. But what I do need to show is that the class of future-pointing vectors $P^{a}$ all have $P^{0}>0$ if at least one of them have $P^{0}>0$.
That is the reason why we choose $P^{a}=(1,0,0,0)$ because then, when we evaluate $P^{a}Q_{a}>0$, all the space-components of $Q_{a}$ are eliminated and we are left with the simple relation that $Q^{a}>0$.
Thus, we have shown basically that the class of future-pointing vectors and the class of past-pointing vectors do not overlap, and that each class can be identified by the sign of the temporal component of the four-vectors.
Am I correct?
13. Jan 1, 2016
### spaghetti3451
Alright, so now let me show the equivalence between statements 1 and 2.
1. A time-orientation is chosen by taking at will some time-like vector, say $U^{a}=(1,0,0,0)$ and designating it to be future-pointing. Any other time-like or null vector $V^{a}$ such that $U^{a}V_{a}>0$ is also future-pointing, whereas if $U^{a}V_{a}<0$, then $V^{a}$ is past-pointing.
2. A four-vector $P^{a}$ is future-pointing if and only if $P^{0}>0$.
If some time-like vector $U^{a}=(1,0,0,0)$ is chosen to be future-pointing, then for any other time-like vector $V^{a}$ with $U^{a}V_{a}>0$, we have
$U^{a}V_{a}>0 \implies U^{0}V_{0}+U^{i}V_{i}>0 \implies U^{0}V^{0}>0 \implies V^{0}>0$.
Therefore, all time-like vectors $V^{a}$ with $V^{0}>0$ are future-pointing.
Similarly, for any other time-like vector $W^{a}$ with $U^{a}W_{a}<0$, we have
$U^{a}W_{a}<0 \implies U^{0}W_{0}+U^{i}W_{i}<0 \implies U^{0}W^{0}<0 \implies W^{0}<0$.
Therefore, all time-like vectors $W^{a}$ with $W^{0}<0$ are future-pointing.
14. Jan 1, 2016
### Staff: Mentor
Correct.
15. Jan 1, 2016
### TSny
I'm not following how you claim that the statement $(P^{0}Q^{0})^{2}>(\vec{P}\cdot{\vec{Q}})^{2}$ implies that either $P^{0}Q^{0}>\vec{P}\cdot{\vec{Q}}$, where the RHS is positive or $P^{0}Q^{0}<\vec{P}\cdot{\vec{Q}}$, where the RHS is negative.
Are you saying that the statement $(P^{0}Q^{0})^{2}>(\vec{P}\cdot{\vec{Q}})^{2}$ by itself implies that if $\vec{P}\cdot{\vec{Q}}$ is positive then $P^{0}Q^{0}>\vec{P}\cdot{\vec{Q}}$?
Suppose $P^{\alpha} = (2, 1, 0, 0)$ and $Q^{\alpha} = (-2, 1, 0, 0)$. Both vectors are timelike. $P^{0}Q^{0} = -4$ while $\vec{P}\cdot{\vec{Q}} = 1$. Then $(P^{0}Q^{0})^{2}>(\vec{P}\cdot{\vec{Q}})^{2}$ and $\vec{P}\cdot{\vec{Q}} > 0$, but it is not true that $P^{0}Q^{0}>\vec{P}\cdot{\vec{Q}}$.
Hope I'm not overlooking something or misinterpreting your statement.
16. Jan 1, 2016
### spaghetti3451
Yes.
Ah! I see! Thanks for pointing out the mistake.
I thought I could use the fact that $x^{2}>y^{2} \implies x>y$ for $y$ positive or $x<y$ for $y$ negative. But, I realise now that it's not so simple, because $x$, in this case $P^{0}Q^{0}$, is itself a product of two numbers.
So, I have to go back to the drawing board and rethink a new proof, or at least, modify the existing proof.
17. Jan 1, 2016
### TSny
Hmm. Even if $x$ were not the product of two numbers, it would still not be true in general that $x^{2}>y^{2} \implies x>y$ for $y$ positive.
You are close. Along with $x^{2}>y^{2}$ you have $x > y$ (from $P^{\alpha}Q_{\alpha} > 0$). From both of these together you can conclude something important about $x$.
18. Jan 1, 2016
### spaghetti3451
Got it!
$x^{2}>y^{2} \implies (x+y)(x-y)>0$.
Now, $x>y \implies x-y>0 \implies x+y>0 \implies x>-y$.
The only way for $x>y$ and $x>-y$ are both valid is if $x>0$, that is $P^{0}Q^{0}>0$.
19. Jan 1, 2016
### spaghetti3451
Is it correct?
20. Jan 1, 2016
### TSny
The middle $\implies$ is of course using both $x-y>0$ and $(x+y)(x-y)>0$.
Yes. Nice.
Draft saved Draft deleted
Similar Discussions: Future-pointing and past-pointing time-like vectors
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https://blogs.princeton.edu/imabandit/2016/05/11/bandit-theory-part-i/?replytocom=368136
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# Bandit theory, part I
This week I’m giving two 90 minutes lectures on bandit theory at MLSS Cadiz. Despite my 2012 survey with Nicolo I thought it would be a good idea to post my lectures notes here. Indeed while much of the material is similar, the style of a mini-course is quite different from the style of a survey. Also, bandit theory has surprisingly progressed since 2012 and many things can now be explained better. Finally in the survey we completely omitted the Bayesian model as we thought that we didn’t have much to add on this topic compared to existing sources (such as the 2011 book by Gittins, Glazebrook, Weber). For a mini-course this concern is irrelevant so I quickly discuss the famous Gittins index and its proof of optimality.
i.i.d. multi-armed bandit, Robbins [1952]
Known parameters: number of arms and (possibly) number of rounds .
Unknown parameters: probability distributions on with mean (notation: ).
Protocol: For each round , the player chooses based on past observations and receives a reward/observation (independently from the past).
Performance measure: The cumulative regret is the difference between the player’s accumulated reward and the maximum the player could have obtained had she known all the parameters,
This problem models the fundamental tension between exploration and exploitation (one wants to pick arms that performed well in the past, yet one needs to make sure that no good option has been missed). Almost every week new applications are found that fit this simple framework and I’m sure you already have some in mind (the most popular one being ad placement on the internet).
i.i.d. multi-armed bandit: fundamental limitations
How small can we expect to be? Consider the -armed case where and where is unknown. Recall from Probability 101 (or perhaps 102) that with expected observations from the second arm there is a probability at least to make the wrong guess on the value of . Now let be the expected number of pulls of arm up to time when . One has
We refer to Bubeck, Perchet and Rigollet [2013] for the details. The important message is that for fixed the lower bound is , while for the worse (which is of order ) it is . In the -armed case this worst-case lower bound becomes (see Auer, Cesa-Bianchi, Freund and Schapire [1995]). The -lower bound is slightly “harder” to generalize to the -armed case (as far as I know there is no known finite-time lower bound of this type), but thankfully it was already all done 30 years ago. First some notation: let and the number of pulls of arm up to time . Note that one has . For let
Theorem [Lai and Robbins [1985]]
Consider a strategy s.t. , we have if . Then for any Bernoulli distributions,
Note that so up to a variance-like term the Lai and Robbins lower bound is . This lower bound holds more generally than just for Bernoulli distributions, see for example Burnetas and Katehakis [1996].
i.i.d. multi-armed bandit: fundamental strategy
Hoeffding’s inequality teaches us that with probability at least , ,
The UCB (Upper Confidence Bound) strategy (Lai and Robbins [1985], Agarwal [1995], Auer, Cesa-Bianchi and Fischer [2002]) is:
The regret analysis is straightforward: on a probability event one has
so that and in fact
i.i.d. multi-armed bandit: going further
• The numerical constant in the UCB regret bound can be replaced by (which is the best one can hope for), and more importantly by slightly modifying the derivation of the UCB one can obtain the Lai and Robbins variance-like term (that is replacing by ): see Cappe, Garivier, Maillard, Munos and Stoltz [2013].
• In many applications one is merely interested in finding the best arm (instead of maximizing cumulative reward): this is the best arm identification problem. For the fundamental strategies see Even-Dar, Mannor and Mansour [2006] for the fixed-confidence setting (see also Jamieson and Nowak [2014] for a recent short survey) and Audibert, Bubeck and Munos [2010] for the fixed budget setting. Key takeaway: one needs of order rounds to find the best arm.
• The UCB analysis extends to sub-Gaussian reward distributions. For heavy-tailed distributions, say with moment for some , one can get a regret that scales with (instead of ) by using a robust mean estimator, see Bubeck, Cesa-Bianchi and Lugosi [2012].
Adversarial multi-armed bandit, Auer, Cesa-Bianchi, Freund and Schapire [1995, 2001]
For , the player chooses based on previous observations, and simultaneously an adversary chooses a loss vector . The player’s loss/observation is . The regret and pseudo-regret are defined as:
Obviously and there is equality in the oblivious case ( adversary’s choices are independent of the player’s choices). The case where is an i.i.d. sequence corresponds to the i.i.d. model we just studied. In particular we already know that is a lower bound on the attainable pseudo-regret.
The exponential weights strategy for the full information case where is observed at the end of round is defined by: play at random from where
In five lines one can show with and a well-chosen learning rate (recall that ):
For the bandit case we replace by in the exponential weights strategy, where
The resulting strategy is called Exp3. The key property of is that it is an unbiased estimator of :
Furthermore with the analysis described above one gets
It only remains to control the variance term, and quite amazingly this is straightforward:
Thus with one gets .
• With the modified loss estimate one can prove high probability bounds on , and by integrating the deviations one can show .
• The extraneous logarithmic factor in the pseudo-regret upper can be removed, see Audibert and Bubeck [2009]. Conjecture: one cannot remove the log factor for the expected regret, that is for any strategy there exists an adaptive adversary such that .
• can be replaced by various measure of “variance” in the loss sequence, see e.g., Hazan and Kale [2009].
• There exist strategies which guarantee simultaneously in the adversarial model and in the i.i.d. model, see Bubeck and Slivkins [2012].
• Many interesting variants: graph feedback structure of Mannor and Shamir [2011] (there is a graph on the set of arms, and when an arm is played one observes the loss for all its neighbors), regret with respect to best sequence of actions with at most switches, switching cost (interestingly in this case the best regret is , see Dekel, Ding, Koren and Peres [2013]), and much more!
Bayesian multi-armed bandit, Thompson [1933]
Here we assume a set of “models” and prior distribution over . The Bayesian regret is defined as
where simply denotes the regret for the i.i.d. model when the underlying reward distributions are . In principle the strategy minimizing the Bayesian regret can be computed by dynamic programming on the potentially huge state space . The celebrated Gittins index theorem gives sufficient condition to dramatically reduce the computational complexity of implementing the optimal Bayesian strategy under a strong product assumption on . Notation: denotes the posterior distribution on at time .
Theorem [Gittins [1979]]
Consider the product and -discounted case: , , , and furthermore one is interested in maximizing . The optimal Bayesian strategy is to pick at time the arm maximizing the Gittins index:
where the expectation is over drawn from with , and the supremum is taken over all stopping times .
Note that the stopping time in the Gittins index definition gives the optimal strategy for a 2-armed game, where one arm’s reward distribution is while the other arm reward’s distribution is with as a prior for .
Proof: The following exquisite proof was discovered by Weber [1992]. Let
be the Gittins index of arm at time , which we interpret as the maximum charge one is willing to pay to play arm given the current information. The prevailing charge is defined as (i.e. whenever the prevailing charge is too high we just drop it to the fair level). We now make three simple observations which together conclude the proof:
• The discounted sum of prevailing charge for played arms is an upper bound (in expectation) on the discounted sum of rewards. Indeed the times at which the prevailing charge are updated are stopping times, and so between two such times the expected sum of discounted reward is smaller than the discounted sum of the fair charge at time which is equal to the prevailing charge at any time in .
• Since the prevailing charge is nonincreasing, the discounted sum of prevailing charge is maximized if we always pick the arm with maximum prevailing charge. Also note that the sequence of prevailing charge does not depend on the algorithm.
• Gittins index does exactly 2. (since we stop playing an arm only at times at which the prevailing charge is updated) and in this case 1. is an equality. Q.E.D.
For much more (implementation for exponential families, interpretation as a multitoken Markov game, …) see Dumitriu, Tetali and Winkler [2003], Gittins, Glazebrook, Weber [2011], Kaufmann [2014].
Bayesian multi-armed bandit, Thompson Sampling (TS)
In machine learning we want (i) strategies that can deal with complicated priors, and (ii) guarantees for misspecified priors. This is why we have to go beyond the Gittins index theory.
In his 1933 paper Thompson proposed the following strategy: sample and play .
Theoretical guarantees for this highly practical strategy have long remained elusive. Recently Agrawal and Goyal [2012] and Kaufmann, Korda and Munos [2012] proved that TS with Bernoulli reward distributions and uniform prior on the parameters achieves (note that this is the frequentist regret!). We also note that Liu and Li [2015] takes some steps in analyzing the effect of misspecification for TS.
Let me also mention a beautiful conjecture of Guha and Munagala [2014]: for product priors, TS is a 2-approximation to the optimal Bayesian strategy for the objective of minimizing the number of pulls on suboptimal arms.
Bayesian multi-armed bandit, Russo and Van Roy [2014] information ratio analysis
Assume a prior in the adversarial model, that is a prior over , and let denote the posterior distribution (given ). We introduce
The key observation is that (recall that )
Indeed, equipped with Pinsker’s inequality and basic information theory concepts one has (we denote for the mutual information conditionally on everything up to time , also denotes the law of conditionally on everything up to time ):
Thus which gives the claim thanks to a telescopic sum. We will use this key observation as follows (we give a sequence of implications leading to a regret bound so that all that is left to do is to check that the first statement in this sequence is true for TS):
Thus writing and we have
For TS the following shows that one can take :
Thus TS always satisfies . Side note: by the minimax theorem this implies the existence of a strategy for the oblivious adversarial model with regret (of course we already proved that such a strategy exist, in fact we even constructed one via exponential weights, but the point is that the proof here does not require any “miracle” –yes exponential weights are kind of a miracle, especially when you consider how the variance of the unbiased estimator gets automatically controlled).
Summary of basic results
• In the i.i.d. model UCB attains a regret of and by Lai and Robbins’ lower bound this is optimal (up to a multiplicative variance-like term).
• In the adversarial model Exp3 attains a regret of and this is optimal up to the logarithmic term.
• In the Bayesian model, Gittins index gives an optimal strategy for the case of product priors. For general priors Thompson Sampling is a more flexible strategy. Its Bayesian regret is controlled by the entropy of the optimal decision. Moreover TS with an uninformative prior has frequentist guarantees comparable to UCB.
This entry was posted in Optimization, Probability theory. Bookmark the permalink.
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https://www.physicsforums.com/threads/fluid-flow-question-through-hose.185661/
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# Fluid flow question through hose
1. Sep 19, 2007
### greydient
Here's a silly question.
If I'm comparing two different sizes of hose, using the same flow rate in gpm, how do I calculate the pressure drops through each for comparison?
I'm considering using hoses with interior diameter .438 and .688, each with a length of 5 inches.
2. Sep 19, 2007
### FredGarvin
I am assuming that you want to measure the delta P, not calculate it. Calculating it is basic stuff.
If you are flowing to atmosphere on one end, you will have to adjust the pressure side of the pump you are using to get the flowrates to be equal between the two hose sizes. You can rely on a pressure gauge right at the outlet of the pump to give you the required delta P data.
3. Sep 19, 2007
### stewartcs
Pressure drop depends on these items. The fluid density, fluid velocity, pipe (or hose) roughness, length of the pipe (or hose), diameter of pipe (or hose), and any elevation changes between the two ends.
A standard equation for pressure drop is given by:
delta p = ((pf*f*L*v^2)/(144*d*2*g)) + ((z*pf)/144)
where,
delta p = pressure drop in lbs/in^2
pf = density of fluid in lbs/ft^3
f = friction factor
L = length in feet
v = velocity of fluid in ft/sec
d = diameter in ft
g = gravitational acceleration in ft/sec^2
z = elevation change in feet
The friction factor, f, is found depending on whether the flow is laminar or turbulent. If you find that the flow is in the critical region (between laminar and turbulent, 2000 > Re < 4000), then emperical testing is more accurate.
Hope this helps...
PS
Make sure your units are the same as shown above!
4. Sep 22, 2007
### jaap de vries
look up Moody chart the rest is standard and described above. (find Re #)
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https://jp.maplesoft.com/support/help/maplesim/view.aspx?path=worksheet/reference/contextmaplein
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Context Bar for Math Input - Maple Help
Context Bar for Math Input
Switch the input display between 2-D Math and Maple Input notation.
This page describes how the context bar can be used to switch the input display between 2-D Math and Maple Input notation at a Maple prompt.
• When Math is selected, the input display mode is 2-D math notation:
• When Text is selected, the input display mode is Maple Input notation (sometimes called 1-D math):
At a Maple prompt, you can toggle the input mode by selecting Math or Text from the context bar.
Note: Set the default input display mode from the Display tab of the Options dialog. See Options>Display.
You can also use the F5 shortcut key, which at a Maple prompt toggles between 2-D math input and Maple Input.
In document mode, the context bar lets you switch between entering plain text and math. For more information on switching between text and math input, see Select Entry Mode.
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http://computer-programming-forum.com/2-vfp/426e05fbfe8391cc.htm
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FP 2.5 Dos - Too many files open
Author Message
FP 2.5 Dos - Too many files open
I am recreating an environment to convert an old FP 2.5 program and i get
the message "Too many files open" when trying to open all the database
tables used by this program. I have tried setting the Files environment
variable in config.sys to both 100 and 200 and i have tried increasing the
buffers variable but i still get the same message. I am running Foxpro from
a Dos command prompt under Windows NT WS 4.0 with SP3.
Does anyone remember the cause of this error, i think it was rather common
some years ago.
David Jenssen
Wed, 04 Oct 2000 03:00:00 GMT
FP 2.5 Dos - Too many files open
What else do you have open in terms of other programs? This sort of problem
happens frequently in 32-bit multi-tasking environs (with several programs
open)and Fox wants more memory to work with.
Mike Ballai
Try DBRITE -- the better FoxPro Tablemaker shareware program
Wed, 04 Oct 2000 03:00:00 GMT
FP 2.5 Dos - Too many files open
Quote:
> I am recreating an environment to convert an old FP 2.5 program and i get
> the message "Too many files open" when trying to open all the database
> tables used by this program. I have tried setting the Files environment
> variable in config.sys to both 100 and 200 and i have tried increasing the
> buffers variable but i still get the same message. I am running Foxpro from
> a Dos command prompt under Windows NT WS 4.0 with SP3.
> Does anyone remember the cause of this error, i think it was rather common
> some years ago.
> David Jenssen
than the extended version. The standard version only supports 25 work areas.
After loading FP type ?VERS() at the command prompt, if the display does not
include (X) after the 2.5 then the standard version is loaded.
To solve the problem assign sufficient extended memory to the app.
Thu, 05 Oct 2000 03:00:00 GMT
FP 2.5 Dos - Too many files open
Quote:
> I am recreating an environment to convert an old FP 2.5 program and i get
> the message "Too many files open" when trying to open all the database
> tables used by this program. I have tried setting the Files environment
> variable in config.sys to both 100 and 200 and i have tried increasing the
CONGIG.SYS? I thought under Windows NT4.0 it is called CONFIG.NT that is
in the \WINNT\SYSTEM32 directory. And be sure to have enough memory so
that you can run the eXtended version (the (X) in the blue start screen).
How that is arranged under NT I'm not sure of it.
Here are my config.nt lines (without the REM lines)
ECHOCONFIG
dos=high, umb
device=%SystemRoot%\system32\himem.sys
files=100
--
Groetjes,
Wim de Lange
Fri, 06 Oct 2000 03:00:00 GMT
FP 2.5 Dos - Too many files open
Quote:
> I am recreating an environment to convert an old FP 2.5 program and i get
> the message "Too many files open" when trying to open all the database
> tables used by this program. I have tried setting the Files environment
> variable in config.sys to both 100 and 200 and i have tried increasing the
CONGIG.SYS? I thought under Windows NT4.0 it is called CONFIG.NT that is
in the \WINNT\SYSTEM32 directory. And be sure to have enough memory so
that you can run the eXtended version (the (X) in the blue start screen).
How that is arranged under NT I'm not sure of it.
Here are my config.nt lines (without the REM lines)
ECHOCONFIG
dos=high, umb
device=%SystemRoot%\system32\himem.sys
files=100
--
Groetjes,
Wim de Lange
|
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|
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/441/6/a/k/
|
# Properties
Label 441.6.a.k Level $441$ Weight $6$ Character orbit 441.a Self dual yes Analytic conductor $70.729$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 441.a (trivial)
## Newform invariants
Self dual: yes Analytic conductor: $$70.7292645375$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 7) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
$$f(q)$$ $$=$$ $$q + 10 q^{2} + 68 q^{4} - 56 q^{5} + 360 q^{8}+O(q^{10})$$ q + 10 * q^2 + 68 * q^4 - 56 * q^5 + 360 * q^8 $$q + 10 q^{2} + 68 q^{4} - 56 q^{5} + 360 q^{8} - 560 q^{10} - 232 q^{11} + 140 q^{13} + 1424 q^{16} - 1722 q^{17} + 98 q^{19} - 3808 q^{20} - 2320 q^{22} - 1824 q^{23} + 11 q^{25} + 1400 q^{26} - 3418 q^{29} + 7644 q^{31} + 2720 q^{32} - 17220 q^{34} - 10398 q^{37} + 980 q^{38} - 20160 q^{40} - 17962 q^{41} + 10880 q^{43} - 15776 q^{44} - 18240 q^{46} + 9324 q^{47} + 110 q^{50} + 9520 q^{52} - 2262 q^{53} + 12992 q^{55} - 34180 q^{58} - 2730 q^{59} - 25648 q^{61} + 76440 q^{62} - 18368 q^{64} - 7840 q^{65} - 48404 q^{67} - 117096 q^{68} + 58560 q^{71} - 68082 q^{73} - 103980 q^{74} + 6664 q^{76} + 31784 q^{79} - 79744 q^{80} - 179620 q^{82} - 20538 q^{83} + 96432 q^{85} + 108800 q^{86} - 83520 q^{88} - 50582 q^{89} - 124032 q^{92} + 93240 q^{94} - 5488 q^{95} + 58506 q^{97}+O(q^{100})$$ q + 10 * q^2 + 68 * q^4 - 56 * q^5 + 360 * q^8 - 560 * q^10 - 232 * q^11 + 140 * q^13 + 1424 * q^16 - 1722 * q^17 + 98 * q^19 - 3808 * q^20 - 2320 * q^22 - 1824 * q^23 + 11 * q^25 + 1400 * q^26 - 3418 * q^29 + 7644 * q^31 + 2720 * q^32 - 17220 * q^34 - 10398 * q^37 + 980 * q^38 - 20160 * q^40 - 17962 * q^41 + 10880 * q^43 - 15776 * q^44 - 18240 * q^46 + 9324 * q^47 + 110 * q^50 + 9520 * q^52 - 2262 * q^53 + 12992 * q^55 - 34180 * q^58 - 2730 * q^59 - 25648 * q^61 + 76440 * q^62 - 18368 * q^64 - 7840 * q^65 - 48404 * q^67 - 117096 * q^68 + 58560 * q^71 - 68082 * q^73 - 103980 * q^74 + 6664 * q^76 + 31784 * q^79 - 79744 * q^80 - 179620 * q^82 - 20538 * q^83 + 96432 * q^85 + 108800 * q^86 - 83520 * q^88 - 50582 * q^89 - 124032 * q^92 + 93240 * q^94 - 5488 * q^95 + 58506 * q^97
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
0
10.0000 0 68.0000 −56.0000 0 0 360.000 0 −560.000
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Atkin-Lehner signs
$$p$$ Sign
$$3$$ $$-1$$
$$7$$ $$-1$$
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 441.6.a.k 1
3.b odd 2 1 49.6.a.a 1
7.b odd 2 1 63.6.a.e 1
12.b even 2 1 784.6.a.c 1
21.c even 2 1 7.6.a.a 1
21.g even 6 2 49.6.c.c 2
21.h odd 6 2 49.6.c.b 2
28.d even 2 1 1008.6.a.y 1
84.h odd 2 1 112.6.a.g 1
105.g even 2 1 175.6.a.b 1
105.k odd 4 2 175.6.b.a 2
168.e odd 2 1 448.6.a.c 1
168.i even 2 1 448.6.a.m 1
231.h odd 2 1 847.6.a.b 1
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7.6.a.a 1 21.c even 2 1
49.6.a.a 1 3.b odd 2 1
49.6.c.b 2 21.h odd 6 2
49.6.c.c 2 21.g even 6 2
63.6.a.e 1 7.b odd 2 1
112.6.a.g 1 84.h odd 2 1
175.6.a.b 1 105.g even 2 1
175.6.b.a 2 105.k odd 4 2
441.6.a.k 1 1.a even 1 1 trivial
448.6.a.c 1 168.e odd 2 1
448.6.a.m 1 168.i even 2 1
784.6.a.c 1 12.b even 2 1
847.6.a.b 1 231.h odd 2 1
1008.6.a.y 1 28.d even 2 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{6}^{\mathrm{new}}(\Gamma_0(441))$$:
$$T_{2} - 10$$ T2 - 10 $$T_{5} + 56$$ T5 + 56 $$T_{13} - 140$$ T13 - 140
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T - 10$$
$3$ $$T$$
$5$ $$T + 56$$
$7$ $$T$$
$11$ $$T + 232$$
$13$ $$T - 140$$
$17$ $$T + 1722$$
$19$ $$T - 98$$
$23$ $$T + 1824$$
$29$ $$T + 3418$$
$31$ $$T - 7644$$
$37$ $$T + 10398$$
$41$ $$T + 17962$$
$43$ $$T - 10880$$
$47$ $$T - 9324$$
$53$ $$T + 2262$$
$59$ $$T + 2730$$
$61$ $$T + 25648$$
$67$ $$T + 48404$$
$71$ $$T - 58560$$
$73$ $$T + 68082$$
$79$ $$T - 31784$$
$83$ $$T + 20538$$
$89$ $$T + 50582$$
$97$ $$T - 58506$$
|
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|
https://freedocs.mi.hdm-stuttgart.de/sd1Median.html
|
## The median of a given sample.
No. 157
### Calculating the median
Q:
We want to extend exercise Adding support to retrieve statistical data. by adding a method int getMedian(). For this purpose our current implementation lacks ordering of input values. Consider the following sample of values:
2, 7, 0, -3, 4
Obtaining the median requires ordering these values:
-3, 0, 2, 4, 7
Thus the given sample's median is 2. Solve this exercise in the following order:
1. For testing and other purposes it is convenient to provide an additional method returning the array of values being added so far:
/**
* @return The array of values entered so far
*/
public int[] getValues() {
...
return ...;
}
### Caution
Do not just return your internal array int[] values! Due to the amortized doubling implementation this will in most cases contain unused positions on top of added values.
You may either construct a suitable copy containing the current elements yourself or get enlightened by reading the API documentation of copyOfRange(...).
2. Provide some tests to assure your sorting implementation works well. You'll implement the actual sorting in the next step. Right now testing for correct sorting will fail (unless a given set of values had already been added in ascending order). A test might look like:
final int[]
unsortedValues = {0, -1, 5, 2, 7, 6},
sortedValues = {-1, 0, 2, 5, 6, 7};
IntegerStore store = new IntegerStore();
for (final int i: unsortedValues) {
}
// Now check your store for correctly sorted order of elements
...
Do not forget to consider value sets which include duplicates and write tests accordingly!
Hint: The Junit Framework provides a (convenience) method assertArrayEquals(...).
3. Modify your addValue(...) method's implementation. Though there are more elaborate sorting methods available in Java we'll do it the hard way ourselves in this exercise. Consider the following example:
store.addValue(1);
store.addValue(3);
Prior to inserting a new value our addValue(...) method shall find a suitable position inside the array of already added values to insert the new value. When adding the last value 3 in the above example the internal array already contains the values (1, 2, 7, 9). Traversing this array shows that the new value of 3 should be inserted between 2 and 7.
Thus a general strategy inserting a new value candidate might be:
1. Find the first index pointing to an existing value being larger or equal to the given candidate. In the above example this index value is 2 pointing to value 7.
If there is no such existing value just add the new value at the array's top end like you did before when not yet bothering about sorting.
2. Shift the right part of the array starting at index 2 in our example one position to the right thus creating a free (denoted by F) insert position:
Index values | 0| 1| 2| 3| 4| 5| ...
-----------------+--+--+--+--+-----+ ...
values oldArray | 1| 2| 7| 9| | |
-----------------+--+--+--+--+-----+ ...
values newArray | 1| 2| F| 7| 9| | ...
You may now insert your latest value 3 at the free index position 2 ending up with a well sorted array (1, 2, 3, 7, 9).
This example just illustrates a (very simple!) sorting algorithm.
Hint: On implementation be very careful with respect to off by one errors you are likely to encounter. The tests you have written beforehand will guide you.
4. Provide a constructor public IntegerStore(final int[] values) in a meaningful way with respect to median calculations.
5. Add a dummy implementation double getMedian(){return 0;} to your class IntegerStore from exercise Adding support to retrieve statistical data. .
6. Provide some tests both for even and uneven sample sizes. All of these will probably fail till you complete your implementation.
7. Finally complete the desired double getMedian() method's implementation and actually test it. There must be at least one element in order to be able returning a meaningful result:
/**
* <dl>
* <dt><b>Precondition:</b></dt>
* <dd>There must be at least one element.</dd>
* </dl>
*
* @return The sample's median.
*/
public double getMedian() {
...
return ... ;
}
8. Implement a main method as in Reading console input asking the user for an arbitrary number of values. Then compute both their average and median like:
How big is your sample? 5
Enter value #1 of 5: 1
Enter value #2 of 5: -2
Enter value #3 of 5: 1
Enter value #4 of 5: 5
Enter value #5 of 5: 2
Your sample's median is: 1.0
A:
1. The copyOfRange(...) method in getValues() returns that portion of our int[] values array actually been filled with data.
2. Provide some tests assuring your sorting implementation works well prior to actually implementing the actual sorting in the next step. Right now testing for correct sorting will fail (unless a given set of values had already been added in ascending order). A test might look like:
final int[]
unsortedValues = {0, -1, 5, 2, 7, 6},
sortedValues = {-1, 0, 2, 5, 6, 7};
IntegerStore store = new IntegerStore();
for (final int i: unsortedValues) {
}
// Now check your store for correctly sorted order of elements
...
Do not forget to consider value sets which include duplicates and write tests accordingly!
Hint: The Junit Framework provides a (convenient) method assertArrayEquals(...).
3. Modify your addValue(...) method's implementation. Though there are more elaborate sorting methods available in Java we'll do it the hard way ourselves in this exercise. Consider the following example:
store.addValue(1);
store.addValue(3);
Prior to inserting a new value our addValue(...) method shall find a suitable position inside the array of already added values to insert the new value. When adding the last value 3 in the above example the internal array already contains the values (1, 2, 7, 9). Traversing this array shows that the new value of 3 should be inserted between 2 and 7.
Thus a general strategy inserting a new value candidate might be:
1. Find the first index pointing to an existing value being larger or equal to the given candidate. In the above example this index value is 2 pointing to value 7.
If there is no such existing value just add the new value at the array's top as you did without bothering about sorting.
2. Shift the right part of the array starting at index 2 in our example one position to the right thus creating a free (denoted by F) insert position:
Index values | 0| 1| 2| 3| 4| 5| ...
-----------------+--+--+--+--+-----+ ...
values oldArray | 1| 2| 7| 9| | |
-----------------+--+--+--+--+-----+ ...
values newArray | 1| 2| F| 7| 9| | ...
You may now insert your latest value 3 at the free index position 2 ending up with a well sorted array (1, 2, 3, 7, 9).
This example just illustrates a (very simple!) sorting algorithm.
Hint: On implementation be very careful with respect to off by one errors you are likely to encounter. The tests you have written beforehand will guide you.
4. The constructor public IntegerStore(final int[] values) internally uses our addValue(...) method thus adding each array value one by one. Consider an alternative naive implementation:
public IntegerStore(final int[] values) {
this.values = values;
}
This will fail in most cases since the array parameter typically contains unsorted values.
Having this constructor in place also simplifies writing tests:
...
@Test
public void testMedian() {
IntegerStore store = new IntegerStore(new int[] {2, 7, 0, -3, 4});
assertArrayEquals(new int[] {-3, 0, 2, 4, 7}, store.getValues());
assertTrue(Math.abs(2. - store.getMedian()) < 1.E-10);
...
5. -
6. @Test
public void testMedian() {
IntegerStore store = new IntegerStore(new int[] {2, 7, 0, -3, 4});
assertArrayEquals(new int[] {-3, 0, 2, 4, 7}, store.getValues());
assertTrue(Math.abs(2. - store.getMedian()) < 1.E-10);
assertArrayEquals(new int[] {-3, 0, 2, 4, 7, 7}, store.getValues());
assertTrue(Math.abs(3. - store.getMedian()) < 1.E-10);
}
7. double getMedian()
8. main(...)
|
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|
http://tex.stackexchange.com/questions/5170/mapsto-vs-rightarrow/5171
|
# Mapsto vs. rightarrow
This is perhaps half a math question and half a typesetting one. In what circumstances do I use \mapsto and when \rightarrow? I feel like the standard seems to be: when you're specifying the operator you use \rightarrow, but if you're just saying that one domain maps to another you use \mapsto. Is that correct?
e.g. I would say Q\times\Gamma\mapsto Q but \delta:Q\times\Gamma\rightarrow Q.
-
You use \mapsto to denote the actual function mapping. For example, consider the function $f:\mathbb N\to\mathbb N$ given by $f(n)=5n$. You could write that second part as $n\mapsto5n$.
The \mapsto notation is useful for talking about a function without inventing a name for it, e.g. "the map $\mathbb{R}\to \mathbb{R}$ given by $x\mapsto x^2$ is not injective". Note that \to is a nice shorthand for \rightarrow, which at the same time is more semantic. – Villemoes Nov 10 '10 at 10:36
I'd prefer using \colon instead of :; in fact I'd even more prefer $f\from\mathbb N\to\mathbb N$, with \newcommand*\from{\colon}. – Hendrik Vogt Nov 10 '10 at 14:41
@Hendrik: I like the idea of using \from. I think I've seen equal numbers of : and \colon in books (or the equivalent spacing) so I think it's just up to personal preference (or editor preference, really). I have no strong feelings on that one. – TH. Nov 11 '10 at 5:43
|
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|
http://cms.math.ca/cmb/msc/32H30?fromjnl=cmb&jnl=CMB
|
location: Publications → journals
Search results
Search: MSC category 32H30 ( Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22} )
Expand all Collapse all Results 1 - 1 of 1
1. CMB 2009 (vol 52 pp. 154)
Ye, Yasheng; Ru, Min
A Big Picard Theorem for Holomorphic Maps into Complex Projective Space We prove a big Picard type extension theorem for holomorphic maps $f\from X-A \rightarrow M$, where $X$ is a complex manifold, $A$ is an analytic subvariety of $X$, and $M$ is the complement of the union of a set of hyperplanes in ${\Bbb P}^n$ but is not necessarily hyperbolically imbedded in ${\Bbb P}^n$. Category:32H30
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https://www.ideals.illinois.edu/handle/2142/16322/browse?rpp=20&sort_by=4&type=periodical&etal=-1&starts_with=A&order=DESC
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# Browse Dissertations and Theses - Geology by Issue
• (2010-05-18)
ABSTRACT We tested an in situ method for monitoring the concentrations of aqueous chemical species and dissolved gases in groundwater. We deployed in situ samplers in 8 wells completed in the glacial Glasford formation ...
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• (2010-05-19)
Density bands in the CaCO3 (aragonite) skeleton of scleractinian corals are commonly used as chronometers, where crystalline couplets of high and low density bands represent the span of one year. Isotopic analysis of these ...
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• (2010-05-19)
The interaction of climate, tectonics, and topography in the Olympic Mountains of Washington State is explored to determine the influence of glaciers on spatially variable erosion and rock uplift rates. As glaciers have ...
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High-resolution particle-image velocimetry (PIV) experiments have been conducted over a fixed-bed to examine the effects of interacting barchan dunes on the flow structure. The barchan dune models were based upon an idealized ...
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A detailed understanding of the climate of the Pleistocene (1,800,000 years ago to 10,000 years ago) is crucial for constructing predictive models of future climate trends. Researchers studying past climate (paleoclimate) ...
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Understanding the composition of Earth’s inner core is crucial for revealing the mechanisms of core formation and the evolution of Earth. The presence of light elements in the Earth’s inner core has been indicated in recent ...
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We tested whether the gene expression of dissimilatory sulfite reductase (dsr mRNA), a critical enzyme in the sulfate reduction pathway, can serve as an indicator of the rate of sulfate reduction in natural systems. We ...
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Ice-walled lake plains (IWLPs) form along glacial margins in areas of stagnating ice. In Illinois, IWLPs tend to have low relief (<7m) and were formed during the last deglaciation of the Lake Michigan lobe (20,800 to 16,000 ...
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This study applies high precision 238U/235U measurement techniques two three geologic settings: basalt differentiation, uranium ore genesis, and the remediation of a uranium-contaminated groundwater system. In the latter ...
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One of the fundamental objectives of the extensive research on Creede district, Colorado, has been to determine the sources, pathways, and interactions of fluids involved in the genesis of the epithermal ores. From the ...
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Passive margin escarpments are large-scale geomorphic features which persist over timescales of tens of millions of years. The maintenance of steep topography over these timescales challenges conventional understanding of ...
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Analysis of sedimentological, stratigraphic, paragenetic and geochemical characteristics of samples from the Early Ordovician Shakopee Dolomite and Everton Formation, and the overlying Middle Ordovician St. Peter Sandstone, ...
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• (1989)
Oxygen isotope evidence from Caradocian Trenton Group brachiopods in the Mohawk Valley of New York suggests that Caradocian oceans were salinity-stratified and dominated at depth by warm, saline waters. $\delta\sp{18}$O ...
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A multidisciplinary study utilizing new ultrahigh-resolution microscopy techniques has been undertaken to reconstruct the paragenesis of Cambrian-age Mt. Simon Sandstone quartz arenites buried at 1.8-2.1 km within the ...
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Magnetic susceptibility (MS) zones, controlled by silt-size magnetite concentrations, have been delineated within oxidized, C horizon Peoria and Loveland Silts along the Illinois and Mississippi Valleys. Lower Peoria and ...
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The response of sediment, vegetation and aquatic environments to climate change during the last glacial--interglacial--glacial intervals were investigated from fossiliferous successions in four breached kettle basins in ...
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The geochemical characteristics of paleofluids in the White River Group played a vital role in controlling zeolitic alteration as well as the formation of calcretes. The White River Group is a terrestrially deposited ...
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Cyclothems record the sedimentary product of cyclicity in relative sea-level on either a regional or global scale, showing both regressive and transgressive phases. This study aims to contribute to our understanding of ...
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Seismic methods using natural earthquakes are commonly applied to investigate the velocity structures of the crust and upper mantle. Among all these methods, seismic tomography is one of the most powerful tools to image ...
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Geologists have long recognized the important role of continental-scale fluid flow as a mechanism for diagenesis, including the dissolution of rock and the deposition of Mississippi Valley-Type (MVT) minerals in sedimentary ...
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https://sofi-northwestern.pure.elsevier.com/en/publications/mechanism-of-manganese-catalyzed-oxygen-evolution-from-experiment-2
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# Mechanism of Manganese-Catalyzed Oxygen Evolution from Experimental and Theoretical Analyses of 18O Kinetic Isotope Effects
Sahr Khan, Ke R. Yang, Mehmed Z. Ertem, Victor S. Batista, Gary W. Brudvig
Research output: Contribution to journalArticlepeer-review
28 Citations (Scopus)
## Abstract
The biomimetic oxomanganese complex [MnIII/IV2(μ-O)2(terpy)2(OH2)2](NO3)3 (1; terpy = 2,2′:6′,2″-terpyridine) catalyzes O2 evolution from water when activated by oxidants, such as oxone (2KHSO5·KHSO4·K2SO4). The mechanism of this reaction has never been characterized, due to the fleeting nature of the intermediates. In the present study, we elucidate the underlying reaction mechanism through experimental and theoretical analyses of competitive kinetic oxygen isotope effects (KIEs) during catalytic turnover conditions. The experimental 18O KIE is a sensitive probe of the highest transition state in the O2-evolution mechanism and provides a strict constraint for calculated mechanisms. The 18O kinetic isotope effect of 1.013 ± 0.003 measured using natural abundance reactants is consistent with the calculated isotope effect of peroxymonosulfate binding to the complex, as described by density functional theory (DFT). This provides strong evidence for peroxymonosulfate binding being both the first irreversible and rate-determining step during turnover, in contrast to the previously held assumption that formation of a high-valent Mn-oxo/oxyl species is the highest barrier step that controls the rate of O2 evolution by this complex. The comparison of the measured and calculated KIEs supplements previous kinetic studies, enabling us to describe the complete mechanism of O2 evolution, starting from when the oxidant first binds to the manganese complex to when O2 is released. The reported findings lay the groundwork for understanding O2 evolution catalyzed by other biomimetic oxomanganese complexes, with features common to those of the O2-evolving complex of photosystem II, providing experimental and theoretical diagnostics of oxygen isotope effects that could reveal the nature of elusive reaction intermediates.
Original language English 7104-7113 10 ACS Catalysis 5 12 https://doi.org/10.1021/acscatal.5b01976 Published - Oct 22 2015
## Keywords
• density functional theory
• manganese complex
• oxygen evolution mechanism
• oxygen isotope effects
• peroxymonosulfate
## ASJC Scopus subject areas
• Catalysis
• Chemistry(all)
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https://motls.blogspot.com/2007/05/noisy-picnic-and-political-correctness.html?m=0?m=1
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## Monday, May 21, 2007 ... //
### Noisy picnic and political correctness
On May 12th, two groups organized a noisy picnic on the Quad's public lawn. Harvard students were everywhere around. Many of them were studying: it was a reading period. Many of them are sensitive and can't concentrate well if there is noise around.
It shouldn't be unexpected that someone called the police. If it were a party I couldn't effectively attend and if there were people around me who would also think that the noise is just too much, I would call police, too.
Police has checked whether the people have had any right to be there. The participants were asked to keep the noise down and the picnic continued. You would think that this story ends up with an acceptable compromise.
Except that there apparently exists a whole official foundation at Harvard whose very goal is to guarantee that peace is not what follows after such picnics. The foundation is called
• Harvard Foundation for Intercultural and Race Relations.
Its director, S. Allen Counter, has made the following breathtaking remarks:
• This ["I Am Harvard" campaign] is an important step to take in what is clearly a racist community, in which police are allowed to use South African apartheid techniques to harass our students. If there had been 60 white students on the lawn, would police ride up on motorcycles with dark shades to make them show their IDs?
Wow. If someone makes a huge mess in front of the buildings where some of the smartest young people on the planet are supposed to study, it is illegitimate to call police because it is a black people's party and everyone - the whole community of Harvard students - is instantly accused of racism and the director of the "intercultural foundation" is black, too.
Counter's "foundation" is clearly meant to be a tool to intimidate students and other members of the community, politicize all questions, and make sure that a pathetic hypocritical ideology is more important than a tolerable atmosphere during the reading period and other values that used to be associated with the world of Academia.
I apologize but under normal circumstances, being black hasn't allowed one to make a huge mess in the middle of Harvard. In the past, everyone would understand that if someone didn't know why the previous sentence is true, his proclamation that "I am Harvard" shouldn't have been uncritically accepted.
These days, the Academia - universities as well as their individual departments - are literally flooded with similar distasteful foundations and committees whose only purpose is to overfill the community with propaganda and fear and to impose very unbalanced, politically biased code of a certain flavor.
We have a lot of committees for diversity and various departments for women's studies, among others. I think that the very name of these institutions is constructed to guarantee that only one type of ideas, one sex, and one race is being "protected" by these institutions. Feminists have a monopoly in the questions about the women's role in the society. Radical blacks have a monopoly in the questions about the interracial relations. Environmentalists have a monopoly in the committees that are dedicated to the questions of the environment.
Everything is designed to protect the totalitarian influence of one ideology and no one seems to care.
Show me a single influential scholar in a department of women's studies who understands the very basic insight about that discipline, namely why virtually all of scholarly feminism is intellectual garbage. Show me a single director of a foundation for diversity who would protect a white person against a black person. Show me a single chair of a deparmental diversity committee who understands that the lack of conservatives at the universities is much more serious a problem that the lack of a certain skin color.
The very structure of these institutions and foundations is designed to help to indoctrinate, intimidate, and radicalize the members of the academic community. The only good sign here is that Lucy Coldwell and other Crimson staff writers realize that something is wrong here, too. They ask Dr. Counter to apologize. I doubt he will.
In a previous incident, S. Allen Counter "accused" the Crimson that some of its writers were active in Hillel. At Harvard, it must apparently be a crime again - or at least is no longer kosher - to be a member of the largest campus organization of what is arguably the smartest nation in the world.
Outrageous institutions producing fear and tension - e.g. the Harvard Foundation for Intercultural and Race Relations - should be abolished as soon as possible unless the society wants the political correctness to reach the same level of madness as a certain ideology did in the 1930s.
And that's the memo.
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https://www.physicsforums.com/threads/expressing-polar-equation-as-a-cartesian-equation.638002/
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# Expressing polar equation as a Cartesian equation
1. Sep 22, 2012
### Bipolarity
1. The problem statement, all variables and given/known data
Express the following equation in Cartesian form
$$r = 1 - cos(θ)$$
2. Relevant equations
$$x = r*cos(θ)$$
$$y = r*sin(θ)$$
$$r^{2} = x^{2} + y^{2}$$
$$tan(θ) = \frac{y}{x}$$
3. The attempt at a solution
I have no idea... a hint would be nice thanks!
BiP
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Sep 22, 2012
### gabbagabbahey
If $x=r\cos\theta$, what is $\cos\theta$? If $x^2+y^2=r^2$, and $r\geq 0$, what is $r$?
3. Sep 22, 2012
### Bipolarity
Thanks!
BiP
Similar Discussions: Expressing polar equation as a Cartesian equation
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https://socratic.org/questions/570516fd11ef6b28bba6ff98
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Chemistry
Topics
Question #6ff98
Jul 5, 2016
$1.87 L$
Explanation:
It may be easily solved by using mole concept as follows:
I assumed that the reactants are completely consumed to form both
$C O$ & $C {O}_{2}$
and they are formed as
$C O \to x \text{ moles}$
$C {O}_{2} \to y \text{ moles}$
We have been given reatants as
$C \to 2 g \to \text{2g"/"12g/mole"=1/6"moles}$
${O}_{2} \to 4 g \to \text{4g"/"32g/mol"=1/8"moles}$
Now 1 mole CO contains 1 mole C and $\frac{1}{2}$ mole ${O}_{2}$
So x mole CO contains x mole C and $\frac{x}{2}$ mole ${O}_{2}$
Similarly 1 mole $C {O}_{2}$ contains 1 mole C and 1 mole ${O}_{2}$
So y mole $C {O}_{2}$ contains y mole C and y mole ${O}_{2}$
We can cobmine these information to form following two equations
Considering Total Carbon
$x + y = \frac{1}{6.} \ldots . . \left(1\right)$
Considering Total Oxygen
$\frac{x}{2} + y = \frac{1}{8.} \ldots . \left(2\right)$
Now subtracting (2) from (1) we can write
$x - \frac{x}{2} = \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24}$
$\therefore \frac{x}{2} = \frac{1}{24} \implies x = \frac{1}{12} m o l$
Plugging the value of x in (1)
$\frac{1}{12} + y = \frac{1}{6}$
$\implies y = \frac{1}{6} - \frac{1}{12} = \frac{2 - 1}{12}$
$\therefore y = \frac{1}{12} m o l$
When the mixture of gas produced is passed through alkali solution $C {O}_{2}$ will be absorbed and the residual gas will be $\frac{1}{12} m o l$ CO which will occupy $\frac{1}{12} \times 22.4 L \approx 1.87 L \text{ at STP}$
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http://physics.stackexchange.com/users/20015/talon
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# Talon
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5 $SU(N)$ Neel manifold
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http://callmeeinstein.blogspot.com.es/2012_09_01_archive.html
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## Saturday, 29 September 2012
### Welcome little Einsteins...
So, this is the first post on our blog's wall ^_^
I really hope this experiment we are starting fits well on your (sometimes) fuzzy minds XD
This forthcoming week we'll learn about some numbers that cannot be expressed as fractions (the so-called irrational numbers) I don't kno why, but I do love these numbers!
One fine example of irrational numbers is the famous $\sqrt{2}$ which you are using everyday without even noticing: DIN A4 papers. In two or three days you will finally know why is this numer related to the paper sheets you write on. There is even a spiral related with the DIN A4 paper sheets which is almost perfectly built, but has some imperfections that will be mended in Unit 7.
Sometimes it is impossible to explain something without using mathematics... It is a strange math-world we are living in!.
BTW: did you know that Futurama's screenwriters are indeed mathematicians, physicists and theoretical engineers? I promise I will tell you more about the hilarious math-jkes it is possible to find in this series.
Anyway, I would like to finish this post with an incredible animated vide showing, among others, the Fibonacci spiral (the one that will be introduced in Uint 7) and that is quite a lot "smoother" than the DIN-A4 spiral. That spiral is featured in the beautiful video on the right.
And DON'T FORGET THIS IS OUR BLOG, so any contribution about maths, science, music, movies or whatever will be welcomed :D
First Challenge of the Week: PILGRIM's PROBLEM
An Italian pilgrim was planning his journey from Rome to Santiago de Compostela. Before arriving to Spain, he wanted to visit 64 different cities using only 15 straight pilgrimages. The map he was currently in possession of, showed the different paths communicating all the cities he wanted to visit.
Would you be able to draw a path using 15 straight lines without removing the pencil from the sheet so the pilgrim manages to complete successfully his trip?
Watch it: You MUST start your trip from the black spot, but you can finish it wherever you want. Note there’s one missing connection between two towns at the bottom of the drawing.
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https://en.m.wikipedia.org/wiki/Galvanic_anode
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# Galvanic anode
A galvanic anode, or sacrificial anode, is the main component of a galvanic cathodic protection (CP) system used to protect buried or submerged metal structures from corrosion.
Example of a galvanic anode on the hull of a ship.
They are made from a metal alloy with a more "active" voltage (more negative reduction potential / more positive electrode potential) than the metal of the structure. The difference in potential between the two metals means that the galvanic anode corrodes, so that the anode material is consumed in preference to the structure. The loss (or sacrifice) of the anode material gives rise to the alternative name of sacrificial anode.
## Theory
In brief, corrosion is a chemical reaction occurring by an electrochemical mechanism (a redox reaction).[1] During corrosion of iron or steel there are two reactions, oxidation (equation 1), where electrons leave the metal (and the metal dissolves, i.e. actual loss of metal results) and reduction, where the electrons are used to convert oxygen and water to hydroxide ions (equation 2):[2]
${\displaystyle {\ce {Fe -> Fe^2+(aq) + 2e-}}}$
(1)
${\displaystyle {\ce {O2 + 2 H2O + 4e- -> 4 OH- (aq)}}}$
(2)
In most environments, the hydroxide ions and ferrous ions combine to form ferrous hydroxide, which eventually becomes the familiar brown rust:[3]
${\displaystyle {\ce {Fe^2+(aq) + 2OH- (aq) -> Fe(OH)2(s)}}}$
(3)
As corrosion takes place, oxidation and reduction reactions occur and electrochemical cells are formed on the surface of the metal so that some areas will become anodic (oxidation) and some cathodic (reduction). Electrons flow from the anodic areas into the electrolyte as the metal corrodes. Conversely, as electrons flow from the electrolyte to the cathodic areas, the rate of corrosion is reduced.[4] (The flow of electrons is in the opposite direction of the flow of electric current.)
As the metal continues to corrode, the local potentials on the surface of the metal will change and the anodic and cathodic areas will change and move. As a result, in ferrous metals, a general covering of rust is formed over the whole surface, which will eventually consume all the metal. This is rather a simplified view of the corrosion process, because it can occur in several different forms.[5]
CP works by introducing another metal (the galvanic anode) with a much more anodic surface, so that all the current will flow from the introduced anode and the metal to be protected becomes cathodic in comparison to the anode. This effectively stops the oxidation reactions on the metal surface by transferring them to the galvanic anode, which will be sacrificed in favour of the structure under protection.[6] More simply put, this takes advantage of the relatively low stability of magnesium, aluminum or zinc metals; they dissolve instead of iron because their bonding is weaker compared to iron, which is bonded strongly via its partially filled d-orbitals.
For this protection to work there must be an electron pathway between the anode and the metal to be protected (e.g., a wire or direct contact) and an ion pathway between both the oxidizing agent (e.g., oxygen and water or moist soil) and the anode, and the oxidizing agent and the metal to be protected, thus forming a closed circuit; therefore simply bolting a piece of active metal such as zinc to a less active metal, such as mild steel, in air (a poor ionic conductor) will not furnish any protection.
## Anode materials
A steel wide-beam canal barge, showing a newly blacked hull and new magnesium anodes.
There are three main metals used as galvanic anodes: magnesium, aluminum and zinc. They are all available as blocks, rods, plates or extruded ribbon. Each material has advantages and disadvantages.
Magnesium has the most negative electropotential of the three (see galvanic series) and is more suitable for areas where the electrolyte (soil or water) resistivity is higher. This is usually on-shore pipelines and other buried structures, although it is also used on boats in fresh water and in water heaters. In some cases, the negative potential of magnesium can be a disadvantage: if the potential of the protected metal becomes too negative, reduction of water or solvated protons may evolve hydrogen atoms on the cathode surface, for instance according to
${\displaystyle {\ce {2 H2O + 2e- -> 2H + 2OH- (aq)}}}$
(4)
leading to hydrogen embrittlement or to disbonding of the coating.[7][8] Where this is a concern, zinc anodes may be used. An aluminum-zinc-tin alloy called KA90 is commonly used in marine and water heater applications.[9]
Zinc and aluminium are generally used in salt water, where the resistivity is generally lower and magnesium dissolves relatively quickly by reaction with water under hydrogen evolution (self-corrosion). Typical uses are for the hulls of ships and boats, offshore pipelines and production platforms, in salt-water-cooled marine engines, on small boat propellers and rudders, and for the internal surface of storage tanks.
Zinc is considered a reliable material, but is not suitable for use at higher temperatures, as it tends to passivate (the oxide layer formed shields from further oxidation); if this happens, current may cease to flow and the anode stops working.[10] Zinc has a relatively low driving voltage, which means in higher-resistivity soils or water it may not be able to provide sufficient current. However, in some circumstances — where there is a risk of hydrogen embrittlement, for example — this lower voltage is advantageous, as overprotection is avoided.[11]
Aluminium anodes have several advantages, such as a lighter weight, and much higher capacity than zinc. However, their electrochemical behavior is not considered as reliable as zinc, and greater care must be taken in how they are used. Aluminium anodes will passivate where chloride concentration is below 1,446 parts per million.[12]
One disadvantage of aluminium is that if it strikes a rusty surface, a large thermite spark may be generated, so its use is restricted in tanks where there may be explosive atmospheres and there is a risk of the anode falling.[8]
Since the operation of a galvanic anode relies on the difference in electropotential between the anode and the cathode, practically any metal can be used to protect some other, providing there is a sufficient difference in potential. For example, iron anodes can be used to protect copper.[13]
## Design considerations
The design of a galvanic anode CP system should consider many factors, including the type of structure, the resistivity of the electrolyte (soil or water) it will operate in, the type of coating and the service life.
The primary calculation is how much anode material will be required to protect the structure for the required time. Too little material may provide protection for a while, but need to be replaced regularly. Too much material would provide protection at an unnecessary cost. The mass in kg is given by equation (5).[14]
Mass = (Current Required x Design Life x 8760) ÷ (Utilisation Factor x Anode Capacity)
(5)
• The design life is in years (1 year = 8760 hours).
• The utilisation factor (UF) of the anode is a constant value, depending on the shape of the anode and how it is attached, which signifies how much of the anode can be consumed before it ceases to be effective. A value of 0.8 indicates that 80% of the anode can be consumed, before it should be replaced. A long slender stand off anode (installed on legs to keep the anode away from the structure) has a UF value of 0.9, whereas the UF of a short, flush mounted anode is 0.8.[14]
• Anode capacity is an indication of how much material is consumed as current flows over time. The value for zinc in seawater is 780 Ah/kg but aluminium is 2000 Ah/kg,[14] which reflects the lower atomic mass of aluminium and means that, in theory, aluminium can produce much more current per weight than zinc before being depleted and this is one of the factors to consider when choosing a particular material.
The amount of current required corresponds directly to the surface area of the metal exposed to the soil or water, so the application of a coating drastically reduces the mass of anode material required. The better the coating, the less anode material is needed.
Once the required mass of material is known, the particular type of anode is chosen. Differently shaped anodes will have a different resistance to earth, which governs how much current can be produced, so the resistance of the anode is calculated to ensure that sufficient current will be available. If the resistance of the anode is too high, either a differently shaped or sized anode is chosen, or a greater quantity of anodes must be used.[14]
The arrangement of the anodes is then planned so as to provide an even distribution of current over the whole structure. For example, if a particular design shows that a pipeline 10 kilometres (6.2 mi) long needs 10 anodes, then approximately one anode per kilometre would be more effective than putting all 10 anodes at one end or in the centre.
• No external power sources required.
• Relatively easy to install.
• Lower voltages and current mean that risk of causing stray current interference on other structures is low.
• Require less frequent monitoring than impressed current CP systems.
• Relatively low risk of overprotection.
• Once installed, testing the system components is relatively simple for trained personnel.
• Current capacity limited by anode mass and self consumption at low current density.
• Lower driving voltage means the anodes may not work in high-resistivity environments.
• Often requires that the protected structure be electrically isolated from other structures and ground.
• Anodes are heavy and will increase water resistance on moving structures or pipe interiors.
• Where D.C. power is available, electrical energy can be obtained more cheaply than by galvanic anodes.
• Where large arrays are used, wiring is needed due to high current flow and need to keep resistance losses low.
• Anodes must be carefully placed to avoid interfering with water flow into the propeller.
• To retain effectiveness, the anodes must be inspected and/or replaced as part of normal maintenance.
## Cost effectiveness
A galvanic anode (sacrificial anode) on a yacht's propeller shaft
As the anode materials used are generally more costly than iron, using this method to protect ferrous metal structures may not appear to be particularly cost effective. However, consideration should also be given to the costs incurred to repair a corroded hull or to replace a steel pipeline or tank because their structural integrity has been compromised by corrosion.
However, there is a limit to the cost effectiveness of a galvanic system. On larger structures, such as long pipelines, so many anodes may be needed that it would be more cost-effective to install impressed current cathodic protection.
## Production of sacrificial anodes
The basic method is to produce sacrificial anodes through a casting process. However, two casting methods can be distinguished.[15]
The high pressure die-casting process for sacrificial anodes is widespread. It is a fully automated machine process. In order for the manufacturing process to run reliably and in a repeatable manner, a modification of the processed sacrificial anode alloy is required. Alternatively, the gravity casting process is used for the production of the sacrificial anodes. This process is performed manually or partially automated. The alloy does not have to be adapted to the manufacturing process, but is designed for 100% optimum corrosion protection.
## Notes
1. ^ Shrier 10:4
2. ^ Peabody p.2
3. ^ Shrier 3:4
4. ^ Peabody p. 21
5. ^ Shrier 1:2
6. ^ Shrier 10:29
7. ^ Peabody p.37
8. ^ a b Schreir 10:44
9. ^ "80251 KA90 Aluminum Alloy Anodes in Hot and Cold Seawater and Brine Environments". ASM International.
10. ^ Baeckmann, Schwenck, Prinz. p.185
11. ^ Shreir 10:43
12. ^ de Rincon, O.; Sanchez, M.; Salas, O.; Romero, G.; Palacios, C.; Basile, J.; Suarez, J.; de Romero, M.; Zamora, R. (2010), "Comparative behavior of sacrificial anodes based on Mg, Zn, and Al alloys in brackish water", Comparative Behavior of Sacrificial Anodes Based on Mg, Zn, and Al Alloys in Brackish Water, NACE, p. 15, retrieved 2013-09-05
13. ^ Shreir 10:12
14. ^ a b c d DNV RP-B401-2005
## References
• A. W. Peabody, Peabody's Control of Pipeline Corrosion, 2nd ed., 2001, NACE International. ISBN 1-57590-092-0
• Shreir L. L. et al., Corrosion Vol. 2, 3rd ed., 1994, ISBN 0-7506-1077-8
• Baeckmann, Schwenck, Prinz. Handbook of Cathodic Corrosion Protection, 3rd ed. 1997. ISBN 0-88415-056-9
• Det Norske Veritas Recommended Practice for Cathodic Protection Design DNV RP-B401-2005
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https://mafiadoc.com/homomorphisms-between-mapping-class-groups_5bbd9ca1097c47e4188b45e6.html
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Homomorphisms between mapping class groups
Nov 8, 2010 - Benson Farb, Chris Leininger and especially Johanna Mangahas for many very interesting conversations on the topic of this paper. The.
HOMOMORPHISMS BETWEEN MAPPING CLASS GROUPS
arXiv:1011.1855v1 [math.GT] 8 Nov 2010
JAVIER ARAMAYONA & JUAN SOUTO Abstract. Suppose that X and Y are surfaces of finite topological type, where X has genus g ≥ 6 and Y has genus at most 2g − 1; in addition, suppose that Y is not closed if it has genus 2g − 1. Our main result asserts that every non-trivial homomorphism Map(X) → Map(Y ) is induced by an embedding, i.e. a combination of forgetting punctures, deleting boundary components and subsurface embeddings. In particular, if X has no boundary then every non-trivial endomorphism Map(X) → Map(X) is in fact an isomorphism. As an application of our main theorem we obtain that, under the same hypotheses on genus, if X and Y have finite analytic type then every non-constant holomorphic map M(X) → M(Y ) between the corresponding moduli spaces is a forgetful map. In particular, there are no such holomorphic maps unless X and Y have the same genus and Y has at most as many marked points as X.
1. Introduction Throughout this article we will restrict our attention to connected orientable surfaces of finite topological type, meaning of finite genus and with finitely many boundary components and/or cusps. We will feel free to think about cusps as marked points, punctures or topological ends. If a surface has empty boundary and no cusps, it is said to be closed. The mapping class group Map(X) of a surface X of finite topological type is the group of isotopy classes of orientation preserving homeomorphisms fixing pointwise the union of the boundary and the set of punctures. We denote by T (X) and by M(X) = T (X)/ Map(X) the Teichm¨ uller space and moduli space of X, respectively. The first author has been partially supported by M.E.C. grant MTM2006/14688. The second author has been partially supported by NSF grant DMS-0706878, NSF Career award 0952106, and the Alfred P. Sloan Foundation. 1
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1.1. The conjecture. The triad formed by the mapping class group Map(X), Teichm¨ uller space T (X) and moduli space M(X) is often compared with the one formed by SLn Z, the symmetric space SOn \ SLn R, and the locally symmetric space SOn \ SLn R/ SLn Z; here SLn Z stands as the paradigm of an arithmetic lattice in a higher rank semisimple algebraic group. This analogy has motivated many, possibly most, advances in the understanding of the mapping class group Map(X). For example, Grossman [15] proved that Map(X) is residually finite; Birman, Lubotzky and McCarthy [7] proved that the Tits alternative holds for subgroups of Map(X); the Thurston classification of elements in Map(X) mimics the classification of elements in an algebraic group [44]; Harvey [18] introduced the curve complex in analogy with the rational Tits’ building; Harer’s [17] computation of the virtual cohomological dimension of Map(X) follows the outline of Borel and Serre’s argument for arithmetic groups [8], etc... On the other hand, the comparison between Map(X) and SLn Z has strong limitations; for instance the mapping class group has finite index in its abstract commensurator [23], does not have property (T) [1] and has infinite dimensional second bounded cohomology [5]. In addition, it is not known if the mapping class group contains finite index subgroups Γ with H 1 (Γ; R) 6= 0. With the dictionary between Map(X) and SLn Z in mind, it is natural to ask to what extent there is an analog of Margulis’ superrigidity in the context of mapping class groups. This question, in various guises, has been addressed by a number of authors in recent times. For instance, Farb-Masur [14] proved that every homomorphism from an irreducible lattice in a higher-rank Lie group to a mapping class group has finite image. Notice that, on the other hand, mapping class groups admit non-trivial homomorphisms into higher-rank lattices [30]. With the same motivation, one may try to understand homomorphisms between mapping class groups; steps in this direction include the results of [2, 3, 19, 22, 25, 37]. In the light of this discussion we propose the following general conjecture, which states that, except in some low-genus cases (discussed in Example 1), some version of Margulis’ superrigidity holds for homomorphisms between mapping class groups: Superrigidity conjecture. Margulis’ superrigidity holds for homomorphisms φ : Map(X) → Map(Y ) between mapping class groups as long as X has at least genus three.
3
The statement of the superrigidity conjecture is kept intentionally vague for a good reason: different formulations of Margulis’ superrigidity theorem suggest different forms of the conjecture. For instance, recall that the geometric version of superrigidity asserts that any homomorphism Γ → Γ0 between two lattices in simple algebraic groups of higher rank is induced by a totally geodesic immersion MΓ → MΓ0 between the locally symmetric spaces associated to Γ and Γ0 . One possible way of interpreting the superrigidity conjecture for mapping class groups is to ask whether every homomorphism between mapping class groups of, say, surfaces of finite analytic type, induces a holomorphic map between the corresponding moduli spaces. Remark. There are examples [2] of injective homomorphisms Map(X) → Map(Y ) which map some pseudo-Anosovs to multi-twists and hence are not induced by any isometric embedding M(X) → M(Y ) for any reasonable choice of metric on M(X) and M(Y ). This is the reason why we prefer not to ask, as done by Farb and Margalit (see Question 2 of [3]), whether homomorphisms between mapping class groups are geometric. The Lie theoretic version of superrigidity essentially asserts that every homomorphism Γ → Γ0 between two irreducible lattices in higher rank Lie groups either has finite image or extends to a homomorphism between the ambient groups. The mapping class group Map(X) is a quotient of the group of homeomorphisms (resp. diffeomorphisms) of X but not a subgroup [39, 36], and thus there is no ambient group as such. A natural interpretation of this flavor of superrigidity would be to ask whether every homomorphism Map(X) → Map(Y ) is induced by a homomorphism between the corresponding groups of homeomorphisms (resp. diffeomorphisms). Finally, one has the folkloric version of superrigidity: every homomorphism between two irreducible higher rank lattices is one of the “obvious” ones. The word “obvious” is rather vacuous; to give it a little bit of content we adopt Maryam Mirzakhani’s version of the conjecture above: every homomorphism between mapping class groups has either finite image or is induced by some manipulation of surfaces. The statement manipulation of surfaces is again vague, but it conveys the desired meaning. 1.2. The theorem. Besides the lack of counterexamples, the evidence supporting the superrigidity conjecture is limited to the results in [3, 19, 22, 25, 37]. The goal of this paper is to prove the conjecture,
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with respect to any of its possible interpretations, under suitable genus bounds. Before stating our main result we need a definition: Definition 1. Let X and Y be surfaces of finite topological type, and consider their cusps to be marked points. Denote by |X| and |Y | the compact surfaces obtained from X and Y by forgetting all their marked points. By an embedding ι:X→Y we will understand a continuous injective map ι : |X| → |Y | with the property that whenever y ∈ ι(|X|) ⊂ |Y | is a marked point of Y in the image of ι, then ι−1 (y) is also a marked point of X. Note that forgetting a puncture, deleting a boundary component, and embedding X as a subsurface of Y are examples of embeddings. Conversely, every embedding is a combination of these three building blocks; compare with Proposition 3.1 below. It is easy to see that every embedding ι : X → Y induces a homomorphism Map(X) → Map(Y ). Our main result is that, as long as the genus of Y is less than twice that of X, the converse is also true: Theorem 1.1. Suppose that X and Y are surfaces of finite topological type, of genus g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. Then every nontrivial homomorphism φ : Map(X) → Map(Y ) is induced by an embedding X → Y . Remark. As we will prove below, the conclusion of Theorem 1.1 also applies to homomorphisms φ : Map(X) → Map(Y ) when both X and Y have the same genus g ∈ {4, 5}. We now give some examples that highlight the necessity for the genus bounds in Theorem 1.1. Example 1. Let X be a surface of genus g ≤ 1; if g = 0 then assume that X has at least four marked points or boundary components. The mapping class group Map(X) surjects onto PSL2 Z ' (Z/2Z) ∗ (Z/3Z). In particular, any two elements α, β ∈ Map(Y ) with orders two and three, respectively, determine a homomorphism Map(X) → Map(Y ); notice that such elements exist if Y is closed, for example. Choosing α and β appropriately, one can in fact obtain infinitely many conjugacy classes of homomorphisms Map(X) → Map(Y ) with infinite image and with the property that every element in the image is either pseudoAnosov or has finite order.
5
Example 1 shows that some lower bound on the genus of X is necessary in the statement of Theorem 1.1. Furthermore, since Map(X) has non-trivial abelianization if X has genus 2, there exist homomorphisms from Map(X) into mapping class groups of arbitrary closed surfaces Y that are not induced by embeddings. On the other hand, we expect Theorem 1.1 to be true for surfaces of genus g ∈ {3, 4, 5}. Remark. Recall that the mapping class group of a punctured disk is a finite index subgroup of the appropriate braid group. In particular, Example 1 should be compared with the rigidity results for homomorphisms between braid groups, and from braid groups into mapping class groups, due to Bell-Margalit [3] and Castel [11]. Next, observe that an upper bound on the genus of the target surface is also necessary in the statement of Theorem 1.1 since, for instance, the mapping class group of every closed surface injects into the mapping class group of some non-trivial connected cover [2]. Moreover, the following example shows that the bound in Theorem 1.1 is in fact optimal: Example 2. Suppose that X has non-empty connected boundary and let Y be the double of X. Let X1 , X2 be the two copies of X inside Y , and for x ∈ X denote by xi the corresponding point in Xi . Given a homeomorphism f : X → X fixing pointwise the boundary and the cusps define fˆ : Y → Y, fˆ(xi ) = (f (x))i ∀xi ∈ Xi The map f → fˆ induces a homomorphism Map(X) → Map(Y ) which is not induced by any embedding. 1.3. Applications. After having established that in Theorem 1.1 a lower bound for the genus of X is necessary and that the upper bound for the genus of Y is optimal, we discuss some consequences of our main result. First, we will observe that, in the absence of boundary, every embedding of a surface into itself is in fact a homeomorphism; in light of this, Theorem 1.1 implies the following: Theorem 1.2. Let X be a surface of finite topological type, of genus g ≥ 4 and with empty boundary. Then any non-trivial endomorphism φ : Map(X) → Map(X) is induced by a homeomorphism X → X; in particular φ is an isomorphism.
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Remark. The analogous statement of Theorem 1.2 for injective endomorphisms was known to be true by the work of Ivanov and McCarthy [25, 24, 37]. Theorem 1.2, as well as other related results discussed in Section 11, are essentially specializations of Theorem 1.1 to particular situations. Returning to the superrigidity conjecture, recall that in order to prove superrigidity for (cocompact) lattices one may associate, to every homomorphism between two lattices, a harmonic map between the associated symmetric spaces, and then use differential geometric arguments to show that this map is a totally geodesic immersion. This is not the approach we follow in this paper, and neither Teichm¨ uller space nor moduli space will play any role in the proof of Theorem 1.1. As a matter of fact, reversing the logic behind the proof of superrigidity, Theorem 1.1 will actually provide information about maps between moduli spaces, as we describe next. Suppose that X and Y are Riemann surfaces of finite analytical type. Endow the associated Teichm¨ uller spaces T (X) and T (Y ) with the standard complex structure. The latter is invariant under the action of the corresponding mapping class group and hence we can consider the moduli spaces M(X) = T (X)/ Map(X), M(Y ) = T (Y )/ Map(Y ) as complex orbifolds. Suppose now that X and Y have the same genus and that Y has at most as many marked points as X. Choosing an identification between the set of marked points of Y and a subset of the set of marked points of X, we obtain a holomorphic map M(X) → M(Y ) obtained by forgetting all marked points of X which do not correspond to a marked point of Y . Different identifications give rise to different maps; we will refer to these maps as forgetful maps. In Section 12 we will prove the following result: Theorem 1.3. Suppose that X and Y are Riemann surfaces of finite analytic type and assume that X has genus g ≥ 6 and Y genus g 0 ≤ 2g − 1; in the equality case g 0 = 2g − 1 assume that Y is not closed. Then, every non-constant holomorphic map f : M(X) → M(Y ) is a forgetful map. As a direct consequence of Theorem 1.3 we obtain:
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Corollary 1.4. Suppose that X and Y are Riemann surfaces of finite analytic type and assume that X has genus g ≥ 6 and Y genus g 0 ≤ 2g − 1; in the equality case g 0 = 2g − 1 assume that Y is not closed. If there is a non-constant holomorphic map f : M(X) → M(Y ), then X and Y have the same genus and X has at least as many marked points as Y . In order to prove Theorem 1.3 we will deduce from Theorem 1.1 that the map f is homotopic to a forgetful map F . The following result, proved in Section 12, will immediately yield the equality between f and F : Proposition 1.5. Let X and Y be Riemann surfaces of finite analytical type and let f1 , f2 : M(X) → M(Y ) be homotopic holomorphic maps. If f1 is not constant, then f1 = f2 . Recall that the Weil-Peterson metric on moduli space is K¨ahler and has negative curvature. In particular, if the moduli spaces M(X) and M(Y ) were closed, then Proposition 1.5 would follow directly from the work of Eells-Sampson [12]. In order to prove Proposition 1.5 we simply ensure that their arguments go through in our context. 1.4. Strategy of the proof of Theorem 1.1. We now give a brief idea of the proof of Theorem 1.1. The main technical result of this paper is the following theorem: Proposition 1.6. Suppose that X and Y are surfaces of finite topological type of genera g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. Every nontrivial homomorphism φ : Map(X) → Map(Y ) maps (right) Dehn twists along non-separating curves to (possibly left) Dehn twist along non-separating curves. Given a non-separating curve γ ⊂ X denote by δγ the Dehn twist associated to γ. By Proposition 1.6, φ(δγ ) is a Dehn twist along some non-separating curve φ∗ (γ) ⊂ Y . We will observe that the map φ∗ preserves disjointness and intersection number 1. In particular, φ∗ maps chains in X to chains in Y . In the closed case, it follows easily that there is a unique embedding X → Y which induces the same map on curves as φ∗ ; this is the embedding provided by Theorem 1.1. In the presence of boundary and/or cusps the argument is rather involved, essentially because one needs to determine which cusps and boundary components are to be filled in.
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Hoping that the reader is now convinced that Theorem 1.1 follows after a moderate amount of work from Proposition 1.6, we sketch the proof of the latter. The starting point is a result of Bridson [9] which asserts that, as long as X has genus at least 3, any homomorphism φ : Map(X) → Map(Y ) maps Dehn twists to roots of multitwists. The first problem that we face when proving Proposition 1.6 is that Bridson’s result does not rule out that φ maps Dehn twists to finite order elements. In this direction, one may ask the following question: Question 1. Suppose that φ : Map(X) → Map(Y ) is a homomorphism between mapping class groups of surfaces of genus at least 3, with the property that the image of every Dehn twist along a non-separating curve has finite order. Is the image of φ finite? The answer to this question is trivially positive if ∂Y 6= ∅, for in this case Map(Y ) is torsion-free. We will also give an affirmative answer if Y has punctures: Theorem 1.7. Suppose that X and Y are surfaces of finite topological type, that X has genus at least 3, and that Y is not closed. Then any homomorphism φ : Map(X) → Map(Y ) which maps a Dehn twist along a non-separating curve to a finite order element is trivial. For closed surfaces Y we only give a partial answer to the above question; more concretely, in Proposition 5.1 we will prove that, as long as the genus of Y is in a suitable range determined by the genus of X, then the statement of Theorem 1.7 remains true. Remark. At the end of section 5 we will observe that a positive answer to question 1 would imply that the abelianization of finite index subgroups in Map(X) is finite. This is conjectured to be the case. We continue with the sketch of the proof of Proposition 1.6. At this point we know that for every non-separating curve γ ⊂ X, the element φ(δγ ) is a root of a multitwist and has infinite order. We may thus associate to γ the multicurve φ∗ (γ) supporting the multitwist powers of φ(δγ ). In principle, and also in practice if Y has sufficiently large genus, φ(δγ ) could permute the components of φ∗ (γ). However, under the genus bounds in Theorem 1.1, we deduce from a result of Paris [41] that this is not the case. Once we know that φ(δγ ) fixes each component of φ∗ (γ), a simple counting argument yields that φ∗ (γ) is actually a single curve. This implies that φ(δγ ) is a root of some power of the Dehn twist along φ∗ (γ). In the last step, which we now describe, we will obtain that φ(δγ ) is in fact a Dehn twist.
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Denote by Xγ the surface obtained by deleting from X an open regular neighborhood of γ, and let Yφ0∗ (γ) be the surface obtained by deleting φ∗ (γ) from Y . The centralizer of the Dehn twist δγ in Map(X) is closely related to Map(Xγ ) and the same is true for the centralizer of φ(δγ ) and Map(Yφ0∗ (γ) ). More concretely, the homomorphism φ induces a homomorphism Map(Xγ ) → Map(Yφ0∗ (γ) ) Moreover, it follows from the construction that φ(δγ ) is in fact a power of the Dehn twist along φ∗ (γ) if the image of this homomorphism is not centralized by any finite order element in Map(Yφ0∗ (γ) ). This will follow from an easy computation using the Riemann-Hurwitz formula together with the next result: Proposition 1.8. Suppose that X and Y are surfaces of finite topological type. If the genus of X is at least 3 and larger than that of Y , then there is no nontrivial homomorphism φ : Map(X) → Map(Y ). Remark. If X is closed, Proposition 1.8 is due to Harvey and Korkmaz [19]. Their argument makes heavy use of torsion in Map(X); therefore, it cannot be used for general surfaces. Once we know that φ(δγ ) is a power of a Dehn twist, it follows from the braid relation that this power has to be ±1, as we needed to prove. This finishes the sketch of the proof of Proposition 1.6 and hence of Theorem 1.1. Before concluding the introduction, we would like to mention a related result due to Bridson and Vogtmann [10] on homomorphisms between outer automorphism groups of free groups, namely: Theorem (Bridson-Vogtmann). Suppose n > 8. If n is even and n < m ≤ 2n, or if n is odd and n < m ≤ 2n − 2, then every homomorphism Out(Fn ) → Out(Fm ) factors through a homomorphism Out(Fn ) → Z/2Z. We remark that in their proof, Bridson and Vogtmann make very heavy use of the presence of rather large torsion subgroups in Out(Fn ). Rather on the contrary, in the present paper torsion is an annoyance. In particular, the proof of the Bridson-Vogtmann theorem and that of Theorem 1.1 are completely different. In spite of that, we would like to mention that the Bridson-Vogtmann theorem played a huge role in this paper: it suggested the possibility of understanding homomorphisms between mapping class groups Map(X) → Map(Y ) under the assumption that the genus of Y is not much larger than that of X.
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Acknowledgements. The authors wish to thank Martin Bridson, Benson Farb, Chris Leininger and especially Johanna Mangahas for many very interesting conversations on the topic of this paper. The authors are also grateful to Michel Boileau and Luis Paris for letting them know about the work of Fabrice Castel. The first author wishes to express his gratitude to Ser Peow Tan and the Institute for Mathematical Sciences of Singapore, where parts of this work were completed. 2. Generalities In this section we discuss a few well-known facts on mapping class groups. See [13, 24] for details. Throughout this article, all surfaces under consideration are orientable and have finite topological type, meaning that they have finite genus, finitely many boundary components and finitely many punctures. We will feel free to consider cusps as marked points, punctures, or ends homeomorphic to S1 × R. For instance, if X is a surface with, say, 10 boundary components and no cusps, by deleting every boundary component we obtain a surface X 0 with 10 cusps and no boundary components. A simple closed curve on a surface is said to be essential if it does not bound a disk containing at most one puncture; we stress that we consider boundary-parallel curves to be essential. From now on, by a curve we will mean an essential simple closed curve. Also, we will often abuse terminology and not distinguish between curves and their isotopy classes. We now introduce some notation that will be used throughout the paper. Let X be a surface and let γ be an essential curve not parallel to the boundary of X. We will denote by Xγ the complement in X of the interior of a closed regular neighborhood of γ; we will refer to the two boundary components of Xγ which appear in the boundary of the regular neighborhood of γ as the new boundary components of Xγ . We will denote by Xγ0 the surface obtained from Xγ by deleting the new boundary components of Xγ ; equivalently, Xγ0 = X \ γ. A multicurve is the union of a, necessarily finite, collection of pairwise disjoint, non-parallel curves. Given two multicurves γ, γ 0 we denote their geometric intersection number by i(γ, γ 0 ). A cut system is a multicurve whose complement is a connected surface of genus 0. Two cut systems are said to be related by an elementary move if they share all curves but one, and the remaining two curves intersect exactly once. The cut system complex of a surface X is the simplicial graph whose vertices are cut systems on X and where two
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cut systems are adjacent if the corresponding cut systems are related by an elementary move. 2.1. Mapping class group. The mapping class group Map(X) of a surface X is the group of isotopy classes of orientation preserving homeomorphisms X → X which fix the boundary pointwise and map every cusp to itself; here, we also require that the isotopies fix the boundary pointwise. We will also denote by Map∗ (X) the group of isotopy classes of all orientation preserving homeomorphisms of X. Observe that Map(X) is a subgroup of Map∗ (X) only in the absence of boundary; in this case Map(X) has finite index in Map∗ (X). While every element of the mapping class group is an isotopy class of homeomorphisms, it is well-known that the mapping class group cannot be realized by a group of diffeomorphisms [39], or even homeomorphisms [36]. However, for our purposes the difference between actual homeomorphisms and their isotopy classes is of no importance. In this direction, and in order to keep notation under control, we will usually make no distinction between mapping classes and their representatives. 2.2. Dehn twists. Given a curve γ on X, we denote by δγ the (right) Dehn twist along γ. It is important to remember that δγ is solely determined by the curve γ and the orientation of X. In other words, it is independent of any chosen orientation of γ. Perhaps the main reason why Dehn twists appear so prominently in this paper is because they generate the mapping class group: Theorem 2.1 (Dehn-Lickorish). If X has genus at least 2, then Map(X) is generated by Dehn twists along non-separating curves. There are quite a few known concrete sets of Dehn twists which generate the mapping class group. We will consider the so-called Humphries generators [21]; see Figure 1 for a picture of the involved curves. a1
b1
a2
b2
a3
c
b3
bg
rk
r1
r2
Figure 1. The Humphries generators: Dehn twists along the curves ai , bi , c and ri generate Map(X).
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Algebraic relations among Dehn twists are often given by particular configurations of curves. We now discuss several of these relations; see [13, 16, 33] and the references therein for proofs and details: Conjugate Dehn twists. For any curve γ ⊂ X and any f ∈ Map(X) we have δf (γ) = f δγ f −1 Hence, Dehn twists along any two non-separating curves are conjugate in Map(X). Conversely, if the Dehn twist along γ is conjugate in Map(X) to a Dehn twist along a non-separating curve, then γ is nonseparating. Observe that Theorem 2.1 and the fact that Dehn twists along any two non-separating curves are conjugate immediately imply the following very useful fact: Lemma 2.2. Let X be a surface of genus at least 3 and let φ : Map(X) → G be a homomorphism. If δγ ∈ Ker(φ) for some γ ⊂ X non-separating, then φ is trivial. Disjoint curves. Suppose γ, γ 0 are disjoint curves, meaning i(γ, γ 0 ) = 0. Then δγ and δγ 0 commute. Curves intersecting once. Suppose that two curves γ and γ 0 intersect once, meaning i(γ, γ 0 ) = 1. Then δγ δγ 0 δγ = δγ 0 δγ δγ 0 This is the so-called braid relation; we say that δγ and δγ 0 braid. It is known [16] that if γ and γ 0 are two curves in X and k ∈ Z is such that |k · i(γ, γ 0 )| ≥ 2, then δγk and δγk0 generate a free group F2 of rank 2. In particular we have: Lemma 2.3. Suppose that k ∈ Z \ {0} and that γ and γ 0 are curves such that δγk and δγk0 satisfy the braid relation, then either γ = γ 0 or k = ±1 and i(γ, γ 0 ) = 1. Chains. Recall that a chain in X is a finite sequence of curves γ1 , . . . , γk such that i(γi , γj ) = 1 if |i − j| = 1 and i(γi , γj ) = 0 otherwise. Let γ1 , . . . , γk be a chain in X and suppose first that k is even. Then the boundary ∂Z of a regular neighborhood of ∪γi is connected and we have (δγ1 δγ2 . . . δγk )2k+2 = δ∂Z If k is odd then ∂Z consists of two components ∂1 Z and ∂2 Z and the appropriate relation is (δγ1 δγ2 . . . δγk )k+1 = δ∂Z1 δ∂Z2 = δ∂Z2 δ∂Z1 These two relations are said to be the chain relations.
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Lanterns. A lantern is a configuration in of seven curves a, b, c, d, x, y and z in X as represented in figure 2.
a
x b
y
d
c z
Figure 2. A lantern If seven curves a, b, c, d, x, y and z in X form a lantern then the corresponding Dehn twists satisfy the so-called lantern relation: δa δb δc δd = δx δy δz Conversely, it is due to Hamidi-Tehrani [16] and Margalit [33] that, under mild hypotheses, any seven curves whose associated Dehn twists satisfy the lantern relation form a lantern. More concretely: Proposition 2.4 (Hamidi-Tehrani, Margalit). Let a, b, c, d, x, y, z be essential curves whose associated Dehn twists satisfy the lantern relation δa δb δc δd = δx δy δz If the curves a, b, c, d, x are paiwise distinct and pairwise disjoint, then a, b, c, d, x, y, z is a lantern. In the course of this paper we will continuously discriminate against separating curves. By a non-separating lantern we understand a lantern with the property that all the involved curves are non-separating. It is well-known, and otherwise easy to see, that X contains a nonseparating lantern if X has genus at least 3. In particular we deduce that, as long as X has genus g ≥ 3, every non-separating curve belongs to a non-separating lantern. 2.3. Centralizers of Dehn twists. Observe that the relation f δγ f −1 = δf (γ) , for f ∈ Map(X) and γ ⊂ X a curve, implies that Z(δγ ) = {f ∈ Map(X) | f (γ) = γ},
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where Z(δγ ) denotes the centralizer of δγ in Map(X). Notice that Z(δγ ) is also equal to the normalizer N (hδγ i) of the subgroup of Map(X) generated by δγ . An element in Map(X) which fixes γ may either switch the sides of γ or may preserve them. We denote by Z0 (δγ ) the group of those elements which preserve sides; observe that Z0 (δγ ) has index at most 2 in Z(δγ ). The group Z0 (δγ ) is closely related to two different mapping class groups. First, let Xγ be the surface obtained by removing the interior of a closed regular neighborhood γ × [0, 1] of γ from X. Every homeomorphism of Xγ fixing pointwise the boundary and the punctures extends to a homeomorphism X → X which is the identity on X \ Xγ . This induces a homomorphism Map(Xγ ) → Map(X); more concretely we have the following exact sequence: (2.1)
0 → Z → Map(Xγ ) → Z0 (δγ ) → 1
Here, the group Z is generated by the difference δη1 δη−1 of the Dehn 2 twists along η1 and η2 , the new boundary curves of Xγ . Instead of deleting a regular neighborhood of γ we could also delete γ from X. Equivalently, let Xγ0 be the surface obtained from Xγ by deleting the new boundary curves of Xγ . Every homeomorphism of X fixing γ induces a homeomorphism of Xγ0 . This yields a second exact sequence (2.2)
0 → hδγ i → Z0 (δγ ) → Map(Xγ0 ) → 1
2.4. Multitwists. To a multicurve η ⊂ X we associate the group Tη = h{δγ , γ ⊂ η}i ⊂ Map(X) generated by the Dehn twists along the components of η. We refer to the elements in Tη as multitwists along η. Observe that Tη is abelian; more concretely, Tη is isomorphic to the free abelian group with rank equal to the number of components of η. Let η ⊂ X be a multicurve. An element f ∈ Tη which does not belong to any Tη0 , for some η 0 properly contained in η, is said to be a generic multitwist along η. Conversely, if f ∈ Map(X) is a multitwist, then the support of f is the smallest multicurve η such that f is a generic multitwist along η. Much of what we just said about Dehn twists extends easily to multitwists. For instance, if η ⊂ X is a multicurve, then we have Tf (η) = f Tη f −1
15
for all f ∈ Map(X). In particular, the normalizer N (Tη ) of Tη in Map(X) is equal to N (Tη ) = {f ∈ Map(X)|f (η) = η} On the other hand, the centralizer Z(Tη ) of Tη is the intersection of the centralizers of its generators; hence Z(Tη ) = {f ∈ Map(X)|f (γ) = γ for every component γ ⊂ η} Notice that N (Tη )/Z(Tη ) acts by permutations on the set of components of η. For further use we observe that if the multicurve η happens to be a cut system, then N (Tη )/Z(Tη ) is in fact isomorphic to the group of permutations of the components of η. Denote by Z0 (Tη ) the subgroup of Z(Tη ) fixing not only the components but also the sides of each component. Notice that Z(Tη )/Z0 (Tη ) is a subgroup of (Z/2Z)|η| and hence is abelian. Observe that it follows from the definition of the mapping class group and from the relation δf (γ) = f δγ f −1 that every Dehn twist along a boundary component of X is central in Map(X). In fact, as long as X has at least genus 3, such Dehn twists generate the center of Map(X): Theorem 2.5. If X has genus at least 3 then the group T∂X generated by Dehn twists along the boundary components of X is the center of Map(X). Moreover, we have 1 → T∂X → Map(X) → Map(X 0 ) → 1 where X 0 is the surface obtained from X by deleting the boundary. Notice that if X is a surface of genus g ∈ {1, 2}, with empty boundary and no marked points, then the center of Map(X) is generated by the hyperelliptic involution. 2.5. Roots. It is a rather surprising, and annoying, fact that such simple elements in Map(X) as Dehn twists have non-trivial roots [34]. Recall that a root of f ∈ Map(X) is an element g ∈ Map(X) for which there is k ∈ Z with f = g k . Being forced to live with roots, we state here a few simple but important observations: Lemma 2.6. Suppose that f ∈ Tη and f 0 ∈ Tη0 are generic multitwists along multicurves η, η 0 ⊂ X. If f and f 0 have a common root, then η = η0. Lemma 2.7. Suppose that f ∈ Tη is a generic multitwist along a multicurve η and f 0 ∈ Map(X) is a root of f . Then f 0 (η) = η and hence f 0 ∈ N (Tη ).
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If η is an essential curve then Tη = hδη i; hence N (Tη ) = Z(δη ) is the subgroup of Map(X) preserving η. Recall that Z0 (δη ) is the subgroup of Z(δη ) which preserves sides of η. Lemma 2.8. Suppose that δη ∈ Map(X) is a Dehn twist along an essential curve η. For f ∈ Z0 (δη ) the following are equivalent: • f is a root of a power of δη , and • the image of f in Map(Xη0 ) under the right arrow in (2.2) has finite order. Moreover, f is itself a power of δη if and only if the image of f in Map(Xη0 ) is trivial. 2.6. Torsion. In the light of Lemma 2.8, it is clear that the existence of roots is closely related to the presence of torsion in mapping class groups. While it is known that every mapping class group always contains a finite index torsion-free subgroup, this is not going to be of much use here. The fact that the mapping class group of a surface with boundary is torsion-free is going to be of more importance. Theorem 2.9. If X is a surface with nonempty boundary, then Map(X) is torsion-free. Similarly, if X has marked points, then finite subgroups of Map(X) are cyclic. The key to understand torsion in mapping class groups is the resolution by Kerckhoff [26] of the Nielsen realization problem: the study of finite subgroups of the mapping class group reduces to the study of groups of automorphism of Riemann surfaces. For instance, it follows from the classical Hurewitz theorem that the order of such a group is bounded from above solely in terms of the genus of the underlying surface. Below we will need the following bound, due to Maclachlan [31] and Nakajima [40], for the order of finite abelian subgroups of Map(X). Theorem 2.10. Suppose that X has genus g ≥ 2. Then Map(X) does not contain finite abelian groups with more than 4g + 4 elements. We remark that if g ≤ 5 all finite subgroups, abelian or not, of Map(X) have been listed [28, 29]. In the sequel we will make use of this list in the case that g = 3, 4. Finally, we observe that a finite order diffeomorphism which is isotopic to the identity is in fact the identity. This implies, for instance, ¯ is obtained from X by filling in punctures, and τ : X → X that if X is a finite order diffeomorphism representing a non-trivial element in ¯ is non-trivial as well. Map(X), then the induced mapping class of X
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2.7. Centralizers of finite order elements. By (2.1) and (2.2), centralizers of Dehn twists are closely related to other mapping class groups. Essentially the same is true for centralizers of other mapping classes. We now discuss the case of torsion elements. The following result follows directly from the work of Birman-Hilden [6]: Theorem 2.11 (Birman-Hilden). Suppose that [τ ] ∈ Map(X) is an element of finite order and let τ : X → X be a finite order diffeomorphism representing [τ ]. Consider the orbifold O = X/hτ i and let O∗ be the surface obtained from O by removing the singular points. Then we have a sequence 1 → h[τ ]i → Z([τ ]) → Map∗ (O∗ ) where Map∗ (O∗ ) is the group of isotopy classes of all homeomorphisms O∗ → O∗ . Hidden in Theorem 2.11 we have the following useful fact: two finite order diffeomorphisms τ, τ 0 : X → X which are isotopic are actually conjugate as diffeomorphisms (see the remark in [4, p.10]). Hence, it follows that the surface O∗ in Theorem 2.11 depends only on the mapping class [τ ]. Abusing notation, in the sequel we will speak about the fixed-point set of a finite order element in Map(X). 3. Homomorphisms induced by embeddings In this section we define what is meant by an embedding ι : X → Y between surfaces. As we will observe, any embedding induces a homomorphism between the corresponding mapping class groups. We will discuss several standard examples of such homomorphisms, notably the so-called Birman exact sequences. We will conclude the section with a few observations that will be needed later on. Besides the possible differences of terminology, all the facts that we will state are either well known or simple observations in 2-dimensional topology. A reader who is reasonably acquainted with [13, 24] will have no difficulty filling the details. 3.1. Embeddings. Let X and Y be surfaces of finite topological type, and consider their cusps to be marked points. Denote by |X| and |Y | the compact surfaces obtained from X and Y , respectively, by forgetting all the marked points, and let PX ⊂ |X| and PY ⊂ |Y | be the sets of marked points of X and Y . Definition. An embedding ι : X → Y is a continuous injective map ι : |X| → |Y | such that ι−1 (PY ) ⊂ PX . An embedding is said to be a homeomorphism if it has an inverse which is also an embedding.
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We will say that two embeddings ι, ι0 : X → Y are equivalent or isotopic if there if a continuous injective map f : |Y | → |Y | which is isotopic (but not necessarily ambient isotopic) to the identity relative to the set PY of marked points of Y and which satisfies f ◦ ι = ι0 . Abusing terminology, we will often say that equivalent embeddings are the same. Given an embedding ι : X → Y and a homeomorphism f : X → X which pointwise fixes the boundary and the marked points of X, we consider the homeomorphism ι(f ) : Y → Y given by ι(f )(x) = (ι◦f ◦ι−1 )(x) if x ∈ ι(X) and ι(f )(x) = x otherwise. Clearly, ι(f ) is a homeomorphism which pointwise fixes the boundary and the marked points of Y . In particular ι(f ) represents an element ι# (f ) in Map(Y ). It is easy to check that we obtain a well-defined group homomorphism ι# : Map(X) → Map(Y ) characterized by the following property: for any curve γ ⊂ X we have ι# (δγ ) = δι(γ) . Notice that this characterization immediately implies that if ι and ι0 are isotopic, then ι# = ι0# . 3.2. Birman exact sequences. As we mentioned above, notable examples of homomorphisms induced by embeddings are the so-called Birman exact sequences, which we now describe. Let X and Y be surfaces of finite topological type. We will say that Y is obtained from X by filling in a puncture if there is an embedding ι : X → Y and a marked point p ∈ PX , such that the underlying map ι : |X| → |Y | is a homeomorphism, and ι−1 (PY ) = PX \ {p}. If Y is obtained from X by filling in a puncture we have the following exact sequence: (3.1)
1
/
π1 (|Y | \ PY , ι(p))
/
Map(X)
ι#
/
Map(Y )
/
1
The left arrow in (3.1) can be described concretely. For instance, if γ is a simple loop in |Y | based ι(p) and avoiding all other marked points of Y , then the image of the element [γ] ∈ π1 (|Y | \ PY , ι(p)) in Map(X) is the difference of the two Dehn twists along the curves forming the boundary of a regular neighborhood of ι−1 (γ). Similarly, we will say that Y is obtained from X by filling in a boundary component if there is an embedding ι : X → Y , with ι−1 (PY ) = PX , and such that the complement in |Y | of the image of the underlying map |X| → |Y | is a disk which does not contain any marked point of
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Y . If Y is obtained from X by filling in a boundary component then we have the following exact sequence: (3.2)
1 → π1 (T 1 (|Y | \ PY )) → Map(X) → Map(Y ) → 1
Here T 1 (|Y | \ PY ) is the unit-tangent bundle of the surface |Y | \ PY . We refer to the sequences (3.1) and (3.2) as the Birman exact sequences. 3.3. Other building blocks. As we will see in the next subsection, any embedding is a composition of four basic building blocks. Filling punctures and filling boundary components are two of them; next, we describe the other two types. Continuing with the same notation as above, we will say that Y is obtained from X by deleting a boundary component if there is an embedding ι : X → Y with ι(PX ) ⊂ PY and such that the complement of the image of the underlying map |X| → |Y | is disk containing exactly one point in PY . If Y is obtained from X by deleting a boundary component then we have (3.3)
1 → Z → Map(X) → Map(Y ) → 1
where, Z is the group generated by the Dehn twist along the forgotten boundary component. Finally, we will say that ι : X → Y is a subsurface embedding if ι(PX ) ⊂ PY and if no component of the complement of the image of the underlying map |X| → |Y | is a disk containing at most one marked point. Notice that if ι : X → Y is a subsurface embedding, then the homomorphism ι# : Map(X) → Map(Y ) is injective if and only if ι is anannular, i.e. if no component of the complement of the image of the underlying map |X| → |Y | is an annulus without marked points; compare with (2.1) above. 3.4. General embeddings. Clearly, the composition of two embeddings is an embedding. For instance, observe that filling in a boundary component is the same as first forgetting it and then filling in a puncture. The following proposition, whose proof we leave to the reader, asserts that every embedding is isotopic to a suitable composition of the elementary building blocks we have just discussed: Proposition 3.1. Every embedding ι : X → Y is isotopic to a composition of the following three types of embedding: filling punctures, deleting boundary components, and subsurface embeddings. In particular, the homomorphism ι# : Map(X) → Map(Y ) is injective if and only if ι is an anannular subsurface embedding.
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Notation. In order to avoid notation as convoluted as T 1 (|Y | \ PY ), most of the time we will drop any reference to the underlying surface |Y | or to the set of marked point PY ; notice that this is consistent with taking the freedom to consider punctures as marked points or as ends. For instance, the Birman exact sequences now read 1 → π1 (Y ) → Map(X) → Map(Y ) → 1, if Y is obtained from X by filling in a puncture, and 1 → π1 (T 1 Y ) → Map(X) → Map(Y ) → 1, if it is obtained filling in a boundary component. We hope that this does not cause any confussion. 3.5. Two observations. We conclude this section with two observations that will be needed below. First, suppose that ι : X → Y is an embedding and let η ⊂ X be a multicurve. The image ι(η) of η in Y is an embedded 1-manifold, but it does not need to be a multicurve. For instance, some component of ι(η) may not be essential in Y ; also two components of ι(η) may be parallel in Y . If this is not the case, that is, if ι(η) is a multicurve in Y , then it is easy to see that ι# maps the subgroup Tη of multitwists supported on η isomorphically onto Tι(η) . We record this observation in the following lemma: Lemma 3.2. Let ι : X → Y be an embedding and let η ⊂ X be a multicurve such that • every component of ι(η) is essential in Y , and • no two components of ι(η) are parallel in Y , Then ι(η) is also a multicurve in Y and the homomorphism ι# maps Tη ⊂ Map(X) isomorphically to Tι(η) ⊂ Map(Y ). Moreover, the image of a generic multitwist in Tη is generic in Tι(η) . Finally, we recall the well-known fact that the Birman exact sequence (3.1) does not split: Lemma 3.3. Suppose that X is a surface of genus g ≥ 3 with empty boundary and a single puncture. If Y is the closed surface obtained from X by filling in the puncture, then the exact sequence (3.1) 1 → π1 (Y ) → Map(X) → Map(Y ) → 1 does not split. Proof. The mapping class group Map(Y ) of the closed surface Y contains a non-cyclic finite subgroup; namely one isomorphic to Z/2Z ×
21
Z/2Z. By Theorem 2.9 such a subgroup does not exist in Map(X), which proves that there is no splitting of (3.1). In Lemma 3.3 we proved that in a very particular situation one of the two Birman exact sequences does not split. Notice however that it follows from Theorem 1.1 that they never do; this also follows from the work of Ivanov-McCarthy [25]. 4. Triviality theorems In this section we remind the reader of two triviality theorems for homomorphisms from mapping class groups to abelian groups and permutation groups; these results are widely used throughout this paper. The first of these results is a direct consequence of Powell’s theorem [42] on the vanishing of the integer homology of the mapping class group of surfaces of genus at least 3: Theorem 4.1 (Powell). If X is a surface of genus g ≥ 3 and A is an abelian group, then every homomorphism Map(X) → A is trivial. We refer the reader to Korkmaz [27] for a discussion of Powell’s theorem and other homological properties of mapping class groups. As a first consequence of Theorem 4.1 we derive the following useful observation: Lemma 4.2. Let X, Y and Y¯ be surfaces of finite topological type, and let ι : Y → Y¯ be an embedding. Suppose that X has genus at least 3 and that φ : Map(X) → Map(Y ) is a homomorphism such that the composition φ¯ = ι# ◦ φ : Map(X) → Map(Y¯ ) is trivial. Then φ is trivial as well. Proof. By Proposition 3.1 the embedding ι : Y → Y¯ is a suitable composition of filling in punctures and boundary components, deleting boundary components and subsurface embeddings. In particular, we may argue by induction and assume that ι is of one of these four types. For the sake of concreteness suppose ι : Y¯ → Y is the embedding associated to filling in a boundary component; the other cases are actually a bit easier and are left to the reader. We have the following diagram: Map(X)
1
/
π1 (T 1 Y¯ )
LLL LLLφ¯ φ LLL L& ι# / Map(Y / Map(Y ) ¯) /
1
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JAVIER ARAMAYONA & JUAN SOUTO
The assumption that φ¯ is trivial amounts to supposing that the image of φ is contained in π1 (T 1 Y¯ ). The homomorphism π1 (T 1 Y¯ ) → π1 (Y¯ ) yields another diagram: Map(X)
1
/
Z
/
π1
JJ JJ φ0 JJ φ JJ J% 1¯ /π (T Y )
¯)
1 (Y
/
1
Since every nontrivial subgroup of the surface group π1 (Y¯ ) has nontrivial homology, we deduce from Theorem 4.1 that φ0 is trivial. Hence, the image of φ is contained in Z. Applying again Theorem 4.1 above we deduce that φ is trivial, as it was to be shown. Before stating another consequence of Theorem 4.1 we need a definition: Definition 2. A homomorphism φ : Map(X) → Map(Y ) is said to be irreducible if its image does not fix any essential curve in Y ; otherwise we say it is reducible. Remark. Recall that we consider boundary parallel curves to be essential. In particular, every homomorphism Map(X) → Map(Y ) is reducible if Y has non-empty boundary. Let φ : Map(X) → Map(Y ) be a reducible homomorphism, where X has genus at least 3, and let η ⊂ Y be a multicurve which is componentwise invariant under φ(Map(X)); in other words, φ(Map(X)) ⊂ Z(Tη ). Moreover, notice that Theorem 4.1 implies that φ(Map(X)) ⊂ Z0 (Tη ), where Z0 (Tη ) is the subgroup of Z(Tη ) consisting of those elements that fix the sides of each component of η. Now let Yγ0 = Y \ η be the surface obtained by deleting η from Y . Composing (2.2) as often as necessary, we obtain an exact sequence as follows: (4.1)
1 → Tη → Z0 (Tη ) → Map(Yη0 ) → 1
The same argument of the proof of Lemma 4.2 shows that φ is trivial if the composition of φ and the right homomorphism (4.1) is trivial. Hence we have: Lemma 4.3. Let X, Y be surfaces of finite topological type. Suppose that X has genus at least 3 and that φ : Map(X) → Map(Y ) is a nontrivial reducible homomorphism fixing the multicurve η ⊂ Y . Then φ(Map(X)) ⊂ Z0 (Tη ) and the composition of φ with the homomorphism (4.1) is not trivial.
23
The second trivially theorem, due to Paris [41], asserts that the mapping class group of a surface of genus g ≥ 3 does not have subgroups of index less than or equal to 4g + 4; equivalently, any homomorphism from the mapping class group into a symmetric group Sk is trivial if k ≤ 4g + 4: Theorem 4.4 (Paris). If X has genus g ≥ 3 and k ≤ 4g + 4, then there is no nontrivial homomorphism Map(X) → Sk where the latter group is the group of permutations of the set with k elements. Before going any further we should mention that in [41], Theorem 4.4 is only stated for closed surfaces. However, the proof works as it is also for surfaces with boundary and or punctures. We leave it to the reader to check that this is the case. As a first consequence of Theorem 4.1 and Theorem 4.4 we obtain the following special case of Proposition 1.8: Proposition 4.5. If X has genus at least 3 and Y at most genus 2, then every homomorphism φ : Map(X) → Map(Y ) is trivial. Proof. Assume for concreteness that Y has genus 2; the cases of genus 0 and genus 1 are in fact easier and are left to the reader. Notice that by Lemma 4.2, we may assume without lossing generality that Y has empty boundary and no marked points. Recall that Map(Y ) has a central element τ of order 2, namely the hyperelliptic involution. As we discussed above, we identify the finite order mapping class τ with one of its finite order representatives, which we again denote by τ . The surface underlying the orbifold Y /hτ i is the 6-punctured sphere S0,6 . By Theorem 2.11 we have the following exact sequence: 1 → hτ i → Map(Y ) → Map∗ (S0,6 ) → 1 where Map∗ (S0,6 ) is, as always, the group of isotopy classes of all orientation preserving homeomorphisms of S0,6 . Therefore, any homomorphism φ : Map(X) → Map(Y ) induces a homomorphism φ0 : Map(X) → Map∗ (S0,6 ) By Paris’ theorem, the homomorphism obtained by composing φ0 with the obvious homomorphism Map∗ (S0,6 ) → S6 , the group of permutations of the punctures, is trivial. In other words, φ0 takes values in Map(S0,6 ). Since the mapping class group of the standard sphere S2 is trivial, Lemma 4.2 implies that φ0 is trivial. Therefore, the image of φ is contained in the abelian subgroup hτ i ⊂ Map(Y ). Finally, Theorem 4.1 implies that φ is trivial, as we had to show.
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JAVIER ARAMAYONA & JUAN SOUTO
5. Getting rid of the torsion We begin this section reminding the reader of a question posed in the introduction: Question 1. Suppose that φ : Map(X) → Map(Y ) is a homomorphism between mapping class groups of surfaces of genus at least 3, with the property that the image of every Dehn twist along a non-separating curve has finite order. Is the image of φ finite? In this section we will give a positive answer to the question above if the genus of Y is exponentially bounded by the genus of X. Namely: Proposition 5.1. Suppose that X and Y are surfaces of finite topological type with genera g and g 0 respectively. Suppose that g ≥ 4 and that either g 0 < 2g−2 − 1 or g 0 = 3, 4. Any homomorphism φ : Map(X) → Map(Y ) which maps a Dehn twist along a non-separating curve to a finite order element is trivial. Under the assumption that Y is not closed, we obtain in fact a complete answer to the question above: Theorem 1.7. Suppose that X and Y are surfaces of finite topological type, that X has genus at least 3, and that Y is not closed. Then any homomorphism φ : Map(X) → Map(Y ) which maps a Dehn twist along a non-separating curve to a finite order element is trivial. Recall that by Theorem 2.9, the mapping class group of a surface with non-empty boundary is torsion-free. Hence we deduce from Lemma 2.2 that it suffices to consider the case that ∂Y = ∅. From now on, we assume that we are in this situation. The proofs of Proposition 5.1 and Theorem 1.7 are based on Theorem 4.1, the connectivity of the cut system complex, and the following algebraic observation: Lemma 5.2. For n ∈ N, n ≥ 2, consider Zn endowed with the standard action of the symmetric group Sn by permutations of the basis elements e1 , . . . , en . If V is a finite abelian group equipped with an Sn action, then for any Sn -equivariant epimorphism φ : Zn → V one of the following two is true: (1) Either the restriction of φ to Zn−1 × {0} is surjective, or (2) V has order at least 2n and cannot be generated by fewer than n elements. Moreover, if (1) does not hold and V 6= (Z/2Z)n then V has at least 2n+1 elements.
25
Proof. Let d be the order of φ(e1 ) in V and observe that, by Sn equivariance, all the elements φ(ei ) also have order d. It follows that (dZ)n ⊂ Ker(φ) and hence that φ descends to an epimorphism φ0 : (Z/dZ)n → V Our first goal is to restrict to the case that d is a power Q of a prime. a In order to do this, consider the prime decomposition d = j pj j of d, where pi 6= pj and ai ∈ N. By the Chinese remainder theorem we have Y a Z/dZ = Z/pj j Z j
Hence, there is a Sn -equivariant isomorphism Y a (Z/dZ)n = (Z/pj j Z)n j a
Consider the projection πj : Zn → (Z/pj j Z)n and observe that if the a restriction to Zn−1 × {0} of φ0 ◦ πj surjects onto φ0 ((Z/pj j Z)n ) for all j, then φ(Zn−1 × {0}) = V . Supposing that this were not the case, replace φ by φ0 ◦ πj and V a by φ((Z/pj j Z)n ). In more concrete terms, we can assume from now on that d = pa is a power of a prime. At this point we will argue by induction. The key claim is the following surely well-known observation: Claim. Suppose that p is prime. The only Sn -invariant subgroups W of (Z/pZ)n are the following: • The trivial subgroup {0}, • (Z/pZ)n itself, • E = {(a, a, . . . , a) ∈ (Z/pZ)n |a = 0, . . . , p − 1}, and • F = {(a1 , . . . , an ) ∈ (Z/pZ)n |a1 + · · · + an = 0}. Proof of the claim. Suppose that W ⊂ (Z/pZ)n is not trivial and take v = (vi ) ∈ W nontrivial. If v cannot be chosen to have distinct entries then W = E. So suppose that this is not case and choose v with two distinct entries, say v1 and v2 . Consider the image v 0 of v under the transposition (1, 2). By the Sn -invariance of W we have v 0 ∈ W and hence v − v 0 ∈ W . By construction, v − v 0 has all entries but the two first ones equal to 0. Moreover, each of the first two entries is the negative of the other one. Taking a suitable power we find that (1, −1, 0, . . . , 0) ∈ W . By the Sn -invariance of W we obtain that every element with one 1, one −1 and 0 otherwise belongs to W . These elements span F .
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JAVIER ARAMAYONA & JUAN SOUTO
We have proved that either W is trivial, or W = E or F ⊂ W . Since the only subgroups containing F are F itself and the total space, the claim follows. Returning to the proof of Lemma 5.2, suppose first that a = 1, i.e. d = p is prime. The kernel of the epimorphism φ0 : (Z/pZ)n → V is a Sn -invariant subspace. Either φ0 is injective, and thus V contains pn ≥ 2n elements, or its kernel is one of the spaces E or F provided by the claim. Since the union of either one of them with (Z/pZ)n−1 × {0} spans (Z/pZ)n , it follows that the restriction of φ to Zn−1 ×{0} surjects onto V . This concludes the proof if a = 1. Suppose that we have proved the result for a − 1. We can then consider the diagram: /
0
0
/
(Z/pa−1 Z)n 0
a−1
φ ((Z/p
/
/
(Z/pa Z)n
(Z/pZ)n
φ0 n
Z) )
/
V
/
0
V /φ ((Z/pa−1 Z)n )
/
/
0
0
Observe that if one of the groups to the left and right of V on the bottom row has at least 2n elements, then so does V . So, if this is not the case we may assume by induction that the restriction of the left and right vertical arrows to (Z/pa−1 Z)n−1 × {0} and (Z/pZ)n−1 × {0} are epimorphisms. This shows that the restriction of φ0 to (Z/pa Z)n−1 ×{0} is also an epimorphism. It follows that either V has at least 2n elements or the restriction of φ to Zn−1 × {0} is surjective, as claimed. Both the equality case and the claim on the minimal number of elements needed to generate V are left to the reader. We are now ready to prove: Lemma 5.3. Given n ≥ 4, suppose that g > 0 is such that 2n−2 −1 > g or g ∈ {3, 4}. If Y is surface of genus g ≥ 3, V ⊂ Map(Y ) is a finite abelian group endowed with an action of Sn , and φ : Zn → V is a Sn -equivariant epimomorphism, then the restriction of φ to Zn−1 × {0} is surjective. Proof. Suppose, for contradiction, that the restriction of φ to Zn−1 ×{0} is not surjective. Recall that by the resolution of the Nielsen realization problem [26] there is a conformal structure on Y such that V can be represented by a group of automorphisms. Suppose first that 2n−2 − 1 > g. Since we are assuming that the restriction of φ to Zn−1 × {0} is not surjective, Lemma 5.2 implies that
27
V has at least 2n elements. Then: 2n = 4(2n−2 − 1) + 4 > 4g + 4, which is impossible since Theorem 2.10 asserts that Map(Y ) does not contain finite abelian groups with more than 4g + 4 elements. Suppose now that g = 4. If n ≥ 5 we obtain a contradiction using the same argument as above. Thus assume that n = 4. Since 24+1 = 32 > 20 = 4 · 4 + 4, it follows from the equality statement in Lemma 5.2 that V is isomorphic to (Z/2Z)4 . Luckily for us, Kuribayashi-Kuribayashi [28] have classified all groups of automorphisms of Riemann surfaces of genus 3 and 4. From their list, more concretely Proposition 2.2 (c), we obtain that (Z/2Z)4 cannot be realized as a subgroup of the group of automorphisms of a surface of genus 4, and thus we obtain the desired contradiction. Finally, suppose that g = 3. As before, this case boils down to ruling out the possibility of having (Z/2Z)4 acting by automorphisms on a Riemann surface of genus 3. This is established in Proposition 1.2 (c) of [28]. This concludes the case g = 3 and thus the proof of the lemma. Remark. One could wonder if in Lemma 5.3 the condition n ≥ 4 is necessary. Indeed it is, because the mapping class group of a surface of genus 3 contains a subgroup isomorphic to (Z/2Z)3 , namely the group H(8, 8) in the list in [28]. After all this immensely boring work, we are finally ready to prove Proposition 5.1. Proof of Proposition 5.1. Recall that a cut system in X is a maximal multicurve whose complement in X is connected; observe that every cut system consists of g curves and that every non-separating curve is contained in some cut system. Given a cut system η consider the group Tη generated by the Dehn twists along the components of η, noting that Tη ' Zg . Any permutation of the components of η can be realized by a homeomorphism of X. Consider the normalizer N (Tη ) and centralizer Z(Tη ) of Tη in Map(X). As mentioned in Section 2.4, we have the following exact sequence: 1 → Z(Tη ) → N (Tη ) → Sg → 1, where Sg denotes the symmetric group of permutations of the components of η. Observe that the action by conjugation of N (Tη ) onto Tη induces an action Sg = N (Tη )/Z(Tη ) y Tη which is conjugate to the standard action of Sg y Zg . Clearly, this action descends to an action Sg y φ(Tη ).
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Seeking a contradiction, suppose that the image under φ of a Dehn twist δγ along a non-separating curve has finite order. Since all the Dehn twists along the components of η are conjugate to δγ we deduce that all their images have finite order; hence φ(Tη ) is generated by finite order elements. On the other hand, φ(Tη ) is abelian because it is the image of an abelian group. Being abelian and generated by finite order elements, φ(Tη ) is finite. It thus follows from Lemma 5.3 that the subgroup of Tη generated by Dehn twists along g − 1 components of η surjects under φ onto φ(Tη ). This implies that φ(Tη ) = φ(Tη0 ) 0 whenever η and η are cut systems which differ by exactly one component. Now, since the cut system complex is connected [20], we deduce that φ(δα ) ∈ φ(Tη ) for every non-separating curve α. Since Map(X) is generated by Dehn twists along non-separating curves, we deduce that the image of Map(X) is the abelian group φ(Tη ). By Theorem 4.1, any homomorphism Map(X) → Map(Y ) with abelian image is trivial, and thus we obtain the desired contradiction. Before moving on we discuss briefly the proof of Theorem 1.7. Suppose that Y is not closed. Then, every finite subgroup of Map(Y ) is cyclic by Theorem 2.9. In particular, the bound on the number of generators in Lemma 5.2 implies that if V ⊂ Map(Y ) is a finite abelian group endowed with an action of Sn and φ : Zn → V is a Sn -equivariant epimomorphism then the restriction of φ to Zn−1 × {0} is surjective. Once this has been established, Theorem 1.7 follows with the same proof, word for word, as Proposition 5.1. Remark. Let X and Y be surfaces, where Y has a single boundary component and no cusps. Let G be a finite index subgroup of Map(X) and let φ : G → Map(Y ) be a homomorphism. A simple modification of a construction due to Breuillard-Mangahas [32] yields a closed surface Y 0 containing Y and a homomorphism φ0 : Map(X) → Map(Y 0 ) such that for all g ∈ G we have, up to isotopy, φ0 (g)(Y ) = Y and φ0 (g)|Y = φ(g). Suppose now that G could be chosen so that there is an epimorphism G → Z. Assume further that φ : G → Map(Y ) factors through this epimorphism and that the image of φ is purely pseudo-Anosov. Then, every element in the image of the extension φ0 : Map(X) → Map(Y ) either has finite order or is a partial pseudo-Anosov. A result of Bridson [9], stated as Theorem 6.1 below, implies that every Dehn twist in
29
Map(X) is mapped to a finite order element in Map(Y ). Hence, the extension homomorphism φ0 produces a negative answer to Question 1. We have hence proved that a positive answer to Question 1 implies that every finite index subgroup of Map(X) has finite abelianization. 6. The map φ∗ In addition to the triviality results given in Theorems 4.1 and 4.4, the third key ingredient in the proof of Theorem 1.1 is the following result due to Bridson [9]: Theorem 6.1 (Bridson). Suppose that X, Y are surfaces of finite type and that X has genus at least 3. Any homomorphism φ : Map(X) → Map(Y ) maps roots of multitwists to roots of multitwists. A remark on the proof of Theorem 6.1. In [9], Theorem 6.1 is proved for surfaces without boundary only. However, Bridson’s argument remains valid if we allow X to have boundary. That the result can also be extended to the case that Y has non-empty boundary needs a minimal argument, which we now give. Denote by Y 0 the surface obtained from Y by deleting all boundary components and consider the homomorphism π : Map(Y ) → Map(Y 0 ) provided by Theorem 2.5. By Bridson’s theorem, the image under π ◦ φ of a Dehn twist δγ is a root of a multitwist. Since the kernel of π is the group of multitwists along the boundary of Y , it follows that φ(δγ ) is also a root of a multitwist, as claimed. A significant part of the sequel is devoted to proving that under suitable assumptions the image of a Dehn twist is in fact a Dehn twist. We highlight the apparent difficulties in the following example: Example 3. Suppose that X has a single boundary component and at least two punctures. By [15], the mapping class group Map(X) is residually finite. Fix a finite group G and an epimorphism π : Map(X) → G. It is easy to construct a connected surface Y on which G acts and which contains |G| disjoint copies Xg (g ∈ G) of X with gXh = Xgh for all g, h ∈ G. Given x ∈ X, denote the corresponding element in Xg by xg . If f : X → X is a homeomorphism fixing pointwise the boundary and punctures, we define fˆ : Y → Y with fˆ(xg ) = (f (x))π([f ])g for xg ∈ Xg and fˆ(y) = π([f ])(y) for y ∈ / ∪g∈G Xg ; here [f ] is the element in Map(X) represented by f .
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JAVIER ARAMAYONA & JUAN SOUTO
Notice that fˆ does not fix the marked points of Y ; in order to by-pass this difficulty, consider Y¯ the surface obtained from Y by forgetting all marked points, and consider fˆ to be a self-homeomorphism of Y¯ . It is easy to see that the map f 7→ fˆ induces a homomorphism φ : Map(X) → Map(Y¯ ) with some curious properties, namely: • If γ ⊂ X is a simple closed curve which bounds a disk with at least two punctures then the image φ(δγ ) of the Dehn twist δγ along γ has finite order. Moreover, δγ ∈ Ker(φ) if and only if δγ ∈ Ker(π). • If γ ⊂ X is a non-separating simple closed curve then φ(δγ ) has infinite order. Moreover, φ(δγ ) is a multitwist if δγ ∈ Ker(π); otherwise, φ(δγ ) is a non-trivial root of a multitwist. Observe that in the latter case, φ(δγ ) induces a non-trivial permutation of the components of the multicurve supporting any of its multitwist powers. This concludes the discussion of Example 3. While a finite order element is by definition a root of a multitwist, Proposition 5.1 ensures that, under suitable bounds on the genera of the surfaces involved, any non-trivial homomorphism Map(X) → Map(Y ) maps Dehn twists to infinite order elements. From now on we assume that we are in the following situation: (*) X and Y are orientable surfaces of finite topological type, of genus g and g 0 respectively, and such that one of the following holds: • Either g ≥ 4 and g 0 ≤ g, or • g ≥ 6 and g 0 ≤ 2g − 1. Remark. It is worth noticing that the reason for the genus bound g ≥ 6 in Theorem 1.1 is that 2g−2 − 1 < 2g − 1 if g < 6. Assuming (*), it follows from Proposition 5.1 that any non-trivial homomorphism φ : Map(X) → Map(Y ) maps Dehn twists δγ along non-separating curves γ to infinite order elements in Map(Y ). Furthermore, it follows from Theorem 6.1 that there is N such that φ(δγN ) is a non-trivial multitwist. We denote by φ∗ (γ) the multicurve in Y supporting φ(δγN ), which is independent of the choice of N by Lemma 2.6. Notice that two multitwists commute if and only if their supports do not intersect; hence, φ∗ preserves the property of having zero intersection number. Moreover, the uniqueness of φ∗ (γ) implies that for
31
any f ∈ Map(X) we have φ∗ (f (γ)) = φ(f )(φ∗ (γ)). Summing up we have: Corollary 6.2. Suppose that X and Y are as in (*) and let φ : Map(X) → Map(Y ) be a non-trivial homomorphism. For every non-separating curve γ ⊂ X, there is a uniquely determined multicurve φ∗ (γ) ⊂ Y with the property that φ(δγ ) is a root of a generic multitwist in Tφ∗ (γ) . Moreover the following holds: • i(φ∗ (γ), φ∗ (γ 0 )) = 0 for any two disjoint non-separating curves γ and γ 0 , and • φ∗ (f (γ)) = φ(f )(φ∗ (γ)) for all f ∈ Map(X). In particular, the multicurve φ∗ (γ) is invariant under φ(Z(δγ )). The remainder of this section is devoted to give a proof of the following result: Proposition 6.3. Suppose that X and Y are as in (*); further, assume that Y is not closed if it has genus 2g − 1. Let φ : Map(X) → Map(Y ) be an irreducible homomorphism. Then, for every non-separating curve γ ⊂ X the multicurve φ∗ (γ) is a non-separating curve. Recall that a homomorphism φ : Map(X) → Map(Y ) is irreducible if its image does not fix any curve in Y , and that if φ is irreducible then ∂Y = ∅; see Definition 2 and the remark following. Before launching the proof of Proposition 6.3 we will establish a few useful facts. Lemma 6.4. Suppose X and Y satisfy (*) and that φ : Map(X) → Map(Y ) is an irreducible homomorphism. Let Y¯ be obtained from Y by filling in some, possibly all, punctures of Y , and let φ¯ = ι# ◦ φ : Map(X) → Map(Y¯ ) be the composition of φ with the homomorphism ι# induced by the embedding ι : Y → Y¯ . For every non-separating curve γ ⊂ X we have: • ι(φ∗ (γ)) is a multicurve, and • φ¯∗ (γ) = ι(φ∗ (γ)). In particular, ι yields a bijection between the components of φ∗ (γ) and φ¯∗ (γ). Proof. First observe that, arguing by induction, we may assume that Y¯ is obtained from Y by filling in a single cusp. We suppose from now on that this is the case and observe that it follows from Lemma 4.2 that φ¯ is not trivial. Notice also that since Y and Y¯ have the same genus, φ¯∗ (γ) is well-defined by Corollary 6.2.
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JAVIER ARAMAYONA & JUAN SOUTO
By definition of φ∗ and φ¯∗ , we can choose N ∈ N such that φ(δγN ) ¯ N ) are generic multitwists in Tφ (γ) and Tφ¯ (γ) . In particular, and φ(δ ∗ γ ∗ it follows from Lemma 3.2 that in order to prove Lemma 6.4 it suffices to show that ι(φ∗ (γ)) does not contain (1) inessential components, or (2) parallel components. Claim 1. ι(φ∗ (γ)) does not contain inessential components. Proof of Claim 1. Seeking a contradiction, suppose that a component η of φ∗ (γ) is inessential in Y¯ . Since Y¯ is obtained from Y by filling in a single cusp, it follows that η bounds a disk in Y with exactly two punctures. Observe that this implies that for any element F ∈ Map(Y ) we have either F (η) = η or i(F (η), η) > 0. On the other hand, if f ∈ Map(X) is such that i(f (γ), γ) = 0 then we have i(φ(f )(η), η) ≤ i(φ(f )(φ∗ (γ)), φ∗ (γ)) = i(φ∗ (f (γ)), φ∗ (γ)) = 0 We deduce that η = φ(f )(η) ⊂ φ∗ (f (γ)) for any such f . Since any two non-separating curves in X are related by an element of Map(X) we obtain: (?) If γ 0 is a non-separating curve in X with i(γ, γ 0 ) = 0 then η = φ(δγ 0 )(η) and η ⊂ φ∗ (γ 0 ). Choose γ 0 ⊂ X so that X \(γ ∪γ 0 ) is connected. It follows from (?) that if γ 00 is any other non-separating curve which either does not intersect γ or γ 0 we have φ(δγ 00 )(η) = η. Since the mapping class group is generated by such curves, we deduce that every element in φ(Map(X)) fixes η, contradicting the assumption that φ is irreducible. This concludes the proof of Claim 1. We use a similar argument to prove that ι(φ∗ (γ)) does not contain parallel components. Claim 2. ι(φ∗ (γ)) does not contain parallel components. Proof of Claim 2. Seeking again a contradiction suppose that there are η 6= η 0 ⊂ φ∗ (γ) whose images in Y¯ are parallel. Hence, η ∪ η 0 bounds an annulus which contains a single cusp. As above, it follows that for any element f ∈ Map(Y ) we have either f (η ∪ η 0 ) = η ∪ η 0 or i(f (η), η) > 0. By the same argument as before, we obtain that φ(Map(X)) preserves η ∪ η 0 . Now, it follows from either Theorem 4.1 or Theorem 4.4 that φ(Map(X)) cannot permute η and η 0 . Hence φ(Map(X)) fixes η, contradicting the assumption that φ is irreducible. As we mentioned above, Lemma 6.4 follows from Claim 1, Claim 2 and Lemma 3.2.
33
Continuing with the preliminary considerations to prove Proposition 6.3, recall that the final claim in Corollary 6.2 implies that φ(δγ ) preserves the multicurve φ∗ (γ). Our next goal is to show that, as long as φ is irreducible, the element φ(δγ ) preserves every component of φ∗ (γ). Lemma 6.5. Suppose that X and Y are as in (*) and let φ : Map(X) → Map(Y ) be an irreducible homomorphism. If γ ⊂ X is a non-separating simple closed curve, then φ(Z0 (δγ )) fixes every component of φ∗ (γ). Hence, φ(Z0 (δγ )) ⊂ Z0 (Tφ∗ (γ) ). Recall that Z0 (δγ ) is the subgroup of Map(X) fixing not only γ but also the two sides of γ and that it has at most index 2 in the centralizer Z(δγ ) of the Dehn twist δγ . Proof. We first prove Lemma 6.5 in the case that Y is closed. As in Section 2, we denote by Xγ the surface obtained by deleting the interior of a closed regular neighborhood of γ from X. Recall that by (2.1) there is a surjective homomorphism Map(Xγ ) → Z0 (δγ ) Consider the composition of this homomorphism with φ and, abusing notation, denote its image by φ(Map(Xγ )) = φ(Z0 (δγ )). By Corollary 6.2, the subgroup φ(Map(Xγ )) of Map(Y ) acts on the set of components of φ∗ (γ) and hence on Y \ φ∗ (γ). Since Y is assumed to be closed and of at most genus 2g − 1 we deduce that Y \ φ∗ (γ) has at most |χ(Y )| = 2g 0 − 2 ≤ 4g − 4 components. Since the surface Xγ has genus g − 1 ≥ 3, we deduce from Theorem 4.4 that φ(Map(Xγ )) fixes each component of Y \ φ∗ (γ). Suppose now that Z is a component of Y \ φ∗ (γ) and let η be the set of components of φ∗ (γ) contained in the closure of Z. Noticing that 4 − 4g ≤ χ(Y ) ≤ χ(Z) ≤ −|η| + 2 we obtain that η consists of at most 4g−2 components. Since φ(Map(Xγ )) fixes Z, it acts on the set of components of η. Again by Theorem 4.4, it follows that this action is trivial, meaning that every component of φ∗ (γ) contained in the closure of Z is preserved. Since Z was arbitrary, we deduce that φ(Map(Xγ ) preserves every component of φ∗ (γ) as claimed. Lemma 4.3 now implies that φ(Z0 (δγ )) = φ(Map(Xγ )) ⊂ Z0 (Tφ∗ (γ) ). This concludes the proof of Lemma 6.5 in the case that Y is closed. We now turn our attention to the general case. Recall that the assumption that φ is irreducible implies that ∂Y = ∅. Let Y¯ be the surface obtained from Y by closing up all the cusps and denote by
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φ¯ : Map(X) → Map(Y¯ ) the composition of φ with the homomorphism ι# : Map(Y ) → Map(Y¯ ) induced by the embedding ι : Y → Y¯ . By the ¯ On the other hand, Lemma 6.4 above, Lemma 6.5 holds true for φ. shows that for any γ ⊂ X non-separating there is a bijection between φ∗ (γ) and φ¯∗ (γ). Thus the claim follows. Note that Lemma 6.5 yields the following sufficient condition for a homomorphism between mapping class groups to be reducible: Corollary 6.6. Suppose that X and Y are as in (*) and let φ : Map(X) → Map(Y ) be a non-trivial homomorphism. Let γ and γ 0 be distinct, disjoint curves on X such that X \ (γ ∪ γ 0 ) is connected. If the multicurves φ∗ (γ) and φ∗ (γ 0 ) share a component, then the homomorphism φ : Map(X) → Map(Y ) is reducible. Proof. Suppose that φ is irreducible and observe that Map(X) is generated by Dehn twists along curves α which are disjoint from γ or γ 0 . For any such α we have δα ∈ Z0 (δγ ) ∪ Z0 (δγ 0 ). In particular, it follows from Proposition 6.5 that φ(Map(X)) fixes every component of φ∗ (γ) ∩ φ∗ (γ 0 ). The assumption that φ was irreducible implies that φ∗ (γ) ∩ φ∗ (γ 0 ) = ∅. We are now ready to prove Proposition 6.3: Proof of Proposition 6.3. Let γ be a non-separating curve on X. Extend γ to a multicurve η ⊂ X with 3g − 3 components γ1 , . . . , γ3g−3 , and such that the surface X \ (γi ∪ γj ) is connected for all i, j. Since δγi and δγj are conjugate in Map(X) we deduce that φ∗ (γi ) and φ∗ (γj ) have the same number K of components for all i, j. Since φ is irreducible, Corollary 6.6 implies that φ∗ (γi ) and φ∗ (γj ) do not share any components for all i 6= j. This shows that ∪i φ∗ (γi ) is the union of (3g − 3)K distinct curves. Furthermore, since δγi and δγj commute, we deduce that ∪i φ∗ (γi ) is a multicurve in Y . Suppose first that Y has genus g 0 ≤ 2g−2. In the light of Lemma 6.4, it suffices to consider the case that Y is closed. Now, the multicurve ∪i φ∗ (γi ) has at most 3g 0 − 3 ≤ 3(2g − 2) − 3 < 6g − 6 components. Hence: 6g − 6 K< ≤ 2, 3g − 3 and thus the multicurve φ∗ (γ) consists of K = 1 components; in other words, it is a curve. It is non-separating because otherwise the multicurve ∪i φ∗ (γi ) would consist of 3g − 3 separating curves, and a closed surface of genus g 0 ≤ 2g − 2 contains at most 2g − 3 disjoint separating curves. This concludes the proof of the proposition in the case that Y has genus at most 2g − 2.
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Suppose now that Y has genus g 0 = 2g − 1 and that Y is not closed. Again by Lemma 6.4, we can assume that Y has a single puncture, which we consider as a marked point. In this case, the multicurve ∪i φ∗ (γi ) consists of at most 3g 0 − 2 = 6g − 5 curves. Since we know that ∪i φ∗ (γi ) is the union of (3g − 3)K distinct curves, we deduce K ≤ 2. In the case that ∪i φ∗ (γi ) has fewer than 6g − 6 components, we proceed as before. Therefore, it remains to rule out the possibility of having exactly 6g − 6 components. Suppose, for contradiction, that ∪i φ∗ (γi ) has 6g − 6 components. Since Y has genus 2g − 1 and exactly one marked point, the complement of ∪i φ∗ (γi ) in Y is a disjoint union of pairs of pants, where exactly one of them, call it P , contains the marked point of Y . Now, the boundary components of P are contained in the image under φ∗ of curves a1 , a2 , a3 ∈ {γ1 , . . . , γ3g−3 }. Assume, for the sake of concreteness, that ai 6= aj whenever i 6= j; the remaining case is dealt with using minor modifications of the argument we give here. Suppose first that the multicurve α = a1 ∪ a2 ∪ a3 does not disconnect X and let α0 6= α be another multicurve with three components satisfying: (1) X \ α0 is connected, (2) i(α, α0 ) = 0, and (3) X \ (γ ∪ γ 0 ) is connected for all γ, γ 0 ∈ α ∪ α0 . Notice that since X \ α and X \ α0 are homeomorphic, there is f ∈ Map(X) with f (α) = α0 . Now, P 0 = φ(f )(P ) is a pair of pants which contains the marked point of Y . Taking into account that ∂P ⊂ φ∗ (α) and ∂P 0 ⊂ φ∗ (α0 ) we deduce from (2) that i(∂P, ∂P 0 ) = ∅ and hence that P = P 0 . Since α0 6= α we may assume, up to renaming, that a1 6⊂ α0 . Since φ(f )(∂P ) = ∂P 0 and ∂P ∩ φ∗ (a1 ) 6= ∅, we deduce that is i such that φ∗ (ai ) ∩ φ∗ (f (a1 )) contains a boundary curve of P . In the light of (3), it follows from Corollary 6.6 that φ is reducible; this contradiction shows that X \ α cannot be connected. If X \α is not connected, then it has two components, as X \(a1 ∪a2 ) is connected. Suppose first that neither of the two components Z1 , Z2 of X \ α is a (possibly punctured) pair of pants and notice that this implies that Z1 and Z2 both have positive genus. Let P1 ⊂ Z1 be an unpunctured pair of pants with boundary ∂P1 = a1 ∪ a2 ∪ a03 and let P2 ⊂ Z2 be second unpunctured a pair of pants with Z2 \ P2 connected and with boundary ∂P2 = a3 ∪a01 ∪a02 where a01 and a02 are not boundary parallel in Z2 ; compare with Figure 3. Notice that Z10 = (Z1 ∪ P2 ) \ P1 is homeomorphic to Z1 . Similarly, Z20 = (Z2 ∪ P1 ) \ P2 is homeomorphic to Z2 . Finally notice also that Zi0 contains the same punctures as Zi
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Figure 3. for i = 1, 2. It follows from the classification theorem of surfaces that there is f ∈ Map(X) with f (Z1 ) = Z10 and f (Z2 ) = Z20 . In particular, f (α) = α0 where α0 = a01 ∪ a02 ∪ a03 . We highlight a few facts: (1) There is f ∈ Map(X) with f (α) = α0 , (2) i(α, α0 ) = 0, and (3) X \ (γ ∪ γ 0 ) is connected for all γ, γ 0 ∈ {a1 , a2 , a01 , a02 }. As above, we deduce that φ(f )(∂P ) = ∂P 0 and that for all i = 1, 2, 3 there is j such that φ∗ (ai ) ∩ φ∗ (f (aj )) contains a boundary curve of P . In the light of (3), it follows again from Corollary 6.6 that φ is reducible. We have reduced to the case that one of the components of X \ α, say Z1 , is a (possibly punctured) pair of pants. We now explain how to reduce to the case that Z1 is a pair of pants without punctures. Let a03 ⊂ Z1 be a curve which, together with a3 , bounds an annulus A ⊂ Z1 such that Z1 \ A does not contain any marked points. Notice that we may assume without loss of generality that the multicurve γ1 ∪· · ·∪γ3g−3 above does not intersect a03 . It follows that i(φ∗ (a03 ), ∪φ∗ (γi )) = 0. Next, observe that a pants decomposition of Y consists of 3(2g − 1) − 3 + 1 = 6g − 5 curves. Since φ∗ (a03 ) has two components and ∪φ∗ (γi ) has 6g − 6 components, we deduce that there exists i such that φ∗ (a03 ) and φ∗ (γi ) share a component. If i 6= 3, property (3) and Corollary 6.6 imply that φ is reducible, since a03 ∪ γi does not separate X. It thus follows that φ∗ (a03 ) and φ∗ (a3 ) share a component, and so ∂P ⊂ φ∗ (a1 ∪ a2 ∪ a03 ). Summing up, it remains to rule out the possibility that Z1 is a pair of pants without punctures. Choose α0 ⊂ X satisfying: (1) α0 bounds a pair of pants in X, (2) i(α, α0 ) = 0, and (3) X \ (γ ∪ γ 0 ) is connected for all γ, γ 0 ∈ α ∪ α0 . Now there is f ∈ Map(X) with f (α) = α0 and we can repeat word by word the argument given in the case that X \ α was connected. After having ruled out all possibilities, we deduce that ∪i φ∗ (γi ) cannot have 6g − 6 components. This concludes the proof of Proposition 6.3.
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7. Proof of Proposition 1.8 In this section we show that every homomorphism Map(X) → Map(Y ) is trivial if the genus of X is larger than that of Y . As a consequence we obtain that, under suitable genus bounds, the centralizer of the image of a non-trivial homomorphism between mapping class groups is torsion-free. Proposition 1.8. Suppose that X and Y are orientable surfaces of finite topological type. If the genus of X is at least 3 and larger than that of Y , then every homomorphism φ : Map(X) → Map(Y ) is trivial. Recall that Proposition 1.8 is due to Harvey-Korkmaz [19] in the case that both surfaces X and Y are closed. Proof. We will proceed by induction on the genus of X. Notice that Proposition 4.5 establishes the base case of the induction and observe that by Lemma 4.2 we may assume that Y is has empty boundary and no cusps. Suppose now that X has genus g ≥ 4 and that we have proved Proposition 1.8 for surfaces of genus g − 1. Our first step is to prove the following: Claim. Under the hypotheses above, every homomorphism Map(X) → Map(Y ) is reducible. Proof of the claim. Seeking a contradiction, suppose that there is an irreducible homomorphism φ : Map(X) → Map(Y ), where Y has smaller genus than X. Let γ ⊂ X be a non-separating curve. Observing that X and Y satisfy (*), we deduce that φ∗ (γ) is a non-separating curve by Proposition 6.3 and that φ(Z0 (δγ )) ⊂ Z0 (δφ∗ (γ) ) by Lemma 6.5. By (2.2), Z0 (δφ∗ (γ) ) dominates Map(Yφ0∗ (γ) ) where Yφ0∗ (γ) = Y \ φ∗ (γ). On the other hand, we have by (2.1) that Z0 (δγ ) is dominated by the group Map(Xγ ) where Xγ is obtained from X by deleting the interior of a closed regular neighborhood of γ. Since φ∗ (γ) is non-separating, the genus of Yφ0∗ (γ) and Xγ is one less than that of Y and X, respectively. The induction assumption implies that the induced homomorphism Map(Xγ ) → Map(Yφ0∗ (γ) ) is trivial. The last claim in Lemma 4.3 proves that the homomorphism Map(Xγ ) → Z0 (δφ∗ (γ) ) ⊂ Map(Y ) is also trivial. We have proved that Z0 (δγ ) ⊂ Ker(φ). Since Z0 (δγ ) contains a Dehn twist along a non-separating curve, we deduce that φ
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is trivial from Lemma 2.2. This contradiction concludes the proof of the claim. Continuing with the proof of the induction step in Proposition 1.8, suppose there exists a non-trivial homomorphism φ : Map(X) → Map(Y ). By the above claim, φ is reducible. Let η ⊂ Y be a maximal multicurve in Y which is componentwise fixed by φ(Map(X)), and notice that φ(Map(X)) ⊂ Z0 (Tη ) by Lemma 4.3. Consider φ0 : Map(X) → Map(Yη0 ), the composition of φ with the homomorphism (4.1). The maximality of the multicurve η implies that φ0 is irreducible. Since the genus of Yη0 is at most equal to that of Y , we deduce from the claim above that φ0 is trivial. Lemma 4.3 implies hence that φ is trivial as well. This establishes Proposition 1.8 As we mentioned before, a consequence of Proposition 1.8 is that, under suitable assumptions, the centralizer of the image of a homomorphism between mapping class groups is torsion-free. Namely, we have: Lemma 7.1. Let X and Y be surfaces of finite topological type, where X has genus g ≥ 3 and Y has genus g 0 ≤ 2g. Suppose moreover that Y has at least one (resp. three) marked points if g 0 = 2g − 1 (resp. g 0 = 2g). If φ : Map(X) → Map(Y ) is a non-trivial homomorphism, then the centralizer of φ(Map(X)) in Map(Y ) is torsion-free. The proof of Lemma 7.1 relies on Proposition 1.8 and the following consequence of the Riemann-Hurwitz formula: Lemma 7.2. Let Y be a surface of genus g 0 ≥ 0 and let τ : Y → Y be a nontrivial diffeomorphism of prime order, representing an element in Map(Y ). Then τ has F ≤ 2g 0 + 2 fixed-points and the underlying 0 surface of the orbifold Y /hτ i has genus at most g¯ = 2g +2−F . 4 Proof. Consider the orbifold Y /hτ i and let F be the number of its singular points; observe that F is also equal to the number of fixed points of τ since τ has prime order p. Denote by |Y /hτ i| the underlying surface of the orbifold Y /hτ i. The Riemann-Hurwitz formula shows that (7.1)
2 − 2g 0 = χ(Y ) = p · χ(|Y /hτ i|) − (p − 1) · F
After some manipulations, (7.1) shows that F =
2g 0 − 2 + p · (2 − 2¯ g) p−1
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where g¯ is the genus of |Y /hτ i|. Clearly, the quantity on the right is maximal if g¯ = 0 and p = 2. This implies that F ≤ 2g 0 + 2, as claimed. Rearranging (7.1), we obtain g¯ =
2g 0 + (2 − F )(p − 1) 2p
Again this is maximal if p is as small as possible, i.e. p = 2. Hence 0 . g¯ ≤ 2g +2−F 4 We are now ready to prove Lemma 7.1. Proof of Lemma 7.1. First, if Y has non-empty boundary there is nothing to prove, for in this case Map(Y ) is torsion-free. Therefore, assume that ∂Y = ∅. Suppose, for contradiction, that there exists [τ ] ∈ Map(Y ) non-trivial, of finite order, and such that φ(Map(X)) ⊂ Z([τ ]). Let τ : Y → Y be a finite order diffeomorphism representing [τ ]. Passing to a suitable power, we may assume that the order of τ is prime. Consider the orbifold Y /hτ i as a surface with the singular points marked, and recall that by Theorem 2.11 we have the following exact sequence: 1
/
h[τ ]i
/
Z([τ ])
β
/
Map∗ (Y /hτ i)
On the other hand, we have by definition 1 → Map(Y /hτ i) → Map∗ (Y /hτ i) → SF → 1 where F is the number of punctures of Y /hτ i. Again, F is equal to the number of fixed points of τ since τ has prime order. Observe that Lemma 7.2 gives that F ≤ 2g 0 + 2 ≤ 4g + 2; hence, it follows from Theorem 4.4 that the composition of the homomorphism Map(X)
φ
/
Z([τ ])
β
/
Map∗ (Y /hτ i)
/
SF
is trivial; in other words, (β ◦ φ)(Map(X)) ⊂ Map(Y /hτ i). Our assumptions on the genus and the marked points of Y imply, by the genus bound in Lemma 7.2, that Y /hτ i has genus less than g. Hence, the homomorphism β ◦ φ : Map(X) → Map(Y /hτ i) is trivial by Proposition 1.8. This implies that the image of φ is contained in the abelian group h[τ ]i. Theorem 4.1 shows hence that φ is trivial, contradicting our assumption. This concludes the proof of Lemma 7.1 The following example shows that Lemma 7.1 is no longer true if Y is allowed to have genus 2g and fewer than 3 punctures.
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Example 4. Let X be a surface with no punctures and such that ∂X = S1 . Let Z be a surface of the same genus as X, with ∂Z = ∅ but with two punctures. Regard X as a subsurface of Z and consider the two-to-one cover Y → Z corresponding to an arc in Z \ X joining the two punctures of Z. Every homomorphism X → X fixing poinwise the boundary extends to a homeomorphism of Z fixing the punctures and which lifts to a unique homeomorphism Y → Y which fixes the two components of the preimage of X under the covering Y → Z. The image of the induced homomorphism Map(X) → Map(Y ) is centralized by the involution τ associated to the two-to-one cover Y → Z. Moreover, if X has genus g then Y has genus 2g and 2 punctures. 8. Proof of Proposition 1.6 We are now ready to prove that under suitable genus bounds, homomorphisms between mapping class groups map Dehn twists to Dehn twists. Namely: Proposition 1.6. Suppose that X and Y are surfaces of finite topological type, of genus g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. Every nontrivial homomorphism φ : Map(X) → Map(Y ) maps (right) Dehn twists along non-separating curves to (possibly left) Dehn twists along non-separating curves. Remark. The reader should notice that the proof of Proposition 1.6 applies, word for word, to homomorphisms between mapping class groups of surfaces of the same genus g ∈ {4, 5}. We will first prove Proposition 1.6 under the assumption that φ is irreducible and then we will deduce the general case from here. Proof of Proposition 1.6 for irreducible φ. Suppose that φ is irreducible and recall that this implies that ∂Y = ∅. Let γ ⊂ X be a nonseparating curve. Thus φ∗ (γ) is also a non-separating curve, by Proposition 6.3. We first show that φ(δγ ) is a power of δφ∗ (γ) . Let Xγ be the complement in X of the interior of a closed regular neighborhood of γ and Yφ0∗ (γ) = Y \ φ∗ (γ) the connected surface obtained from Y by removing φ∗ (γ). We have that: (?) Xγ and Yφ0∗ (γ) have genus g − 1 ≥ 3 and g 0 − 1 ≤ 2g − 2 respectively. Moreover, observe that Yφ0∗ (γ) has two more punctures than Y ; in particular, Yγ0 has at least 3 punctures if it has genus 2g − 2.
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By (2.1) and (2.2) we have epimorphisms Map(Xγ ) → Z0 (φ(δγ ))
and
Z0 (δφ∗ (γ) ) → Map(Yφ0∗ (γ) ).
In addition, we know that φ(Z0 (δγ )) ⊂ Z0 (δφ∗ (γ) ) by Lemma 6.5. Composing all these homomorphisms we get a homomorphism φ0 : Map(Xγ ) → Map(Yφ0∗ (γ) ) It follows from Lemma 2.2 that the restriction of φ to Z0 (δγ ) is not trivial because the latter contains a Dehn twist along a non-separating curve; Lemma 4.3 implies that φ0 is not trivial either. Since δγ centralizes Z0 (δγ ), it follows that φ0 (δγ ) ∈ Map(Yφ0∗ (γ) ) centralizes the image of φ0 . Now, the definition of φ∗ (γ) implies that some power of φ(δγ ) is a power of the Dehn twist δφ∗ (γ) . Hence, the first claim of Lemma 2.8 yields that φ0 (δγ ) has finite order, and thus φ0 (δγ ) ∈ Map(Yφ0∗ (γ) ) is a finite order element centralizing φ(Map(Xγ )). By (?), Lemma 7.1 applies and shows that φ0 (δγ ) is in fact trivial. The final claim of Lemma 2.8 now shows that φ(δγ ) is a power of δφ∗ (γ) ; in other words, there exists N ∈ Z \ {0} such that φ(δγ ) = δφN∗ (γ) . It remains to prove that N = ±1. Notice that N does not depend on the particular non-separating curve γ since any two Dehn twists along non-separating curves are conjugate. Consider a collection γ1 , . . . , γn of non-separating curves on X, with γ = γ1 , such that the Dehn twists δγi generate Map(X) and i(γi , γj ) ≤ 1 for all i, j (compare with Figure 1). Observe that the N -th powers of the Dehn twists along the curves {φ∗ (γi )} generate φ(Map(X)). It follows hence from the assumption that φ is irreducible that the curves {φ∗ (γi )} fill Y (compare with the proof of Lemma 10.1 below). Thus, since φ∗ preserves disjointness by Corollary 6.2, there exists γ 0 ∈ {γ1 , . . . , γn } such that i(γ, γ 0 ) = 1 and i(φ∗ (γ), φ∗ (γ 0 )) ≥ 1. Since i(γ, γ 0 ) = 1, the Dehn twists δγ and δγ 0 braid. Thus, the N -th powers δφN∗ (γ) = φ(δγ ) and δφN∗ (γ 0 ) = φ(δγ 0 ) of the Dehn twists along φ∗ (γ) and φ∗ (γ 0 ) also braid. Since i(φ∗ (γ), φ∗ (γ 0 )) ≥ 1, Lemma 2.3 shows that i(φ∗ (γ), φ∗ (γ 0 )) = 1 and N = ±1, as desired. Before moving on, we remark that in final argument of the proof of the irreducible case of Theorem 1.6 we have proved the first claim of the following lemma: Lemma 8.1. Suppose that X, Y are as in the statement of Proposition 1.6, and let and φ : Map(X) → Map(Y ) be an irreducible homomorphism. Then the following holds: • i(φ∗ (γ), φ∗ (γ 0 )) = 1 for all curves γ, γ 0 ⊂ X with i(γ, γ 0 ) = 1.
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• If a, b, c, d, x, y and z is a lantern with the property that no two curves chosen among a, b, c, d and x separate X, then φ∗ (a), φ∗ (b), φ∗ (c), φ∗ (d), φ∗ (x), φ∗ (y) and φ∗ (z) is a lantern in Y . We prove the second claim. By the irreducible case of Proposition 1.6 we know that if γ is any component of the lantern in question, then φ∗ (γ) is a single curve and φ(δγ ) = δφ∗ (γ) . In particular notice that the Dehn-twists along φ∗ (a), φ∗ (b), φ∗ (c), φ∗ (d), φ∗ (x), φ∗ (y) and φ∗ (z) satisfy the lantern relation. Since a, b, c, d, x are pairwise disjoint, Corollary 6.2 yields that the curves φ∗ (a), φ∗ (b), φ∗ (c), φ∗ (d), φ∗ (x) are also pairwise disjoint. Moreover, the irreducibility of φ, the assumption that that no two curves chosen among a, b, c, d and x separate X, and Corollary 6.6 imply that the curves φ∗ (a), φ∗ (b), φ∗ (c), φ∗ (d) and φ∗ (x) are pairwise distinct. Thus, the claim follows from Proposition 2.4. We are now ready to treat the reducible case of Proposition 1.6. Proof of Proposition 1.6 for reducible φ. Let φ : Map(X) → Map(Y ) be a non-trivial reducible homomorphism, and let η be the maximal multicurve in Y which is componentwise fixed by φ(Map(X)). Recall the exact sequence (4.1): 1 → Tη → Z0 (Tη ) → Map(Yη0 ) → 0 Lemma 4.3 shows that φ(Map(X)) ⊂ Z0 (Tη ) and that the composition φ0 : Map(X) → Map(Yη0 ) of φ and the homomorphism Z0 (Tη ) → Map(Yη0 ) is not trivial. Observe that φ0 is irreducible because η was chosen to be maximal. The surface Yη0 may well be disconnected; if this is the case, Map(Yη0 ) is by definition the direct product of the mapping class groups of the connected components of Yη0 . Noticing that the sum of the genera of the components of Yη0 is bounded above by the genus of Y , it follows from the bound g 0 ≤ 2g − 1 and from Proposition 1.8 that Yη0 contains at a single component Yη00 on which φ(Map(X)) acts nontrivially. Hence, we can apply the irreducible case of Proposition 1.6 and deduce that φ0 : Map(X) → Map(Yη00 ) maps Dehn twists to possibly left Dehn twists. Conjugating φ by an outer automorphism of Map(X) we may assume without loss of generality that φ0 maps Dehn twists to Dehn twists. Suppose now that a, b, c, d, x, y and z form a lantern in X as in Lemma 8.1; such a lantern exists because X has genus at least 3. By Lemma 8.1 we obtain that the images of these curves under φ0∗ also form a lantern. In other words, if S ⊂ X is the four-holed sphere with
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boundary a ∪ b ∪ c ∪ d then there is an embedding ι : S → Yη00 ⊂ Yη0 such that for any γ ∈ {a, . . . , z} we have φ0 (δγ ) = δι(γ) Identifying Yη00 with a connected component of Yη0 = Y \ η we obtain an embedding ˆι : S → Y . We claim that for any γ in the lantern a, b, c, d, x, y, z we have φ(δγ ) = δˆι(γ) . A priori we only have that, for any such γ, both φ(δγ ) and δˆι(γ) project to the same element δι(γ) under the homomorphism Z0 (Tη ) → Map(Yη0 ). In other words, there is τγ ∈ Tη with φ(δγ ) = δˆι(γ) τγ . Observe that since any two curves γ, γ 0 in the lantern a, b, c, d, x, y, z are non-separating, the Dehn twists δγ and δγ 0 are conjugate in Map(X). Therefore, their images under φ are also conjugate in φ(Map(X)) ⊂ Z0 (Tη ). Since Tη is central in Z0 (Tη ), it follows that in fact τγ = τγ 0 for any two curves γ and γ 0 in the lantern. Denote by τ the element of Tη so obtained. On the other hand, both δa , . . . , δz and δˆι(a) , . . . , δˆι(z) satisfy the lantern relation and, moreover, τ commutes with everything. Hence 1 = φ(δa )φ(δb )φ(δc )φ(δd )φ(δz )−1 φ(δy )−1 φ(δx )−1 = −1 −1 −1 −1 = δˆι(a) τ δˆι(b) τ δˆι(c) τ δˆι(d) τ τ −1 δˆι−1 δˆι(y) τ δˆι(x) = (z) τ −1 −1 = δˆι(a) δˆι(b) δˆι(c) δˆι(d) δˆι−1 (z) δˆ ι(y) δˆ ι(x) τ = τ
Hence, we have proved that φ(δa ) = δˆι(a) τ = δˆι(a) In other words, the image under φ of the Dehn twist along some, and hence every, non-separating curve is a Dehn twist. 9. Reducing to the irreducible In this section we explain how to reduce the proof of Theorem 1.1 to the case of irreducible homomorphisms between mapping class groups of surfaces without boundary. 9.1. Weak embeddings. Observe there are no embeddings X → Y if X has no boundary but Y does (compare with Corollary 11.1 below). We are going to relax the definition of embedding to allow for this possibility. For this purpose, it is convenient to regard X and Y as possibly non-compact surfaces without marked points; recall that we declared ourselves to be free to switch between cusps, marked points and ends.
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Definition. Let X and Y be possibly non-compact surfaces of finite topological type without marked points. A weak embedding ι : X → Y is a topological embedding of X into Y . Given two surfaces X and Y without marked points there are two, ˆ and Yˆ with sets P ˆ and P ˆ essentially unique, compact surfaces X X Y ˆ \ P ˆ and Y = Yˆ \ P ˆ . We will of marked points and with X = X X Y say that a weak embedding ι : X → Y is induced by an embedding ˆ P ˆ ) → (Yˆ , P ˆ ) if there is a homeomorphism f : Y → Y which ˆι : (X, X Y is isotopic to the identity relative to PYˆ , and ˆι|X = f ◦ ι. It is easy to describe which weak embeddings are induced by embeddings: A weak embedding ι : X → Y is induced by an embedding if and only if the image ι(γ) of every curve γ ⊂ X which bounds a ˆ containing at most one marked point bounds a disk in Yˆ disk in X which again contains at most one marked point. Since ι(γ) bounds a disk without punctures if γ does, we can reformulate this equivalence in terms of mapping classes: Lemma 9.1. A weak embedding ι : X → Y is induced by an embedding if and only if δι(γ) is trivial in Map(Y ) for every, a fortiori non-essential, curve γ ⊂ X which bounds a disk with a puncture. Notice that in general a weak embedding X → Y does not induce a homomorphism Map(X) → Map(Y ). On the other hand, the following proposition asserts that if a homomorphism Map(X) → Map(Y ) is, as far as it goes, induced by a weak embedding, then it is induced by an actual embedding. Proposition 9.2. Let X and Y be surfaces of finite type and genus at least 3. Suppose that φ : Map(X) → Map(Y ) is a homomorphism such that there is a weak embedding ι : X → Y with the property that for every non-separating curve γ ⊂ X we have φ(δγ ) = δι(γ) . Then φ is induced by an embedding X → Y . Proof. Suppose that a ⊂ X bounds a disk with one puncture and consider the lantern in X given in Figure 4. We denote the boldprinted curves by a, b, c, d and the dotted lines by x, y, z; observe that a is the only non-essential curve in the lantern. By the lantern relation and because a is not essential we have (9.1)
1 = δa = δx δy δz δb−1 δc−1 δd−1
The images under ι of the curves a, b, c, d, x, y, z also form a lantern in Y and hence we obtain (9.2)
−1 −1 −1 δι(a) = δι(x) δι(y) δι(z) δι(b) δι(c) δι(d)
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Figure 4. A lantern in X where one of the curves is non-essential and all the others are non-separating. The assumption in the Proposition implies that the image under the homomorphism φ of the right side of (9.1) is equal to the right side of (9.2). This implies that δι(a) is trivial. Lemma 9.1 shows now that the weak embedding ι is induced by an embedding, which we again denote by ι. Let ι# the homomorphism induced by ι. Since, by assumption, φ(δγ ) = δι(γ) = ι# (δγ ) for all non-separating curves γ, and since the Dehn twists along these curves generate the mapping class group, we deduce that φ = ι# . In particular, φ is induced by an embedding, as we needed to prove. 9.2. Down to the irreducible case. Armed with Proposition 9.2, we now prove that it suffices to establish Theorem 1.1 for irreducible homomorphisms. Namely, we have: Lemma 9.3. Suppose that Theorem 1.1 holds for irreducible homomorphisms. Then it also holds for reducible ones. Proof. Let X and Y be surfaces as in the statement of Theorem 1.1 and suppose that φ : Map(X) → Map(Y ) is a non-trivial reducible homomorphism. Let η be a maximal multicurve in Y whose every component of η is invariant under φ(Map(X)); by Lemma 4.3, φ(Map(X)) ⊂ Z0 (Tη ). Consider, as in the proof of Proposition 1.6, the composition φ0 : Map(X) → Map(Yη0 ) of φ and the homomorphism in (4.1). Lemma 4.2 shows that φ0 is non-trivial; moreover, it is irreducible by the maximality of η. Now, Proposition 1.6 implies that for any γ non-separating both φ(δγ ) = δφ∗ (γ) and φ0 (δγ ) = δφ0∗ (γ) are Dehn twists. As in the proof of the
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reducible case of Proposition 1.6 we can consider Yη0 = Y \ η as a subsurface of Y . Clearly, φ∗ (γ) = φ0∗ (γ) after this identification. Assume that Theorem 1.1 holds for irreducible homomorphisms. Since φ0 is irreducible, we obtain an embedding ι : X → Yη0 inducing φ0 . Consider the embedding ι : X → Yη0 as a weak embedding ˆι : X → Y . By the above, φ(δγ ) = δˆι(γ) , for every γ ⊂ X nonseparating. Finally, Proposition 9.2 implies that φ is induced by an embedding. 9.3. No factors. Let φ : Map(X) → Map(Y ) be a homomorphism as in the statement of Theorem 1.1. We will say that φ factors if there ¯ an embedding ¯ι : X → X, ¯ and a homomorphism are a surface X, ¯ → Map(Y ) such that the following diagram commutes: φ¯ : Map(X) (9.3)
Map(X)
LLL LLLφ LLL L& / ¯ Map(Y ) Map(X) ¯ ι#
φ¯
Since the composition of two embeddings is an embedding, we deduce that φ is induced by an embedding if φ¯ is. Since a homomorphism Map(X) → Map(Y ) may factor only finitely many times, we obtain: Lemma 9.4. If Proposition 1.6 holds for homomorphisms φ : Map(X) → Map(Y ) which do not factor, then it holds in full generality. Our next step is to prove that any irreducible homomorphism φ : Map(X) → Map(Y ) factors if X has boundary. We need to establish the following result first: Lemma 9.5. Suppose that X and Y are as in the statement of Theorem 1.1 and let φ : Map(X) → Map(Y ) be an irreducible homomorphism. Then the centralizer of φ(Map(X)) in Map(Y ) is trivial. Proof. Suppose, for contradiction, that there is a non-trivial element f in Z(φ(Map(X))); we will show that φ is reducible. Noticing that the genus bounds in Theorem 1.1 are more generous than those in Lemma 7.1, we deduce from the latter that f has infinite order. Let γ ⊂ X be a non-separating curve and recall that φ(δγ ) is a Dehn twist by Proposition 1.6. Since f commutes with φ(δγ ) it follows that f is not pseudo-Anosov. In particular, f must be reducible; let η be the canonical reducing multicurve associated to f [7]. Since φ(Map(X)) commutes with f we deduce that φ(Map(X)) preserves η. We will
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prove that φ(Map(X)) fixes some component of η, obtaining hence a contradiction to the assumption that φ is irreducible. The arguments are very similar to the arguments in the proof of Lemma 6.4 and Lemma 6.5. First, notice that the same arguments as the ones used to prove Lemma 6.4 imply that some component of η is fixed if some component of Y \η is a disk or an annulus. Suppose that this is not the case. Then Y \ η has at most 2g 0 − 2 ≤ 4g − 4 components. Hence Theorem 4.4 implies that φ(Map(X)) fixes every component of Y \ η. Using again that no component of Y \η is a disk or an annulus we deduce that every such component C has at most 2g 0 + 2 ≤ 4g − 2 boundary components. Hence Theorem 4.4 implies that φ(Map(X)) fixes every component of ∂C ⊂ η. We have proved that some component of η is fixed by φ(Map(X)) and hence that φ is reducible, as desired. We can now prove: Corollary 9.6. Suppose that X and Y are as in Theorem 1.1 and that ∂X 6= ∅. Then every irreducible homomorphism φ : Map(X) → Map(Y ) factors. Proof. Let X 0 = X \ ∂X be the surface obtained from X by deleting the boundary and consider the associated embedding ι : X → X 0 . By Theorem 2.5, the homomorphism ι# : Map(X) → Map(X 0 ) fits in the exact sequence 1 → T∂X → Map(X) → Map(X 0 ) → 1 where T∂X is the center of Map(X). It follows from Lemma 9.5 that if φ is irreducible, then T∂X ⊂ Ker(φ). We have proved that φ descends to φ0 : Map(X 0 ) → Map(Y ) and hence that φ factors as we needed to show. Combining Lemma 9.3, Lemma 9.4 and Corollary 9.6 we deduce: Proposition 9.7. Suppose that Theorem 1.1 holds if • X and Y have no boundary, and • φ : Map(X) → Map(Y ) is irreducible and does not factor. Then, Theorem 1.1 holds in full generality.
10. Proof of Theorem 1.1 In this section we prove the main result of this paper, whose statement we now recall:
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Theorem 1.1. Suppose that X and Y are surfaces of finite topological type, of genus g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. Then every nontrivial homomorphism φ : Map(X) → Map(Y ) is induced by an embedding X → Y . Remark. As mentioned in the introduction, the same conclusion as in Theorem 1.1 applies for homomorphisms φ : Map(X) → Map(Y ) if both X and Y have the same genus g ∈ {4, 5}. This will be shown in the course of the proof. By Proposition 9.7 we may assume that X and Y have no boundary, that φ is irreducible and that it does not factor. Moreover, by Proposition 1.6, the image of a Dehn twist δγ along a non-separating curve is either the right or the left Dehn twist along the non-separating curve φ∗ (γ). Notice that, up to composing φ with an outer automorphism of Map(Y ) induced by an orientation reversing homeomorphism of Y , we may actually assume that φ(δγ ) is actually a right Dehn twist for some, and hence every, non-separating curve γ ⊂ X. In light of this, from now on we will assume without further notice that we are in the following situation: Standing assumptions: X and Y have no boundary; φ is irreducible and does not factor; φ(δγ ) = δφ∗ (γ) for all γ ⊂ X non-separating. Under these assumptions, we now prove φ is induced by a homeomorphism. We will make extensive use of the concrete set of generators of Map(X) given in Figure 1, which we include here as Figure 5 for convenience. The reader should have Figure 5 constantly in mind through the rest of this section. a1
b1
a2
b2
a3
c
b3
bg
rk
r1
r2
Figure 5. Dehn twists along the curves ai , bi , c and ri generate Map(X). Notice that the sequence a1 , b1 , a2 , b2 , . . . , ag , bg in Figure 5 forms a chain; we will refer to it as the ai bi -chain. We refer to the multicurve
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r1 ∪ · · · ∪ rk as the ri -fan. The curve c would be worthy of a name such as el pendejo or el pinganillo but we prefer to call it simply the curve c. Observe that all the curves in Figure 5 are non-separating. Hence, it follows from Proposition 6.3 that φ∗ (γ) is a non-separating curve for any curve γ in the collection ai , bi , ri , c. We claim that the images under φ∗ of all these curves in fill Y . Lemma 10.1. The image under φ∗ of the ai bi -chain, the ri -fan and the c-curve fill Y . Proof. Since the Dehn twists along the curves ai , bi , ri , c generate Map(X), any curve in Y which is fixed by the images under φ of all these Dehn twists is fixed by φ(Map(X)). Noticing that the image under φ of a Dehn twist along any of ai , bj , rl , c is a Dehn twist along the φ∗ -image of the curve, the claim follows since φ is assumed to be irreducible. Suppose that γ, γ 0 are two distinct elements of the collection ai , bi , ri , c. We now summarize several of the already established facts about the relative positions of the curves φ∗ (γ), φ∗ (γ 0 ): (1) If i(γ, γ 0 ) = 0 then i(φ∗ (γ), φ∗ (γ 0 )) = 0 by Corollary 6.2. (2) If γ, γ 0 are distinct and disjoint, and X \ (γ ∪ γ 0 ) is connected, then φ∗ (γ) 6= φ∗ (γ 0 ) by Corollary 6.6. (3) If i(γ, γ 0 ) = 1 then i(φ∗ (γ), φ∗ (γ 0 ) = 1 by Lemma 8.1. Notice that these properties do not ensure that φ∗ (ri ) 6= φ∗ (rj ) if i 6= j. We denote by R ⊂ Y the maximal multicurve with the property that each one of its components is homotopic to one of the curves φ∗ (ri ). Notice that R = ∅ if and only if X has at most a puncture and that in any case R has at most as many components as curves has the ri -fan. The following lemma follows easily from (1), (2) and (3) above: Lemma 10.2. With the notation of Figure 5 the following holds: • The image under φ∗ of the ai bi -chain is a chain of the same length in Y . • Every component of the multicurve R intersects the φ∗ -image of the ai bi -chain exactly in the component φ∗ (bg ). • The curve φ∗ (c) is disjoint from every curve in R, intersects φ∗ (b2 ) exactly once, and is disjoint from the images of the other curves in the ai bi -chain. At first glance, Lemma 10.2 yields the desired embedding without any further work, but this is far from true. A first problem is that R may have too few curves. Also, the curves in the ri -fan come equipped with a natural ordering and that we do not know yet that φ∗ preserves
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this ordering. Before tackling these problems, we clarify the position of φ∗ (c): Lemma 10.3. Let Z be a regular neighborhood of the ai bi -chain, noting that c ⊂ Z. Then there is an orientation preserving embedding F : Z → Y such that φ∗ (γ) = F (γ) for γ = ai , bi , c and i = 1, . . . , g. Proof. The image under φ∗ of the ai bi -chain is a chain of the same length, by Lemma 10.2. Let Z 0 be a regular neighborhood of the φ∗ image of the ai bi -chain. Since regular neighborhoods of any two chains of the same length are homeomorphic in an orientation preserving manner, there is an orientation preserving embedding F : Z → Z0 with F (ai ) = φ∗ (ai ) and F (bi ) = φ∗ (bi ) for all i. It remains to prove that F can be chosen so that F (c) = φ∗ (c). Let Z0 ⊂ Z be the subsurface of X filled by a1 , b1 , a2 , b2 and observe that, up to isotopy, c ⊂ Z0 . The boundary of Z0 is connected and, by the chain relation (see Section 2) we can write the Dehn twist along ∂Z0 as: δ∂Z0 = (δa1 δb2 δa2 δb2 )10 Hence we have φ(δ∂Z0 ) = (φ(δa1 )φ(δb2 )φ(δa2 )φ(δb2 ))10 = (δφ∗ (a1 ) δφ∗ (b2 ) δφ∗ (a2 ) δφ∗ (b2 ) )10 = (δF (a1 ) δF (b2 ) δF (a2 ) δF (b2 ) )10 = δF (∂Z0 ) where the last equality follows again from the chain relation. Since c is disjoint from ∂Z0 we have that δc and δ∂Z0 commute. Hence φ∗ (c) does not intersect F (∂Z0 ). On the other hand, since φ∗ (c) intersects φ∗ (b2 ) ⊂ F (Z0 ), we deduce from Lemma 10.2 that φ∗ (c) ⊂ F (Z0 ). Observe now that F (Z) \ (∪φ∗ (ai ) ∪ φ∗ (bi )) ' Z \ (∪ai ∪ bi ) is homeomorphic to an annulus A. It follows from Lemma 10.2 that the intersection of φ∗ (c) with A is an embedded arc whose endpoints are in the subsegments of ∂A corresponding to φ∗ (b2 ). There are two choices for such an arc. However, there is an involution τ : F (Z) → F (Z) with τ (φ∗ (ai )) = φ∗ (ai ) and τ (φ∗ (bi )) = φ∗ (bi ) and which interchanges these two arcs. It follows that, up to possibly replacing F by τ ◦ F , we have F (c) = φ∗ (c), as we needed to prove. At this point we are ready to prove the first cases of Theorem 1.1.
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Proof of Theorem 1.1 (X is closed or has one puncture). Let Z be as in Lemma 10.3 and note that, from the assumptions on X, the homomorphism σ# : Map(Z) → Map(X) induced by the embedding σ : Z → X is surjective. Let φˆ : Map(Z) → Map(Y ) be the composition of σ# and φ. By Lemma 10.3, φˆ is induced by an embedding of F :Z →Y. Suppose first that X has one puncture. In particular, there is a weak embedding X → Z ⊂ X which is homotopic to the identity X → X. The composition of this weak embedding X → Z and of the embedding F : Z → Y is a weak embedding which, in the sense of Proposition 9.2, induces φ. It follows from Proposition 9.2 that φ is induced by an embedding, as we needed to prove. The case that X is closed is slightly more complicated. The assumption that φ is irreducible and that a collection of curves in F (Z) fills Y , implies that Y \ F (Z) is a disk containing at most one puncture. If Y \ F (Z) is a disk without punctures, then the we can clearly extend the map F to a continuous injective map X → Y . Since any continuous injective map between closed connected surfaces is a homeomorphism, it is a fortiori an embedding and we are done in this case. It remains to rule out the possibility that X is closed and Y has one puncture. Suppose that this is the case and let Y¯ be the surface obtained from Y by filling in its unique puncture. We can now apply the above argument to the induced homomorphism φ¯ : Map(X) → Map(Y¯ ), to deduce that φ¯ is induced by an embedding X → Y¯ . Since any embedding from a closed surface is a homeomorphism we deduce that φ¯ is an isomorphism. Consider φ ◦ φ¯−1 : Map(Y¯ ) → Map(Y ) and notice that composing φ ◦ φ¯−1 with the filling-in homomorphism Map(Y ) → Map(Y¯ ) we obtain the identity. Hence, φ ◦ φ¯−1 is a splitting of the Birman exact sequence 1 → π1 (Y¯ ) → Map(Y ) → Map(Y¯ ) → 1, which does not exist by Lemma 3.3. It follows that Y cannot have a puncture, as we needed to prove. We continue with the preparatory work needed to prove Theorem 1.1 in the general case. From now on we assume that X has at least 2 punctures. Standing assumption: X has at least 2 punctures. Continuing with the proof of Theorem 1.1, we prove next Y has the same genus as X.
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Lemma 10.4. Both surfaces X and Y have the same genus g. Proof. With the same notation as in Lemma 10.3 we need to prove that S = Y \ F (Z) is a surface of genus 0. By Lemma 10.1 the arcs ρi = φ∗ (ri ) ∩ S fill S. Denote by S¯ the surface obtained by attaching a disk along F (∂Z) ⊂ ∂S and notice that the arcs ρi can be extended ¯ Moreover, every curve in S¯ to a collection of disjoint curves ρ¯i in S. either agrees or intersects one of the curves ρ¯i more than once, which is impossible if S has genus at least 1; this proves Lemma 10.4. Notice that if η ⊂ X is separating, all we know about φ(δη ) is that it is a root of a multitwist by Bridson’s Theorem 6.1; in particular, φ(δη ) may be trivial or have finite order. If this is not the case, we denote by φ∗ (η) the multicurve supporting any multitwist power of φ(δη ). Observe that if η bounds a disk with punctures then, up to replacing the ai bi -chain by another such chain, we may assume that i(η, ai ) = i(η, bi ) = 0 for all i. In particular, φ∗ (η) does not intersect any of the curves φ∗ (ai ) and φ∗ (bi ). It follows that no component of φ∗ (η) is non-separating. We record our conclusions: Lemma 10.5. Suppose that η ⊂ X bounds a disk with punctures and that φ(δη ) has infinite order. Then every component of the multicurve φ∗ (η) separates Y . Our next goal is to bound the number of cusps of Y : S Lemma 10.6. Every connected component of Y \ ( i φ∗ (ai ) ∪ R) contains at most single puncture. In particular Y has at most as many punctures as X. Recall that R ⊂ Y is the maximal multicurve with the property that each one of its components is homotopic to one of the curves φ∗ (ri ). Proof. Observe that Lemma 10.1 and Lemma 10.3 imply that the union of R and the image under φ∗ of the ai bi -chain fill Y . In particular, every component of the complement in Y of the union of R and all the curves φ∗ (ai ) and φ∗ (bi ) contains at most one puncture of Y . It follows from Lemma 10.2 that the multicurve ∪φ∗ (bi ) does not separate any of the components of the complement of (∪φ∗ (ai )) ∪ R in Y . We have proved the first claim. It follows again from Lemma 10.2 that the multicurve ∪φ∗ (ai ) ∪ R separates Y into at most k components where k ≥ 2 is the number of punctures of X. Thus, Y has at most as many punctures as X. So far, we do not know much about the relative positions of the curves in R; this will change once we have established the next three lemmas.
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Lemma 10.7. Suppose that a, b ⊂ X are non-separating curves that bound an annulus A. Then φ∗ (a) and φ∗ (b) bound an annulus A0 in Y ; moreover, if A contains exactly one puncture and φ∗ (a) 6= φ∗ (b), then A0 also contains exactly one puncture. Proof. Notice that A is disjoint from a chain of length 2g − 1. Since φ∗ maps chains to chains (Lemma 10.2), since it preserves disjointness (Corollary 6.2) and since Y has the same genus as X (Lemma 10.4), we deduce that φ∗ (∂A) consists of non-separating curves which are contained in an annulus in Y . The first claim follows. Suppose that φ∗ (a) 6= φ∗ (b); up to translating by a mapping class, we may assume that a = a1 and that b is a curve disjoint from (∪ai )∪(∪ri ) and with i(b, b1 ) = 1 and i(b, bi ) = 0 for i = 2, . . . , g (compare with the dashed curve in Figure 6). Since φ∗ preserves disjointness and a1
b1
a2
b
b2
a3
b3
c
bg
rk
r1
r2
Figure 6. intersection number one (Lemma 8.1), it follows that the annulus A0 bounded by φ∗ (a) = φ∗ (a1 ) and contained in one of the two S φ∗ (b) is S connected components of Y \ ( i φ∗ (ai ) ∪ i φ∗ (ri )) adjacent to φ∗ (a1 ). By Lemma 10.6, each one of these components contains at most a puncture, and thus the claim follows. Lemma 10.8. Let γ, γ 0 ⊂ X be non-separating curves bounding an annulus with one puncture. Then φ∗ (γ) 6= φ∗ (γ 0 ). Proof. We will prove that if φ∗ (γ) = φ∗ (γ 0 ), then φ factors in the sense of (9.3); notice that this contradicts our standing assumption. Suppose φ∗ (γ) = φ∗ (γ 0 ), noting that Proposition 1.6 implies that φ(δγ ) = φ(δγ 0 ). Let p be the puncture in the annulus bounded by ¯ surface obtained from X by filling in the γ and γ 0 . Consider the X puncture p and the Birman exact sequence (3.1): ¯ p) → Map(X) → Map(X) ¯ →1 1 → π1 (X, ¯ Let α ∈ π1 (X, ¯ p) be the unique associated to the embedding X → X. essential simply loop contained in the annulus bounded by γ ∪ γ 0 . The
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image of α under the left arrow of the Birman exact sequence is δγ δγ−1 0 . ¯ Hence, α belongs to the kernel of φ. Since π1 (X, p) has a set of generators consisting of translates of α by Map(X) we deduce that that ¯ p) ⊂ Ker(φ). This shows that φ : Map(X) → Map(Y ) factors π1 (X, ¯ and concludes the proof of Lemma 10.8. through Map(X) Lemma 10.9. Let a, b ⊂ X be non-separating curves which bound an annulus with exactly two punctures. Then φ∗ (a) and φ∗ (b) bound an annulus A0 ⊂ Y with exactly two punctures. Moreover, if x ⊂ A is any non-separating curve in X separating the two punctures of A, then φ∗ (x) ⊂ A0 and separates the two punctures of A0 . Proof. Let x ⊂ A be a curve as in the statement. Suppose first that φ∗ (a) 6= φ∗ (b). Consider the annuli A0 , A01 and A02 in Y with boundaries ∂A0 = φ∗ (a) ∪ φ∗ (b), ∂A01 = φ∗ (a) ∪ φ∗ (x), ∂A02 = φ∗ (x) ∪ φ∗ (b). By Lemmas 10.7 and 10.8, the annuli A01 and A02 contain exactly one puncture. Finally, since φ∗ (x) does not intersect φ∗ (a)∪φ∗ (b), it follows that A0 = A01 ∪ A02 and the claim follows. It remains to rule out the possibility that φ∗ (a) = φ∗ (b). Seeking a contradiction, suppose that this is the case. Consider curves d, c, y, z as in Figure 7 and notice that a, b, c, d, x, y, z is a lantern, and that y
x
d a
b
z c
Figure 7. The back dots represent cusps c, d are not essential. In particular, the lantern relation reduces to δa δb = δx δy δz . Applying φ we obtain δφ2∗ (a) = δφ∗ (x) δφ∗ (y) φ(δz ) By Bridson’s theorem, φ(δz ) is a root of a multitwist. Since δa and δz commute, we have that δφ2∗ (a) φ(δz )−1 is also a root of a multitwist. By the same arguments as above, there are annuli A01 , A02 in Y , each containing at most one puncture, with boundaries ∂A01 = φ∗ (a) ∪ φ∗ (x), ∂A02 = φ∗ (a) ∪ φ∗ (y)
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Observe that i(φ∗ (x), φ∗ (y)) is even. If i(φ∗ (x), φ∗ (y)) > 2, then by [16, Theorem 3.10] the element δφ∗ (x) δφ∗ (y) is relatively pseudo-Anosov, and hence not a multitwist. If i(φ∗ (x), φ∗ (y)) = 2, then we are in the situation of Figure 8, meaning that we can extend φ∗ (a), φ∗ (x), φ∗ (y)
Figure 8. The solid lines are φ∗ (a), φ∗ (x) and φ∗ (y) and the black dots are cusps. ˆ φ∗ (x), φ∗ (y), zˆ with cˆ, dˆ not-essential and ˆb to a lantern φ∗ (a), ˆb, cˆ, d, non-separating. From the lantern relation we obtain: δφ−1 δ −1 δ = δz−1 ˆ δˆb ∗ (y) φ∗ (x) φ∗ (a) This implies that φ(δz ) = δz−1 ˆ δˆb δφ∗ (a) is a multitwist whose support contains non-separating components. This contradicts Lemma 10.5 and so we deduce that, if φ∗ (a) = φ∗ (b) then φ∗ (x) and φ∗ (y) cannot have positive intersection number. Finally, we treat the case i(φ∗ (x), φ∗ (y)) = 0. Since x and y are disjoint from a, it follows that the left side of δφ−1 δ −1 δ 2 = φ(δz ) ∗ (x) φ∗ (y) φ∗ (a) is a multitwist supported on a multicurve contained in φ∗ (a) ∪ φ∗ (x) ∪ φ∗ (y). Since these three curves are non-separating, it follows from Lemma 10.5 that φ(δz ) = Id. This shows that φ∗ (a) = φ∗ (x) = φ∗ (y). Since a and x bound an annulus which exactly one puncture, we get a contradiction to Lemma 10.8. Thus, we have proved that φ∗ (a) 6= φ∗ (b); this concludes the proof of Lemma 10.9 We are now ready to finish the proof of Theorem 1.1. Proof of Theorem 1.1. Continuing with the same notation and standing assumptions, we now introduce orderings on the ri -fan and the multicurve R ⊂ Y . In order to do so, observe that the union of the multicurve ∪ai and any of the curves in the ri -fan separates X. Similarly, notice that by Lemma 10.2 the union of the multicurve ∪φ∗ (ai ) and any of the components of R is a multicurve consisting of g + 1 nonseparating curves. Since Y has genus g, by Lemma 10.4, we deduce
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that the union of the multicurve ∪φ∗ (ai ) and any of the components of R separates Y . We now define our orderings: • Given two curves ri , rj in the ri -fan we say that ri ≤ rj if ri and c are in the same connected component of X \(a1 ∪· · ·∪ag ∪rj ). Notice that the labeling in Figure 5 is such that ri ≤ rj for i ≤ j. • Similarly, given two curves r, r0 ∈ R we say that r ≤ r0 if r and φ∗ (c) are in the same connected component of X \ (φ∗ (a1 ) ∪ · · · ∪ φ∗ (ag ) ∪ r0 ). The minimal element of the ri -fan, the curve r1 in Figure 5, is called the initial curve in the ri -fan; we define the initial curve of the multicurve R in an analogous way. We claim that its image under φ∗ is the initial curve of R: Claim. φ∗ (r1 ) is the initial curve in R. Proof of the claim. Suppose, for contradiction, that φ∗ (r1 ) is not the initial curve in R. Consider, besides the curves in Figure 5, a curve c0 as in Figure 9. In words, c and c0 bound an annulus with exactly two punctures and (10.1)
i(c0 , ri ) = 0 ∀i ≥ 2 and i(c0 , ai ) = 0 ∀i
Notice that by Lemma 10.9, φ∗ (c) and φ∗ (c0 ) bound an annulus A which contains exactly two punctures. a1
b1
a2
b2
a3
c
b3
c'
bg
rk
r1
r2
Figure 9. The dotted curve c0 and c bound an annulus with two punctures. Since φ(r1 ) is not the initial curve, then i(φ∗ (c0 ), ∪φ∗ (rj )) = 0 for all j, as i(c0 , rj ) = 0 for all j > 1. Also, by disjointness i(φ∗ (c0 ), φ∗ (ai )) = 0 for all i. Since the boundary ∂A = φ∗ (c) ∪ φ∗ (c0 ) of the annulus A is disjoint of ∪φ∗ (ai ) ∪ φ∗ (ri ) it is contained in one of the connected components of X \ (∪φ∗ (ai ) ∪ φ∗ (ri )). However, each one of these components contains at most one puncture, by Lemma 10.6. This contradicts Lemma 10.9, and thus we have established the claim.
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We are now ready to prove that φ∗ induces an order preserving bijection between the ri -fan and the multicurve R. Denote the curves in R by ri0 , labeled in such a way that ri0 ≤ rj0 if i ≤ j. By the previous claim, φ∗ (r1 ) = r10 . Next, consider the curve r2 , and observe that r1 and r2 bound an annulus with exactly one puncture. Hence, Lemma 10.8 yields that φ∗ (r1 ) = r10 and φ∗ (r2 ) also bound an annulus with exactly one puncture. In particular, φ∗ (r2 ) cannot be separated from r10 by any component of R. This proves that φ∗ (r2 ) = r20 . We now consider the curve r3 . The argument just used for r2 implies that either φ∗ (r3 ) = r30 or φ∗ (r3 ) = r10 . The latter is impossible, as the curves r1 and r3 bound an annulus with exactly two punctures and hence so do φ∗ (r1 ) = r10 and φ∗ (r3 ), by Lemma 10.9. Thus φ∗ (r3 ) = r30 . Repeating this argument as often as necessary we obtain that the map φ∗ induces an injective, order preserving map from the ri -fan to R. Since by definition R has at most as many components as the ri -fan, we have proved that this map is in fact an order preserving bijection. Let Z ⊂ X be a regular neighborhood of the ai bi -chain, and recall c ⊂ Z. By Lemma 10.3 there is an orientation preserving embedding F : Z → Y such that φ∗ (γ) = F (γ) for γ = ai , bi , c (i = 1, . . . , g). We choose Z so that it intersects every curve in the ri -fan in a segment. Observe that Lemma 10.2 implies that F can be isotoped so that F (Z ∩ (∪ri )) = F (Z) ∩ R The orderings of the ri -fan and of R induce orderings of Z ∩ (∪ri ) and Z ∩ R. Since the map φ∗ preserves both orderings we deduce that F preserves the induced orderings of Z ∩ (∪ri ) and F (Z) ∩ R.
Z ∩ r2 Z ∩ r1 ∂Z
∂Z
Figure 10. Attaching the first (left) and second (right) annuli along ∂Z. Let k be the number of curves in the ri -fan, and thus in R. We successively attach k annuli along the boundary ∂Z of Z, as indicated in Figure 10. In this way we get a surface Z1 naturally homeomorphic to X. We perform the analogous operation on ∂F (Z), thus obtaining
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a surface Z2 which is naturally homeomorphic to Y . Since the map φ∗ is preserves the orderings of the ri -fan and of R, we get that the homeomorphism F : Z → F (Z) extends to a homeomorphism F¯ : X → Y such that F¯ (γ) = φ∗ (γ) for every curve γ in the collection ai , bi , c, ri . It follows that the homomorphisms φ and F¯# both map the Dehn twist along γ to the Dehn twist along φ∗ (γ) and, in particular, to the same element in Map(Y ). Since the Dehn twists along the curves ai , bi , c, ri generate Map(X), we deduce φ = F# . This finishes the proof of Theorem 1.1. 11. Some consequences of Theorem 1.1 We now present several consequences of Theorem 1.1; each of them results from imposing extra conditions on the surfaces involved and then reinterpreting the word “embedding” in that specific situation. Namely, observe that Proposition 3.1 immediately implies the following: Corollary 11.1. Suppose that X and Y are surfaces of finite topological type and that ι : X → Y is an embedding. (1) If X is closed, i.e. if X has neither boundary nor marked points, then ι is a homeomorphism. (2) If X has no boundary, then ι is obtained by forgetting a (possibly empty) collection of punctures of X. In particular, ι# : Map(X) → Map(Y ) is surjective, and it is injective if and only if ι is a homeomorphism. (3) If X = Y and X has no boundary, then ι is a homeomorphism. (4) If X = Y and ι is a subsurface embedding, then ι is (isotopic to) a homeomorphism. Combining the first part of Corollary 11.1 and Theorem 1.1, we obtain: Corollary 11.2. Suppose that X and Y are surfaces of finite topological type, of genus g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. If X is closed then every nontrivial homomorphism φ : Map(X) → Map(Y ) is induced by a homeomorphism X → Y ; in particular φ is an isomorphism.
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As mentioned in the introduction, if there are no restrictions on the genus of Y then Corollary 11.2 is far from true. Indeed, Theorem 1 of [2] shows that for every closed surface X there exist a closed surface Y and an injective homomorphism Map(X) → Map(Y ). Moving away from the closed case, if X is allowed to have marked points and/or boundary then there are numerous non-trivial embeddings of X into other surfaces. That said, the second part of Corollary 11.1 tells us that if X has no boundary, then every subsurface embedding of X into another surface is necessarily a homeomorphism. Hence we have: Corollary 11.3. Suppose that X and Y are surfaces of finite topological type, of genus g ≥ 6 and g 0 ≤ 2g − 1 respectively; if Y has genus 2g − 1, suppose also that it is not closed. If X has empty boundary then any injective homomorphism φ : Map(X) → Map(Y ) is induced by a homeomorphism X → Y ; in particular φ is an isomorphism. Again, if there are no restrictions on the genus of Y then Corollary 11.3 is simply not true; see Section 2 of [25] and Theorem 2 of [2]. By Corollary 11.1 (3), if X has no boundary then any embedding ι : X → X is a homeomorphism. Observing that Theorem 1.1 applies for homomorphisms between surfaces of the same genus g ≥ 4, (see the remark following the statement of the theorem) we deduce: Theorem 1.2. Let X be a surface of finite topological type, of genus g ≥ 4 and with empty boundary. Then any non-trivial endomorphism φ : Map(X) → Map(X) is induced by a homeomorphism X → X; in particular φ is an isomorphism. Note that Theorem 1.2 fails if X has boundary. However, by Corollary 11.1 (4), any subsurface embedding X → X is isotopic to a homeomorphism. Therefore, we recover the following result due to IvanovMcCarthy [25] (see [22] and [37] for related earlier results): Corollary 11.4 (Ivanov-McCarthy). Let X be a surface of finite topological type, of genus g ≥ 4. Then any injective homomorphism φ : Map(X) → Map(X) is induced by a homeomorphism X → X; in particular φ is an isomorphism. 12. Proof of Theorem 1.3 Given a Riemann surface X of finite analytic type, endow the associated Teichm¨ uller space T (X) with the standard complex structure.
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Recall that Map(X) acts discretely on T (X) by biholomorphic automorphisms. In particular, we can consider the moduli space M(X) = T (X)/ Map(X) as a complex orbifold; by construction it is a good orbifold, meaning that its universal cover is a manifold. Suppose now that Y is another Riemann surface of finite analytic type. We will consider maps f : M(X) → M(Y ) in the category of orbifolds. Since M(X) and M(Y ) are both good obifolds we can associate to every such map f a homomorphism f∗ : Map(X) → Map(Y ) and a holomorphic map f˜ : T (X) → T (Y ) which is f∗ -equivariant, that is, ˜ ˜ f (γx) = f∗ (γ) f (x) ∀γ ∈ Map(X) and x ∈ T (X) and such that the following diagram commutes: T (X)
M(X)
f
/
/
T (Y )
M(Y )
Here both vertical arrows are the standard projections. Remark. In the remainder of this section we will treat M(X) and M(Y ) as if they were manifolds. This is justified by two observations. First, every statement we make holds indistinguishable for manifolds and for orbifolds. And second, in all our geometric arguments we could pass to a manifold finite cover and work there. We hope that this does not cause any confusion. Suppose now that X and Y have the same genus and that Y has at most as many marked points as X. Choosing an identification between the set of marked points of Y and a subset of the set of marked points of X, we obtain a holomorphic map M(X) → M(Y ) obtained by forgetting all marked points of X which do not correspond to a marked point of Y . Different identifications give rise to different maps; we will refer to these maps as forgetful maps.
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In the rest of the section we will prove Theorem 1.3, whose statement we now recall: Theorem 1.3. Suppose that X and Y are Riemann surfaces of finite analytic type and assume that X has genus g ≥ 6 and Y genus g 0 ≤ 2g − 1; if g 0 = 2g − 1 assume further that Y is not closed. Then, every non-constant holomorphic map f : M(X) → M(Y ) is a forgetful map. In order to prove Theorem 1.3, we will first deduce from Theorem 1.1 that there is a forgetful map F : M(X) → M(Y ) homotopic to f ; then we will modify an argument due to Eells-Sampson to conclude that that f = F . In fact we will prove, without any assumptions on the genus, that any two homotopic holomorphic maps between moduli spaces are equal: Proposition 1.5. Let X and Y be Riemann surfaces of finite analytic type and let f1 , f2 : M(X) → M(Y ) be homotopic holomorphic maps. If f1 is not constant, then f1 = f2 . Armed with Proposition 1.5, we now conclude the proof of Theorem 1.3. Proof of Theorem 1.3 from Proposition 1.5. Suppose that f : M(X) → M(Y ) is holomorphic and not constant. It follows from the latter assumption and from Proposition 1.5 that f is not homotopic to a constant map. In particular, the induced homomorphism f∗ : Map(X) → Map(Y ) is non-trivial. Thus, it follows from Theorem 1.1 that f∗ is induced by an embedding. Now, since X has empty boundary, Corollary 11.1 (2) tells us that every embedding X → Y is obtained by filling in a collection of punctures of X. It follows that there is a forgetful map F : M(X) → M(Y ) with F∗ = f∗ . We deduce that F and f are homotopic to each other because the universal cover T (Y ) of M(Y ) is contractible. Hence, Proposition 1.5 shows that f = F , as we needed to prove. The remainder of this section is devoted to prove Proposition 1.5. Recall at this point that T (X) admits many important Map(X)-invariant metrics. In particular, we will endow: • T (X) with McMullen’s K¨ahler hyperbolic metric [38], and • T (Y ) with the Weil-Petersson metric.
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The reason why we do not endow T (X) with the Weil-Petersson metric is encapsulated in the following observation: Lemma 12.1. Every holomorphic map f : T (X) → T (Y ) is Lipschitz. Proof. Denote by T (X)T and T (Y )T the Teichm¨ uller spaces of X and Y , respectively, both equipped with the Teichm¨ uller metric. Consider f as a composition of maps T (X)
Id
/
T (X)T
f
/
T (Y )T
Id
/
T (Y )
By [38, Theorem 1.1] the first arrow is bi-lipschitz. By Royden’s theorem [43], the middle map is 1-Lipschitz. Finally, the last arrow is also Lipschitz because the Teichm¨ uller metric dominates the Weil-Petersson metric up to a constant factor [38, Proposition 2.4]. We will also need the following fact from Teichm¨ uller theory: Lemma 12.2. There exists a collection {Ki }n∈N of subsets of M(X) with the following properties: S • M(X) = n∈N Ki , • Kn ⊂ Kn+1 for all n, • there is L > 0 such that Kn+1 is contained within distance L of Kn for all n, and • the co-dimension one volume of ∂Kn decreases exponentially when n → ∞. Recall that T (X), and hence M(X), has been endowed with McMullen’s K¨ahler hyperbolic metric. Proof. Let M(X) be the Deligne-Mumford compactification of the moduli space M(X); recall that points Z ∈ M(X) \ M(X) are surfaces with k nodes (k ≥ 1). Wolpert [45] proved that every point in M(X) \ M(X) has a small neighborhood UZ in M(X) whose intersection UZ = UZ ∩ M(X) with M(X) is bi-holomorphic to a neighborhood of (0, . . . , 0) in ((D∗ )k × (D)dimC (T (X))−k )/G where G is a finite group; here D∗ and D are the punctured and unpunctured open unit disks in C. We may assume, without loss of generality, that UZ ' ((D∗ )k × (D)dimC (T (X))−k )/G where D ⊂ D is the disk of Euclidean radius 21 centered at 0.
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Endow now D∗ and D with the hyperbolic metric. For n ∈ N ∪ {0} let Dn ⊂ D be the disk such that the hyperbolic distance between ∂D∗ and ∂Dn∗ is equal to n in D∗ . We set: UZ (n) = ((Dn∗ )k × (Dn )dimC (T (X))−k )/G Observe that, with respect to the hyperbolic metric, the volume of ∂UZ (n) decreases exponentially with n. Since M(X) \ M(X) is compact, we can pick finitely many sets UZ1 , . . . , UZr such that M(X) \ ∪i UZi is compact. For n ∈ N we set Kn = M(X) \ ∪i UZi (n) By construction, M(X) = ∪n Kn and Kn ⊂ Kn+1 ∀n We claim that the sets Kn satisfy the rest of the desired properties. First, recall that Theorem 1.1 of [38] implies that the Teichm¨ uller and K¨ahler hyperbolic metrics on M(X) are bi-Lipschitz equivalent to each other. In particular, it suffices to prove the claim if we consider M(X) equipped with the Teichm¨ uller metric. It is due to Royden [43] that the Teichm¨ uller metric agrees with the Kobayashi metric. It follows that the inclusion UZi ⊂ M(X) is 1-Lipschitz when we endow UZi with the product of hyperbolic metrics and the M(X) with the Teichm¨ uller metric. p By the choice of Dn , every point in UZi (n + 1) is within distance dimC (T (X)) of UZi (n) with respect to the hyperbolic metric. Hence, the same is true with respect to the Teichm¨ uller metric. Therefore, Kn+1 is contained within a fixed Teichm¨ uller distance of Kn . Noticing that ∂Kn ⊂ ∪i=1,...,r ∂UZi (n), that the volume of ∂UZi (n) decreases exponentially with respect to the hyperbolic metric, and that 1-Lipschitz maps contract volume, we deduce that the volume of ∂Kn also decreases exponentially with respect to the Teichm¨ uller metric. This concludes the proof of Lemma 12.2. We are almost ready to prove Proposition 1.5. We first remind the reader of a few facts and definitions on the energy of maps. Suppose that N and M are Riemannian manifolds and that f : N → M is a smooth map. The energy density of f at x ∈ N is defined to be: Ex (f ) =
dim RN X i=1
kdfx vi k2M
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where v1 , . . . , vdimR N is an arbitrary orthonormal basis of Tx M . The energy of f is then the integral of the energy density: Z Ex (f )d volN (x) E(f ) = N
Here d volN is the Riemannian volume form of N . Suppose now that N and M are K¨ahler and let ωN and ωM be the respective K¨ahler forms. Recall that dimC N ωN = ωX ∧ · · · ∧ ωX
is a volume form on N ; more concretely, it is a constant multiple of the Riemannian volume form d volX , where the constant depends only on dimC N . Pulling back the K¨ahler form ωM via f : N → M , we also have the dimC N −1 top-dimensional form (f ∗ ωM )ωN on N . A local computation due to Eells and Sampson [12] shows that for all x ∈ N we have (12.1)
dimC N −1 Ex (f )d volN ≥ c · (f ∗ ωM )ωN
where c > 0 is a constant which again only depends on the dimension dimC N . Moreover, equality holds in (12.1) if and only if f is holomorphic at x. Remark. We stress that the proof of (12.1) is infinitesimal. In particular, it is indifferent to any global geometric property of the involved manifolds such as completeness. We finally have all the ingredients needed to prove Proposition 1.5: Proof of Proposition 1.5. Suppose that f0 , f1 : M(X) → M(Y ) are holomorphic maps and recall that we have endowed M(Y ) with the Weil-Petersson metric and M(X) with McMullen’s K¨ahler hyperbolic metric. We remind the reader that both metrics are K¨ahler and have finite volume. Suppose that f0 and f1 are homotopic and let Fˆ : [0, 1] × M(X) → M(Y ) be a homotopy (as orbifold maps). The Weil-Petersson metric is negatively curved but not complete. However, it is geodesically convex. This allows to consider also the straight homotopy F : [0, 1] × M(X) → M(Y ), F (t, x) = ft (x) determined by the fact that t 7→ ft (x) is the geodesic segment joining f0 (x) and f1 (x) in the homotopy class of Fˆ ([0, 1] × {x}). Clearly, ft is smooth for all t.
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Given a vector V ∈ Tx M(X) the vector field t 7→ d(ft )x V is a Jacobi field along t 7→ ft (x). Since the Weil-Peterson metric is negatively curved, the length of Jacobi fields is a convex function. Now, Lemma 12.1 gives that f0 and f1 are Lipschitz, and therefore the length of d(ft )x V is bounded by the length of V times a constant which depends neither on t nor on x. It follows that the maps ft : M(X) → M(Y ) are uniformly Lipschitz. In particular, they have finite energy E(ft ) < ∞. In fact, the same convexity property of Jacobi fields shows that, for any x, the function t 7→ Ex (ft ) is convex. This implies that the energy function t 7→ E(ft ) is also convex. Moreover, it is strictly convex unless both holomorphic maps f0 and f1 either agree or are constant. Since the last possibility is ruled out by our assumptions we have: Fact. Either f0 = f1 or the function t 7→ E(ft ) is strictly convex.
Supposing that f0 6= f1 we may assume that E(f0 ) ≥ E(f1 ). By the fact above, for all t ∈ (0, 1): we have (12.2)
E(ft ) < E(f0 )
We are going to derive a contradiction to this assertion. In order to do so, let Kn ⊂ M(X) be one of the sets provided by Lemma 12.2 and denote by ωX and ωY the K¨ahler forms of M(X) and M(Y ) respectively. Since the K¨ahler forms are closed, we deduce from Stokes theorem that Z dim (T (X))−1 d (F ∗ ωY )ωX C 0= [0,t]×Kn Z dim (T (X))−1 = (F ∗ ωY )ωX C ∂([0,t]×Kn ) Z Z dimC (T (X))−1 dim (T (X))−1 ∗ = (F ωY )ωX − (F ∗ ωY )ωX C {t}×Kn {0}×Kn Z dim (T (X))−1 + (F ∗ ωY )ωX C [0,t]×∂Kn Z Z dimC (T (X))−1 dim (T (X))−1 ∗ = (ft ωY )ωX − (f0∗ ωY )ωX C Kn Kn Z dim (T (X))−1 + (F ∗ ωY )ωX C [0,t]×∂Kn
Below we will prove: R dim (T (X))−1 Claim. limn→∞ [0,t]×∂Kn (F ∗ ωY )ωX C = 0.
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Assuming the claim we conclude with the proposition. From the claim and the computation above we obtain: Z Z dimC (T (X))−1 dimC (T (X))−1 ∗ ∗ =0 − (f0 ωY )ωX lim (ft ωY )ωX n→∞
Kn
Kn
Taking into account that both maps ft and f0 are Lipschitz and that M(X) has finite volume, we deduce that Z Z dimC (T (X))−1 dim (T (X))−1 ∗ (ft ωY )ωX = (f0∗ ωY )ωX C M(X)
M(X)
We obtain now from (12.1) Z dim (T (X))−1 E(ft ) ≥ c (ft∗ ωY )ωX C M(X) Z dim (T (X))−1 =c (f0∗ ωY )ωX C = E(f0 ) M(X)
where the last equality holds because f0 is holomorphic. This contradicts (12.2). It remains to prove the claim. Proof of the claim. Let d = dimR T (X) and fix (t, x) ∈ [0, 1] × ∂Kn . Let E1 , . . . , Ed be an orthonormal basis of T(t,x) ([0, 1] × ∂Kn ). We have ∗ (F ωY )(E1 , E2 ) · ωX (E3 , E4 ) · . . . · ωX (Ed−1 , Ed ) = hdF(t,x) E1 , i · dF(t,x) E2 iY hE3 , iE4 iX . . . hEd−1 , Ed iX = kdF(t,x) k2 where h·, ·iX and h·, ·iY are the Riemannian metrics on M(X) and M(Y ) and where kdF(t,x) k is the operator norm of dF(t,x) . From this computation we deduce that there is a constant c > 0 depending only on the dimension such that Z Z dim (T (X))−1 ∗ C ≤c (F ωY )ωX kdF(t,x) k2 d vol[0,t]×∂Kn (t, x) [0,t]×∂Kn
[0,t]×∂Kn
Recall that F : [0, 1] × M(X) → M(Y ) is the straight homotopy between the holomorphic (and hence Lipschitz) maps f0 and f1 . Let L be a Lipschitz constant for these maps and fix, once and for all, a point x0 ∈ K0 ⊂ M(X). As we mentioned above, the restriction of F to {t} × M(X) is L-Lipschitz for all t. Hence, the only direction that ∂ dF(t,x) can really increase is the ∂t direction. Since F is the straight
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homotopy, we have ∂ kdF(t,x) kY = dM(Y ) (f0 (x), f1 (x)) ∂t ≤ 2LdM(X) (x, x0 ) + dM(Y ) (f0 (x0 ), f1 (x0 )) It follows that there are constants A, B depending only on L and the base point x0 such that for all (t, x) we have kdF(t,x) k ≤ A · dM(X) (x0 , x)2 + B Summing up we have Z dim (T (X))−1 ∗ C ≤ (12.3) (F ωY )ωX [0,t]×∂Kn 2 ≤ A · max dM(X) (x, x0 ) + B vol(∂Kn ) x∈∂Kn
By construction, maxx∈∂Kn dM(X) (x, x0 ) is bounded from above by a linear function of n. On the other hand, vol(∂Kn ) decreases exponentially. This implies that the right side of (12.3) tends to 0 with n → ∞. This proves the claim. Having proved the claim, we have concluded the proof of Proposition 1.5. References [1] J. Andersen, Mapping Class Groups do not have Kazhdan’s Property (T), math.QA/0706.2184v1. [2] J. Aramayona, C. Leininger and J. Souto, Injections of mapping class groups, Geom. Topol. 13 (2009), no. 5. [3] R. Bell and D. Margalit, Braid groups and the co-Hopfian property, J. Algebra 303 (2006). [4] M. Bestvina, T. Church and J. Souto, Some groups of mapping classes not realized by diffeomorphisms, to appear in Commentarii Mathematici Helvetici. [5] M. Bestvina and K. Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002). [6] J. Birman and H. Hilden, On isotopies of homeomorphisms of Riemann surfaces, Annals of Math., 97 (1973). [7] J. Birman, A. Lubotzky and J. McCarthy, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983). [8] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973). [9] M. Bridson, Semisimple actions of mapping class groups on CAT(0) spaces, preprint, arXiv:0908.0685. [10] M. Bridson and K. Vogtmann, Abelian covers of graphs and maps between outer automorphism groups of free groups, preprint , arXiv:1007.2598. [11] F. Castel, Repr´esentations g´eom´etriques des groupes de tresses, preprint.
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[12] J. Eells, J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964). [13] B. Farb and D. Margalit, A primer on mapping class groups, to appear in Princeton University Press. [14] B. Farb, H. Masur, Superrigidity and mapping class groups, Topology 37, No.6 (1998). [15] E. Grossman, On the residual finiteness of certain mapping class groups, J. London Math. Soc. (2) 9 (1974/75) [16] H. Hamidi-Tehrani, Groups generated by positive multitwists and the fake lantern problem, Algebr. Geom. Topol. 2 (2002) [17] J. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986). [18] W. Harvey, Boundary structure of the modular group, in Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference Ann. of Math. Stud., 97, Princeton Univ. Press, 1981. [19] W. Harvey and M. Korkmaz, Homomorphisms from mapping class groups, Bull. London Math. Soc. 37 (2005), no. 2. [20] A. Hatcher and W. Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980). [21] S. P. Humphries, Generators for the mapping class group, in Topology of lowdimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977), pp. 44–47, Lecture Notes in Math., 722, Springer, Berlin, 1979. [22] N. Ivanov, Automorphisms of Teichm¨ uller modular groups, in Topology and geometry—Rohlin Seminar, 199–270, Lecture Notes in Math., 1346, Springer, Berlin, 1988. [23] N. Ivanov, Automorphism of complexes of curves and of Teichm¨ uller spaces, Internat. Math. Res. Notices 1997. [24] N. Ivanov, Mapping class groups, in Handbook of Geometric Topology, NorthHolland, 2002. [25] N. Ivanov and J. McCarthy, On injective homomorphisms between Teichm¨ uller modular groups. I., Invent. Math. 135 (1999), no. 2. [26] S. Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983). [27] M. Korkmaz, Low-dimensional homology groups of mapping class groups: a survey, Turkish J. Math. 26 (2002), no. 1. [28] A. Kuribayashi and I. Kuribayashi, Automorphism groups of compact Riemann surfaces of genera three and four, J. Pure Appl. Algebra 65 (1990). [29] A. Kuribayashi and I. Kuribayashi, On automorphism groups of compact Riemann surfaces of genus 5, Proc. Japan Acad. Ser. A Math. Sci. 63 (1987). [30] E. Looijenga, Prym representations of mapping class groups, Geometria Dedicata 64, (1997). [31] C. Maclachlan, Abelian groups of automorphisms of compact Riemann surfaces, Proc. London Math. Soc. (3) 15 (1965). [32] J. Mangahas, Uniform uniform exponential growth of subgroups of the mapping class group, Geom. Funct. Anal. 19 (2010), no. 5. [33] D. Margalit, A lantern lemma, Algebr. Geom. Topol. 2 (2002). [34] D. Margalit and S. Schleimer, Dehn twists have roots, Geometry and Topology 13 (2009).
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[35] G. A. Margulis, Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than 1, Invent. Math. 76 (1984), no. 1. [36] V. Markovic, Realization of the mapping class group by homeomorphisms, Invent. Math. 168 (2007), no. 3. [37] J. McCarthy, Automorphisms of surface mapping class groups. A recent theorem of N. Ivanov, Invent. Math. 84 (1986), no. 1. [38] C. T. McMullen, The moduli space of Riemann surfaces is K¨ ahler hyperbolic, Ann. of Math. (2) 151 (2000), no. 1. [39] S. Morita, Characteristic classes of surface bundles, Invent. Math. 90 (1987), no. 3. [40] S. Nakajima, On abelian automorphism groups of algebraic curves, J. London Math. Soc. (2) 36 (1987) [41] L. Paris, Small index subgroups of the mapping class group, to appear in Journal of Group Theory. [42] J. Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978). [43] H. L. Royden, Automorphisms and isometries of Teichm¨ uller space, in Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) pp. 369–383 Ann. of Math. Studies, No. 66. Princeton Univ. Press, Princeton, N.J. [44] W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988). [45] S. Wolpert, Riemann surfaces, moduli and hyperbolic geometry, in Lectures on Riemann Surfaces, World Scientific, 1989.
Department of Mathematics, National University of Ireland, Galway. [email protected] Department of Mathematics, University of Michigan, Ann Arbor. [email protected]
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https://www.physicsforums.com/threads/extrinsic-intrinsic-curvature.30000/
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# Extrinsic/Intrinsic curvature
1. Jun 9, 2004
### Gza
Could someone give me an intuitive example of extrinsic and intrinsic curvature. That would be much appreciated, thanks in advance.
2. Jun 9, 2004
Last edited by a moderator: Apr 20, 2017
3. Jun 10, 2004
### Gza
Yes, that was very helpful. I had to dig up a softer book on a treatment of tensors, but it still served its purpose, thanks again.
4. Jun 11, 2004
### pmb_phy
The cylinder is an excellant example of zero curvature. It is also an excellant example of a manifold for which there are infinitely many geodesics between any two points on the surface.
Pete
5. Jun 12, 2004
### Gza
Maybe i'm referring to the wrong concept, but I thought a circle had a curvature inverse of its radius, so wouldn't the curved part of the cylinder have curvature?
6. Jun 12, 2004
### pmb_phy
You're refering to a different kind of curvature. In the case of the cylinder - when someone says that the surface has zero curvature they mean that there is no "intrinsic" curvature. However it does have an "extrinsic" curvature.
Pete
7. Sep 9, 2004
### mathwonk
As I recall, again from reading Spivak some 35 years ago, Gaussian curvature of a surface at a point p, may be defined as the product of the curvature of the two (perpendicular) curves through p having respectively maximum and minimum curvature as curves. So for a cylinder, you are right that the curve of maximal curvature through the point is a circle of positive curvature, but the curve through the point with minimum curvature is a line with curvature zero, so the product, the curvature of the surface, is zero. Intuitively this is true because the cylinder can be flattened out without tearing it, so really it is not curved as a surface.
I do not know what intrinsic and extrinsic curvature mean but i can guess. Curvatiure is determined by a way of emasuring lengths i.e. a "metric". If a surface like a doughnut for instance is embedded in three space then there are many ways to define a length on it. There is the "extrinsic length" which is just the restriction to the doughnut of the notion of euclidean length. The associated curvatuire would be the extrinsic curvature. E.g. it was extrinsic curvature we were discussing above for the cylinder.
But it seems intuitively clear to me that we could define length differently, in a such a way that the length on (the surface of) a doughnut agreed with the extrinsic length on a cylinder and then the curvature of a doughnut surface would be zero.
So really all curvature is intrinsic, since it is determined by the metric, but you may call the metric and the associated curvature extrinsic if ity happens to agree with that of the embedding space. This is just a plausible guess, but not an uninformed one.
Similar Discussions: Extrinsic/Intrinsic curvature
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https://cran.dcc.uchile.cl/web/packages/poppr/readme/README.html
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# Poppr version 2
## What is poppr?
Poppr is an R package designed for analysis of populations with mixed modes of sexual and clonal reproduction. It is built around the framework of adegenet’s genind and genlight objects and offers the following implementations:
• clone censoring of populations at any of multiple levels of a hierarchy
• convenient counting of multilocus genotypes and sub-setting of populations with multiple levels of hierarchy
• define multilocus genotypes
• calculation of indices of genotypic diversity, evenness, richness, and rarefaction
• drawing of dendrograms with bootstrap support for genetic distances
• drawing of minimum spanning networks for genetic distances
• calculation of the index of association ($I_A$) or ($\bar{r}_d$)
• batch processing on any server that has R (≥ 2.15.1) installed
• calculation of Bruvo’s distance for microsatellite (SSR) markers (implemented in C for speed)
• import of data from and export to GenAlEx
### New in version 2.0:
• handling of genomic SNP data
• custom multilocus genotype definitions
• collapse multilocus lineages by genetic distance
• calculate reticulate minimum spanning networks
• calculate index of association in a sliding window across snps
• bootstrapping of MLG diversity statistics
• interactive exploration of minimum spanning networks
• and more!
For full details, see the NEWS file or type in your R console:
``news(Version >= "2.0.0", package = "poppr")``
## Citation
If you use poppr at all, please specify the version and cite:
Kamvar ZN, Tabima JF, Grünwald NJ. (2014) Poppr: an R package for genetic analysis of populations with clonal, partially clonal, and/or sexual reproduction. PeerJ 2:e281 https://doi.org/10.7717/peerj.281
If you use poppr in a presentation please mention it as the poppr R package, specify the version, and use our logo: (png) | (svg).
Additionally, if you use any following functionalities:
• minimum spanning networks with reticulation
• collapsing multilocus genotypes into multilocus lineages with `mlg.filter()`
• custom multilocus genotype definitions with `mlg.custom()`
• index of association for genomic data with `win.ia()` or `samp.ia()`
• bootstrapping any genetic distance with genind, genlight, or genpop objects with `aboot()`
Kamvar ZN, Brooks JC and Grünwald NJ (2015) Novel R tools for analysis of genome-wide population genetic data with emphasis on clonality. Front. Genet. 6:208. doi: 10.3389/fgene.2015.00208
You can obtain citation information in R by typing:
``citation(package = "poppr")``
## Installation
### From CRAN
To install, make sure R is at least version 2.15.1 (the authors recommend ≥ 3.0), and in your console, type:
``install.packages("poppr")``
### Stable version
New features are occasionally added to {poppr}, but it can take time for it to get to CRAN. If you know that you want the latest version of {poppr}, (which will contain bug fixes and new features to be included in future releases), then you can use the custom R-Universe repository, which is updated hourly: https://zkamvar.r-universe.dev/ui#builds
To install poppr from the R-Universe, you can use the following code:
``````universe <- c("https://zkamvar.r-universe.dev", "https://cloud.r-project.org")
install.packages("poppr", repos = universe)``````
The universe repository also contain up-to-date versions of {adegenet} and {hierfstat}, which are commonly used in conjunction with {poppr} and are notoriously out of date on CRAN.
### Unstable/Development versions
All Development versions of {poppr} will be on GitHub, but need to be compiled.
To install this package from github, make sure you have the following:
• Xcode (OSX) OR Rtools (Windows)
• {remotes} (to install, use: `install.packages("remotes")`)
For Linux users, make sure that the function `getOption("unzip")` returns `"unzip"` or `"internal"`. If it does not, then run `options(unzip = "internal")`.
Once you have {remotes} and a C compiler installed, you can use the `install_github()` function to install the current version from github.
All new features in testing will be released on different branches. These features will be in various stages of development and may or may not be documented. Install with caution. The below command would install features on the branch called “devel”. Note that these branches might be out of date from the main branch. Note: if you don’t have LaTeX installed, you should set `build_vignettes = FALSE`.
``````remotes::install_github(repo = "grunwaldlab/poppr@devel", build_vignettes = TRUE)
library("poppr")``````
## Help / Documentation
### R documentation
To access a descriptive index of help files in poppr, type in your console:
``package?poppr``
### Vignettes
A few vignettes have been written for poppr:
Title Command
Algorightms and Equations `vignette("algo", "poppr")`
Data import and manipulation `vignette("poppr_manual", "poppr")`
Multilocus Genotype Analysis `vignette("mlg", "poppr")`
### User Group
Users who have any questions/comments/suggestions regarding any version of poppr (stable or development) should direct their comments to the Poppr google group
### Book/Primer
In Spring of 2014, Dr. Niklaus J. Grünwald, Dr. Sydney E. Everhart and Zhian N. Kamvar wrote a primer for population genetic analysis in R located at https://grunwaldlab.github.io/Population_Genetics_in_R.
## Contributing
Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms. If you wish to contribute code to poppr, please fork the repository and create a pull request with your added feature.
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https://www.groundai.com/project/higher-order-terms-in-the-inflaton-potential-and-the-lower-bound-on-the-tensor-to-scalar-ratio-r/
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Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
# Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r
C. Destri Dipartimento di Fisica G. Occhialini, Università Milano-Bicocca and INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italia. H. J. de Vega LPTHE, Université Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Laboratoire Associé au CNRS UMR 7589, Tour 24, 5ème. étage, Boite 126, 4, Place Jussieu, 75252 Paris, Cedex 05, France Observatoire de Paris, LERMA. Laboratoire Associé au CNRS UMR 8112.
61, Avenue de l’Observatoire, 75014 Paris, France.
N. G. Sanchez Observatoire de Paris, LERMA. Laboratoire Associé au CNRS UMR 8112.
61, Avenue de l’Observatoire, 75014 Paris, France.
July 18, 2019
###### Abstract
The MCMC analysis of the CMB+LSS data in the context of the Ginsburg-Landau approach to inflation indicated that the fourth degree double–well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lower bound for the ratio of the tensor to scalar fluctuations and as most probable value , within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index and ratio . Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg-Landau class too. The theoretical values in the plane for all double well inflaton potentials in the Ginsburg-Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region . The upper border of the banana-shaped region is given by the fourth order double–well potential and provides an upper bound for the ratio . The lower border of is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio . For example, the current best value of the spectral index , implies is in the interval: . Interestingly enough, this range is within reach of forthcoming CMB observations.
###### pacs:
98.80.Cq,05.10.Cc,11.10.-z
## I Introduction
The current WMAP data are validating the single field slow-roll scenario WMAP5 (). Single field slow-roll models provide an appealing, simple and fairly generic description of inflation libros (); revius (). This inflationary scenario can be implemented using a scalar field, the inflaton with a Lagrangian density
L=a3(t)[˙φ22−(∇φ)22a2(t)−V(φ)], (1)
where is the inflaton potential. Since the universe expands exponentially fast during inflation, gradient terms are exponentially suppressed and can be neglected. At the same time, the exponential stretching of spatial lengths classicalize the physics and permits a classical treatment. One can therefore consider an homogeneous and classical inflaton field which obeys the evolution equation
¨φ+3H(t)˙φ+V′(φ)=0, (2)
in the isotropic and homogeneous Friedmann-Robertson-Walker (FRW) metric
ds2=dt2−a2(t)d→x2, (3)
which is sourced by the inflaton. Here stands for the Hubble parameter. The energy density and the pressure for a spatially homogeneous inflaton are given by
ρ=˙φ22+V(φ),p=˙φ22−V(φ). (4)
The scale factor obeys the Friedmann equation,
H2(t)=13M2Pl[12˙φ2+V(φ)]. (5)
In order to have a finite number of inflation efolds, the inflaton potential must vanish at its absolute minimum
V′(φmin)=V(φmin)=0. (6)
These two conditions guarantee that inflation is not eternal. Since the inflaton field is space-independent inflation is followed by a matter dominated era (see for example ref. bibl ()).
Inflation as known today should be considered as an effective theory, that is, it is not a fundamental theory but a theory of a condensate (the inflaton field) which follows from a more fundamental one. In order to describe the cosmological evolution it is enough to consider the effective dynamics of such condensates. The inflaton field may not correspond to any real particle (even unstable) but is just an effective description while the microscopic description should come from a Grand Unification theory (GUT) model.
At present, there is no derivation of the inflaton model from a microscopic GUT theory. However, the relation between the effective field theory of inflation and the microscopic fundamental theory is akin to the relation between the effective Ginsburg-Landau theory of superconductivity gl () and the microscopic BCS theory, or like the relation of the sigma model, an effective low energy theory of pions, photons and nucleons (as skyrmions), with the corresponding microscopic theory: quantum chromodynamics (QCD).
In the absence of a microscopic theory of inflation, we find that the Ginsburg-Landau approach is a powerful effective theory description. Such effective approach has been fully successful in several branches of physics when the microscopic theory is not available or when it is very complicated to solve in the regime considered. This is the case in statistical physics, particle physics and condensed matter physics. Such GL effective theory approach permits to analyse the physics in a quantitative way without committing to a specific model gl ().
The Ginsburg-Landau framework is not just a class of physically well motivated inflaton potentials, among them the double and single well potentials. The Ginsburg-Landau approach provides the effective theory for inflation, with powerful gain in the physical insight and analysis of the data. As explained in this paper and shown in the refs. mcmc ()-bibl (), the analysis of the present set of CMB+LSS data with the effective theory of inflation, favor the double well potential. Of course, just analyzing the present data without this powerful physical theory insight, does not allow to discriminate between classes of models, and so, very superficially and incompletely, it would seem that almost all the potentials are still at the same footing, waiting for the new data to discriminate them.
In the Ginsburg-Landau spirit the potential is a polynomial in the field starting by a constant term gl (). Linear terms can always be eliminated by a constant shift of the inflaton field. The quadratic term can have a positive or a negative sign associated to unbroken symmetry (chaotic inflation) or to broken symmetry (new inflation), respectively.
As shown in refs. mcmc (); bibl () a negative quadratic term and a negligible cubic term in new inflation provides a very good fit to the CMB+LSS data, (the inflaton starts at or very close to the false vacuum ). The analysis in refs.mcmc (); bibl () showed that chaotic inflation is clearly disfavoured compared with new inflation. Namely, inflaton potentials with are favoured with the inflaton starting to evolve at .
We can therefore ignore the linear and cubic terms in . I f we restrict ourselves for the moment to fourth order polynomial potentials, eq.(6) and imply that the inflaton potential is a double well (broken symmetric) with the following form:
V(φ)=−12m2φ2+14λφ4+m44λ=14λ(φ2−m2λ)2. (7)
The mass term and the coupling are naturally expressed in terms of the two energy scales which are relevant in this context: the energy scale of inflation and the Planck mass GeV,
m=M2MPl,λ=y8N(MMPl)4. (8)
Here is the quartic coupling.
The MCMC analysis of the CMB+LSS data combined with the theoretical input above yields the value for the coupling mcmc (); bibl (). turns out to be order one consistent with the Ginsburg-Landau formulation of the theory of inflation bibl ().
According to the current CMB+LSS data, this fourth order double–well potential of new inflation yields as most probable values: mcmc (); bibl (). This value for is within reach of forthcoming CMB observations apjnos (). For the best fit value , the inflaton field exits the horizon in the negative concavity region intrinsic to new inflation. We find for the best fit mcmc (); bibl (),
M=0.543×1016GeV for the scale of inflation andm=1.21×1013GeV for the inflaton mass. (9)
It must be stressed that in our approach the amplitude of scalar fluctuations allows us to completely determine the energy scale of inflation which turns out to coincide with the Grand Unification energy scale (well below the Planck energy scale). Namely, we succeed to derive the energy scale of inflation without the knowledge of the value of from observations. guarantees the validity of the effective theory approach to inflation. The fact that the inflaton mass is implies the appearance of infrared phenomenon as the quasi-scale invariance of the primordial power.
Since the inflaton potential must be bounded from below , the highest degree term must be even and with a positive coefficient. Hence, we consider polynomial potentials of degree where .
The request of renormalizability restricts the degree of the inflaton potential to four. However, since the theory of inflation is an effective theory, potentials of degrees higher than four are in principle acceptable.
A given Ginsburg-Landau potential will be reliable provided it is stable under the addition to the potential of terms of higher order. Namely, adding to the th order potential further terms of order and should only produce small changes in the observables. Otherwise, the description obtained could not be trusted. Since, the highest degree term must be even and positive, this implies that all even terms of order higher or equal than four should be positive.
Moreover, when expressed in terms of the appropriate dimensionless variables, a relevant dimensionless coupling constant can be defined by rescaling the inflaton field. This coupling turns out to be of order where is the number of efolds since the cosmologically relevant modes exit the horizon till the end of inflation showing that the slow-roll approximation is in fact an expansion in 1sN (). It is then natural to introduce as coupling constant . This is consistent with the stability of the results in the above sense. Generally speaking, the Ginsburg-Landau approach makes sense for small or moderate coupling.
Odd terms in the inflaton field are allowed in in the effective theory of inflation. Choosing an even function of implies that is a symmetry of the inflaton potential. At the moment, as stated in ciri (); bibl (), we do not see reasons based on fundamental physics to choose a zero or a nonzero cubic term, which is the first non-trivial odd term. Only the phenomenology, that is the fit to the CMB+LSS data, decides on the value of the cubic and the higher order odd terms. The MCMC analysis of the WMAP plus LSS data shows that the cubic term is negligible and therefore can be ignored for new inflation mcmc (); bibl (). CMB data have also been analyzed at the light of slow-roll inflation in refs. otros ().
In the present paper we systematically study the effects produced by higher order terms () in the inflationary potential on the observables and .
We show in this paper that all curves for a large class of double–well potentials of arbitrary high order in new inflation fall inside the universal banana region depicted in fig. 10. Moreover, we find that the curves for even double–well potentials with arbitrarily positive higher order terms lie inside the universal banana region [fig. 10]. This is true for arbitrarily large values of the coefficients in the potential.
Furthermore, the inflaton field may be a condensate of fermion-antifermion pairs in a grand unified theory (GUT) in the inflationary background. In this paper we explicitly write down in closed form the inflaton potential dynamically generated as the effective potential of fermions in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg-Landau class of potentials considered in this paper. We find that the corresponding curves lie inside the universal banana region provided the one-loop part of the inflaton potential is at most of the same order as the tree level piece. Therefore, a lower bound for the ratio tensor/scalar fluctuations is present for all potentials above mentioned. For the current best value of the spectral index bibl (); WMAP5 () the lower bound turns out to be .
Namely, the shape of the banana region fig. 10 combined with the value for the spectral index yields the lower bound . If one consider low enough values for (in disagreement with observations) can be arbitrarily small within the GL class of inflaton potentials.
The upper border of the universal region tells us that for . Therefore, we have inside the region within the large class of potentials considered here
0.021
Interestingly enough is within reach, although borderline for the Planck satellite apjnos ().
Among the simplest potentials in the Ginsburg-Landau class, the one that best reproduces the present CMB+LSS data, is the fourth order double–well potential eq.(7), yielding as most probable values: . Our work here shows that adding higher order terms to the inflaton potential does not really improve the data description in spite of the addition of new free parameters. Therefore, the fourth order double–well potential gives a robust and stable description of the present CMB/LSS data and provides clear predictions to be contrasted with the forthcoming CMB observations apjnos ().
There is an abundant literature on slow-roll inflationary potentials and the cosmological parameters and including new inflation and in particular hilltop inflation lily (); otros2 (); otros3 (); otros4 ().
The question on whether a lower bound for is found or not depends on whether the Ginsburg-Landau (G-L) effective field approach to inflation is used or not. Namely, within the G-L approach, the new inflation double well potential determines a banana shaped relationship which for the observed value determines a lower bound on . The analysis of the CMB+LSS data within the G-L approach which we performed in refs. mcmc (); bibl () shows that new inflation is preferred by the data with respect to chaotic inflation for fourth degree potentials, and that the lower bound on is then present. Without using the powerful physical G-L framework such discrimination between the two classes of inflation models is not possible and the lower bound for does not emerge. Other references in the field (i. e. lily (); kinney08 (); PeirisEasther ()) do not work within the Ginsburg-Landau framework, do not find lower bounds for and cannot exclude arbitrarily small values for , much smaller than our lower bound .
This paper is organized as follows: in section II we present in general inflaton potentials of arbitrary high degree, specializing then to fourth and sixth–order polynomial potentials and displaying their corresponding curves. Sec. III contains the th order double–well polynomial inflaton potentials with arbitrary random coefficients and their curves. Sec. IV presents the limits of these polynomial potentials and we present in sec. V the exponential potential and its infinite coupling limit. In sec. V we compute the inflaton potential from dynamically generated fermion condensates in a de Sitter space-time displaying their curves. Finally, we present and discuss the universal banana region in sec. VII together with our conclusions.
## Ii Physical parametrization for inflaton potentials
We start by writing the inflaton potential in dimensionless variables as ciri ()
V(φ)=M4v(φMPl), (10)
where is the energy scale of inflation and is a dimensionless function of the dimensionless field argument . Without loss of generality we can set . Moreover, provided we can choose without loss of generality .
In the slow-roll regime, higher time derivatives in the equations of motion can be neglected with the final well known result for the number of efolds
N=−∫ϕendϕexitdϕv(ϕ)v′(ϕ), (11)
where is the inflaton field at horizon exit. To leading order in we can take to be the value at which attains its absolute minimum , which must be zero since inflation must stop after a finite number of efolds bibl ().
Then, in chaotic inflation we have , with for , while in new inflation we have with for . We consider potentials that can be expanded in Taylor series around , with a non-vanishing quadratic (mass) term.
It is convenient to rescale the inflaton field in order to conveniently parametrize the higher order potential. We define a coupling parameter by rescaling the inflaton and its potential keeping invariant the quadratic term, that is
v(ϕ)=1gv1(ϕ√g) (12)
For a potential expanded in power series around we write:
v1(u)=c0∓12u2+∑k≥3ckkuk (13)
Then, replacing
u=ϕ√g, (14)
we find
v(ϕ)=c0g∓12ϕ2+∑k≥3gk/2−1kckϕk. (15)
The positive sign in the quadratic term corresponds to chaotic inflation (in which case ), while the negative sign corresponds to new inflation (in which case is chosen such that vanishes at its absolute minimum).
Clearly plus the set of coefficients provide an overcomplete parametrization of the inflaton potential which we will now reduce. In the case of chaotic inflation a convenient choice is , so that
v(ϕ)=12ϕ2+√gc33ϕ3+g4ϕ4+∑k≥5gk/2−1kckϕk[chaotic inflation] (16)
which represents a generic higher order perturbation of the trinomial chaotic inflation studied in refs. mcmc ().
In the case of new inflation, where , it is more convenient to set without loss of generality that . In order to have appropriate inflation, must be the absolute minimum of and the closest one to the origin on the positive semi–axis. That is,
v′1(1)=−1+∑k≥3ck=0 (17)
and then fixes from eq.(12) the constant term in the potential
c0=12−∑k≥3ckk (18)
We thus get for the inflaton potential
v1(u)=12(1−u2)+∑k≥3ckk(uk−1)[new inflation], (19)
corresponding to
v(ϕ)=12(1g−ϕ2)+∑k≥3ckk(gk/2−1ϕk−1g)[new inflation] (20)
For the coupling and the field using eq.(14),
g=1ϕ2min=M2Plφ2min,u=ϕϕmin=φφmin. (21)
From eq.(11) it now follows that the parameter can be expressed as the integral
y(u)=8∫uumindxv1(x)v′1(x),u≡√gϕexit, (22)
where,
g=y(u)8N, (23)
with for chaotic inflation and for new inflation. Eq.(22) can be regarded as a parametrization of and in terms of the rescaled exit field . Clearly, as a function of , is uniformly of order . is numerically of order as long as is of order one. As we shall see, typically both at horizon exit and are of order one. We have for new inflation and for chaotic inflation.
In what follows we therefore use instead of as a coupling constant and make contact with eq.(10) by setting
φ=MPl√8Nyu,V(φ)=8NM4yv1(√y8NφMPl). (24)
We can easily read from this equation the order of magnitude of and since is given by eq.(9) and and are of order one. Hence, and .
As we will see below, the coupling (or ) is the most relevant coupling since it is related to the inflaton rescaling: the tensor–scalar ratio and the spectral index vary in a more relevant manner with than with the rest of the parameters in the potential eq.(15).
By construction the function has the following properties
• ;
• for in chaotic inflation;
• for in new inflation;
• as ;
• as in chaotic inflation;
• as in new inflation.
In terms of this parametrization and to leading order in , the tensor to scalar ratio and the spectral index read:
r=y(u)N[v′1(u)v1(u)]2,ns−1=−38r+y(u)4Nv′′1(u)v1(u) (25)
Notice that both and are of order for generic inflation potentials in this Ginsburg-Landau framework as we see from eq.(25). Moreover, the running of the scalar spectral index from eq.(24) and its slow-roll expression turn out to be of order
dnsdlnk=−y2(u)32N2{v′1(u)v′′′1(u)v21(u)+3[v′1(u)]4v41(u)−4[v′1(u)]2v′′1(u)v31(u)}.
and therefore can be neglected bibl (). Such small estimate for is in agreement with the present data WMAP5 () and makes the running unobservable for a foreseeable future.
Since can be inverted for any , these two relations can also be regarded as parametrizations and in terms of the coupling constant .
We are interested in the region of the plane obtained from eq.(25) by varying (or ) and the other parameters in the inflaton potential. We call this region.
From now on, we will restrict to new inflation.
For a generic [with the required global properties described above] we can determine the asymptotic of , since they follow from the weak coupling limit and from the strong coupling limit . When , then and from the property above,
r=8N+O(u−1)=0.13333…+O(u−1) (26)
and
ns=1−2N+O(u−1)=0.9666…+O(u−1). (27)
When we have in new inflation and then,
ns≃1+2Nlogu⟶−∞,r≃−8Nu2loguv1(0)⟶0+. (28)
We see that in the strong coupling regime becomes very small and becomes well below unity. However, the slow-roll approximation is valid for and in any case, the WMAP+LSS results exclude WMAP5 (). Therefore, the strong coupling limit is ruled out.
Eq.(25) for can be rewritten using eq.(22) in the suggestive form,
r=64Ny(u)[dlny(u)du]−2 (29)
Since may be small only in case is large (the logarithmic derivative of has a milder effect for large .) Therefore, we only find in a strong coupling regime. Notice that is much smaller than in the strong coupling regime [eq.(21)].
Let us now study large classes of physically meaningful inflaton potentials in order to provide generic bounds on the region of the plane within an interval of surely compatible with the WMAP+LSS data for , namely . To gain insight into the problem, we consider first the cases amenable to an analytic treatment, leaving the generic cases to a numerical investigation. As we will see below, the boundaries of the region turn out to be described parametrically by the analytic formulas (32) and (50).
### ii.1 The fourth degree double–well inflaton potential
The case when the is the standard double–well quartic polynomial
has been studied in refs. mcmc (); bibl (). In the general framework outlined above we have for this case,
v1(u)=14(u2−1)2=14−12u2+14u4,λ=y8N(MMPl)4,m=M2MPl. (30)
By explicitly evaluating the integral in eq. (22) one obtains
y(u)=u2−1−logu2, (31)
and then, from eq. (25)
ns=1−1N3u2+1(1−u2)2(u2−1−logu2),r=1N16u2(1−u2)2(u2−1−logu2) (32)
where . As required by the general arguments above, is a monotonically decreasing function of , ranging from till when increases from till . In particular, when vanishes quadratically as,
y(u)u→1−=12(1−u2)2.
The concavity of the potential eq.(30) for the inflaton field at horizon crossing takes the value
v′′1(u)=3u2−1.
We see that vanishes at , that is at . (This is usually called the spinodal point revi ()). Therefore,
v′′1(u)>0fory<0.431946…andv′′1(u)<0fory>0.431946…. (33)
Our MCMC analysis of the CMB+LSS data combined with the theoretical model eq.(30) yields mcmc (); bibl () deep in the negative concavity region .
The negative concavity case for is specific to new inflation eq.(30). can be expressed as a linear combination of the observables and as
ns−1+38r=y(u)4Nv′′1(u)v1(u)
As expected in the general framework presented above, the limit implies weak coupling , that is, the potential is quadratic around the absolute minimum and we find,
nsy→0=1−2N,ry→0=8N,uy→0=1, (34)
which coincide with and for the monomial quadratic potential in chaotic inflation.
In the limit which implies (strong coupling), we have
uy→+∞=e−(y+1)/2→0+
and
nsy≫1=1−yN,ry≫1=16yNe−y−1. (35)
Notice that the slow-roll approximation is no longer valid when the coefficient of becomes much larger than unity. Hence, the results in eq.(35) are valid for . We see that in this strong coupling regime (see fig. 1), becomes very small and becomes well below unity. However, the WMAP+LSS results exclude WMAP5 (). Therefore, this strong coupling limit is ruled out.
For the fourth order double–well inflaton potential, the relation defined by eq.(32) is a single curve depicted with dotted lines in fig. 1. It represents the upper border of the banana shaped region in fig. 1.
Notice that there is here a maximum value for , namely with bibl (). The curve has here two branches: the lower branch in which increases with increasing and the upper branch in which decreases with increasing .
### ii.2 The sixth–order double–well inflaton potential
We consider here new inflation described by a six degree even polynomial potential with broken symmetry. According to eq. (10) and eq. (12) we then have
V(φ)=M4gv1(√gφMPl),v1(u)=c0−12u2+c44u4+c66u6. (36)
where for stability we assume . Moreover, if we regard this case as a higher order correction to the quartic double–well potential, then is positive.
The inflaton potential eq.(36) is a particular case of eq.(13). The conditions eqs. (17) and (18) that the absolute minimum of be at yields
c4+c6=1,c0=12−14c4−16c6 (37)
It is convenient to use as free parameter so that and . Thus,
v1(u)=12(1−u2)−1−b4(1−u4)−b6(1−u6)=112(1−u2)2(3+b+2bu2) (38)
where in order to ensure that .
The integral in eq. (22) can be explicitly evaluated with the result
y(u)=8∫u1dxv1(x)v′1(x)=23(u2−1)−13(3+b)logu2+(1+b)23blog1+bu21+b (39)
According to the general arguments presented above [see the lines below eq. (22)] one can verify that is a monotonically decreasing function of for , where .
The scalar index and the tensor–scalar ratio are evaluated from eq. (25) as
r=yN[12u(1+bu2)(1−u2)(3+b+2bu2)]2,ns=1−38r+3y(u)N5bu4+3(1−b)u2−1(1−u2)2(3+b+2bu2) (40)
Various curves are plotted in fig. 1 for several values of in the interval sweeping the region . We see that for increasing [namely, for increasing sextic coupling and decreasing quartic coupling, see eq.(38)] the curves move down and right, sweeping the banana-shape region depicted on fig. 1.
Clearly, is a variable more relevant than . Changing moves and in the whole available range of values, while changing only amounts to displacements transverse to the banana region in the plane. In particular, for a given becomes smaller for increasing .
We see in fig. 1 two important limiting curves: the and the curves. When the function reduces to the fourth order double-well potential eq.(30) and we recover its characteristic curve . When the potential has no quartic term and reduces to the quadratic plus sixth order potential:
v1(u)b→1=16(1−u2)2(2+u2)=13−12u2+16u6. (41)
In summary, the quadratic plus quartic broken–symmetry potential describes the upper/left border of the banana–shaped region of fig. 1, while the quadratic plus sextic broken–symmetry potential describes its lower/right border.
## Iii Higher–order even polynomial double-well inflaton potentials
The generalization of the sixth order inflaton potential with broken symmetry to arbitrarily higher orders is now straightforward:
V(φ)=M4gv1(√gφMPl),v1(u)=12(1−u2)+n∑k=2c2k2k(u2k−1), (42)
with the constraint eq.(17)
n∑k=2c2k=1 (43)
which guarantees that is an extreme of .
We consider here the case when all higher coefficients are positive or zero :
c2k≥0,k=2,…,n
such that is the unique positive minimum.
We determine the shape of the region for arbitrary positive or zero values of the coefficients [subject to the constraint (43)], performing a large number of simulations with different setups. After producing coefficients we numerically computed the function following eq.(22)
y(u)=4∫1udxx1−x2+∑nk=2c2kk(x2k−1)1−∑nk=2c2kx2k−2
and obtain the curves from eq. (25) by plotting directly vs. .
Uniform distributions of coefficients are obtained by setting
c2k=(n∑j=1logξj)−1logξk,k=1,2,…,n (44)
where the numbers are independently and uniformly distributed in the unit interval. We used the parametrization eq.(44) also when the are chosen according to other rules.
For example, in figs. 2-3 we plot the results when , that is for the ten degree polynomial. In this case we let and take independently the values or , for a total of 78 distinct configurations of coefficients. For better clarity, in figs. 2-3 we also include the two border cases and .
For higher values of we extracted the numbers at random within the unit interval. In particular, for the highest case considered, , we used three distributions: in the first, the were all extracted independently and uniformly over the unit interval; in the second we set and extracted the independently and uniformly; in the third we picked at random four freely varying and fixed to 1 the remaining 45 ones (that is we picked at random four possibly non–zero , setting the rest to zero); the values of the four free were chosen at random in the same set of values of the case. The results of these simulations are shown in fig. 5.
As evident from fig. 3, where the curves are split in upper/lower branches with growing/decreasing and especially from fig. 5, the case of the quadratic plus th order polynomial provides a bound to the banana region from below. That is, for any fixed value of , the quadratic plus th order polynomial provides the lowest value for .
One sees from fig. 5 that some blue curves go beyond the slashed red curve for the quadratic plus potential on the right upper border of the banana region . Namely, the right upper border of the region is not given by the quadratic plus potential while this potential provides the lower border of the region.
We performed many other tests with intermediate values of and several other distributions, including other dependent distributions, with characteristic values for growing linearly with or decreasing in a power–like or exponential way. In all cases, the results were consistent with those given above.
It is also important to observe that the class of potentials considered, that is arbitrary even polynomials with positive or zero couplings, is a class of weakly coupled models. This is evident from fig. 4, were is plotted vs. the coupling , which remains of order one when decreases well below the current experimental limits. This weak coupling is the reason why the addition of higher even monomials to these potentials causes only minor quantitative changes to the shape of the curves.
The inflaton potential eq.(42) in the original inflaton field takes therefore the form
V(φ)=4NM4y(u)⎧⎨⎩1−y(u)8Nφ2M2Pl+n∑k=2c2kk(y(u)8N)kφ2kM2kPl⎫⎬⎭,
Therefore, since the coupling is we have the -th term in the potential suppressed by the -th power of as well as by the factor .
In particular, the quartic term
y(u)c432N(MMPl)4φ4
possesses a very small quartic coupling since . Notice that these suppression factors are natural in the GL approach and come from the ratio of the two relevant energy scales here: the Planck mass and the inflation scale . When the GL approach is not used these suppression factors do not follow in general.
The validity of the GL approach relies on the wide separation between the scale of inflation and the higher energy scale (corresponding to the underlying unknown microscopic theory as discussed in ref. 1sN ().) It is not necessary to require in the GL approach but to impose 1sN ()
V(φ)≪M4Pland hencev1(ϕ√g)≪1012g.
This last condition gives an upper bound for the inflaton field depending on the large argument behavior of . We get for example:
φ≪106MPlforv1(u)u→∞∼u2,φ≪2600MPlforv1(u)u→∞∼u4.
The validity of the effective GL theory relies on that separation of scales and the GL approach allows to determine the scale of inflation as GeV (at the GUT scale) and well below the Planck scale using the amplitude of the scalar fluctuations from the CMB data mcmc (); bibl ().
Inflaton potentials containing terms of arbitrary high order in the inflaton are considered in ref. lily (), sec. 25.3.2 without using the GL approach and within the small field hypothesis . Smallness conditions on the expansion coefficients are required in ref. lily (). This is actually not needed in the GL approach, whose validity relies only on the wide separation of scales between and , at least in the case of even polynomials with positive coefficients.
## Iv The quadratic plus the 2nth order double-well inflaton potential
In order to find the observationally interesting right and down border of the banana we consider the quadratic plus the th order potential for new inflation ho (),
v1(u)=12(1−u2)+12n(u2n−1). (45)
As in the general case eq.(19), we choose the absolute minimum at . The customary relation eq.(22) takes here the form ho (),
y(u)=4n∫1udxxn(1−x2)+x2n−11−x2n−2where0
This integral can be expressed as a sum of terms including logarithms and arctangents PBM ().
In the weak coupling limit and take the values of the quadratic monomial potential eqs.(26)-(27) ho (); bibl ():
ns−1y→0=−2N=−0.0333…,ry→0=8N=0.1333…, (47)
while in the strong coupling limit at fixed and take the values
ns≃1+2Nlogu⟶−∞,r≃−16Nnn−1u2logu⟶0+,
in accordance with the general formula eq.(28). In fig. 6 we plot vs. for the potential eq.(45) and the exponents and . We see that for vs. tends towards a limiting curve. For we reach the upper end of the curve [the monomial quadratic potential eq.(47)] while for large the left and lower end of the curve is reached. However, the current CMB–LSS data rule out this strong coupling part of the curve for .
### iv.1 The n→∞ limit at fixed u.
Let us first compute eq.(46) for at fixed . Since in the integrand of eq.(46),
limn→∞x2n=0.
and eq.(46) reduces to
y(u)n→∞=4n∫1udxx[n(1−x2)−1]=2[u2−1−lnu2+O(1n)].
Hence, eq.(46) becomes
y(u)n→∞=2(−lnu2−1+u2)where0
which is just twice the result found in the quartic double–well potential, eq. (31). Notice that eq.(45) in the limit becomes
limn→∞v1(u)={12(1−u2)foru<1+∞foru>1.. (49)
From eqs.(25), (45) and (48) we find for and in the limit
ns−1n→∞=−1N2u2+1(1−u2)2(−lnu2−1+u2), (50) (51) rn→∞=8Nu2(1−u2)2(−lnu2−1+u2). (52)
Now, in the limiting cases and (at ), that is, the strong coupling limit and the the weak coupling limit , respectively, we obtain from eqs.(50)
limu→
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http://tex.stackexchange.com/questions/180177/reduce-line-height-in-p-type-table-cells
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# Reduce line height in p type table cells
I need to set a big table and want to compress it in a way that it fits on one page. The table contains a column of type p with text breaking over multiple lines. Now I want to reduce the overall line spacing. Usually, I'm using a \renewcommand{\arraystretch}{0.9} for that, but that does not seem to work for p columns. See the following example (I set the spacing to 0.5 to make my goal more clear):
\documentclass[ngerman]{scrbook}
\begin{document}
{
\renewcommand{\arraystretch}{0.5} % this reduces the vertical spacing between rows
\begin{table}
\centering
\begin{tabular}{l p{5cm}}
\hline
row one &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog. \\
row two \\
row three \\
\hline
\end{tabular}
\end{table}
}
\end{document}
This produces the following result:
Beside the spacing between the rows (green arrow), I would like to reduce the line spacing in between the "the quick brown fox" lines as well (red arrow). Any hints strongly appreciated.
-
You can use & \baselineskip=10pt for example, to change it locally. I guess that it is not the best solution, but it works. – Sigur May 24 '14 at 16:38
Thank you, I defined a command for that, which makes it a bit less repetitive. Still, if anybody has a global solution (wrt table) that would be great. – qqilihq May 24 '14 at 16:59
The result is disastrous, in my opinion. But here it is, without extra packages and extra commands.
\documentclass[ngerman]{scrbook}
\begin{document}
\begin{table}
\renewcommand{\arraystretch}{0.5} % this reduces the vertical spacing between rows
\begin{tabular}{l p{5cm}}
\hline
row one &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog. \\
row two \\
row three \\
\hline
\end{tabular}
\end{table}
\end{document}
Note that the setting to \baselinestretch (made by \linespread) and to \arraystretch are local to the table environment; you don't need to have them outside the environment which, on the other hand, makes a group so that the previous values will be reverted at \end{table}.
-
the "paragraphed" material would really look better ragged right. – barbara beeton May 24 '14 at 20:44
@barbarabeeton I think there's no mending that can improve that disaster. – egreg May 24 '14 at 20:54
\usepackage{array}
Then
\newcolumntype{P}[1]{>{\small}{p{#1}}
or
\newcolumntype{P}[1]{>{\linespread{.9}}{p{#1}}
If you think you can get away with squeezing the linespacing while keeping the text size.
Then use P{..} instead of p{..}
-
Both of them do not work for me unfortunately, I'm getting the error Paragraph ended before \newcol@ was complete. [] while building. – qqilihq May 25 '14 at 7:36
@qqilihq Then you have a missing } – David Carlisle May 25 '14 at 8:09
It enough to use the \setstretch command from the setspace package. As the row could be undistinguishable, for better readability I introduced a minimal spacing between rows (expressed in ex units, so that it varies with the fontsize) through the cellspace package. I used booktabs in order to have a better vertical spacing for the horizontal lines. Finally, you can play with the fontsize in the table. I give an example with \footnotesize:
\documentclass[ngerman]{scrbook}
\usepackage{setspace}
\usepackage{booktabs}
\usepackage{xcolor}
\usepackage{cellspace}
\setlength\cellspacetoplimit{0.8ex}
\begin{document}
Text text text text text text text text text text text text text text text text text text text text text text text text tex text.
\begin{table}[!htbp]
\centering\footnotesize\setstretch{0.5}
\begin{tabular}{Sl p{5cm}}
\toprule
row one &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog. \\
row two &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.\\
row three &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.\\
\bottomrule
\end{tabular}
\end{table}
\end{document}
-
Note: in my first attempt to give an answer -- since unfortunately I'm still not familiar with SE -- I made a terrible mess from which I was (in this moment) unable to (re)edit my answer and correct in last second observed error in it. Sorry for this. Now I try to correct this and all puts on right place.
Well, meanwhile you got good answers from others, so I added main just to eliminate my previous (locked) mess.
Answer: If you explicitly (again) declare font family in the table environment, for examaple with \rmfamily, than work the following MWE:
\documentclass{article}
\usepackage[active,floats,tightpage]{preview} %just for showing only table
\begin{document}
\begin{table}[h!]\centering
\linespread{0.8} % this decrease the vertical spacing between lines
\rmfamily % without this, \linespread doesn't give expected effect
% to be honest, I do not know, why this is necessary
\begin{tabular}{l p{5cm}}
\hline
row one &
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog.
the quick brown fox jumps over the lazy dog. \\
row two & \\
row three & \\
\hline
\end{tabular}
\end{table}
\end{document}
I tested above MWE with article package since I newer use scrbook. I believe/hope, that it also should work with scrbook.
The declaration of \rmfamiliy (or for example \sffamily, which I usually use in my tables) inside table environment make \linespread{<reduction factor>} active in all table cells. Why it is necessary, I do not know.
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https://infoscience.epfl.ch/record/129945
|
Infoscience
Journal article
# Second-order hyperbolic S.P.D.E.'s driven by homogeneous Gaussian noise on a hyperplane
We study a class of hyperbolic stochastic partial di®erential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions di®er. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.
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https://www.physicsforums.com/threads/magnetic-vector-potential-of-infinite-wire.119419/
|
# Magnetic vector potential of infinite wire
1. May 1, 2006
### siddharth
I don't know if this thread belongs in Introductory Physics or here, so please feel free to move it if you wish.
The question is
Find the vector potential a distance $r$ from an infinite straight wire carrying a current $I$
I know that the vector potential can be given by
$$\frac{\mu_0}{4 \pi} \int \frac{I \vec{dl}}{r}$$
The problem is that in this case, the wire goes to infinity. So that that doesn't work.
I tried it in another way. Since $$B = \nabla \times A$$ and the direction of A is generally the direction of the current, it reduces to
$$\left(\frac{d A_r}{dz} - \frac{ d A_z}{dr}\right) \hat{e_{\phi}} = \frac{\mu_0 I}{2 \pi r} \hat{e_{\phi}}$$
ie,
$$\frac{d A_z}{dr} = -\frac{\mu_0 I}{2 \pi r}$$
and
$$A = -\frac{\mu_0 I}{2 \pi} ln\left(\frac{r}{r_0}\right) \hat{e_z}$$
Is that right? Also, how can we generally say that A is along the direction of the current?
Last edited: May 1, 2006
2. May 1, 2006
### Tom Mattson
Staff Emeritus
No, it's fine here.
Yes, it does. The improper integral you would obtain does in fact converge.
I don't think so, but it looks like it's close. What's $r_0$?
You needn't say that at all. Remember that the potentials are related to the physical fields via differential operators. That relationship affords you some gauge freedom. You can replace $\vec{A}$ with $\vec{A}+\nabla\chi$ provided that $\chi$ is continuously differentiable. You will get the same magnetic field, even if $\nabla\chi$ isn't in the direction of the current.
3. May 1, 2006
### siddharth
Does it?
Doing it that way, I get
$$A = \left(\frac{\mu_0 I}{4 \pi}\right) ln(\sec \theta + \tan \theta)$$
where $\theta$ is the angle made between the lines joining the point where I'm finding the potential to the center of the wire and the ends.
So as $\theta$ goes to pi/2 or -pi/2, doesn't it diverge?
$r_0$ is some point where I have defined A to be 0.
Yeah, I understand. But the thing is, in most cases A in fact does point along the direction of the current.
4. May 1, 2006
### Physics Monkey
Hi siddharth,
The integral defining A does indeed diverge, however it is possible to extract a finite part which produces the correct physics. Extracting the finite parts from such integrals is a fairly common technique for dealing with these infinite geometries.
In your case the integral you want to do (after a change of variables) is $$\frac{\mu_0 I}{4 \pi} \int^{\Lambda}_{-\Lambda} dz \frac{1}{\sqrt{\rho^2 + z^2}},$$ which you can write as $$\frac{\mu_0 I}{2 \pi} \int^\Lambda_0 dz \frac{1}{\sqrt{\rho^2 + z^2}} = \frac{\mu_0 I}{2 \pi} \log{\left(\frac{\Lambda}{\rho} + \sqrt{1 + \frac{\Lambda^2}{\rho^2}} \right)}$$. For large cutoff you can approximate the argument of the log as $$\frac{\mu_0 I}{2 \pi} \log{\left(\frac{2 \Lambda}{\rho} \right)} = - \frac{\mu_0 I}{2 \pi} \log{\left(\frac{\rho}{\rho_0}\right)} + \frac{\mu_0 I}{2 \pi} \log{\left(\frac{2 \Lambda}{\rho_0}\right)}$$. Now look what has happened! Yes, the vector potential is formally infinite if you let the cutoff go to infinity, but all the physical results (magnetic field) are independent of the cutoff. You are able to extract the relevant physics from a formally divergent integral. Needless to say, this is a very powerful methodology that you will meet again and again as you progress through physics.
Also, the vector potential often points along the current because in the Coulomb gauge one has the formula $$\vec{A} = \frac{\mu_0}{4 \pi} \int d^3 x' \frac{\vec{J}(\vec{x}')}{|\vec{x}-\vec{x}'|}$$. It's clear then that as long as the current points in one direction, A will point in that direction in the Coulomb gauge.
Hope this helps.
Last edited: May 1, 2006
5. May 2, 2006
### siddharth
That's fantastic!
I'm curious, why does it work? How come the relevant physics comes out so nicely?
Thanks a ton for your help.
Last edited: May 2, 2006
6. May 2, 2006
### Tom Mattson
Staff Emeritus
I was wrong about that, as PM pointed out. You have to do some mathematical trickery that I had forgotten about (it's been a while).
As I said, that's a choice. You can choose the gauge that's convenient for you.
7. May 2, 2006
### Physics Monkey
Isn't it cool! Physics is so awesome.
What's going on is essentially a separation of different scales. As far as charged particles close to a long wire are concerned, it doesn't matter how long the wire is as long as it's very long. You could never figure out what the length of the wire is by performing local experiments. Since the length of the wire is unobservable, you might suspect that it enters the vector potential only as a pure gauge term. This suspicion is confirmed when you carry out the calculation, and you can easily check for yourself that is indeed possible to eliminate $$\Lambda$$ by choosing a different gauge. It is quite instructive to carry out calculations of this type for a variety of infinite geometries. You will find that the infinite geometry gives you some divergence, but the divergence is always unobservable. Such calculations give you glimpse of the very subtle and deep nature of field theory. It's all very beautiful stuff really.
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# A rectangular picture is surrounded by a boarder, as shown
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A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder?
A. 10
B. 15
C. 30
D. 40
E. 60
[Reveal] Spoiler: OA
Last edited by Bunuel on 25 Jul 2013, 02:59, edited 1 time in total.
Renamed the topic, edited the question, added the OA and the image.
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### Show Tags
17 Aug 2010, 18:54
kwhitejr wrote:
FIGURE: Imagine a rectangle within a rectangle. Every side of the interior rectangle is 2 inches from the congruous side of the larger rectangle.
A rectangular picture is surrounded by a border, as shown in the figure above. Without the border the length of the picture is twice the width. If the area of the border is 196 square inches, what is the length, in inches, of the picture, excluding the border?
A. 10
B. 15
C. 30
D. 40
E. 60
Length of the outer rectangle - L, Breadth of the outer rectangle - B.
Length of the inner rectangle - l, Breadth of the inner rectangle - b.
Now given that - L*B = 196 sq. unit and l = 2b.
Also l = L - 4 and b = B - 4
Hence area of the outer rectangle (border area) = 196 - Area of the inner rectangle
(L * B) = 196 - (l*b)
((l+4) * (b+4)) = 196 - (l*b)
Simplifying => (lb + 4l + 4b + 16) = (196 - lb)
(4l + 4b) = 180
(4(2b) + 4b) = 180
12b = 180
b = 15, l = 30.
Hence the length of the inner rectangle or picture is 30 units. Answer C.
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### Show Tags
17 Aug 2010, 19:15
Ans : C
Assume the length of inner rectangle as L and the width as w then L = 2W
so the length of outer rectange will be L+4 and width as W+4
The area of border is
area of outer rectangle - area of inner rectangle
[(L+4)*(W+4)]- [ L * W] =196
4L +4W +16 = 196
substituting L = 2W we get
12W = 180
W= 15
L = 2W = 30
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25 Jul 2013, 02:55
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How to attach a picture to the first post?
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25 Jul 2013, 03:00
Expert's post
thewind wrote:
How to attach a picture to the first post?
Done. Thank you. +1.
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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26 Jul 2013, 23:37
In border area there are 4 square , two simillar rectangle and two another similar rectangle
L= length of inner rectangle, l= width of inner rectangle
Given L= 2l ,
Border area 196= 4 square ( 2*2) + 2 rectangle (2*l)+ 2 rectangle (2*L)
196= 16+ 2*L+ 2*L + L/2*2+L/2*2
180=6L
L= 30.
Hope the approach is correct
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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29 Oct 2013, 03:02
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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03 Jun 2015, 15:48
Expert's post
Hi All,
Many Test Takers would use an algebraic approach to solving this problem (which is fine). Since the prompt asks for the length of the picture and the answer are NUMBERS, we can TEST THE ANSWERS.
We're given some facts to work with:
1) The length of the picture is TWICE its width
2) The area of the BORDER is 196 sq. inches
3) The border "adds 4" to the length and width of the picture
We're asked for the LENGTH of the picture.
Since the Length is TWICE the width, chances are that we're looking for an answer that is TWICE another answer (which means either 30 & 15 or 60 & 30).
IF.....
Length = 30
Width = 15
Area of picture = 450
Total Length = 34
Total Width = 19
Total area = 646
Total area - picture area = 646 - 450 = 196. This is a MATCH for what we were told, so this MUST be the answer.
[Reveal] Spoiler:
C
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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6480 Location: Pune, India Followers: 1760 Kudos [?]: 10497 [2] , given: 206 Re: A rectangular picture is surrounded by a boarder, as shown [#permalink] ### Show Tags 03 Jun 2015, 21:26 2 This post received KUDOS Expert's post kwhitejr wrote: Attachment: Rectangular.jpg A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A. 10 B. 15 C. 30 D. 40 E. 60 Here is a 20 second estimation method: Say the width of the picture is b. Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it. 12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40. The only option is (C) Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches. So 12b = 196 - 16 = 180 b = 15 So length = 30 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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04 Jun 2015, 00:37
C
(l+4) (b+4) - lb = 196
l+b = 45
if l=2b then b=15 and l=30
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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07 Jun 2015, 03:47
VeritasPrepKarishma wrote:
kwhitejr wrote:
Attachment:
Rectangular.jpg
A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder?
A. 10
B. 15
C. 30
D. 40
E. 60
Here is a 20 second estimation method:
Say the width of the picture is b.
Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it.
12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40.
The only option is (C)
Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches.
So 12b = 196 - 16 = 180
b = 15
So length = 30
Hi karishma,
I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b.
Can you please explain this in detail.
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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08 Jun 2015, 07:56
Expert's post
akhil911 wrote:
VeritasPrepKarishma wrote:
kwhitejr wrote:
Attachment:
The attachment Rectangular.jpg is no longer available
A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder?
A. 10
B. 15
C. 30
D. 40
E. 60
Here is a 20 second estimation method:
Say the width of the picture is b.
Area of the frame can be approximated to 2*b + 2*b + 2*2b + 2*2b = 12b. Some area is left out here. Ignore it.
12b is a bit less than 196 so b would be more than 10 but less than 20. So length is more than 20 but less than 40.
The only option is (C)
Alternatively, if you want to find the exact value, the area of the left out region is 4 squares of 2*2 i.e. 16 square inches.
So 12b = 196 - 16 = 180
b = 15
So length = 30
Hi karishma,
I did not understand how you can approximate area of the frame as 2*b + 2*b + 2*2b + 2*2b = 12b.
Can you please explain this in detail.
Attachment:
Approx Area.jpg [ 332.5 KiB | Viewed 1459 times ]
The shaded region is approximately 2b + 2b + 4b + 4b. The four little squares (with question marks) is the only area unaccounted for.
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Re: A rectangular picture is surrounded by a boarder, as shown [#permalink]
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23 Jun 2015, 06:10
Hey,
I started with calculating the area of the frame.
The small corners (red rectangles): We know that the frame is 2 wide from every side. So each of the red rectangles will have an area of 2^2 = 4. We have four of those, so 4*4 = 16.
The green rectangles: 2*2w = 4w. We have two of those, so 2*4w = 8w.
The black (remaining two rectangles): 2*w = 2w. We have two of those, so 2*2w = 4w.
Adding the different areas gives as the total frame area: 16 + 12w
From the stem we know that 16 + 12w = 196.
So, w = 15 and the length is 30.
Attachments
frame.png [ 5.87 KiB | Viewed 1299 times ]
Re: A rectangular picture is surrounded by a boarder, as shown [#permalink] 23 Jun 2015, 06:10
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https://forum.mysensors.org/topic/11421/read-the-digoo-dg-r8h-temp-humidity-sensor/3
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# Read the Digoo DG-R8H temp/humidity sensor
• Hi there all,
I know that usually all the node is maked by DIY... and there is some that are really greate.
But before knowing MySensore I have bought 8 pieces of Digoo DG-R8H sensors.
This one are really nice at less than 4 Euro. But have not display
I make it work using OpenMqttGateway but I want to try the MySensors also if possible.
So is there anyone that have use this sensors please ?
Thanks all
Denis
• @DenisJ these sensors are not compatible with mysensors. You can however setup a separate mysensors network and run these at the same time.
• Yes in the mean time I understand that MySensor have all the personalized ask/answer structure.
But I still study cause I like much this type of home network.
Anyway maybe there can be a personalized gateway part only for the incompatible sensors.
I'll try to study it when I'll be more "old" in this
Thanks a lot for the answer
Denis
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http://www.gnu.org/software/gsl/manual/html_node/Vector-operations.html
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Next: , Previous: Exchanging elements, Up: Vectors [Index]
#### 8.3.8 Vector operations
Function: int gsl_vector_add (gsl_vector * a, const gsl_vector * b)
This function adds the elements of vector b to the elements of vector a. The result a_i \leftarrow a_i + b_i is stored in a and b remains unchanged. The two vectors must have the same length.
Function: int gsl_vector_sub (gsl_vector * a, const gsl_vector * b)
This function subtracts the elements of vector b from the elements of vector a. The result a_i \leftarrow a_i - b_i is stored in a and b remains unchanged. The two vectors must have the same length.
Function: int gsl_vector_mul (gsl_vector * a, const gsl_vector * b)
This function multiplies the elements of vector a by the elements of vector b. The result a_i \leftarrow a_i * b_i is stored in a and b remains unchanged. The two vectors must have the same length.
Function: int gsl_vector_div (gsl_vector * a, const gsl_vector * b)
This function divides the elements of vector a by the elements of vector b. The result a_i \leftarrow a_i / b_i is stored in a and b remains unchanged. The two vectors must have the same length.
Function: int gsl_vector_scale (gsl_vector * a, const double x)
This function multiplies the elements of vector a by the constant factor x. The result a_i \leftarrow x a_i is stored in a.
Function: int gsl_vector_add_constant (gsl_vector * a, const double x)
This function adds the constant value x to the elements of the vector a. The result a_i \leftarrow a_i + x is stored in a.
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https://human.libretexts.org/Courses/College_of_the_Canyons/English_101%3A_Grammar_Guide_(Kaiserman)/02%3A_Syntax/2.3%3A_Compound_Sentences_-_Joining_Clauses_with_Coordination
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2.3: Compound Sentences - Joining Clauses with Coordination
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A compound sentence consists of two independent clauses joined by coordination. Coordination connects the two clauses in a way that emphasizes both clauses equally. Consider these two sentences:
Original sentences: I spent my entire paycheck last week. I am staying home this weekend.
In their current form, these sentences contain two separate ideas that may or may not be related. Am I staying home this week because I spent my paycheck, or is there another reason for my lack of enthusiasm to leave the house? To indicate a relationship between the two ideas, we can use the coordinating conjunction so:
Revised sentence: I spent my entire paycheck last week, so I am staying home this weekend.
The revised sentence illustrates that the two ideas are connected. Notice that the sentence retains two independent clauses (I spent my entire paycheck; I am staying home this weekend) because each can stand alone as a complete idea.
Coordinating Conjunctions
A coordinating conjunction is a word that joins two independent clauses. The most common coordinating conjunctions are for, and, nor, but, or, yet, and so. Note that a comma precedes the coordinating conjunction when it joins two independent clauses.
Table $$\PageIndex{1}$$: Coordinating Conjunctions
Independent Clause
Coordinating Conjunction
Independent Clause
Revised Sentence
I will not be attending the dance.
For (indicates a reason or cause)
I have no one to go with.
I will not be attending the dance, for I have no one to go with.
Posters announcing the dance are everywhere.
And (joins to ideas)
Teachers have talked about it in class.
Posters announcing the dance are everywhere, and teachers have talked about it in class.
Jessie isn’t going to be at the dance.
Nor (indicates a negative)
Tom won’t be there either.
Jessie isn’t going to be at the dance, nor will Tom be there.
The fundraisers are hoping for a record-breaking attendance.
But, yet (both words indicate a contrast; but is more commonly used)
I don’t think many people are going.
The fundraisers are hoping for a record-breaking attendance, but I don’t think many people are going.
OR
The fundraisers are hoping for a record breaking attendance, yet I don’t think many people are going.
I might go to the next fundraising event.
Or (offers an alternative)
I might donate some money to the cause.
I might go to the next fundraising event, or I might donate some money to the cause.
Buying a new Dress is expensive.
So (indicates a result)
By staying home I will save money.
Buying a new dress is expensive, so by staying home I will save money.
Tip
To help you remember the seven coordinating conjunctions, think of the acronym FANBOYS: for, and, nor, but, or, yet, so. Remember that when you use a coordinating conjunction to connect independent clauses, a comma should precede the conjunction. (Exception: the comma is sometimes left out when the clauses are short and closely related. Example: John drove and I gave directions.)
Another method of joining two independent clauses with related and equal ideas is to use a conjunctive adverb and a semicolon. Like coordinating conjunctions, conjunctive adverbs can join independent clauses and indicate a particular relationship between them, but conjunctive adverbs create a stronger break between the clauses than coordinating conjunction do. Read the following sentences:
Original sentences: Bridget wants to take part in the next Olympics. She trains every day.
Since these sentences contain two equal and related ideas, they may be joined using a conjunctive adverb. Now, read the revised sentence:
Revised sentence: Bridget wants to take part in the next Olympics; therefore, she trains every day.
The revised sentence explains the relationship between Bridget’s desire to take part in the next Olympics and her daily training. Notice that the conjunctive adverb comes after a semicolon that separates the two clauses and is followed by a comma. The table below lists common conjunctive adverbs and demonstrates their function.
Table $$\PageIndex{2}$$: Conjunctive Adverbs
Function
Example
Also, furthermore, moreover, besides
Alicia was late for class and stuck in traffic; furthermore, her shoe heel had broken and she had forgotten her lunch.
Comparison
similarly, likewise
Recycling aluminum cans is beneficial to the environment; similarly, reusing plastic bags and switching off lights reduces waste.
Contrast
Most people do not walk to work; instead, they drive or take the train.
Emphasis
namely, certainly, indeed
The Siberian tiger is a rare creature; indeed, there are fewer than five hundred left in the wild.
Cause and Effect
accordingly, consequently, hence, thus
I missed my train this morning; consequently, I was late for my meeting.
Time
finally, next, subsequently, then
Tim crossed the barrier, jumped over the wall, and pushed through the hole in the fence; finally, he made it to the station.
Exercise
Combine each sentence pair into a single sentence using either a coordinating conjunction or a conjunctive adverb:
1. Pets are not allowed in Mr. Taylor’s building. He owns several cats and a parrot.
2. New legislation prevents drivers from sending or reading text messages while driving. Many people continue to use their phones illegally.
3. The coroner concluded that the young man had taken a lethal concoction of drugs. By the time his relatives found him, nothing could be done.
4. Amphibians are vertebrates that live on land and in the water. Flatworms are invertebrates that live only in water.
5. Ashley carefully fed and watered her tomato plants all summer. The tomatoes grew juicy and ripe.
6. When he lost his car key, Simon attempted to open the door with a wire hanger, a credit card, and a paper clip. He called the manufacturer for advice.
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https://blog.catprosystems.com/commit-logs/postgresql-10.13/
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# PostgreSQL 10.13 commit log
## Stamp 10.13.
commit : a411361705cdf0c0d63d1de231d7ea33a030b4f9
author : Tom Lane <[email protected]>
date : Mon, 11 May 2020 17:12:38 -0400
committer: Tom Lane <[email protected]>
date : Mon, 11 May 2020 17:12:38 -0400
M configure
M configure.in
M doc/bug.template
M src/include/pg_config.h.win32
M src/interfaces/libpq/libpq.rc.in
M src/port/win32ver.rc
## Translation updates
commit : ce0bbdda3e3c2101efbb0a8915e9d057606059dc
author : Peter Eisentraut <[email protected]>
date : Mon, 11 May 2020 13:26:52 +0200
committer: Peter Eisentraut <[email protected]>
date : Mon, 11 May 2020 13:26:52 +0200
Source-Git-URL: https://git.postgresql.org/git/pgtranslation/messages.git
Source-Git-Hash: 7176d722099b6a56e0aec6f32a195ff77babe844
M src/backend/po/de.po
M src/backend/po/es.po
M src/backend/po/ru.po
M src/backend/po/sv.po
M src/bin/pg_dump/po/de.po
M src/bin/pg_dump/po/fr.po
M src/bin/pg_dump/po/ru.po
M src/bin/pg_dump/po/sv.po
M src/bin/psql/po/ru.po
M src/bin/psql/po/sv.po
M src/bin/scripts/po/de.po
M src/bin/scripts/po/fr.po
M src/bin/scripts/po/ru.po
M src/bin/scripts/po/sv.po
M src/pl/plpgsql/src/po/ru.po
## Release notes for 12.3, 11.8, 10.13, 9.6.18, 9.5.22.
commit : 65b58d98916b55697230c53d053cb2a3defb7d7a
author : Tom Lane <[email protected]>
date : Sun, 10 May 2020 15:06:00 -0400
committer: Tom Lane <[email protected]>
date : Sun, 10 May 2020 15:06:00 -0400
M doc/src/sgml/release-10.sgml
## Prevent archive recovery from scanning non-existent WAL files.
commit : 660f1fc40d7a09e9486284d0858168703b9adf11
author : Fujii Masao <[email protected]>
date : Wed, 8 Apr 2020 00:49:29 +0900
committer: Fujii Masao <[email protected]>
date : Wed, 8 Apr 2020 00:49:29 +0900
Previously when there were multiple timelines listed in the history file
of the recovery target timeline, archive recovery searched all of them,
starting from the newest timeline to the oldest one, to find the segment
the segment until it reached the timeline that the segment belonged to.
These scans for non-existent segment could be harmful on the recovery
performance especially when archival area was located on the remote
storage and each scan could take a long time.
To address the issue, this commit changes archive recovery so that
it skips scanning the timeline that the segment to read doesn't belong to.
Per discussion, back-patch to all supported versions.
Author: Kyotaro Horiguchi, tweaked a bit by Fujii Masao
Reviewed-by: David Steele, Pavel Suderevsky, Grigory Smolkin
Discussion: https://postgr.es/m/[email protected]
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/transam/xlog.c
## pg_restore: Provide file name with one failure message
commit : f8635747ee9c07844819075675b2c5c07a7e016e
author : Alvaro Herrera <[email protected]>
date : Fri, 8 May 2020 19:38:46 -0400
committer: Alvaro Herrera <[email protected]>
date : Fri, 8 May 2020 19:38:46 -0400
Almost all error messages already include file name where relevant, but
this one had been overlooked. Repair.
Backpatch to 9.5.
Discussion: https://postgr.es/m/CAH503wA_VOrcKL_43p9atRejCDYmOZ8MzfK9S6TJrQqBqNeAXA@mail.gmail.com
Reviewed-by: Álvaro Herrera <[email protected]>
M src/bin/pg_dump/pg_backup_directory.c
## Fix inconsistency in pg_buffercache docs.
commit : b50712ba7530361a345ae01e5d929b3e6f46a0dc
author : Amit Kapila <[email protected]>
date : Fri, 8 May 2020 09:07:14 +0530
committer: Amit Kapila <[email protected]>
date : Fri, 8 May 2020 09:07:14 +0530
Commit 6e654546fb avoids locking bufmgr partitions to make pg_buffercache
less disruptive on production systems but forgot to update the docs.
Reviewed-by: Amit Kapila
Backpatch-through: 10
Discussion: https://postgr.es/m/CA+fd4k6sD8oeP1qJbFAor=rCpYckU9DsywHiYx3x5Hz5Z8Ua_w@mail.gmail.com
M doc/src/sgml/pgbuffercache.sgml
## Report missing wait event for timeline history file.
commit : 3a48740e898c7586d119bd821572265418ad7b43
author : Fujii Masao <[email protected]>
date : Fri, 8 May 2020 10:36:40 +0900
committer: Fujii Masao <[email protected]>
date : Fri, 8 May 2020 10:36:40 +0900
TimelineHistoryRead and TimelineHistoryWrite wait events are reported
during waiting for a read and write of a timeline history file, respectively.
However, previously, TimelineHistoryRead wait event was not reported
TimelineHistoryWrite was not reported while writeTimeLineHistory() was
writing one line with the details of the timeline split, at the end.
This commit fixes these issues.
Back-patch to v10 where wait events for a timeline history file was added.
Author: Masahiro Ikeda
Reviewed-by: Michael Paquier, Fujii Masao
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/transam/timeline.c
## Fix YA text phrase search bug.
commit : 26cf16a9336101504c17e4bf7f6b6208c71bfa47
author : Tom Lane <[email protected]>
date : Thu, 7 May 2020 15:59:52 -0400
committer: Tom Lane <[email protected]>
date : Thu, 7 May 2020 15:59:52 -0400
checkcondition_str() failed to report multiple matches for a prefix
pattern correctly: it would dutifully merge the match positions, but
then after exiting that loop, if the last prefix-matching word had
had no suitable positions, it would report there were no matches.
The upshot would be failing to recognize a match that the query
should match.
It looks like you need all of these conditions to see the bug:
* a phrase search (else we don't ask for match position details)
* a prefix search item (else we don't get to this code)
* a weight restriction (else checkclass_str won't fail)
Noted while investigating a problem report from Pavel Borisov,
though this is distinct from the issue he was on about.
Back-patch to 9.6 where phrase search was added.
M src/test/regress/expected/tstypes.out
M src/test/regress/sql/tstypes.sql
## Heed lock protocol in DROP OWNED BY
commit : 4d21263fffd2d5aebeb2e52dbaaa31d3ba16d51e
author : Alvaro Herrera <[email protected]>
date : Wed, 6 May 2020 12:29:41 -0400
committer: Alvaro Herrera <[email protected]>
date : Wed, 6 May 2020 12:29:41 -0400
We were acquiring object locks then deleting objects one by one, instead
of acquiring all object locks first, ignoring those that did not exist,
and then deleting all objects together. The latter is the correct
protocol to use, and what this commits changes to code to do. Failing
to follow that leads to "cache lookup failed for relation XYZ" error
reports when DROP OWNED runs concurrently with other DDL -- for example,
a session termination that removes some temp tables.
Author: Álvaro Herrera
Reported-by: Mithun Chicklore Yogendra (Mithun CY)
Discussion: https://postgr.es/m/CADq3xVZTbzK4ZLKq+dn_vB4QafXXbmMgDP3trY-GuLnib2Ai1w@mail.gmail.com
M src/backend/catalog/dependency.c
M src/backend/catalog/pg_shdepend.c
M src/backend/commands/subscriptioncmds.c
M src/include/catalog/dependency.h
## Handle spaces for Python install location in MSVC scripts
commit : 307ed98b01394488b9bd1dfa7a851a219c7e27ab
author : Michael Paquier <[email protected]>
date : Wed, 6 May 2020 21:08:31 +0900
committer: Michael Paquier <[email protected]>
date : Wed, 6 May 2020 21:08:31 +0900
Attempting to use an installation path of Python that includes spaces
caused the MSVC builds to fail. This fixes the issue by using the same
quoting method as ad7595b for OpenSSL.
Author: Victor Wagner
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M src/tools/msvc/Mkvcbuild.pm
## Get rid of trailing semicolons in C macro definitions.
commit : 49718aa9ee5ee9a667cdd50e659687490716c94a
author : Tom Lane <[email protected]>
date : Fri, 1 May 2020 17:28:01 -0400
committer: Tom Lane <[email protected]>
date : Fri, 1 May 2020 17:28:01 -0400
Writing a trailing semicolon in a macro is almost never the right thing,
because you almost always want to write a semicolon after each macro
call instead. (Even if there was some reason to prefer not to, pgindent
would probably make a hash of code formatted that way; so within PG the
rule should basically be "don't do it".) Thus, if we have a semi inside
the macro, the compiler sees "something;;". Much of the time the extra
empty statement is harmless, but it could lead to mysterious syntax
errors at call sites. In perhaps an overabundance of neatnik-ism, let's
run around and get rid of the excess semicolons whereever possible.
The only thing worse than a mysterious syntax error is a mysterious
syntax error that only happens in the back branches; therefore,
backpatch these changes where relevant, which is most of them because
most of these mistakes are old. (The lack of reported problems shows
that this is largely a hypothetical issue, but still, it could bite
us in some future patch.)
John Naylor and Tom Lane
Discussion: https://postgr.es/m/CACPNZCs0qWTqJ2QUSGJ07B7uvAvzMb-KbG2q+oo+J3tsWN5cqw@mail.gmail.com
M contrib/btree_gist/btree_ts.c
M contrib/btree_gist/btree_utils_num.h
M contrib/pg_trgm/trgm.h
M contrib/pgcrypto/crypt-blowfish.c
M src/backend/utils/sort/gen_qsort_tuple.pl
M src/bin/pg_dump/pg_backup_archiver.h
M src/include/access/nbtree.h
M src/port/qsort.c
M src/port/qsort_arg.c
## Fix full text search to handle NOT above a phrase search correctly.
commit : 072a863275e93147cf5987b915815e041322b8be
author : Tom Lane <[email protected]>
date : Mon, 27 Apr 2020 12:21:04 -0400
committer: Tom Lane <[email protected]>
date : Mon, 27 Apr 2020 12:21:04 -0400
Queries such as '!(foo<->bar)' failed to find matching rows when
implemented as a GiST or GIN index search. That's because of
failing to handle phrase searches as tri-valued when considering
a query without any position information for the target tsvector.
We can only say that the phrase operator might match, not that it
does match; and therefore its NOT also might match. The previous
coding incorrectly inverted the approximate phrase result to
decide that there was certainly no match.
To fix, we need to make TS_phrase_execute return a real ternary result,
and then bubble that up accurately in TS_execute. As long as we have
to do that anyway, we can simplify the baroque things TS_phrase_execute
was doing internally to manage tri-valued searching with only a bool
as explicit result.
For now, I left the externally-visible result of TS_execute as a plain
bool. There do not appear to be any outside callers that need to
distinguish a three-way result, given that they passed in a flag
saying what to do in the absence of position data. This might need
to change someday, but we wouldn't want to back-patch such a change.
Although tsginidx.c has its own TS_execute_ternary implementation for
use at upper index levels, that sadly managed to get this case wrong
as well :-(. Fixing it is a lot easier fortunately.
Per bug #16388 from Charles Offenbacher. Back-patch to 9.6 where
phrase search was introduced.
Discussion: https://postgr.es/m/[email protected]
M src/test/regress/data/tsearch.data
M src/test/regress/expected/tsearch.out
M src/test/regress/expected/tstypes.out
M src/test/regress/sql/tsearch.sql
M src/test/regress/sql/tstypes.sql
## Fix error case for CREATE ROLE ... IN ROLE.
commit : 287f6d2d96ddca279518348f88667d9ef10028b5
date : Sat, 25 Apr 2020 05:10:13 +0100
date : Sat, 25 Apr 2020 05:10:13 +0100
CreateRole() was passing a Value node, not a RoleSpec node, for the
newly-created role name when adding the role as a member of existing
roles for the IN ROLE syntax.
This mistake went unnoticed because the node in question is used only
for error messages and is not accessed on non-error paths.
In older pg versions (such as 9.5 where this was found), this results
in an "unexpected node type" error in place of the real error. That
node type check was removed at some point, after which the code would
accidentally fail to fail on 64-bit platforms (on which accessing the
Value node as if it were a RoleSpec would be mostly harmless) or give
an "unexpected role type" error on 32-bit platforms.
Fix the code to pass the correct node type, and add an lfirst_node
assertion just in case.
Per report on irc from user m1chelangelo.
Backpatch all the way, because this error has been around for a long
time.
M src/backend/commands/user.c
## Update Windows timezone name list to include currently-known zones.
commit : 40d4bc5acd0aeaf4fbbd4716a22f998b2580f42b
author : Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 17:53:23 -0400
committer: Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 17:53:23 -0400
Thanks to Juan José Santamaría Flecha.
Discussion: https://postgr.es/m/[email protected]
M src/bin/initdb/findtimezone.c
M src/tools/win32tzlist.pl
## Improve placement of "display name" comment in win32_tzmap[] entries.
commit : 4985b3b84918025f65b268df08d00c214411ebff
author : Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 17:21:44 -0400
committer: Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 17:21:44 -0400
Sticking this comment at the end of the last line was a bad idea: it's
not particularly readable, and it tempts pgindent to mess with line
breaks within the comment, which in turn reveals that win32tzlist.pl's
clean_displayname() does the wrong thing to clean up such line breaks.
While that's not hard to fix, there's basically no excuse for this
arrangement to begin with, especially since it makes the table layout
needlessly vary across back branches with different pgindent rules.
Let's just put the comment inside the braces, instead.
win32tzlist.pl to match; there's no actual data change.
Per odd-looking results from Juan José Santamaría Flecha.
Back-patch, since the point is to make win32_tzmap[] look the
same in all supported branches again.
Discussion: https://postgr.es/m/[email protected]
M src/bin/initdb/findtimezone.c
M src/tools/win32tzlist.pl
## Update time zone data files to tzdata release 2020a.
commit : 898921a18959a1c2e5a960ae13642462d7a74393
author : Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 10:54:47 -0400
committer: Tom Lane <[email protected]>
date : Fri, 24 Apr 2020 10:54:47 -0400
DST law changes in Morocco and the Canadian Yukon.
Historical corrections for Shanghai.
The America/Godthab zone is renamed to America/Nuuk to reflect
current English usage; however, the old name remains available as a
compatibility link.
M src/timezone/data/tzdata.zi
## Remove some unstable parts from new TAP test for archive status check
commit : 3d9cae5adb1668212c9816777849c7577dcaf346
author : Michael Paquier <[email protected]>
date : Fri, 24 Apr 2020 11:34:06 +0900
committer: Michael Paquier <[email protected]>
date : Fri, 24 Apr 2020 11:34:06 +0900
The test is proving to have timing issues when looking at archive status
files on standbys after crash recovery, while other parts of the test
rely on pg_stat_archiver as a wait point to make sure that a given state
of the archiving is reached. The coverage is not heavily impacted by
the removal those extra tests.
Per reports from several buildfarm animals, like crake, piculet,
culicidae and francolin.
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M src/test/recovery/t/020_archive_status.pl
## Fix handling of WAL segments ready to be archived during crash recovery
commit : 02657c42199cd992eedc99a9cbc1f2c43ad5b208
author : Michael Paquier <[email protected]>
date : Fri, 24 Apr 2020 08:48:45 +0900
committer: Michael Paquier <[email protected]>
date : Fri, 24 Apr 2020 08:48:45 +0900
78ea8b5 has fixed an issue related to the recycling of WAL segments on
standbys depending on archive_mode. However, it has introduced a
regression with the handling of WAL segments ready to be archived during
crash recovery, causing those files to be recycled without getting
archived.
This commit fixes the regression by tracking in shared memory if a live
cluster is either in crash recovery or archive recovery as the handling
of WAL segments ready to be archived is different in both cases (those
WAL segments should not be removed during crash recovery), and by using
this new shared memory state to decide if a segment can be recycled or
not. Previously, it was not possible to know if a cluster was in crash
recovery or archive recovery as the shared state was able to track only
if recovery was happening or not, leading to the problem.
A set of TAP tests is added to close the gap here, making sure that WAL
segments ready to be archived are correctly handled when a cluster is in
archive or crash recovery with archive_mode set to "on" or "always", for
both standby and primary.
Reported-by: Benoît Lobréau
Author: Jehan-Guillaume de Rorthais
Reviewed-by: Kyotaro Horiguchi, Fujii Masao, Michael Paquier
Discussion: https://postgr.es/m/20200331172229.40ee00dc@firost
Backpatch-through: 9.5
M src/backend/access/transam/xlog.c
M src/backend/access/transam/xlogarchive.c
M src/include/access/xlog.h
A src/test/recovery/t/020_archive_status.pl
## docs: land height is "elevation", not "altitude"
commit : b0b216853883d2384c70fff66cae26b7d54cbc16
author : Bruce Momjian <[email protected]>
date : Wed, 22 Apr 2020 16:23:19 -0400
committer: Bruce Momjian <[email protected]>
date : Wed, 22 Apr 2020 16:23:19 -0400
See https://mapscaping.com/blogs/geo-candy/what-is-the-difference-between-elevation-relief-and-altitude
No patching of regression tests.
Reported-by: [email protected]
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/ddl.sgml
## Fix memory leak in libpq when using sslmode=verify-full
commit : 1bb0293d844538ee39b14a7965a9ea7e10dcae93
author : Michael Paquier <[email protected]>
date : Wed, 22 Apr 2020 07:27:53 +0900
committer: Michael Paquier <[email protected]>
date : Wed, 22 Apr 2020 07:27:53 +0900
Checking if Subject Alternative Names (SANs) from a certificate match
with the hostname connected to leaked memory after each lookup done.
This is broken since acd08d7 that added support for SANs in SSL
certificates, so backpatch down to 9.5.
Author: Roman Peshkurov
Reviewed-by: Hamid Akhtar, Michael Paquier, David Steele
Discussion: https://postgr.es/m/CALLDf-pZ-E3mjxd5=bnHsDu9zHEOnpgPgdnO84E2RuwMCjjyPw@mail.gmail.com
Backpatch-through: 9.5
M src/interfaces/libpq/fe-secure-openssl.c
## Fix possible crash during FATAL exit from reindexing.
commit : e6c17c85ac9e5c6ff2c4feeca913216baeb5afb6
author : Tom Lane <[email protected]>
date : Tue, 21 Apr 2020 15:58:42 -0400
committer: Tom Lane <[email protected]>
date : Tue, 21 Apr 2020 15:58:42 -0400
index.c supposed that it could just use a PG_TRY block to clean up the
state associated with an active REINDEX operation. However, that code
doesn't run if we do a FATAL exit --- for example, due to a SIGTERM
shutdown signal --- while the REINDEX is happening. And that state does
get consulted during catalog accesses, which makes it problematic if we
do any catalog accesses during shutdown --- for example, to clean up any
temp tables created in the session.
If this combination of circumstances occurred, we could find ourselves
trying to access already-freed memory. In debug builds that'd fairly
reliably cause an assertion failure. In production we might often
get away with it, but with some bad luck it could cause a core dump.
Another possible bad outcome is an erroneous conclusion that an
index-to-be-accessed is being reindexed; but it looks like that would
be unlikely to have any consequences worse than failing to drop temp
tables right away. (They'd still get dropped by the next session that
uses that temp schema.)
To fix, get rid of the use of PG_TRY here, and instead hook into
the transaction abort mechanisms to clean up reindex state.
Per bug #16378 from Alexander Lakhin. This has been wrong for a
very long time, so back-patch to all supported branches.
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/transam/xact.c
M src/backend/catalog/index.c
M src/include/catalog/index.h
## Fix minor violations of FunctionCallInvoke usage protocol.
commit : 0d0a0e4c253eb0f5220f9fe8296cdeac0daae662
author : Tom Lane <[email protected]>
date : Tue, 21 Apr 2020 14:23:42 -0400
committer: Tom Lane <[email protected]>
date : Tue, 21 Apr 2020 14:23:42 -0400
Working on commit 1c455078b led me to check through FunctionCallInvoke
call sites to see if every one was being honest about (a) making sure
that fcinfo.isnull is initially false, and (b) checking its state after
the call. Sure enough, I found some violations.
The main one is that finalize_partialaggregate re-used serialfn_fcinfo
without resetting isnull, even though it clearly intends to cater for
serialfns that return NULL. There would only be an issue with a
non-strict serialfn, since it's unlikely that a serialfn would return
NULL for non-null input. We have no non-strict serialfns in core, and
there may be none in the wild either, which would account for the lack
of complaints. Still, it's clearly wrong, so back-patch that fix to
9.6 where finalize_partialaggregate was introduced.
Also, arrayfuncs.c and rowtypes.c contained various callers that were
not bothering to check for result nulls. While what's being called is
a comparison or hash function that probably *shouldn't* return null,
that's a lousy excuse for not having any check at all. There are
existing places that just Assert(!fcinfo->isnull) in comparable
situations, so I added that to the places that were calling btree
comparison or hash support functions. In the places calling
boolean-returning equality functions, it's quite cheap to have them
treat isnull as FALSE, so make those places do that. Also remove some
"locfcinfo->isnull = false" assignments that are unnecessary given the
assumption that no previous call returned null. These changes seem like
mostly neatnik-ism or debugging support, so I didn't back-patch.
M src/backend/executor/nodeAgg.c
M src/include/fmgr.h
## doc: change SGML markup "figure" to "example"
commit : de56dafeede6e64afac57aaaf5c505ee5de09ca4
author : Bruce Momjian <[email protected]>
date : Mon, 20 Apr 2020 21:41:13 -0400
committer: Bruce Momjian <[email protected]>
date : Mon, 20 Apr 2020 21:41:13 -0400
Reported-by: Jürgen Purtz
Discussion: https://postgr.es/m/[email protected]
Author: Jürgen Purtz
Backpatch-through: 9.5
M doc/src/sgml/func.sgml
## Allow pg_read_all_stats to access all stats views again
commit : d0bb66572e3326b40515cbf62ec11b3339bbf914
author : Magnus Hagander <[email protected]>
date : Mon, 20 Apr 2020 12:53:40 +0200
committer: Magnus Hagander <[email protected]>
date : Mon, 20 Apr 2020 12:53:40 +0200
The views pg_stat_progress_* had not gotten the memo that
make a pass over all text-returning pg_stat_xyz functions that could
return "insufficient privilege" and make sure they also respect
Reported-by: Andrey M. Borodin
Reviewed-by: Andrey M. Borodin, Kyotaro Horiguchi
Discussion: https://postgr.es/m/[email protected]
## Fix race conditions in synchronous standby management.
commit : 63ecdaf758c56c183ed76c02e169c9c5504e6693
author : Tom Lane <[email protected]>
date : Sat, 18 Apr 2020 14:02:44 -0400
committer: Tom Lane <[email protected]>
date : Sat, 18 Apr 2020 14:02:44 -0400
We have repeatedly seen the buildfarm reach the Assert(false) in
SyncRepGetSyncStandbysPriority. This apparently is due to failing to
consider the possibility that the sync_standby_priority values in
shared memory might be inconsistent; but they will be whenever only
some of the walsenders have updated their values after a change in
the synchronous_standby_names setting. That function is vastly too
complex for what it does, anyway, so rewriting it seems better than
trying to apply a band-aid fix.
Furthermore, the API of SyncRepGetSyncStandbys is broken by design:
it returns a list of WalSnd array indexes, but there is nothing
guaranteeing that the contents of the WalSnd array remain stable.
Thus, if some walsender exits and then a new walsender process
takes over that WalSnd array slot, a caller might make use of
WAL position data that it should not, potentially leading to
incorrect decisions about whether to release transactions that
are waiting for synchronous commit.
To fix, replace SyncRepGetSyncStandbys with a new function
SyncRepGetCandidateStandbys that copies all the required data
from shared memory while holding the relevant mutexes. If the
associated walsender process then exits, this data is still safe to
make release decisions with, since we know that that much WAL *was*
sent to a valid standby server. This incidentally means that we no
longer need to treat sync_standby_priority as protected by the
SyncRepLock rather than the per-walsender mutex.
SyncRepGetSyncStandbys is no longer used by the core code, so remove
it entirely in HEAD. However, it seems possible that external code is
relying on that function, so do not remove it from the back branches.
Instead, just remove the known-incorrect Assert. When the bug occurs,
the function will return a too-short list, which callers should treat
as meaning there are not enough sync standbys, which seems like a
reasonably safe fallback until the inconsistent state is resolved.
Moreover it's bug-compatible with what has been happening in non-assert
builds. We cannot do anything about the walsender-replacement race
condition without an API/ABI break.
The bogus assertion exists back to 9.6, but 9.6 is sufficiently
different from the later branches that the patch doesn't apply at all.
I chose to just remove the bogus assertion in 9.6, feeling that the
probability of a bad outcome from the walsender-replacement race
condition is too low to justify rewriting the whole patch for 9.6.
Discussion: https://postgr.es/m/[email protected]
M src/backend/replication/syncrep.c
M src/backend/replication/walsender.c
M src/include/replication/syncrep.h
M src/include/replication/walsender_private.h
## Use a slightly more liberal regex to detect Visual Studio version
commit : ddac64f2d6fbdf04529a85a05c52728175bf5c17
author : Andrew Dunstan <[email protected]>
date : Fri, 17 Apr 2020 14:55:55 -0400
committer: Andrew Dunstan <[email protected]>
date : Fri, 17 Apr 2020 14:55:55 -0400
Apparently in some language versions of Visual Studio nmake outputs some
material after the version number and before the end of the line. This
has been seen in Chinese versions. Therefore, we no longer demand that
the version string comes at the end of a line.
Per complaint from Cuiping Lin.
Backpatch to all live branches.
M src/tools/msvc/VSObjectFactory.pm
## Fix cache reference leak in contrib/sepgsql.
commit : f4a42005613bf279b4c1d203112c0583cbbf498e
author : Tom Lane <[email protected]>
date : Thu, 16 Apr 2020 14:45:54 -0400
committer: Tom Lane <[email protected]>
date : Thu, 16 Apr 2020 14:45:54 -0400
fixup_whole_row_references() did the wrong thing with a dropped column,
resulting in a commit-time warning about a cache reference leak.
I (tgl) added a test case exercising this, but back-patched the test
only as far as v10; the patch didn't apply cleanly to 9.6 and it
didn't seem worth the trouble to adapt it. The bug is pretty old
though, so apply the code change all the way back.
Michael Luo, with cosmetic improvements by me
Discussion: https://postgr.es/m/BYAPR08MB5606D1453D7F50E2AF4D2FD29AD80@BYAPR08MB5606.namprd08.prod.outlook.com
M contrib/sepgsql/dml.c
M contrib/sepgsql/expected/dml.out
M contrib/sepgsql/sql/dml.sql
## Fix minor memory leak in pg_dump
commit : e7887fe00db214b141a29f4298c7bb6536292a7e
author : Michael Paquier <[email protected]>
date : Wed, 15 Apr 2020 15:56:52 +0900
committer: Michael Paquier <[email protected]>
date : Wed, 15 Apr 2020 15:56:52 +0900
A query used to read default ACL information from the catalogs did not
free a set of PQExpBuffer.
Oversight in commit e2090d9, so backpatch down to 9.6.
Author: Jie Zhang
Discussion: https://postgr.es/m/05bcbc5857f948efa0b451b85a48ae10@G08CNEXMBPEKD06.g08.fujitsu.local
Backpatch-through: 9.6
M src/bin/pg_dump/pg_dump.c
## Repair last commit's new wait_for_catchup() call.
commit : aca51181baf9ec3ddcac6707bf6a6a5014f7543b
date : Mon, 13 Apr 2020 21:10:06 -0700
date : Mon, 13 Apr 2020 21:10:06 -0700
The function had a different API in v10. Per buildfarm.
M src/test/recovery/t/010_logical_decoding_timelines.pl
## Add a wait_for_catchup() before immediate stop of a test master.
commit : ab7699e86c161960c44b51d1a7e6d32784cf5299
date : Mon, 13 Apr 2020 18:47:28 -0700
date : Mon, 13 Apr 2020 18:47:28 -0700
Per buildfarm member hoverfly, a slow walsender could make the test
fail. Back-patch to v10, where the test was introduced.
Discussion: https://postgr.es/m/[email protected]
M src/test/recovery/t/010_logical_decoding_timelines.pl
## Clear dangling pointer to avoid bogus EXPLAIN printout in a corner case.
commit : 1e6bb6125f33eeb2e6cc00e6af8777bdbe9a3786
author : Tom Lane <[email protected]>
date : Sat, 11 Apr 2020 12:29:06 -0400
committer: Tom Lane <[email protected]>
date : Sat, 11 Apr 2020 12:29:06 -0400
ExecReScanHashJoin will destroy the join's hash table if it expects
that the inner relation will produce different rows on rescan.
Up to now it's not bothered to clear the additional pointer to that
hash table that exists in the child HashState node. However, it's
possible for the query to terminate without building a fresh hash
table (this happens if the outer relation is found to be empty
during the final rescan). So we can end with a dangling pointer
to a deleted hash table. That was harmless originally, but since
9.0 EXPLAIN ANALYZE has used that pointer to print hash table
statistics. In debug builds this reproducibly results in garbage
statistics. In non-debug builds there's frequently no ill effects,
but in principle one could get wrong EXPLAIN ANALYZE output, or
perhaps even a crash if free() has released the hashtable memory
back to the OS.
To fix, just make sure we clear the additional pointer when destroying
the hash table. In problematic cases, EXPLAIN ANALYZE will then print
no hashtable statistics (reverting to its pre-9.0 behavior). This isn't
ideal, but since the problem manifests only in unusual corner cases,
it's hard to justify taking any risks to do better in the back
branches. A follow-on patch will improve matters in HEAD.
Konstantin Knizhnik and Tom Lane, per diagnosis by Thomas Munro
of a trouble report from Alvaro Herrera.
Discussion: https://postgr.es/m/[email protected]
M src/backend/executor/nodeHashjoin.c
## Doc: clarify locking requirements for ALTER TABLE ADD FOREIGN KEY.
commit : 61a9b814c553439854e9515ecb6458f77402443a
author : Tom Lane <[email protected]>
date : Fri, 10 Apr 2020 13:12:58 -0400
committer: Tom Lane <[email protected]>
date : Fri, 10 Apr 2020 13:12:58 -0400
The docs explained that a SHARE ROW EXCLUSIVE lock is needed on the
referenced table, but failed to say the same about the table being
altered. Since the page says that ACCESS EXCLUSIVE lock is taken
unless otherwise stated, this left readers with the wrong conclusion.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/ref/alter_table.sgml
## Doc: sync CREATE GROUP syntax synopsis with CREATE ROLE.
commit : 8f111150e68a0560dae67dda628296d5a26817b7
author : Tom Lane <[email protected]>
date : Fri, 10 Apr 2020 10:44:10 -0400
committer: Tom Lane <[email protected]>
date : Fri, 10 Apr 2020 10:44:10 -0400
CREATE GROUP is an exact alias for CREATE ROLE, and CREATE USER is
almost an exact alias, as can easily be confirmed by checking the
code. So the man page syntax descriptions ought to match up. The
last few additions of role options seem to have forgotten to update
create_group.sgml, though. Fix that, and add a naggy reminder to
create_role.sgml in hopes of not forgetting again.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/ref/create_group.sgml
## Further cleanup of ts_headline code.
commit : 9be664d715ebcb7265c6f3e2bdba89de2b45d66c
author : Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 15:38:43 -0400
committer: Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 15:38:43 -0400
Suppress a probably-meaningless uninitialized-variable warning
(induced by my previous patch, I'm sorry to say).
Improve mark_hl_fragments()'s test for overlapping cover strings:
it failed to consider the possibility that the current string is
strictly within another one. That's unlikely given the preceding
splitting into MaxWords fragments, but I don't think it's impossible.
Discussion: https://postgr.es/m/[email protected]
M src/backend/tsearch/wparser_def.c
## Doc: improve documentation about ts_headline() function.
commit : 2971180929b6d3902ea31b3274929955b05e2f5e
author : Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 15:11:08 -0400
committer: Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 15:11:08 -0400
Now that I've had my nose in that code, I thought the docs about
it left something to be desired.
M doc/src/sgml/textsearch.sgml
## Fix default text search parser's ts_headline code for phrase queries.
commit : 5f7247b3ba6b7a7e92bcf2e15a6b75223c5d3dea
author : Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 13:19:23 -0400
committer: Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 13:19:23 -0400
This code could produce very poor results when asked to highlight a
string based on a query using phrase-match operators. The root cause
is that hlCover(), which is supposed to find a minimal substring that
matches the query, was written assuming that word position is not
significant. I'm only 95% convinced that its algorithm was correct even
for plain AND/OR queries; but it definitely fails completely for phrase
matches, causing it to possibly not identify a cover string at all.
Hence, rewrite hlCover() with a less-tense algorithm that just tries
all the possible substrings, earlier and shorter ones first. (This is
not as bad as it sounds performance-wise, because all of the string
matching has been done already: the repeated tsquery match checks
boil down to pointer comparisons.)
Unfortunately, since that approach produces more candidate cover
strings than before, it also exposes that there were bugs in the
heuristics in mark_hl_words() for selecting a best cover string.
Fixes there include:
* Do not apply the ShortWord filter to words that appear in the query.
* Remove a misguided optimization for quickly rejecting a cover.
* Fix order-of-operation bug that could cause computation of a
wrong figure of merit (poslen) when shortening a cover.
* Change the preference rule so that candidate headlines that do not
include their whole cover string (after MaxWords trimming) are lowest
priority, since they may not actually satisfy the user's query.
This results in some changes in existing regression test cases,
but they all seem reasonable. Note in particular that the tests
involving strings like "1 2 3" were previously being affected by
the ShortWord filter, masking the normal matching behavior.
Per bug #16345 from Augustinas Jokubauskas; the new test cases are
based on that example. Back-patch to 9.6 where phrase search was
Discussion: https://postgr.es/m/[email protected]
M src/backend/tsearch/wparser_def.c
M src/test/regress/expected/tsearch.out
M src/test/regress/sql/tsearch.sql
## Cosmetic improvements for default text search parser's ts_headline code.
commit : afab3998685f61d07c3ae05bf22fc5f2a0e92557
author : Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 12:37:00 -0400
committer: Tom Lane <[email protected]>
date : Thu, 9 Apr 2020 12:37:00 -0400
This code was woefully unreadable and under-commented. Try to improve
if-tests more readable, using boolean type where appropriate, etc.
There are a couple of tiny coding improvements too, but this commit
includes (I hope) no behavioral change.
Nonetheless, back-patch as far as 9.6, because a followup bug-fixing
commit depends on this.
Discussion: https://postgr.es/m/[email protected]
M src/backend/tsearch/wparser_def.c
## Fix pg_dump/pg_restore to restore event trigger comments later.
commit : 830471e0dcf67b12f229bfa9489643eb108f580f
author : Tom Lane <[email protected]>
date : Wed, 8 Apr 2020 11:23:39 -0400
committer: Tom Lane <[email protected]>
date : Wed, 8 Apr 2020 11:23:39 -0400
Repair an oversight in commit 8728b2c70: if we're postponing restore
of event triggers to the end, we must also postpone restoring any
comments on them, since of course we cannot create the comments first.
(This opens yet another opportunity for an event trigger to bollix
the restore, but there's no help for that.)
Per bug #16346 from Alexander Lakhin.
Like the previous commit, back-patch to all supported branches.
Hamid Akhtar and Tom Lane
Discussion: https://postgr.es/m/[email protected]
M src/bin/pg_dump/pg_backup_archiver.c
## Fix circle_in to accept "(x,y),r" as it's advertised to do.
commit : 4c7a311a2df9b3b91285def8de2e1308f90e9e21
author : Tom Lane <[email protected]>
date : Tue, 7 Apr 2020 20:50:02 -0400
committer: Tom Lane <[email protected]>
date : Tue, 7 Apr 2020 20:50:02 -0400
Our documentation describes four allowed input syntaxes for circles,
but the regression tests tried only three ... with predictable
consequences. Remarkably, this has been wrong since the circle
datatype was added in 1997, but nobody noticed till now.
David Zhang, with some help from me
Discussion: https://postgr.es/m/[email protected]
M src/test/regress/expected/circle.out
M src/test/regress/sql/circle.sql
## Adjust bytea get_bit/set_bit to cope with bytea strings > 256MB.
commit : 889786e0e8c1eba9e770d173bbef2244f67e72c9
author : Tom Lane <[email protected]>
date : Tue, 7 Apr 2020 16:30:55 -0400
committer: Tom Lane <[email protected]>
date : Tue, 7 Apr 2020 16:30:55 -0400
Since the existing bit number argument can't exceed INT32_MAX, it's
not possible for these functions to manipulate bits beyond the first
256MB of a bytea value. However, it'd be good if they could do at
least that much, and not fall over entirely for longer bytea values.
Adjust the comparisons to be done in int64 arithmetic so that works.
Also tweak the error reports to show sane values in case of overflow.
Also add some test cases to improve the miserable code coverage
of these functions.
Apply patch to back branches only; HEAD has a better solution
as of commit 26a944cf2.
Extracted from a much larger patch by Movead Li
Discussion: https://postgr.es/m/[email protected]
M src/test/regress/expected/strings.out
M src/test/regress/sql/strings.sql
## Preserve clustered index after rewrites with ALTER TABLE
commit : cef2b8d52c59168bf34c22bff0ed98fea7232981
author : Michael Paquier <[email protected]>
date : Mon, 6 Apr 2020 11:05:57 +0900
committer: Michael Paquier <[email protected]>
date : Mon, 6 Apr 2020 11:05:57 +0900
A table rewritten by ALTER TABLE would lose tracking of an index usable
for CLUSTER. This setting is tracked by pg_index.indisclustered and is
controlled by ALTER TABLE, so some extra work was needed to restore it
properly. Note that ALTER TABLE only marks the index that can be used
for clustering, and does not do the actual operation.
Author: Amit Langote, Justin Pryzby
Reviewed-by: Ibrar Ahmed, Michael Paquier
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M src/backend/commands/tablecmds.c
M src/backend/utils/cache/lsyscache.c
M src/include/utils/lsyscache.h
M src/test/regress/expected/alter_table.out
M src/test/regress/sql/alter_table.sql
## Use TransactionXmin instead of RecentGlobalXmin in heap_abort_speculative().
commit : 0e708d3115958ffcd8e91123f405dc482871abf6
author : Andres Freund <[email protected]>
date : Sun, 5 Apr 2020 17:47:30 -0700
committer: Andres Freund <[email protected]>
date : Sun, 5 Apr 2020 17:47:30 -0700
There's a very low risk that RecentGlobalXmin could be far enough in
the past to be older than relfrozenxid, or even wrapped
around. Luckily the consequences of that having happened wouldn't be
too bad - the page wouldn't be pruned for a while.
Avoid that risk by using TransactionXmin instead. As that's announced
via MyPgXact->xmin, it is protected against wrapping around (see code
Author: Andres Freund
Discussion: https://postgr.es/m/[email protected]
Backpatch: 9.5-
M src/backend/access/heap/heapam.c
## Save errno across LWLockRelease() calls
commit : 038c9bbe9b6193cf8eeea3f7485134ef17fd947b
author : Peter Eisentraut <[email protected]>
date : Sun, 5 Apr 2020 10:02:00 +0200
committer: Peter Eisentraut <[email protected]>
date : Sun, 5 Apr 2020 10:02:00 +0200
Fixup for "Drop slot's LWLock before returning from SaveSlotToPath()"
Reported-by: Michael Paquier <[email protected]>
M src/backend/replication/slot.c
## Fix bugs in gin_fuzzy_search_limit processing.
commit : 44c763fe993013d44404116872780e1acdfa8988
author : Tom Lane <[email protected]>
date : Fri, 3 Apr 2020 13:15:30 -0400
committer: Tom Lane <[email protected]>
date : Fri, 3 Apr 2020 13:15:30 -0400
entryGetItem()'s three code paths each contained bugs associated
with filtering the entries for gin_fuzzy_search_limit.
decided to filter an item. If we ran out of items on the current
page and needed to advance to the next, what would actually happen
the random dropItem() test would accept one of the same items it'd
previously rejected, and we'd move on --- but it could take awhile
with small gin_fuzzy_search_limit. To add insult to injury, this
case would inevitably cause entryLoadMoreItems() to decide it needed
to re-descend from the root, making things even slower.
The posting-list path failed to implement gin_fuzzy_search_limit
filtering at all, so that all entries in the posting list would
be returned.
The bitmap-result path used a "gotitem" variable that it failed to
update in the one place where it'd actually make a difference, ie
at the one "continue" statement. I think this was unreachable in
practice, because if we'd looped around then it shouldn't be the
case that the entries on the new page are before advancePast.
Still, the "gotitem" variable was contributing nothing to either
clarity or correctness, so get rid of it.
Refactor all three loops so that the termination conditions are
The code coverage report showed that we had no coverage at all for
the re-descend-from-root code path in entryLoadMoreItems(), which
seems like a very bad thing, so add a test case that exercises it.
simplistic test case that at least hits those code paths a little bit.
Back-patch to all supported branches.
Discussion: https://postgr.es/m/CAEknJCdS-dE1Heddptm7ay2xTbSeADbkaQ8bU2AXRCVC2LdtKQ@mail.gmail.com
M src/backend/access/gin/ginget.c
M src/test/regress/expected/gin.out
M src/test/regress/sql/gin.sql
## Fix bogus CALLED_AS_TRIGGER() defenses.
commit : 85f0d470380902c8c62d0165c349c82d81c3e056
author : Tom Lane <[email protected]>
date : Fri, 3 Apr 2020 11:24:56 -0400
committer: Tom Lane <[email protected]>
date : Fri, 3 Apr 2020 11:24:56 -0400
contrib/lo's lo_manage() thought it could use
trigdata->tg_trigger->tgname in its error message about
not being called as a trigger. That naturally led to a core dump.
unique_key_recheck() figured it could Assert that fcinfo->context
is a TriggerData node in advance of having checked that it's
being called as a trigger. That's harmless in production builds,
and perhaps not that easy to reach in any case, but it's logically
wrong.
The first of these per bug #16340 from William Crowell;
the second from manual inspection of other CALLED_AS_TRIGGER
call sites.
Back-patch the lo.c change to all supported branches, the
other to v10 where the thinko crept in.
Discussion: https://postgr.es/m/[email protected]
M contrib/lo/lo.c
M src/backend/commands/constraint.c
## doc: remove unnecessary INNER keyword
commit : de7561f7d87df7dff8c6b29ac0d6435795d42372
author : Bruce Momjian <[email protected]>
date : Thu, 2 Apr 2020 17:42:09 -0400
committer: Bruce Momjian <[email protected]>
date : Thu, 2 Apr 2020 17:42:09 -0400
A join that was added in commit 9b2009c4cf that did not use the INNER
keyword but the existing query used it. It was cleaner to remove the
existing INNER keyword.
Reported-by: Peter Eisentraut
Backpatch-through: 9.5
M doc/src/sgml/pgbuffercache.sgml
commit : 8a043d8673289c2a0c6256fc15cc641bb91c5674
author : Bruce Momjian <[email protected]>
date : Thu, 2 Apr 2020 17:27:43 -0400
committer: Bruce Momjian <[email protected]>
date : Thu, 2 Apr 2020 17:27:43 -0400
Reported-by: Peter Eisentraut
Backpatch-through: 9.5
M doc/src/sgml/func.sgml
## psql: do file completion for \gx
commit : a936012d6b2c9b05b856b3fc936fb2ac6af09164
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 23:01:33 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 23:01:33 -0400
This was missed when the feature was added.
Reported-by: Vik Fearing
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 10
M src/bin/psql/tab-complete.c
## makefile: use proper linker flags for C++ compiles
commit : f1e8362aefc866a6f75b6b41edccd03d51235d17
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 22:26:11 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 22:26:11 -0400
Add CFLAGS_SL flags for C++ compiles, which adds needed -fPIC linker
flag.
Reported-by: Oleksii Kliukin
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 10 only
M src/Makefile.shlib
## doc: remove mention of bitwise operators as solely type-limited
commit : 67427a159b0b5d9091ace90990950a926e46cc89
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 18:44:29 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 18:44:29 -0400
There are other operators that have limited number data type support, so
just remove the sentence.
Reported-by: Sergei Agalakov
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/func.sgml
## doc: clarify hierarchy of objects: global, db, schema, etc.
commit : 4bd53803ef73b43124693e4a96e973e9329b8361
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 18:10:39 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 18:10:39 -0400
The previous wording was confusing because it wasn't in decreasing order
and had to backtrack. Also clarify role/user wording.
Reported-by: [email protected]
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/ddl.sgml
M doc/src/sgml/manage-ag.sgml
## doc: restore wording from recent patch "rolled back to"
commit : b9d94670c1d9b9a6604bb5cd80f77e93aee4e776
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:52:48 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:52:48 -0400
Reported-by: Tom Lane
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5 - 12
M doc/src/sgml/mvcc.sgml
## doc: clarify when row-level locks are released
commit : 5e6a44e47f738373b686ad1b0bf8bcb40c6058c0
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:27:32 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:27:32 -0400
They are released just like table-level locks. Also clean up wording.
Reported-by: [email protected]
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/mvcc.sgml
## doc: add namespace column to pg_buffercache example query
commit : 7c8fb4a5e229547882db0577aacc85c18803f8bd
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:16:33 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:16:33 -0400
Without the namespace, the table name could be ambiguous.
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/pgbuffercache.sgml
## doc: clarify which table creation is used for inheritance part.
commit : 690e4648719183b0527b6c20a87798e5bd6282e4
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:07:43 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 17:07:43 -0400
Previously people might assume that the partition syntax version of
CREATE TABLE is to be used for the inheritance partition table example;
mention that the non-partitioned version should be used.
Reported-by: [email protected]
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 10
M doc/src/sgml/ddl.sgml
## doc: adjust UPDATE/DELETE's FROM/USING to match SELECT's FROM
commit : b8c651b75b2133d843b4fbbd52254b55792339cd
author : Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 16:31:44 -0400
committer: Bruce Momjian <[email protected]>
date : Tue, 31 Mar 2020 16:31:44 -0400
Previously the syntax and wording were unclear.
Reported-by: Alexey Bashtanov
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/ref/delete.sgml
M doc/src/sgml/ref/update.sgml
## Teach pg_ls_dir_files() to ignore ENOENT failures from stat().
commit : 83f7761d84e6b9879decd223b0e172afcb1426d8
author : Tom Lane <[email protected]>
date : Tue, 31 Mar 2020 12:57:55 -0400
committer: Tom Lane <[email protected]>
date : Tue, 31 Mar 2020 12:57:55 -0400
Buildfarm experience shows that this function can fail with ENOENT
if some other process unlinks a file between when we read the directory
entry and when we try to stat() it. The problem is old but we had
not noticed it until 085b6b667 added regression test coverage.
To fix, just ignore ENOENT failures. There is one other case that
this might hide: a symlink that points to nowhere. That seems okay
though, at least better than erroring.
Back-patch to v10 where this function was added, since the regression
test cases were too.
Discussion: https://postgr.es/m/[email protected]
## Back-patch addition of stack overflow and interrupt checks for lquery.
commit : 8b902e438608c2ef7d3875a74a81e66735fab358
author : Tom Lane <[email protected]>
date : Tue, 31 Mar 2020 11:37:44 -0400
committer: Tom Lane <[email protected]>
date : Tue, 31 Mar 2020 11:37:44 -0400
Experimentation shows that it's not hard at all to drive the
old implementation of "ltree ~ lquery" match to stack overflow,
so throw in a check_stack_depth() call, as I just did in HEAD.
I wasn't able to make it take a long time, because all the
pathological cases I tried hit stack overflow first; but
I bet there are some others that do take a long time, so add
CHECK_FOR_INTERRUPTS() too.
Discussion: https://postgr.es/m/CAP_rww=waX2Oo6q+MbMSiZ9ktdj6eaJj0cQzNu=Ry2cCDij5fw@mail.gmail.com
M contrib/ltree/lquery_op.c
## Be more careful about extracting encoding from locale strings on Windows.
commit : d59e83cf5925620703a32cc40f9f75bbb90956e8
author : Tom Lane <[email protected]>
date : Mon, 30 Mar 2020 11:14:58 -0400
committer: Tom Lane <[email protected]>
date : Mon, 30 Mar 2020 11:14:58 -0400
GetLocaleInfoEx() can fail on strings that setlocale() was perfectly
happy with. A common way for that to happen is if the locale string
is actually a Unix-style string, say "et_EE.UTF-8". In that case,
what's after the dot is an encoding name, not a Windows codepage number;
blindly treating it as a codepage number led to failure, with a fairly
silly error message. Hence, check to see if what's after the dot is
all digits, and if not, treat it as a literal encoding name rather than
a codepage number. This will do the right thing with many Unix-style
locale strings, and produce a more sensible error message otherwise.
Somewhat independently of that, treat a zero (CP_ACP) result from
GetLocaleInfoEx() as meaning that we must use UTF-8 encoding.
Back-patch to all supported branches.
Juan José Santamaría Flecha
Discussion: https://postgr.es/m/[email protected]
M src/port/chklocale.c
## Doc: correct misstatement about ltree label maximum length.
commit : e4e07cca5a8a86bedcd874a6f674550407d35555
author : Tom Lane <[email protected]>
date : Sun, 29 Mar 2020 18:54:19 -0400
committer: Tom Lane <[email protected]>
date : Sun, 29 Mar 2020 18:54:19 -0400
The documentation says that the max length is 255 bytes, but
code inspection says it's actually 255 characters; and relevant
lengths are stored as uint16 so that that works.
M doc/src/sgml/ltree.sgml
## Protect against overflow of ltree.numlevel and lquery.numlevel.
commit : 2618ac6c6535171f4993a38e3410955e1c2a2073
author : Tom Lane <[email protected]>
date : Sat, 28 Mar 2020 17:09:51 -0400
committer: Tom Lane <[email protected]>
date : Sat, 28 Mar 2020 17:09:51 -0400
These uint16 fields could be overflowed by excessively long input,
producing strange results. Complain for invalid input.
Likewise check for out-of-range values of the repeat counts in lquery.
(We don't try too hard on that one, notably not bothering to detect
if atoi's result has overflowed.)
Also detect length overflow in ltree_concat.
In passing, be more consistent about whether "syntax error" messages
include the type name. Also, clarify the documentation about what
the size limit is.
This has been broken for a long time, so back-patch to all supported
branches.
Nikita Glukhov, reviewed by Benjie Gillam and Tomas Vondra
Discussion: https://postgr.es/m/CAP_rww=waX2Oo6q+MbMSiZ9ktdj6eaJj0cQzNu=Ry2cCDij5fw@mail.gmail.com
M contrib/ltree/expected/ltree.out
M contrib/ltree/ltree.h
M contrib/ltree/ltree_io.c
M contrib/ltree/ltree_op.c
M contrib/ltree/sql/ltree.sql
M doc/src/sgml/ltree.sgml
## Ensure snapshot is registered within ScanPgRelation().
commit : a0e2a178c6409db195e8e902e4ac279ad60777cb
author : Andres Freund <[email protected]>
date : Sat, 28 Mar 2020 11:52:11 -0700
committer: Andres Freund <[email protected]>
date : Sat, 28 Mar 2020 11:52:11 -0700
In 9.4 I added support to use a historical snapshot in
ScanPgRelation(), while adding logical decoding. Unfortunately a
conflict with the concurrent removal of SnapshotNow was incorrectly
resolved, leading to an unregistered snapshot being used.
It is not correct to use an unregistered (or non-active) snapshot for
snapshot to be invalidated.
Luckily it seems unlikely to actively cause problems in practice, as
ScanPgRelation() requires that we already have a lock on the relation,
we only look for a single row, and we don't appear to rely on the
result's tid to be correct. It however is clearly wrong and potential
negative consequences would likely be hard to find. So it seems worth
backpatching the fix, even without a concrete hazard.
Discussion: https://postgr.es/m/[email protected]
Backpatch: 9.5-
M src/backend/utils/cache/relcache.c
## Ensure that plpgsql cleans up cleanly during parallel-worker exit.
commit : 42d3649b58f4bd5f06b5e20c24439a9d72bc45b6
author : Tom Lane <[email protected]>
date : Thu, 26 Mar 2020 18:06:55 -0400
committer: Tom Lane <[email protected]>
date : Thu, 26 Mar 2020 18:06:55 -0400
plpgsql_xact_cb ought to treat events XACT_EVENT_PARALLEL_COMMIT and
XACT_EVENT_PARALLEL_ABORT like XACT_EVENT_COMMIT and XACT_EVENT_ABORT
respectively, since its goal is to do process-local cleanup. This
oversight caused plpgsql's end-of-transaction cleanup to not get done
in parallel workers. Since a parallel worker will exit just after the
transaction cleanup, the effects of this are limited. I couldn't find
any case in the core code with user-visible effects, but perhaps there
are some in extensions. In any case it's wrong, so let's fix it before
it bites us not after.
evaluation resources in DO blocks. There's no live bug there, but it's
quite unobvious what's happening; at least I thought so. This isn't
related to the other issue, except that I found both things while poking
at expression-evaluation performance.
Back-patch the plpgsql_xact_cb fix to 9.5 where those event types
were introduced, and the DO-block commentary to v11 where DO blocks
gained the ability to issue COMMIT/ROLLBACK.
Discussion: https://postgr.es/m/[email protected]
M src/pl/plpgsql/src/pl_exec.c
## Drop slot's LWLock before returning from SaveSlotToPath()
commit : f36a10434a31bdf6298071c1ddf8d151d103d9fa
author : Peter Eisentraut <[email protected]>
date : Thu, 26 Mar 2020 11:51:39 +0100
committer: Peter Eisentraut <[email protected]>
date : Thu, 26 Mar 2020 11:51:39 +0100
When SaveSlotToPath() is called with elevel=LOG, the early exits didn't
release the slot's io_in_progress_lock.
This could result in a walsender being stuck on the lock forever. A
possible way to get into this situation is if the offending code paths
are triggered in a low disk space situation.
Discussion: https://www.postgresql.org/message-id/flat/56a138c5-de61-f553-7e8f-6789296de785%402ndquadrant.com
M src/backend/replication/slot.c
## Add regression tests for constraint errors in partitioned tables.
commit : 2060999a4d6e4b946a3f032bdd3df1c55ac855b3
author : Andres Freund <[email protected]>
date : Mon, 23 Mar 2020 14:24:06 -0700
committer: Andres Freund <[email protected]>
date : Mon, 23 Mar 2020 14:24:06 -0700
While #16293 only applied to 11 (and 10 to some degree), it seems best
to add tests to all branches with partitioning support.
Reported-By: Daniel WM
Author: Andres Freund
Bug: #16293
Discussion: https://postgr.es/m/[email protected]
Backpatch: 10-
M src/test/regress/expected/inherit.out
M src/test/regress/sql/inherit.sql
## Fix potential crash after constraint violation errors in partitioned tables.
commit : 44170a58092d74913779181392015c9994a2dfc3
author : Andres Freund <[email protected]>
date : Mon, 23 Mar 2020 13:57:43 -0700
committer: Andres Freund <[email protected]>
date : Mon, 23 Mar 2020 13:57:43 -0700
During the reporting of constraint violations for partitioned tables,
ExecPartitionCheckEmitError(), ExecConstraints(),
ExecWithCheckOptions() set the slot descriptor of the input slot to
the root partition's tuple desc. That's generally problematic when
the slot could be used by other routines, but can cause crashes after
the introduction of slots with "fixed" tuple descriptors in
The problem likely escaped detection so far for two reasons: First,
currently the only known way that these routines are used with a
partitioned table that is not "owned" by partitioning code is when
"fast defaults" are used for the child partition. Second, as an error
is raised afterwards, an "external" slot that had its descriptor
changed, is very unlikely to continue being used.
Even though the issue currently is only known to cause a crash for
11 (as that has both fast defaults and "fixed" slot descriptors), it
seems worth applying the fix to 10 too. Potentially changing random
slots is hazardous.
Regression tests will be added in a separate commit, as it seems best
to add them for master and 12 too.
Reported-By: Daniel WM
Author: Andres Freund
Bug: #16293
Discussion: https://postgr.es/m/[email protected]
Backpatch: 11, 10 only
M src/backend/executor/execMain.c
## Doc: explain that LIKE et al can be used in ANY (sub-select) etc.
commit : a7500cce1ef27a319b3d88d9466f71539c187966
author : Tom Lane <[email protected]>
date : Mon, 23 Mar 2020 12:42:15 -0400
committer: Tom Lane <[email protected]>
date : Mon, 23 Mar 2020 12:42:15 -0400
This wasn't stated anywhere, and it's perhaps not that obvious,
since we get questions about it from time to time. Also undocumented
was that the parser actually translates these into operators.
Discussion: https://postgr.es/m/CAFj8pRBkvZ71BqGKZnBBG4=0cKG+s50Dy+DYmrizUKEpAtdc+w@mail.gmail.com
M doc/src/sgml/func.sgml
## Fix our getopt_long's behavior for a command line argument of just "-".
commit : ef7d6d79af43b168caf3ecc5847dcf47032b2253
author : Tom Lane <[email protected]>
date : Mon, 23 Mar 2020 11:58:01 -0400
committer: Tom Lane <[email protected]>
date : Mon, 23 Mar 2020 11:58:01 -0400
src/port/getopt_long.c failed on such an argument, always seeing it
as an unrecognized switch. This is unhelpful; better is to treat such
an item as a non-switch argument. That behavior is what we find in
GNU's getopt_long(); it's what src/port/getopt.c does; and it is
required by POSIX for getopt(), which getopt_long() ought to be
generally a superset of. Moreover, it's expected by ecpg, which
intends an argument of "-" to mean "read from stdin". So fix it.
that was miserably underdocumented. I had to reverse-engineer it
from the code.
Per bug #16304 from James Gray. Back-patch to all supported branches,
since this has been broken forever.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/ref/ecpg-ref.sgml
M src/port/getopt_long.c
## Doc: Fix type of some storage parameters in CREATE TABLE page
commit : 48f57efa49a735873afd3921c67117b8722b75a8
author : Michael Paquier <[email protected]>
date : Mon, 23 Mar 2020 13:38:20 +0900
committer: Michael Paquier <[email protected]>
date : Mon, 23 Mar 2020 13:38:20 +0900
autovacuum_vacuum_scale_factor and autovacuum_analyze_scale_factor have
been documented as "float4", but "floating type" is used in this case
for GUCs and relation options in the documentation.
Author: Atsushi Torikoshi
Discussion: https://postgr.es/m/CACZ0uYFf_p9BpbjLccx3CA=eM1Hk2Te=ULY4iptGLUhL-JxCPA@mail.gmail.com
Backpatch-through: 9.5
M doc/src/sgml/ref/create_table.sgml
## Revert "Skip WAL for new relfilenodes, under wal_level=minimal."
commit : 0a6c9c66da26751322d90f75c872c350376cf55e
date : Sun, 22 Mar 2020 09:24:09 -0700
date : Sun, 22 Mar 2020 09:24:09 -0700
This reverts commit cb2fd7eac285b1b0a24eeb2b8ed4456b66c5a09f. Per
numerous buildfarm members, it was incompatible with parallel query, and
a test case assumed LP64. Back-patch to 9.5 (all supported versions).
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/config.sgml
M doc/src/sgml/perform.sgml
M src/backend/access/gist/gistbuild.c
M src/backend/access/gist/gistutil.c
M src/backend/access/gist/gistxlog.c
M src/backend/access/heap/heapam.c
M src/backend/access/heap/rewriteheap.c
M src/backend/access/nbtree/nbtsort.c
M src/backend/access/rmgrdesc/gistdesc.c
M src/backend/access/transam/xact.c
M src/backend/access/transam/xlogutils.c
M src/backend/bootstrap/bootparse.y
M src/backend/catalog/storage.c
M src/backend/commands/cluster.c
M src/backend/commands/copy.c
M src/backend/commands/createas.c
M src/backend/commands/matview.c
M src/backend/commands/tablecmds.c
M src/backend/nodes/copyfuncs.c
M src/backend/nodes/equalfuncs.c
M src/backend/nodes/outfuncs.c
M src/backend/parser/gram.y
M src/backend/parser/parse_utilcmd.c
M src/backend/storage/buffer/bufmgr.c
M src/backend/storage/lmgr/lock.c
M src/backend/storage/smgr/md.c
M src/backend/storage/smgr/smgr.c
M src/backend/utils/cache/relcache.c
M src/backend/utils/misc/guc.c
M src/backend/utils/misc/postgresql.conf.sample
M src/include/access/gist_private.h
M src/include/access/gistxlog.h
M src/include/access/heapam.h
M src/include/access/rewriteheap.h
M src/include/catalog/storage.h
M src/include/nodes/parsenodes.h
M src/include/storage/bufmgr.h
M src/include/storage/lock.h
M src/include/storage/smgr.h
M src/include/utils/rel.h
M src/include/utils/relcache.h
D src/test/recovery/t/018_wal_optimize.pl
M src/test/regress/expected/alter_table.out
M src/test/regress/expected/create_table.out
M src/test/regress/sql/alter_table.sql
M src/test/regress/sql/create_table.sql
## Skip WAL for new relfilenodes, under wal_level=minimal.
commit : 9d6215205e5afe3062294c081dec4c9c41a12a5b
date : Sat, 21 Mar 2020 09:38:26 -0700
date : Sat, 21 Mar 2020 09:38:26 -0700
Until now, only selected bulk operations (e.g. COPY) did this. If a
given relfilenode received both a WAL-skipping COPY and a WAL-logged
operation (e.g. INSERT), recovery could lose tuples from the COPY. See
src/backend/access/transam/README section "Skipping WAL for New
RelFileNode" for the new coding rules. Maintainers of table access
methods should examine that section.
To maintain data durability, just before commit, we choose between an
fsync of the relfilenode and copying its contents to WAL. A new GUC,
wal_skip_threshold, guides that choice. If this change slows a workload
that creates small, permanent relfilenodes under wal_level=minimal, try
adjusting wal_skip_threshold. Users setting a timeout on COMMIT may
need to adjust that timeout, and log_min_duration_statement analysis
will reflect time consumption moving to COMMIT from commands like COPY.
Internally, this requires a reliable determination of whether
current relfilenode. Introduce rd_firstRelfilenodeSubid. Amend the
specification of rd_createSubid such that the field is zero when a new
rel has an old rd_node. Make relcache.c retain entries for certain
dropped relations until end of transaction.
Back-patch to 9.5 (all supported versions). This introduces a new WAL
record type, XLOG_GIST_ASSIGN_LSN, without bumping XLOG_PAGE_MAGIC. As
always, update standby systems before master systems. This changes
sizeof(RelationData) and sizeof(IndexStmt), breaking binary
compatibility for affected extensions. (The most recent commit to
affect the same class of extensions was
089e4d405d0f3b94c74a2c6a54357a84a681754b.)
Kyotaro Horiguchi, reviewed (in earlier, similar versions) by Robert
Haas. Heikki Linnakangas and Michael Paquier implemented earlier
designs that materially clarified the problem. Reviewed, in earlier
designs, by Andrew Dunstan, Andres Freund, Alvaro Herrera, Tom Lane,
Fujii Masao, and Simon Riggs. Reported by Martijn van Oosterhout.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/config.sgml
M doc/src/sgml/perform.sgml
M src/backend/access/gist/gistbuild.c
M src/backend/access/gist/gistutil.c
M src/backend/access/gist/gistxlog.c
M src/backend/access/heap/heapam.c
M src/backend/access/heap/rewriteheap.c
M src/backend/access/nbtree/nbtsort.c
M src/backend/access/rmgrdesc/gistdesc.c
M src/backend/access/transam/xact.c
M src/backend/access/transam/xlogutils.c
M src/backend/bootstrap/bootparse.y
M src/backend/catalog/storage.c
M src/backend/commands/cluster.c
M src/backend/commands/copy.c
M src/backend/commands/createas.c
M src/backend/commands/matview.c
M src/backend/commands/tablecmds.c
M src/backend/nodes/copyfuncs.c
M src/backend/nodes/equalfuncs.c
M src/backend/nodes/outfuncs.c
M src/backend/parser/gram.y
M src/backend/parser/parse_utilcmd.c
M src/backend/storage/buffer/bufmgr.c
M src/backend/storage/lmgr/lock.c
M src/backend/storage/smgr/md.c
M src/backend/storage/smgr/smgr.c
M src/backend/utils/cache/relcache.c
M src/backend/utils/misc/guc.c
M src/backend/utils/misc/postgresql.conf.sample
M src/include/access/gist_private.h
M src/include/access/gistxlog.h
M src/include/access/heapam.h
M src/include/access/rewriteheap.h
M src/include/catalog/storage.h
M src/include/nodes/parsenodes.h
M src/include/storage/bufmgr.h
M src/include/storage/lock.h
M src/include/storage/smgr.h
M src/include/utils/rel.h
M src/include/utils/relcache.h
A src/test/recovery/t/018_wal_optimize.pl
M src/test/regress/expected/alter_table.out
M src/test/regress/expected/create_table.out
M src/test/regress/sql/alter_table.sql
M src/test/regress/sql/create_table.sql
## Back-patch log_newpage_range().
commit : 43434ed94d80b4a181d5d9dc6bda585a9267eb1e
date : Sat, 21 Mar 2020 09:38:33 -0700
date : Sat, 21 Mar 2020 09:38:33 -0700
Back-patch a subset of commit 9155580fd5fc2a0cbb23376dfca7cd21f59c2c7b
to v11, v10, 9.6, and 9.5. Include the latest repairs to this function.
Use a new XLOG_FPI_MULTI value instead of reusing XLOG_FPI. That way,
if an older server reads WAL from this function, that server will PANIC
instead of applying just one page of the record. The next commit adds a
call to this function.
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/rmgrdesc/xlogdesc.c
M src/backend/access/transam/xlog.c
M src/backend/replication/logical/decode.c
M src/include/catalog/pg_control.h
## During heap rebuild, lock any TOAST index until end of transaction.
commit : 78a34c68920a544292d54f60af561c267b95f64d
date : Sat, 21 Mar 2020 09:38:26 -0700
date : Sat, 21 Mar 2020 09:38:26 -0700
swap_relation_files() calls toast_get_valid_index() to find and lock
this index, just before swapping with the rebuilt TOAST index. The
latter function releases the lock before returning. Potential for
mischief is low; a concurrent session can issue ALTER INDEX ... SET
(fillfactor = ...), which is not alarming. Nonetheless, changing
pg_class.relfilenode without a lock is unconventional. Back-patch to
9.5 (all supported versions), because another fix needs this.
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/heap/tuptoaster.c
M src/backend/commands/cluster.c
## Fix cosmetic blemishes involving rd_createSubid.
commit : 40348680003d637e2068fd4981216f51bff8762b
date : Sat, 21 Mar 2020 09:38:26 -0700
date : Sat, 21 Mar 2020 09:38:26 -0700
Remove an obsolete comment from AtEOXact_cleanup(). Restore formatting
of a comment in struct RelationData, mangled by the pgindent run in
commit 9af4159fce6654aa0e081b00d02bca40b978745c. Back-patch to 9.5 (all
supported versions), because another fix stacks on this.
M src/backend/utils/cache/relcache.c
M src/include/utils/rel.h
## docs: use alias in WHERE clause of full text search example
commit : 514aca63ea565b23756282bd6c77eb30fc9398b7
author : Bruce Momjian <[email protected]>
date : Fri, 20 Mar 2020 20:19:32 -0400
committer: Bruce Momjian <[email protected]>
date : Fri, 20 Mar 2020 20:19:32 -0400
The current doc query specified an alias in the FROM clause and used in
it the target list, but not in the WHERE clause.
Reported-by: [email protected]
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M doc/src/sgml/textsearch.sgml
## Turn off deprecated bison warnings under MSVC
commit : 3163349fd7fe0115b021bfa1fbe4990143957814
author : Andrew Dunstan <[email protected]>
date : Fri, 20 Mar 2020 13:55:15 -0400
committer: Andrew Dunstan <[email protected]>
date : Fri, 20 Mar 2020 13:55:15 -0400
These are disabled by the configure code, so this is just fixing an
inconsistency in the MSVC code.
Backpatch to all live branches.
M src/tools/msvc/pgbison.pl
## pg_upgrade: make get_major_server_version() err msg consistent
commit : c9c042dded8792913a0387bd7e9a0d8f7be00978
author : Bruce Momjian <[email protected]>
date : Thu, 19 Mar 2020 15:20:55 -0400
committer: Bruce Momjian <[email protected]>
date : Thu, 19 Mar 2020 15:20:55 -0400
This patch fixes the error message in get_major_server_version() to be
"could not parse version file", and uses the full file path name, rather
than just the data directory path.
Also, commit 4109bb5de4 added the cause of the failure to the "could
not open" error message, and improved quoting. This patch backpatches
the "could not open" cause to PG 12, where it was first widely used, and
backpatches the quoting fix in that patch to all supported releases.
Reported-by: Tom Lane
Discussion: https://postgr.es/m/[email protected]
Author: Dagfinn Ilmari Mannsåker
Backpatch-through: 9.5
commit : f4efb46d2230ef19165fec78b5c41a78cf6e1213
author : Fujii Masao <[email protected]>
date : Wed, 18 Mar 2020 23:07:17 +0900
committer: Fujii Masao <[email protected]>
date : Wed, 18 Mar 2020 23:07:17 +0900
This commit corrects the descriptions of RecoveryWalAll and RecoveryWalStream
wait events in the documentation.
Back-patch to v10 where those wait events were added.
Author: Fujii Masao
Reviewed-by: Kyotaro Horiguchi, Atsushi Torikoshi
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/monitoring.sgml
## Add missing errcode() in a few ereport calls.
commit : 569f9354bb438520296790aee27960634e3465f8
author : Amit Kapila <[email protected]>
date : Wed, 18 Mar 2020 09:46:52 +0530
committer: Amit Kapila <[email protected]>
date : Wed, 18 Mar 2020 09:46:52 +0530
This will allow to specifying SQLSTATE error code for the errors in the
missing places.
Backpatch-through: 9.5
Discussion: https://postgr.es/m/CA+fd4k6N8EjNvZpM8nme+y+05mz-SM8Z_BgkixzkA34R+ej0Kw@mail.gmail.com
M src/backend/storage/page/bufpage.c
## Doc: clarify behavior of "anyrange" pseudo-type.
commit : 3c871d1ead20e6744403e2180d704dd09fd8c2d6
author : Tom Lane <[email protected]>
date : Tue, 17 Mar 2020 15:05:17 -0400
committer: Tom Lane <[email protected]>
date : Tue, 17 Mar 2020 15:05:17 -0400
I noticed that we completely failed to document the restriction
that an "anyrange" result type has to be inferred from an "anyrange"
input. The docs also were less clear than they could be about the
relationship between "anyrange" and "anyarray".
It's been like this all along, so back-patch.
M doc/src/sgml/extend.sgml
## Use pkg-config, if available, to locate libxml2 during configure.
commit : d67d7243f914f99bd1103f811efd320c987db2bc
author : Tom Lane <[email protected]>
date : Tue, 17 Mar 2020 12:09:27 -0400
committer: Tom Lane <[email protected]>
date : Tue, 17 Mar 2020 12:09:27 -0400
If pkg-config is installed and knows about libxml2, use its information
rather than asking xml2-config. Otherwise proceed as before. This
patch allows "configure --with-libxml" to succeed on platforms that
have pkg-config but not xml2-config, which is likely to soon become
a typical situation.
The old mechanism can be forced by setting XML2_CONFIG explicitly
(hence, build processes that were already doing so will certainly
not need adjustment). Also, it's now possible to set XML2_CFLAGS
and XML2_LIBS explicitly to override both programs.
There is a small risk of this breaking existing build processes,
if there are multiple libxml2 installations on the machine and
pkg-config disagrees with xml2-config about which to use. The
only case where that seems really likely is if a builder has tried
to select a non-default xml2-config by putting it early in his PATH
rather than setting XML2_CONFIG. Plan to warn against that in the
minor release notes.
Back-patch to v10; before that we had no pkg-config infrastructure,
and it doesn't seem worth adding it for this.
Hugh McMaster and Tom Lane; Peter Eisentraut also made an earlier
attempt at this, from which I lifted most of the docs changes.
Discussion: https://postgr.es/m/CAN9BcdvfUwc9Yx5015bLH2TOiQ-M+t_NADBSPhMF7dZ=pLa_iw@mail.gmail.com
M configure
M configure.in
M doc/src/sgml/installation.sgml
## Avoid holding a directory FD open across assorted SRF calls.
commit : 5e4a0b7194b9b53eeedc718fde1430eb649b8b62
author : Tom Lane <[email protected]>
date : Mon, 16 Mar 2020 21:05:29 -0400
committer: Tom Lane <[email protected]>
date : Mon, 16 Mar 2020 21:05:29 -0400
This extends the fixes made in commit 085b6b667 to other SRFs with the
same bug, namely pg_logdir_ls(), pgrowlocks(), pg_timezone_names(),
pg_ls_dir(), and pg_tablespace_databases().
expecting to clean up resources during a ValuePerCall SRF's final
call.
Back-patch to all supported branches, since these functions were
all born broken.
Justin Pryzby, with cosmetic tweaks by me
Discussion: https://postgr.es/m/[email protected]
M contrib/pgrowlocks/pgrowlocks.c
M doc/src/sgml/xfunc.sgml
M src/include/funcapi.h
M src/test/regress/expected/misc_functions.out
M src/test/regress/sql/misc_functions.sql
## Plug memory leak
commit : c6b75b3f14fd4ff973ad3d2e2cfe42b5639bd101
author : Alvaro Herrera <[email protected]>
date : Mon, 16 Mar 2020 16:27:13 -0300
committer: Alvaro Herrera <[email protected]>
date : Mon, 16 Mar 2020 16:27:13 -0300
Introduced by b08dee24a557. Noted by Coverity.
M src/bin/pg_dump/pg_dump.c
## C comment: correct commented bytes of max_cached_tuplebufs
commit : 170679216d225d979daf2651f2bf73bc08ffdd26
author : Bruce Momjian <[email protected]>
date : Sat, 14 Mar 2020 17:36:54 -0400
committer: Bruce Momjian <[email protected]>
date : Sat, 14 Mar 2020 17:36:54 -0400
The comment said ~8MB, but it is actually ~64MB.
Reported-by: Kuntal Ghosh
Discussion: https://postgr.es/m/CAGz5QC+GGmHdnxp04B6wcLz2Zcd_HU+wCBrsPyOZP62-BJghig@mail.gmail.com
Backpatch-through: 9.5-10
M src/backend/replication/logical/reorderbuffer.c
## Restructure polymorphic-type resolution in funcapi.c.
commit : 61d14971dade445cca407660609793dfdb727538
author : Tom Lane <[email protected]>
date : Sat, 14 Mar 2020 14:42:22 -0400
committer: Tom Lane <[email protected]>
date : Sat, 14 Mar 2020 14:42:22 -0400
resolve_polymorphic_tupdesc() and resolve_polymorphic_argtypes() failed to
cover the case of having to resolve anyarray given only an anyrange input.
The bug was masked if anyelement was also used (as either input or
output), which probably helps account for our not having noticed.
While looking at this I noticed that resolve_generic_type() would produce
the wrong answer if asked to make that same resolution. ISTM that
resolve_generic_type() is confusingly defined and overly complex, so
rather than fix it, let's just make funcapi.c do the specific lookups
it requires for itself.
With this change, resolve_generic_type() is not used anywhere, so remove
it in HEAD. In the back branches, leave it alone (complete with bug)
just in case any external code is using it.
While we're here, make some other refactoring adjustments in funcapi.c
with an eye to upcoming future expansion of the set of polymorphic types:
* Simplify quick-exit tests by adding an overall have_polymorphic_result
flag. This is about a wash now but will be a win when there are more
flags.
* Reduce duplication of code between resolve_polymorphic_tupdesc() and
resolve_polymorphic_argtypes().
* Don't bother to validate correct matching of anynonarray or anyenum;
the parser should have done that, and even if it didn't, just doing
"return false" here would lead to a very confusing, off-point error
message. (Really, "return false" in these two functions should only
occur if the call_expr isn't supplied or we can't obtain data type
info from it.)
* For the same reason, throw an elog rather than "return false" if
we fail to resolve a polymorphic type.
The bug's been there since we added anyrange, so back-patch to
all supported branches.
Discussion: https://postgr.es/m/[email protected]
M src/backend/utils/fmgr/funcapi.c
M src/test/regress/expected/rangetypes.out
M src/test/regress/sql/rangetypes.sql
## Doc: fix mistaken reference to "PG_ARGNULL_xxx()" macro.
commit : 00f38866f7e966ac4c48c6b027e2666c3ab29398
author : Tom Lane <[email protected]>
date : Fri, 13 Mar 2020 12:49:10 -0400
committer: Tom Lane <[email protected]>
date : Fri, 13 Mar 2020 12:49:10 -0400
This should of course be just "PG_ARGISNULL()".
Also reorder a couple of paras to make the discussion of PG_ARGISNULL
less disjointed.
Back-patch to v10 where the error was introduced.
Laurenz Albe and Tom Lane, per an anonymous docs comment
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/xfunc.sgml
## Preserve replica identity index across ALTER TABLE rewrite
commit : 02530da73f0438f7c2073267de6fe2be84f592d7
author : Peter Eisentraut <[email protected]>
date : Fri, 13 Mar 2020 11:28:11 +0100
committer: Peter Eisentraut <[email protected]>
date : Fri, 13 Mar 2020 11:28:11 +0100
If an index was explicitly set as replica identity index, this setting
was lost when a table was rewritten by ALTER TABLE. Because this
setting is part of pg_index but actually controlled by ALTER
TABLE (not part of CREATE INDEX, say), we have to do some extra work
to restore it.
Based-on-patch-by: Quan Zongliang <[email protected]>
Discussion: https://www.postgresql.org/message-id/flat/[email protected]
M src/backend/commands/tablecmds.c
M src/backend/utils/cache/lsyscache.c
M src/include/utils/lsyscache.h
M src/test/regress/expected/replica_identity.out
M src/test/regress/sql/replica_identity.sql
## Fix nextXid tracking bug on standbys (9.5-11 only).
commit : 05e0aff58446203d01dfc16717866df769e4e25e
author : Thomas Munro <[email protected]>
date : Thu, 12 Mar 2020 18:06:54 +1300
committer: Thomas Munro <[email protected]>
date : Thu, 12 Mar 2020 18:06:54 +1300
RecordKnownAssignedTransactionIds() should never move
nextXid backwards. Before this commit, that could happen
latestObservedXid.
One consequence is that a well timed XLOG_CHECKPOINT_ONLINE
could cause hot standby feedback messages to get confused
and report an xmin from a future epoch, potentially allowing
vacuum to run too soon on the primary.
Repair, by making sure RecordKnownAssignedTransactionIds()
can only move nextXid forwards.
In release 12 and master, this was already done by commit
2fc7af5e, which consolidated similar code and straightened
out this bug. Back-patch to supported releases before that.
Discussion: https://postgr.es/m/[email protected]
M src/backend/storage/ipc/procarray.c
## Fix test case instability introduced in 085b6b667.
commit : 064e029e60a516dea6566652d729419a51294ac2
author : Tom Lane <[email protected]>
date : Wed, 11 Mar 2020 18:23:57 -0400
committer: Tom Lane <[email protected]>
date : Wed, 11 Mar 2020 18:23:57 -0400
I forgot that the WAL directory might hold other files besides WAL
segments, notably including new segments still being filled.
That means a blind test for the first file's size being 16MB can
fail. Restrict based on file name length to make it more robust.
Per buildfarm.
M src/test/regress/expected/misc_functions.out
M src/test/regress/sql/misc_functions.sql
## Add pg_dump support for ALTER obj DEPENDS ON EXTENSION
commit : d04e342ba404171c706f96e501865fe0d5f6b1e5
author : Alvaro Herrera <[email protected]>
date : Wed, 11 Mar 2020 16:54:54 -0300
committer: Alvaro Herrera <[email protected]>
date : Wed, 11 Mar 2020 16:54:54 -0300
pg_dump is oblivious to this kind of dependency, so they're lost on
dump/restores (and pg_upgrade). Have pg_dump emit ALTER lines so that
they're preserved. Add some pg_dump tests for the whole thing, also.
Reviewed-by: Tom Lane (offlist)
Reviewed-by: Ibrar Ahmed
Reviewed-by: Ahsan Hadi (who also reviewed commit 899a04f5ed61)
Discussion: https://postgr.es/m/[email protected]
M src/bin/pg_dump/common.c
M src/bin/pg_dump/pg_dump.c
M src/bin/pg_dump/pg_dump.h
M src/test/modules/test_pg_dump/t/001_base.pl
## Avoid holding a directory FD open across pg_ls_dir_files() calls.
commit : 05283dd5b5792b094b8211d46fef1082d411e679
author : Tom Lane <[email protected]>
date : Wed, 11 Mar 2020 15:28:00 -0400
committer: Tom Lane <[email protected]>
date : Wed, 11 Mar 2020 15:28:00 -0400
This coding technique is undesirable because (a) it leaks the FD for
the rest of the transaction if the SRF is not run to completion, and
(b) allocated FDs are a scarce resource, but multiple interleaved
uses of the relevant functions could eat many such FDs.
In v11 and later, a query such as "SELECT pg_ls_waldir() LIMIT 1"
yields a warning about the leaked FD, and the only reason there's
no warning in earlier branches is that fd.c didn't whine about such
leaks before commit 9cb7db3f0. Even disregarding the warning, it
wouldn't be too hard to run a backend out of FDs with careless use
of these SQL functions.
Hence, rewrite the function so that it reads the directory within
a single call, returning the results as a tuplestore rather than
via value-per-call mode.
There are half a dozen other built-in SRFs with similar problems,
but let's fix this one to start with, just to see if the buildfarm
finds anything wrong with the code.
In passing, fix bogus error report for stat() failure: it was
whining about the directory when it should be fingering the
individual file. Doubtless a copy-and-paste error.
Back-patch to v10 where this function was added.
Justin Pryzby, with cosmetic tweaks and test cases by me
Discussion: https://postgr.es/m/[email protected]
M src/test/regress/expected/misc_functions.out
M src/test/regress/sql/misc_functions.sql
## Avoid duplicates in ALTER ... DEPENDS ON EXTENSION
commit : 3dfd2d6cd28a125edc4761eaefaa1193f111459d
author : Alvaro Herrera <[email protected]>
date : Wed, 11 Mar 2020 11:04:59 -0300
committer: Alvaro Herrera <[email protected]>
date : Wed, 11 Mar 2020 11:04:59 -0300
If the command is attempted for an extension that the object already
depends on, silently do nothing.
In particular, this means that if a database containing multiple such
entries is dumped, the restore will silently do the right thing and
record just the first one. (At least, in a world where pg_dump does
dump such entries -- which it doesn't currently, but it will.)
Backpatch to 9.6, where this kind of dependency was introduced.
Reviewed-by: Ibrar Ahmed, Tom Lane (offlist)
Discussion: https://postgr.es/m/[email protected]
M src/backend/catalog/pg_depend.c
M src/backend/commands/alter.c
M src/include/catalog/dependency.h
M src/test/modules/test_extensions/expected/test_extdepend.out
M src/test/modules/test_extensions/sql/test_extdepend.sql
## Fix pg_dump/pg_restore to restore event triggers later.
commit : 475b061c867557499559227d743b332c257033a3
author : Tom Lane <[email protected]>
date : Mon, 9 Mar 2020 14:58:11 -0400
committer: Tom Lane <[email protected]>
date : Mon, 9 Mar 2020 14:58:11 -0400
Previously, event triggers were restored just after regular triggers
(and FK constraints, which are basically triggers). This is risky
since an event trigger, once installed, could interfere with subsequent
restore commands. Worse, because event triggers don't have any
particular dependencies on any post-data objects, a parallel restore
would consider them eligible to be restored the moment the post-data
phase starts, allowing them to also interfere with restoration of a
whole bunch of objects that would have been restored before them in
a serial restore. There's no way to completely remove the risk of a
misguided event trigger breaking the restore, since if nothing else
it could break other event triggers. But we can certainly push them
to later in the process to minimize the hazard.
To fix, tweak the RestorePass mechanism introduced by commit 3eb9a5e7c
so that event triggers are handled as part of the post-ACL processing
pass (renaming the "REFRESH" pass to "POST_ACL" to reflect its more
general use). This will cause them to restore after everything except
matview refreshes, which seems OK since matview refreshes really ought
to run in the post-restore state of the database. In a parallel
restore, event triggers and matview refreshes might be intermixed,
but that seems all right as well.
Also update the code and comments in pg_dump_sort.c so that its idea
of how things are sorted agrees with what actually happens due to
the RestorePass mechanism. This is mostly cosmetic: it'll affect the
order of objects in a dump's TOC, but not the actual restore order.
But not changing that would be quite confusing to somebody reading
the code.
Back-patch to all supported branches.
Fabrízio de Royes Mello, tweaked a bit by me
Discussion: https://postgr.es/m/CAFcNs+ow1hmFox8P--3GSdtwz-S3Binb6ZmoP6Vk+Xg=K6eZNA@mail.gmail.com
M src/bin/pg_dump/pg_backup_archiver.c
M src/bin/pg_dump/pg_backup_archiver.h
M src/bin/pg_dump/pg_dump_sort.c
## Fix bug that causes to report waiting in PS display twice, in hot standby.
commit : e9c4eaacdd555c19ded1bdd8c03718eb33b7c3b6
author : Fujii Masao <[email protected]>
date : Tue, 10 Mar 2020 00:14:43 +0900
committer: Fujii Masao <[email protected]>
date : Tue, 10 Mar 2020 00:14:43 +0900
Previously "waiting" could appear twice via PS in case of lock conflict
in hot standby mode. Specifically this issue happend when the delay
in WAL application determined by max_standby_archive_delay and
max_standby_streaming_delay had passed but it took more than 500 msec
to cancel all the conflicting transactions. Especially we can observe this
easily by setting those delay parameters to -1.
The cause of this issue was that WaitOnLock() and
the process title in that case. This commit prevents
ResolveRecoveryConflictWithVirtualXIDs() from reporting waiting
in case of lock conflict, to fix the bug.
Back-patch to all back branches.
Reviewed-by: Fujii Masao
Discussion: https://postgr.es/m/CA+fd4k4mXWTwfQLS3RPwGr4xnfAEs1ysFfgYHvmmoUgv6Zxvmg@mail.gmail.com
M src/backend/storage/ipc/standby.c
## Avoid assertion failure with targeted recovery in standby mode.
commit : b366e51729bb98506769b4f62bc3cf753d156464
author : Fujii Masao <[email protected]>
date : Mon, 9 Mar 2020 15:31:31 +0900
committer: Fujii Masao <[email protected]>
date : Mon, 9 Mar 2020 15:31:31 +0900
At the end of recovery, standby mode is turned off to re-fetch the last
valid record from archive or pg_wal. Previously, if recovery target was
reached and standby mode was turned off while the current WAL source
was stream, recovery could try to retrieve WAL file containing the last
valid record unexpectedly from stream even though not in standby mode.
This caused an assertion failure. That is, the assertion test confirms that
WAL file should not be retrieved from stream if standby mode is not true.
This commit moves back the current WAL source to archive if it's stream
even though not in standby mode, to avoid that assertion failure.
This issue doesn't cause the server to crash when built with assertion
disabled. In this case, the attempt to retrieve WAL file from stream not
in standby mode just fails. And then recovery tries to retrieve WAL file
from archive or pg_wal.
Back-patch to all supported branches.
Author: Kyotaro Horiguchi
Reviewed-by: Fujii Masao
Discussion: https://postgr.es/m/[email protected]
M src/backend/access/transam/xlog.c
## Fix typo
commit : 5c2e2a2227ea60fbd7518ba357c2c0193fa62fea
author : Peter Eisentraut <[email protected]>
date : Sat, 7 Mar 2020 08:51:59 +0100
committer: Peter Eisentraut <[email protected]>
date : Sat, 7 Mar 2020 08:51:59 +0100
## Fix the name of the first WAL segment file, in docs.
commit : 7a00f50ea63175447b7621bb94e8341bf1c34a9c
author : Fujii Masao <[email protected]>
date : Tue, 3 Mar 2020 12:22:04 +0900
committer: Fujii Masao <[email protected]>
date : Tue, 3 Mar 2020 12:22:04 +0900
Previously the documentation explains that WAL segment files
start at 000000010000000000000000. But the first WAL segment file
that initdb creates is 000000010000000000000001 not
000000010000000000000000. This change was caused by old
commit 8c843fff2d, but the documentation had not been updated
a long time.
Back-patch to all supported branches.
Author: Fujii Masao
Reviewed-by: David Zhang
Discussion: https://postgr.es/m/CAHGQGwHOmGe2OqGOmp8cOfNVDivq7dbV74L5nUGr+3eVd2CU2Q@mail.gmail.com
M doc/src/sgml/wal.sgml
## Doc: correct thinko in pg_buffercache documentation.
commit : e2ff91b4c36c582c695a69864dd7b4c988202bfe
author : Tom Lane <[email protected]>
date : Fri, 28 Feb 2020 11:29:59 -0500
committer: Tom Lane <[email protected]>
date : Fri, 28 Feb 2020 11:29:59 -0500
Access to this module is granted to the pg_monitor role, not
pg_read_all_stats. (Given the view's performance impact,
it seems wise to be restrictive, so I think this was the
correct decision --- and anyway it was clearly intentional.)
Per bug #16279 from Philip Semanchuk.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/pgbuffercache.sgml
## createdb: Fix quoting of --encoding, --lc-ctype and --lc-collate
commit : 240c7c75f3a9946509c9c6f9f5062b56cec627ae
author : Michael Paquier <[email protected]>
date : Thu, 27 Feb 2020 11:21:14 +0900
committer: Michael Paquier <[email protected]>
date : Thu, 27 Feb 2020 11:21:14 +0900
The original coding failed to properly quote those arguments, leading to
failures when using quotes in the values used. As the quoting can be
encoding-sensitive, the connection to the backend needs to be taken
before applying the correct quoting.
Author: Michael Paquier
Reviewed-by: Daniel Gustafsson
Discussion: https://postgr.es/m/[email protected]
Backpatch-through: 9.5
M src/bin/scripts/createdb.c
## Doc: discourage use of partial indexes for poor-man's-partitioning.
commit : 1de4a823f9dea3bdc2dba2fe0b9b90c06cfd6fbb
author : Tom Lane <[email protected]>
date : Wed, 19 Feb 2020 18:52:18 -0500
committer: Tom Lane <[email protected]>
date : Wed, 19 Feb 2020 18:52:18 -0500
Creating a bunch of non-overlapping partial indexes is generally
a bad idea, so add an example saying not to do that.
Back-patch to v10. Before that, the alternative of using (real)
partitioning wasn't available, so that the tradeoff isn't quite
so clear cut.
Discussion: https://postgr.es/m/CAKVFrvFY-f7kgwMRMiPLbPYMmgjc8Y2jjUGK_Y0HVcYAmU6ymg@mail.gmail.com
M doc/src/sgml/indices.sgml
## Fix typo
commit : 7d8346b2f42fc7311ccac08870c21a9763c43824
author : Peter Eisentraut <[email protected]>
date : Wed, 19 Feb 2020 20:52:42 +0100
committer: Peter Eisentraut <[email protected]>
date : Wed, 19 Feb 2020 20:52:42 +0100
Reported-by: Daniel Verite <[email protected]>
M src/common/unicode_norm.c
## Fix confusion about event trigger vs. plain function in plpgsql.
commit : 6af63cf8c0b905f5c20cecff03b30ef52594e5f9
author : Tom Lane <[email protected]>
date : Wed, 19 Feb 2020 14:44:58 -0500
committer: Tom Lane <[email protected]>
date : Wed, 19 Feb 2020 14:44:58 -0500
The function hash table keys made by compute_function_hashkey() failed
to distinguish event-trigger call context from regular call context.
This meant that once we'd successfully made a hash entry for an event
trigger (either by validation, or by normal use as an event trigger),
an attempt to call the trigger function as a plain function would
find this hash entry and thereby bypass the you-can't-do-that check in
do_compile(). Thus we'd attempt to execute the function, leading to
strange errors or even crashes, depending on function contents and
server version.
To fix, add an isEventTrigger field to PLpgSQL_func_hashkey,
paralleling the longstanding infrastructure for regular triggers.
This fits into what had been pad space, so there's no risk of an ABI
break, even assuming that any third-party code is looking at these
hash keys. (I considered replacing isTrigger with a PLpgSQL_trigtype
enum field, but felt that that carried some API/ABI risk. Maybe we
should change it in HEAD though.)
Per bug #16266 from Alexander Lakhin. This has been broken since
event triggers were invented, so back-patch to all supported branches.
Discussion: https://postgr.es/m/[email protected]
M src/pl/plpgsql/src/pl_comp.c
M src/pl/plpgsql/src/plpgsql.h
M src/test/regress/expected/event_trigger.out
M src/test/regress/sql/event_trigger.sql
## Fix mesurement of elapsed time during truncating heap in VACUUM.
commit : 79f344d52bd51611bff655a97a89c62118aaa5ee
author : Fujii Masao <[email protected]>
date : Wed, 19 Feb 2020 20:37:26 +0900
committer: Fujii Masao <[email protected]>
date : Wed, 19 Feb 2020 20:37:26 +0900
VACUUM may truncate heap in several batches. The activity report
is logged for each batch, and contains the number of pages in the table
before and after the truncation, and also the elapsed time during
the truncation. Previously the elapsed time reported in each batch was
the total elapsed time since starting the truncation until finishing
each batch. For example, if the truncation was processed dividing into
three batches, the second batch reported the accumulated time elapsed
during both first and second batches. This is strange and confusing
because the number of pages in the table reported together is not
total. Instead, each batch should report the time elapsed during
only that batch.
The cause of this issue was that the resource usage snapshot was
initialized only at the beginning of the truncation and was never
reset later. This commit fixes the issue by changing VACUUM so that
the resource usage snapshot is reset at each batch.
Back-patch to all supported branches.
Reported-by: Tatsuhito Kasahara
Author: Tatsuhito Kasahara
Discussion: https://postgr.es/m/CAP0=ZVJsf=NvQuy+QXQZ7B=ZVLoDV_JzsVC1FRsF1G18i3zMGg@mail.gmail.com
M src/backend/commands/vacuumlazy.c
## Stop demanding that top xact must be seen before subxact in decoding.
commit : b448aa44170b6f67fdb34d4a85610949f15cef96
author : Amit Kapila <[email protected]>
date : Wed, 12 Feb 2020 12:00:01 +0530
committer: Amit Kapila <[email protected]>
date : Wed, 12 Feb 2020 12:00:01 +0530
Manifested as
ERROR: subtransaction logged without previous top-level txn record
this check forbids legit behaviours like
- First xl_xact_assignment record is beyond reading, i.e. earlier
restart_lsn.
- After restart_lsn there is some change of a subxact.
- After that, there is second xl_xact_assignment (for another subxact)
revealing the relationship between top and first subxact.
Such a transaction won't be streamed anyway because we hadn't seen it in
full. Saying for sure whether xact of some record encountered after
the snapshot was deserialized can be streamed or not requires to know
whether it wrote something before deserialization point --if yes, it
hasn't been seen in full and can't be decoded. Snapshot doesn't have such
info, so there is no easy way to relax the check.
Reported-by: Hsu, John
Diagnosed-by: Arseny Sher
Author: Arseny Sher, Amit Kapila
Reviewed-by: Amit Kapila, Dilip Kumar
Backpatch-through: 9.5
Discussion: https://postgr.es/m/[email protected]
M contrib/test_decoding/Makefile
A contrib/test_decoding/expected/subxact_without_top.out
A contrib/test_decoding/specs/subxact_without_top.spec
M src/backend/replication/logical/reorderbuffer.c
## Teach pg_dump to dump comments on RLS policy objects.
commit : f9d7bb68da30b9b91e7ac440103a3e5ddeaf412a
author : Tom Lane <[email protected]>
date : Mon, 17 Feb 2020 18:40:02 -0500
committer: Tom Lane <[email protected]>
date : Mon, 17 Feb 2020 18:40:02 -0500
This was unaccountably omitted in the original RLS patch.
The SQL syntax is basically the same as for comments on triggers,
so crib code from dumpTrigger().
Per report from Marc Munro. Back-patch to all supported branches.
Discussion: https://postgr.es/m/[email protected]
M src/bin/pg_dump/pg_dump.c
## Add description about LogicalRewriteTruncate wait event into document.
commit : 1beab076cefe70d90f839583e880bb97af1fa6f5
author : Fujii Masao <[email protected]>
date : Mon, 17 Feb 2020 15:33:32 +0900
committer: Fujii Masao <[email protected]>
date : Mon, 17 Feb 2020 15:33:32 +0900
Back-patch to v10 where commit 249cf070e3 introduced
LogicalRewriteTruncate wait event.
Author: Fujii Masao
Reviewed-by: Michael Paquier
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/monitoring.sgml
## Doc: fix old oversights in GRANT/REVOKE documentation.
commit : a56c495873c8a507534c3a98217664d2684497a5
author : Tom Lane <[email protected]>
date : Wed, 12 Feb 2020 14:13:13 -0500
committer: Tom Lane <[email protected]>
date : Wed, 12 Feb 2020 14:13:13 -0500
The GRANTED BY clause in GRANT/REVOKE ROLE has been there since 2005
but was never documented. I'm not sure now whether that was just an
oversight or was intentional (given the limited capability of the
option). But seeing that pg_dumpall does emit code that uses this
option, it seems like not documenting it at all is a bad idea.
Also, when we upgraded the syntax to allow CURRENT_USER/SESSION_USER
as the privilege recipient, the role form of GRANT was incorrectly
not modified to show that, and REVOKE's docs weren't touched at all.
Although I'm not that excited about GRANTED BY, the other oversight
seems serious enough to justify a back-patch.
Discussion: https://postgr.es/m/[email protected]
M doc/src/sgml/ref/grant.sgml
M doc/src/sgml/ref/revoke.sgml
## Document the pg_upgrade -j/--jobs option as taking an argument
commit : 9193627732da5ac6b773b242ce0be8ce7e0031ab
author : Peter Eisentraut <[email protected]>
date : Tue, 11 Feb 2020 23:47:36 +0100
committer: Peter Eisentraut <[email protected]>
date : Tue, 11 Feb 2020 23:47:36 +0100
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https://infoscience.epfl.ch/record/228889
|
## Optimal control for power generating kites
Numerical solutions for optimal power generation in a pumping power cycle for Airborne Wind Energy is presented. The problem is essentially an infinite horizon optimal control problem which is then attempted to solve by three methods, finite time horizon approximation, search for the optimal periodic limit cycle and time transformation of the infinite horizon to a finite half-open space. We find the optimal periodic limit cycle formulation to be the most computationally efficient (least time consuming) of the three formulations. While the finite time approximation yields a solution close to the optimal limit cycle, it suffers due to nonlinearities in the system failing to give a consistent limit cycle and also requires large computational time. The time transformation method fails to solve the problem at all as it requires problems to have solutions, exponentially converging to a steady state which is not the case for our system in the time domain.
Year:
2014
Laboratories:
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|
http://mathhelpforum.com/calculus/186803-proving-root-cubic-polynomial-print.html
|
# Proving the root of a cubic polynomial
• August 27th 2011, 11:15 AM
terrorsquid
Proving the root of a cubic polynomial
How, would I go about proving the root exists for:
$x^3+5x^2-4x-1$ in the interval [0,1]
I'm a little lost as to how I should start.
Thanks.
• August 27th 2011, 11:18 AM
Ackbeet
Re: Proving the root of a cubic polynomial
Try using the Intermediate Value Theorem. Does that give you any ideas?
• August 27th 2011, 08:04 PM
terrorsquid
Re: Proving the root of a cubic polynomial
It seems like I'm not doing anything though :D f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?
Am I missing any steps in the proof? Just lean on the theorem and do nothing?
• August 27th 2011, 08:49 PM
Prove It
Re: Proving the root of a cubic polynomial
Quote:
Originally Posted by terrorsquid
It seems like I'm not doing anything though :D f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?
Am I missing any steps in the proof? Just lean on the theorem and do nothing?
If the function goes from negative to positive, or vice versa, then it must cross the x-axis somewhere in between. That's all you need to do :)
• August 27th 2011, 09:05 PM
CaptainBlack
Re: Proving the root of a cubic polynomial
Quote:
Originally Posted by Prove It
If the function goes from negative to positive, or vice versa, then it must cross the x-axis somewhere in between. That's all you need to do :)
Continuous function
CB
• August 28th 2011, 10:12 AM
Prove It
Re: Proving the root of a cubic polynomial
Quote:
Originally Posted by CaptainBlack
Continuous function
CB
That is very true, and I should have pointed it out, but since polynomials are continuous and the function given by the OP is a polynomial, I thought it went without speaking. But thanks :)
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|
http://mathhelpforum.com/advanced-algebra/167280-number-homomorphisms-between-two-groups.html
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# Thread: Number of homomorphisms between two groups
1. ## Number of homomorphisms between two groups
Hi,
The exact question in the book is "Determine the number of homomorphisms from the additive group Z15 to the additive group Z10" (Zn is cyclic group of integers mod n under addition)
Now if the question asks to find the number of homomorphisms from Z15 onto Z10, then by the First Isomorphism Theorem I can prove that none exit. But if homomorphisms from Z15 into Z10 are allowed to be counted, how do I do it?
2. You've got a pretty good start - the idea is to use the First Isomorphism Theorem. You more or less identified that $\displaystyle \mathbb{Z}_{15}$ needs to map onto some kind of subgroup of $\displaystyle \mathbb{Z}_{10}$. It can't be $\displaystyle \mathbb{Z}_{10}$, because $\displaystyle 15/K=10$ has no integer solution. So there are three other possibilities: $\displaystyle \mathbb{Z}_{15}$ maps into (the subgroup isomorphic to) $\displaystyle \mathbb{Z}_{5}$, $\displaystyle \mathbb{Z}_{2}$, or $\displaystyle \{e\}$.
Try applying a similar argument.
3. Originally Posted by sashikanth
Hi,
The exact question in the book is "Determine the number of homomorphisms from the additive group Z15 to the additive group Z10" (Zn is cyclic group of integers mod n under addition)
Now if the question asks to find the number of homomorphisms from Z15 onto Z10, then by the First Isomorphism Theorem I can prove that none exit. But if homomorphisms from Z15 into Z10 are allowed to be counted, how do I do it?
Let f be a homomorphism from Z15 to Z10. The image of f has to be a subgroup of Z10. Thus, the possible cases are |im f|=1, 2, 5, 10 by Lagrange's theorem. The kernel of f also has to be a subgroup of Z15. Thus, by the first isomophism theorem, |im f| has to be either 1 or 5.
Case 1: |im f|=1. There is only one such homomorphism, a trivial one.
Case 2: |im f|=5. There are four such homomorphisms, i.e., \eulerphi(5) = 4.
For case 2, f(1) has to generate the group, im f. It follows that the number of choices for f(1) is \eulerphi(5) = 4.
Thus, the total number is 5.
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# find the number of homomorphusm
Click on a term to search for related topics.
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https://www.physicsforums.com/threads/definition-of-a-rotating-frame-in-gr.380136/
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# Definition of a rotating frame in GR?
1. Feb 20, 2010
### bcrowell
Staff Emeritus
What is a definition in GR that correctly captures the concept that a frame is rotating? Is it enough to say that it's stationary but not static?
2. Feb 20, 2010
### atyy
Last edited: Feb 21, 2010
3. Feb 21, 2010
### edpell
One observes no fictitious centrifugal force. ?
4. Feb 21, 2010
### bcrowell
Staff Emeritus
Thanks for the link, atyy! Hmm...I think what he's saying with the timelike congruences is essentially equivalent to the idea that a particular observer can check whether the Sagnac effect exists. For instance, say you have a rotating disk. You can make a timelike congruence consisting of world-lines at rest relative to the axis, or a congruence consisting of world-lines at rest relative to the disk. In the latter case, you get a Sagnac effect at every point in space.
I guess my question was awfully vague, but this may help to point me in the right direction to make it more well defined. It seems straightforward to define the right notion for a local observer: do you get a Sagnac effect? I had in mind more the question of whether there was any way to say anything globally.
I don't think this works, because by the equivalence principle a centrifugal force is equivalent to a gravitational force.
5. Feb 21, 2010
### atyy
So I googled a bit and came across Ashtekar and Magnon, 1975 about the Sagnac effect in GR. They discuss two definitions of rotation which are absolute. One is the rotation of a timelike vector field, the other is the rotation of a Fermi transported tetrad. And somehow the Sagnac effect links both of them, and they also say rotation is only a "local" concept in GR. I haven't read the paper beyond that.
6. Feb 21, 2010
### bcrowell
Staff Emeritus
Cool, thanks! That makes sense to me. The Sagnac effect is something you can measure locally, and the absence of a Sagnac effect (locally) is equivalent to staticity (locally). So I think the answer to my original question is probably that there is no way to say in general whether a frame is globally rotating, but you can do it locally, and my proposed definition works.
Similar Discussions: Definition of a rotating frame in GR?
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https://www.lessonplanet.com/teachers/the-antarctic-ecosystem-where-would-it-be-without-krill
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# The Antarctic Ecosystem: Where Would It Be Without Krill?
##### This The Antarctic Ecosystem: Where Would It Be Without Krill? lesson plan also includes:
Students investigate the importance of krill to the Antarctic ecosystem by researching the animals that depend on it and drawing a food web. They conclude by writing paragraphs explaining the potential consequences of a decline in krill populations.
Concepts
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https://www.physicsforums.com/threads/why-does-the-gravitational-force-decrease-below-the-earths-surface.908462/
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# Why does the gravitational force decrease below the Earth's surface?
1. Mar 21, 2017
### Steven Hansel
1. The problem statement, all variables and given/known data
Why does gravity force decreases below earth's surface?
2. Relevant equations
F = G (m1 m2)/r^2
F = force of gravity
G = Universal gravity constant
m1 and m2 = mass of the objects
r = distance between two objects
g = GM/r^2
g = gravity of the object
G = universal gravity constant
M = mass of the object
r = distance/radius between two objects
a = g
g1 = g0 (1-h/r)
g1 = gravity below earth surface
g0 = gravity in the earth surface
h = height of the object
r = distance between two objects
3. The attempt at a solution
I'm really confused on why does gravity force decreases below earth's surface. Gravity becomes stronger when the radius/distance become shorter between two objects. Now, an object is getting shorter radius/distance to the planet why the gravitational force decreases? Isn't it supposed to be stronger? I looked up at the internet and it said "The body will be attracted by the mass of the Earth which is enclosed in a sphere of radius (R - h)" Does this mean that gravity decreases because there are mass in that enclosed sphere?
So, will the gravitational force increases if i create a really deep hole below earth surface and put an object into the deep hole?
Last edited: Mar 21, 2017
2. Mar 21, 2017
### Bandersnatch
Can you write down the gravitational force equation and list all the variables in it?
3. Mar 21, 2017
### Steven Hansel
Done!
4. Mar 21, 2017
### Bandersnatch
Ok, consider an uniform solid sphere (a ball) composed of some material of density ρ. The sphere has mass M and radius R. Can you express the mass of the sphere in terms of its radius and density?
5. Mar 21, 2017
### Steven Hansel
Msphere = 4/3π.r^3.p
i think replace M with volume of a sphere and density of the sphere? into the equation of g = 4π.r^3.p/3.(r-h)^2
Correct me if i'm wrong thanks!
6. Mar 21, 2017
### Bandersnatch
so far so good.
Forget h. We're looking at gravitational acceleration at the surface of the sphere.
You forgot G and the factor of 1/3 from the volume equation. The equation should read:
$g=G \frac{4 \pi R^3 \rho}{3 r^2}$
Where R is the radius of the sphere and r is the distance to the centre of the gravitational field. When you're above the surface of a sphere, these two are different. But they're equal when standing on the surface of a sphere, which lets you write:
$g=CR$ where C are all the constants grouped together.
Is everything clear so far? Can you see what happens if you dig down?
7. Mar 21, 2017
### Steven Hansel
Wow, thanks! that really give me an insight, i was confused at the sphere part but now i understand. thanks again!
8. Mar 21, 2017
### PeroK
If you put an object in a very deep hole, then the Earth's mass above the object will be trying to pull it out of the hole, and no longer be pulling it towards the centre.
9. Mar 21, 2017
### Steven Hansel
That really helped me more, because of the radius decreasing as we go to the core of the earth, the mass of earth/radius into the core also decreases. thanks a lot!
10. Mar 21, 2017
### Staff: Mentor
That's not a good description as it contradicts the shell theorem. The object should feel no net force from any of the planet's mass above it. It only feels force from the mass below it, and said mass is less the deeper the object is.
11. Mar 21, 2017
### BvU
For the benefit of Steven:
It looks as if PerOk and Gneill disagree. They don't. They just have a different idea of 'above'. For P it's in a direction away from the object and away from the center of the earth towards the surface and for GNeill it's everything that's further away from the center of the earth than the object. PeroK: dome, Neill: shell.
Makes a difference.
The nice thing is that indeed the 'above' from PerOk and his 'below' (but outside the sphere with a radius equal to the distance from the object to the center of the earth) exactly compensate each other: no net force as Gneill states.
Draft saved Draft deleted
Similar Discussions: Why does the gravitational force decrease below the Earth's surface?
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https://www.physicsforums.com/threads/angular-momentum-along-a-sloping-line.823882/
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Homework Help: Angular momentum along a sloping line
1. Jul 18, 2015
rpthomps
1. The problem statement, all variables and given/known data
A 1.0 kg particle is moving at a constant 3.5 m/s along the line y=0.62x +1.4, where x and y are in meters and where the motion is toward the positive x and y directions. Find its angular momentum about the origin
2. Attempt at a solution
$L=Iw\\\\L=myv\\\\L=(1)(0.62x+1.4)(3.5)$
Not sure what to do with x though. If I set x=0, this just evaluates the momentum at a point not over the line. The line is infinite, so I would have thought the momentum evaluates to infinity as well but the answer is 4.2
2. Jul 18, 2015
Suraj M
Firstly, how did you get this formula? By the definition?
Rethink your substitution for y. What is $y$ by definition?
3. Jul 19, 2015
rpthomps
You're right. There is a problem with my relationship.
The trig part doesn't seem to simplify to nicely though...
4. Jul 19, 2015
haruspex
What is this point P you have chosen? Just consider the point where the trajectory crosses the y axis.
5. Jul 19, 2015
rpthomps
Can I use that position because angular momentum will be conserved for the whole trip and thus will be the same along the path of the mass and the position you suggested is the simplest to calculate?
6. Jul 19, 2015
haruspex
Yes.
7. Jul 19, 2015
rpthomps
Then thank you sir for your help! Really appreciated.
8. Jul 21, 2015
Suraj M
OP, since you've got the answer, it might help you in the future to know the formula for the perpendicular distance of a point from a line, which would simplify the calculation as there would be no angle involved in the calculation.
Do you happen to have a formula like that? if you did you'll get your d and hence answer would just be mvd.
9. Jul 26, 2015
rpthomps
Thank you.
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http://talkstats.com/threads/statistical-test.74466/
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# Statistical test
#### Shailee
##### New Member
Null Hypothesis : Mean of Intra-subject Time to Haemostasis (TTH) = > 10 min
Alternate Hypothesis : Mean of Intra-subject Time to Haemostasis (TTH) </= 10 min
Sample Size : = 70
I have TTH values for all the 70 samples as performed during the study.
I calculated values for (TTH - 10) for all samples.
After this, I performed paired sample t test, at significance 0.05 , two tailed for values of (TTH) & (TTH-10) (https://www.socscistatistics.com/tests/ttestdependent/default.aspx)
The value of p is .01081. The result is significant at p < .05.
Please help to know if this means that the null hypothesis is rejected in favour of alternate hypothesis.
Last edited:
#### GretaGarbo
##### Human
I performed paired sample t test,
Where do the pairs comes from? No, I don't think this is correct.
Null Hypothesis : Mean of Intra-subject Time to Haemostasis (TTH) = > 10 min
You can just do:
t = (mean(TTH) - 10)/(s/sqrt(70))
where s is the standard deviation.
If the t is less than -1.64 then the null hypothesis will be rejected. Example: t= -2.5 will reject the null hypothesis.
That is for a one sided test. For a two sided test the absolute value of t needs to be larger than 2.
#### Shailee
##### New Member
I am sharing the calculation.
Treatment 1 = TTH for all 70 samples
Treatment 2 = TTH - 10 for all 70 samples.
#### Attachments
• 100.8 KB Views: 3
#### Shailee
##### New Member
I have used attached reference for my study.
If you can, please help to know how analysis was performed, I can perform my analysis accordingly.
#### Attachments
• 99.9 KB Views: 1
• 64.5 KB Views: 1
#### GretaGarbo
##### Human
I don't understand this. You used a pairwise test. Did the patients go twice with the ambulance?
The numbers in the first slide does not match the numbers in the next. Also there it sayes n= 167 not 70.
The much lower median as compared to the mean indicates a very skewed distribution or outliers.
#### Shailee
##### New Member
Apologies for the confusion.
I am sharing a reference study, I am trying to run my study in a similar way.
Can you help to know what data was collected and how analysis is performed for the attached reference study.
#### Attachments
• 99.9 KB Views: 1
• 64.5 KB Views: 1
#### GretaGarbo
##### Human
I am sorry but I am not so good in English.
What is "Haemostasis "? Does it have something to do with blod?
Waht is "ambulation"? Does it have something to do with walking? (I thought it was about the ambulance!
What is the sample size? Is it 70? Or much larger?
Where does the data comes from? Have you done the measurements and created them yourself?
What is your reasearch question? What is it you want to investigate? What is it you want to conclude?
Try to answer these with very simple English.
#### Shailee
##### New Member
Research Question: How much time does it take to stop bleeding (Haemostasis) after transracial catheterisation.
Study product: Chitosan dressing used to stop bleeding from puncture site
Method : Chitosan dressing was applied on the puncture site to stop bleeding.
Sample Size: 70
I have data for each patient:
Patient 1 : time to stop bleeding = 4 min
Patient 2: time to stop bleeding = 7 min
Patient 3: ...
....
...
Patient 70: time to stop bleeding = 5 min
Mean time to stop bleeding = 5.43 +/- 1.36 minutes.
I want to conclude that this mean time to stop bleeding is lesser as compared to standard ( as per literature standard time tostados top bleeding is 10 minutes)
Let me know if further information is required.
#### GretaGarbo
##### Human
Now it is more clear. There is no pairing.
You just have the mean and need to do a confidence interval.
So if "1.36" is the standard deviation( s), then you will get that a confidence interval this way:
mean +/- t*s/sqrt(n)
where "t" comes from the t-distribution and gives a 95% confidence interval. t=1.99 here. sqrt(n) means the square root of n and n is 70.
A 95% confidence interval:
5.43 +/- 1.99*1.36/sqrt(70)
gives:
[5.106523 ; 5.753477]
Since the confidence interval does not include "10" the hypothesis that the population mean is equal to 10 is rejected.
(Dou you prefer a t-test? It would reject the null hypotesis with a very low p-value (1.633491e-39))
There might be a skewness in your data since the mean is larger than the median. But with 70 observation the confidence interval will be approximately valid by the central limit theorem.
#### Shailee
##### New Member
How do I perform a t test and get a p value to reject the null hypothesis.
I was referring to that attached reference.
Attached reference has ambulation time. and has a p value of <0.0001 to reject the null hypothesis.
In my case I am trying to check similar analysis with time to stop bleeding.
If you can, do let me know how data might be collected and testes performed for attached reference and if I can use similar theories for my study for time to stop bleeding.
#### Attachments
• 99.9 KB Views: 3
• 64.5 KB Views: 3
#### GretaGarbo
##### Human
mean +/- t*s/sqrt(n)
A 95% confidence interval:
5.43 +/- 1.99*1.36/sqrt(70)
gives:
[5.106523 ; 5.753477]
A t-test and a confidence interval is very similar. Actually there is a correspondence between t-test and confidence intervals (That is called the correspondence theorem and is written in Casella-Berger for the more statistical oriented people.)
A t-test. You can do it like this:
t_obs = (mean - 10)/(s/sqrt(n))
Now, if the observed t-value (t_obs) is larger in absolute value that the critical t-value of 1.99, then it is statistically significant.
Whith your values it would be:
t_obs = (5.43 - 10) /(1.36/sqrt(70)) = -28.11424
And that is really larger in absolute value than 1.99. Its p-value would be 1.633491e-39, which is very close to zero.
This is based on my assumption that the standarddeviation is 1.36.
Code:
mn <- 5.43
std <- 1.36
n <- 70
qt(0.975, n-1)
mn + c(-1 , +1)*1.99*std/sqrt(n)
(mn -10)/(std/sqrt(n))
2*pt(-28.11, 70-1)
#### GretaGarbo
##### Human
Let's see now: Inter-national is between nations. So I believe that inter-personal is between persons. But an intra-net is within a company. So I assume that an intra-individual will be within the individual.
But why measure within the individual? Isn't the question if the mean between individuals will be ca: 10 minutes?
"The intra subject difference... was analysed with a paired t-test". I don't understand this. If you take the paired difference of an individual it will be about 0. Or is there an treatent of before-treatment and after-treatmen?
#### Shailee
##### New Member
Thanks for your inputs. If t test is similar to Confidence Interval, I will just go ahead with confidence interval.
Also is it possible to find confidence interval for below outcome.
Patient comfort levels as assessed by verbal inquiry:
Excellent - 59 patients
Good - 11 patients
Fair - 0 patients
Not acceptable 0 patients.
#### Shailee
##### New Member
Let's see now: Inter-national is between nations. So I believe that inter-personal is between persons. But an intra-net is within a company. So I assume that an intra-individual will be within the individual.
But why measure within the individual? Isn't the question if the mean between individuals will be ca: 10 minutes?
"The intra subject difference... was analysed with a paired t-test". I don't understand this. If you take the paired difference of an individual it will be about 0. Or is there an treatent of before-treatment and after-treatmen?
I don't understand how the test was performed, this was available in literature and so I was referring to the same.
#### GretaGarbo
##### Human
I don't understand how the test was performed, this was available in literature and so I was referring to the same.
I don't understand that either. You must know more about that than I do. Does it make any sense to do a pairwise test?
- - - -
Also is it possible to find confidence interval for below outcome.
Patient comfort levels as assessed by verbal inquiry:
Excellent - 59 patients
Good - 11 patients
Fair - 0 patients
Not acceptable 0 patients.
You could do a confidence interval for the proportion "excellent" and "good"
- - -
Also I note that you have written in several threads about the same problems. Please don't do that. Now, both I and @hlsmith have tried to answer the same question.
#### hlsmith
##### Not a robit
Just provide a link to the paper you keep referencing. That would clear up the issues. I am assuming the study design for the referenced study is different from what you have done or they just did the wrong analyses or reported it incorrectly (which isn't uncommon).
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http://cogsci.stackexchange.com/users/2611/xsi
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http://cms.math.ca/cjm/msc/32W20?fromjnl=cjm&jnl=CJM
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location: Publications → journals
Search results
Search: MSC category 32W20 ( Complex Monge-Ampere operators )
Expand all Collapse all Results 1 - 3 of 3
1. CJM Online first
Zheng, Tao
The Chern-Ricci flow on Oeljeklaus-Toma manifolds We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that, after an initial conformal change, the flow converges, in the Gromov-Hausdorff sense, to a torus with a flat Riemannian metric determined by the OT-manifolds themselves. Keywords:Chern-Ricci flow, Oeljeklaus-Toma manifold, Calabi-type estimate, Gromov-Hausdorff convergenceCategories:53C44, 53C55, 32W20, 32J18, 32M17
2. CJM 2013 (vol 66 pp. 1413)
Zhang, Xi; Zhang, Xiangwen
Generalized Kähler--Einstein Metrics and Energy Functionals In this paper, we consider a generalized Kähler-Einstein equation on Kähler manifold $M$. Using the twisted $\mathcal K$-energy introduced by Song and Tian, we show that the existence of generalized Kähler-Einstein metrics with semi-positive twisting $(1, 1)$-form $\theta$ is also closely related to the properness of the twisted $\mathcal K$-energy functional. Under the condition that the twisting form $\theta$ is strictly positive at a point or $M$ admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized Kähler-Einstein metric implies a Moser-Trudinger type inequality. Keywords:complex Monge--Ampère equation, energy functional, generalized Kähler--Einstein metric, Moser--Trudinger type inequalityCategories:53C55, 32W20
3. CJM 2009 (vol 62 pp. 218)
Xing, Yang
The General Definition of the Complex Monge--Ampère Operator on Compact Kähler Manifolds We introduce a wide subclass ${\mathcal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that ${\mathcal F}(X,\omega)$ is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class. Keywords:complex Monge--Ampère operator, compact Kähler manifoldCategories:32W20, 32Q15
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https://arxiv.org/abs/hep-ex/9910030
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Full-text links:
hep-ex
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# Title: Search for the Weak Decay of a Lightly Bound H Dibaryon
Authors: The KTeV Collaboration
Abstract: We present results of a search for a neutral, six-quark, dibaryon state called the \h, a state predicted to exist in several theoretical models. Observation of such a state would signal the discovery of a new form of hadronic matter. Analyzing data collected by experiment E799-II, using the KTeV detector at Fermilab, we searched for the decay $H^0 \to \Lambda p \piminus$ and found no candidate events. We exclude the region of lightly bound mass states just below the $\Lambda\Lambda$ mass threshold, $2.194~\gev < M_H < 2.231$~\gev, with lifetimes from $\sim$$5 \times 10^{-10}~sec to \sim$$1 \times 10^{-3}$~sec.
Comments: 4 pages, 5 figures. Submitted to Physical Review Letters Subjects: High Energy Physics - Experiment (hep-ex) Journal reference: Phys.Rev.Lett.84:2593-2597,2000 DOI: 10.1103/PhysRevLett.84.2593 Report number: Fermilab pub-99/305-E Cite as: arXiv:hep-ex/9910030 (or arXiv:hep-ex/9910030v1 for this version)
## Submission history
From: Rbd [view email]
[v1] Fri, 15 Oct 1999 15:45:33 GMT (23kb)
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https://en.wikiversity.org/wiki/Electromagnetic_wave
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# Electromagnetic wave
Subject classification: this is a physics resource.
Search for Electromagnetic wave on Wikipedia.
## Electromagnetic wave
Electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.
Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with other charged particles.
Vector equation of Electromagnetic wave
${\displaystyle \nabla \cdot E=0}$
${\displaystyle \nabla \times E={\frac {1}{T}}E}$
${\displaystyle \nabla \cdot B=0}$
${\displaystyle \nabla \times B={\frac {1}{T}}B}$
Electromagnetic wave equation
${\displaystyle \nabla ^{2}E=-\omega E}$
${\displaystyle \nabla ^{2}B=-\omega B}$
Electromagnetic wave function
${\displaystyle E=ASin\omega t}$
${\displaystyle B=ASin\omega t}$
${\displaystyle \omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}$
${\displaystyle T=\mu \epsilon }$
Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena.
EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total (relativistic) mass, is not zero so they are still affected by gravity.
Electromagnetic radiation travels as a moment at speed
${\displaystyle v=\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}$
Carry energy level
${\displaystyle E=pv=pC=p\lambda f=hf}$
Where
${\displaystyle h=p\lambda }$
From above
${\displaystyle p={\frac {h}{\lambda }}}$
${\displaystyle \lambda ={\frac {h}{p}}={\frac {C}{f}}}$
Electromagnetic radiation is in the form of a Quanta , h , whose rest mass is zero . EM travels as Electromagnetic wave at speed of light carries an energy level of a Photon , hf
Photon (Quanta's energy) . ${\displaystyle E_{h}=hf=h({\frac {\omega }{2\pi }})=\hbar \omega }$
Quanta (Massless particle) . ${\displaystyle h=p\lambda }$
Moment. ${\displaystyle p={\frac {h}{\lambda }}=h{\frac {k}{2\pi }}=\hbar k}$
### Electromagnetic spectrum
The wavefront of electromagnetic waves emitted from a point source (such as a lightbulb) is a sphere. The position of an electromagnetic wave within the electromagnetic spectrum could be characterized by either its frequency of oscillation or its wavelength
The Electromagnetic spectrum includes, in order of increasing frequency and decreasing wavelength:
Electromagnetic radiation carries an energy level
${\displaystyle E=pv=pC=p\lambda f=hf}$
This energy is quantized by a quantity called quanta
${\displaystyle h=p\lambda }$
Electromagnetic radiation carries an energy level
${\displaystyle E=hf}$
This energy is quantized by a quantity called quanta
${\displaystyle h=p\lambda }$
Which displays a duality of Wave-Particle like
Wave like . ${\displaystyle \lambda ={\frac {h}{p}}}$
Particle like . ${\displaystyle p={\frac {h}{\lambda }}}$
There are two states that photon are found Radiant Photon and Electric Photon
Radiant Photon is found at threshold frequency , fo
${\displaystyle f=f_{o}={\frac {C}{\lambda _{o}}}}$
${\displaystyle E=hf_{o}}$
${\displaystyle h=p\lambda _{o}}$
${\displaystyle p={\frac {h}{\lambda _{o}}}}$
${\displaystyle \lambda _{o}={\frac {h}{p}}={\frac {C}{f_{o}}}}$
Electric Photon is found at frequency greater than the threshold frequency , f > fo
${\displaystyle f>f_{o}>{\frac {C}{\lambda _{o}}}}$
${\displaystyle E=hf}$
${\displaystyle h=p\lambda }$
${\displaystyle p={\frac {h}{\lambda }}}$
${\displaystyle \lambda _{o}={\frac {h}{p}}={\frac {C}{f}}}$
Photon cannot exist in 2 states at the same time
${\displaystyle \Delta p\Delta \lambda >{\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}={\frac {\hbar }{2}}}$
#### Penertration
Radiant photon (Beta photon) does not penertrate into matter . Eletric photon (Gamma photon) peneratrates into matter to create heat transfer in matter and can free electron from matter's substances' atom accoding to Photoelectric effect
#### Deflection
Photon enters a magnetic field will be deflected
Alpha photon will be deflected upward
Beta photon will be not be deflected and travel straight
Gamma photon will be deflected downward
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http://physics.stackexchange.com/users/10347/emarti?tab=activity&sort=revisions
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# emarti
less info
reputation
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bio website location age member for 3 years, 1 month seen Jul 7 '13 at 22:47 profile views 135
# 12 Revisions
Feb 10 revised What would happen if Large Hadron Collider would collide electrons? added 40 characters in body Feb 5 revised Why Does Light Not Become Polarized In A Magnetic and/or Electric Field? added 701 characters in body Jan 13 revised Can all quantum superpositions be realized experimentally? added 512 characters in body Jan 11 revised Alkali atom in oscilating electromagnetic field added 181 characters in body Jan 5 revised What is the simplest possible topological Bloch function? changed link Jan 3 revised How many ways are there to distribute M excitations of N identical particles among K=3 quantum harmonic oscillators? added 83 characters in body Dec 31 revised What is the difference between a photon and a phonon? added 60 characters in body Dec 31 revised Why is quantum entanglement so important? added 706 characters in body Dec 23 revised Superposition of electromagnetic waves added 426 characters in body Dec 18 revised Amplitude of an electromagnetic wave containing a single photon added the other missing $V$ to $E_peak$, moved $\mu_0$ to the Dec 18 revised Schrodinger's equation (explanation to non physicist) added 1 characters in body Dec 18 revised Amplitude of an electromagnetic wave containing a single photon changed "factor of 2" to "factor of 1/2"
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https://docs.starknet.io/docs/Fees/fee-mechanism/
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# Fee Mechanism
In this section, we will review StarkNet Alpha 0.8.0 fee mechanism. If you want to skip the motivation and deep dive into the mechanism, you can skip directly to the final formula.
## Introduction
Users can specify the maximum fee that they are willing to pay for a transaction via the max_fee field.
The only limitation on the sequencer (enforced by the StarkNet OS) is that the actual fee charged is bounded by max_fee, but for now, StarkWare’s sequencer will only charge the fee required to cover the proof cost (potentially less than the max fee).
Presently, the sequencer only takes into account L1 costs involving proof submission. There are two components affecting the L1 footprint of a transaction:
## Fee Units
The fee is denominated in ETH (this may change in future versions). Each transaction is associated with a gas estimate (explained below), and combining this with the gas price yields the estimated fee.
## How much fee is charged? High-level overview
### Computation
Let’s analyze the correct metric for measuring transaction complexity. For simplicity, we will ignore Cairo’s builtins for the sake of the explanation, then see later how to refer to them.
#### Without builtins
Recall that a Cairo program execution yields an execution trace. When proving a StarkNet block, we aggregate all the transactions appearing in that block to the execution trace.
StarkNet’s prover generates proofs for execution traces, up to some maximal length $L$ (Derived from the specs of the proving machine and the desired proof latency). Tracking the execution trace length associated with each transaction is simple. Each assertion over field elements (such as verifying addition/multiplication over the field) requires the same, constant number of trace cells (this is where our “no-builtins” assumption kicks in! Obviously Pedersen occupies more trace cells than addition). Therefore, in a world without builtins, the fee of the transaction is correlated with $\text{TraceCells}[tx]/L$.
The Cairo execution trace is separated – and each builtin has its own slot. We have to mind this slot allocation when determining the fee.
Let’s go over a concrete example first. For example, imagine the following trace that the prover will occupy:
(up to) 500,000,000 Cairo Steps(up to) 20,000,000 Pedersen hashes(up to) 4,000,000 signature verifications(up to) 10,000,000 range checks
The proof will be closed and sent to L1 when any of these components becomes full. It’s important to realize that the division to builtins must be predetermined! We can’t decide on the fly to have proof with 20,000,001 Pedersen and nothing else.
Suppose, for example, that a transaction uses 10,000 Cairo steps and 500 Pedersen hashes. We can squeeze at most 40,000 such transactions into our hypothetical trace (20,000,000/500). Therefore, its gas price will be correlated with 1/40,000 the cost of submitting proof. Notice we completely ignored the number of Cairo steps this transaction performance estimation, as it is not the limiting factor (since 500,000,000/10,000 > 20,000,000/500). With this example in mind, we can now formulate the exact fee associated with L2 computation.
#### General Case
For each transaction, the sequencer calculates a vector CairoResourceUsage holding:
• Number of Cairo steps
• Number of applications of each Cairo builtin (e.g., five range checks and two Pedersens)
The sequencer crosses this information with the CairoResourceFeeWeights vector. For each resource type (step or a specific builtin application), CairoResourceFeeWeights has an entry that specifies the relative gas cost of that component in the proof. Going back to the above example, if the cost of submitting a proof with 20,000,000 Pedersen hashes is roughly 5m gas, then the weight of the Pedersen builtin is 0.25 gas per application (5,000,000/20,000,000). The sequencer has a pre-defined weights vector, in accordance with the proof parameters.
The sequencer will charge only according to the limiting factor! Therefore the fee is correlated with:
$\max_k[\text{CairoResourceUsage}_k \cdot \text{CairoResourceFeeWeights}_k]$
Where $k$ here enumerates the Cairo resource components, namely: number of steps and built-ins used.
The weights in 0.8.0 are:
Cairo stepECDSArange checkbitwisePedersen
0.05 gas/step25.6 gas/application0.4 gas/application12.8 gas/application0.4 gas/application
### On Chain Data
The on-chain data associated with a transaction is composed of three parts
• l2→l1 messages
• deployed contracts
Whenever a transaction updates a key at the storage of some contract, the following 32 byte words reach L1 as calldata:
• number of updated keys in that contract
• key to update
• new value
##### info
Note that only the most recent value reaches L1. That is, the transaction's fee only depends on the number of unique storage updates (if the same storage cell is updated multiple times within the transaction, the fee remains that of a single update).
Let $c_w$ denote the L1 calldata cost of a 32 byte word, measured in gas. With 16 gas per byte we have $c_w=16\cdot 32=512$. Consequently, the associated storage update fee for a transaction updating $n$ unique contracts and $m$ unique keys is:
$\text{gas\_price}\cdot c_w\cdot\underbrace{(2n+2m)}_{\text{number of words}}$
##### tip
Note that there are many possible improvements to the above pessimistic estimation that will be gradually presented in future versions of StarkNet. For example, if different transactions within the same block update the same storage cell, there is no need to charge both of them (only the latest value reaches L1). In the future, StarkNet may include a refund mechanism for such cases.
#### L2→L1 Messages
When a transaction which raises the send_message_to_l1 syscall is included in a state update, the following data reaches L1:
• payload (list of field elements)
Consequently, the fee associated with a single l2→l1 message is:
$\text{gas\_price}\cdot c_w\cdot(3+\text{payload\_size})$
#### Deployed Contracts
When a transactions which raises the deploy syscall is included in a state update, the following data reaches L1:
• class hash
• number of constructor arguments
• constructor arguments
Consequently, the fee associated with a single deployment is:
$\text{gas\_price}\cdot c_w\cdot(3+\text{\#\text{ of constructor arguments}})$
## Overall Fee
The fee for a transaction with:
• Cairo usage represented by the vector $v$ (the entries of $v$ correspond to the number of steps and number of applications per builtin)
• $n$ unique contract updates
• $m$ unique key updates
• $t$ messages with payload sizes $q_1,...,q_t$
• $\ell$ deployments with number of constructor arguments $c_1,...,c_\ell$
is given by:
$F = \text{gas\_price}\cdot\left(\max_k v_k w_k + c_w\left(2(n+m) + 3t + \sum\limits_{i=1}^t q_i + 3\ell + \sum\limits_{i=1}^\ell c_i\right)\right)$
where $w$ is the weights vector discussed above and $c_w$ is the calldata cost (in gas) per 32 byte word.
## When is the fee charged?
The fee is charged atomically with the transaction execution on L2. The StarkNet OS injects a transfer of the fee-related ERC-20, with an amount equal to the fee paid, sender equals to the transaction submitter, and the sequencer as a receiver.
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https://www.physicsforums.com/threads/relative-velocity-and-momentum.276249/
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# Relative velocity and momentum
1. Dec 1, 2008
### Maiia
1. The problem statement, all variables and given/known data
Tｏｎｙ （ｏｆ ｍａｓｓ ５０ｋｇ）ｃｏａｓｔｓ ｏｎ ｈｉｓ ｂｉｃｙｃｌｅ （ｏｆ ｍａｓｓ ５ ｋｇ）ａｔ ａ ｃｏｎｓｔａｎｔ ｓｐｅｅｄ ｏｆ ６ｍ／ｓ， ｃａｒｒｙｉｎｇ ａ １２ ｋｇ ｐａｃｋ． Ｔｏｎｙ ｔｈｒｏｗｓ ｈｉｓ ｐａｃｋ ｆｏｒｗａｒｄ， ｉｎ ｔｈｅ ｄｉｒｅｃｔｉｏｎ ｏｆ ｈｉｓ ｍｏｔｉｏｎ， ａｔ ２ｍ／ｓ ｒｅｌａｔｉｖｅ ｔｏ ｔｈｅ ｓｐｅｅｄ ｏｆ ｔｈｅ ｂｉｃｙｃｌｅ ｊｕｓｔ ｂｅｆｏｒｅ ｔｈｅ ｔｈｒｏｗ． Ｗｈａｔ ｉｓ ｔｈｅ ｉｎｉｔｉａｌ ｍｏｍｅｎｔｕｍ ｏｆ ｔｈｅ ｓｙｓｔｅｍ （Ｔｏｎｙ， ｔｈｅ ｂｉｃｙｃｌｅ， ａｎｄ ｔｈｅ ｐａｃｋ）？
Ａｎｓｗｅｒ ｉｎ ｕｎｉｔｓ ｏｆ ｋｇｍ／ｓ．
Ｄｏｅｓ ｒｅｌａｔｉｖｅ ｖｅｌｏｃｉｔｙ ｈｅｒｅ ｍｅａｎ ｔｈａｔ ｔｈｅ ｐａｃｋ ｉｓ ａｃｔｕａｌｌｙ ｍｏｖｉｎｇ ａｔ ８ｍ／ｓ？Ｉ＇ｍ ａ ｌｉｔｔｌｅ ｃｏｎｆｕｓｅｄ ａｓ ｔｏ ｗｈａｔ ｒｅｌａｔｉｖｅ ｖｅｌｏｃｉｔｙ ｉｓ． To get initial momentum, I ｗｏｕｌｄ ｊｕｓｔ ａｄｄ ａｌｌ ｔｈｅｉｒ ｍｏｍｅｎｔｕｍｓ ｔｏｇｅｔｈｅｒ， ｒｉｇｈｔ？Ｂｅｃａｕｓｅ ｔｈｅｙ ｈａｖｅ ｄｉｆｆｅｒｅｎｔ ｓｐｅｅｄｓ？ Ｂｅｃａｕｓｅ Ｉ don't think Ｉ would be able to add their masses together and multiply by the velocity.
2. Dec 1, 2008
### turin
Yes, relative to the speed of the bike just means that you should imagine that the bike is at rest and the earth is moving 6 m/s backward. So, yes, the pack is moving at 8 m/s relative to the earth. However, are you sure this is relevant to the question that the problem asks?
3. Dec 1, 2008
### Maiia
hmm i guess not b/c the pack should be moving at the same speed as the boy and the bike..but it would be if i were asked to find the momentum of the system after the pack was thrown i think..
4. Dec 1, 2008
Careful ...
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https://space.stackexchange.com/questions/59175/how-to-find-the-hyperbolic-angle-given-the-mean-anomaly
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How to find the hyperbolic angle given the mean anomaly?
I'm modelling a hyperbolic gravity assist trajectory around Jupiter and trying to calculate the coordinates for each hour interval before/after passing periapsis. I've calculated $$M_h = 0.0176$$ is the mean anomaly 1 hour from periapsis, but how can I determine the corresponding hyperbolic angle, i.e solve this equation for H, given e = 1.3893:
$$M_h = 0.0176 = e~\rm sinh\it(H) - H$$
Using iterative calculations I know the answer is approximately $$H = 0.04$$, but I'm hoping to solve the equation above "precisely".
Like the corresponding eccentric anomaly for elliptical orbits, there is no closed-form formula for going from mean anomaly to hyperbolic anomaly.
You're going to have to use some sort of numerical method to go in that direction. Newton-Raphson tends to converge quickly enough.
$${\displaystyle x_{n+1}=x_{n}-{\frac {f(x_{n})}{f'(x_{n})}}}$$
With Mean anomaly at the chosen time as $$M$$, we'll look for zeroes on the function: $$f(H_n) = e \sinh H_n - H_n -M$$ And we'll need its first derivative: $$f'(H_n) = e \cosh H_n - 1$$
And we'll iterate with:
$$H_{n+1} = H_n - \frac{e \sinh H_n - H_n -M}{e \cosh H_n -1}$$
In almost every case I've used it, it's been useful to set the initial guess of the hyperbolic anomaly $$H_0$$ equal to the Mean Anomaly $$M$$. Given your chosen parameters of eccentricity $$e = 1.3893$$ and mean anomaly $$M = 0.0176$$, these are the values pulled up from a quick Google Sheets Spreadsheet:
Iteration Hyperbolic Anomaly
$$H_0$$ $$\underline{0.0}176$$
$$H_1$$ $$\underline{0.0451}9085695$$
$$H_2$$ $$\underline{0.045154584}33$$
$$H_3$$ $$\underline{0.04515458422}$$
... ...
Newton-Raphson's convergence is typically quadratic, resulting in roughly doubling the number of correct digits each iteration. We're at the three significant figures of your mean anomaly value by $$H_1$$, and by $$H_3$$ the iterated value doesn't change under the floating-point precision Google Sheets can handle.
One more thing: The convergence of using the Newton-Raphson method above with Kepler's equations gets slower as orbital eccentricity approaches $$e=1$$. If Orbital eccentricity was $$e=1.01$$, it would take until $$H_7$$ to get three significant figures stable from the specified Mean Anomaly. At $$e=1.001, H_{21}$$, and $$e=1.0001, H_{74}$$, and so forth. If your hyperbolas are extremely near-parabolic, you may need to look into an alternate method to calculate position as a function of time.
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|
http://roy-t.nl/index.php/tag/math/
|
## Thesis: upper sets in partially ordered sets
Today I finally finished my thesis. It’s topic was to count the number of upper sets in partially ordered sets Which is quite a hard problem since it’s in the complexity class #P-Complete (that’s the class of counting the solutions to the decision problems in NP-complete). All and all I’m quite pleased with the result. Although the upper bound is still $O(2^{n})$, (can’t quite get under there without solving P=NP and winning a million dollars) I’ve manged to find a solution that has a best case of $O(n)$ both in time and memory complexity. With a particularly large data set the brute-force algorithm took over 2 hours to complete while my algorithm took 0.025 seconds. Now that’s what I’d call a speed gain (and yes it was a real life data set, no tricks here). You can see this for yourself in the graph at the bottom of this post the ‘naïeve algoritme’ is the brute force approach, the ‘Familiealgoritme zonder uptrie’ is the first version of my algorithm, the ‘Familiealgoritme met uptrie’ is the final version of my algorithm. It uses a trie like data structure to speed up searching and uses a lot less memory. Note that the graph has a logarithmic scale.
Unfortunately for most readers my thesis is in Dutch, but I’ve translated the abstract to English:
Counting the number of upper sets in partially ordered sets gives us a unique number that can be used to compare sets. This number is like the fingerprint of a set. Until now there isn’t, as to my knowledge, an efficient algorithm to calculate this number. This meant that the number had to be calculated either by hand or by using a brute force approach. Using a brute force approach leads quickly to problems, even for trivially small data sets since this means that you have to generate 2^n subsets and check each of these subsets on upwards closure. When calculating by hand you can use symmetry but this menial process can take a lot of time and is error prone. In this thesis I present an algorithm that can calculate exact, and usually fast, the number of upper sets in a partially ordered set.
You can download my thesis here: Upper sets in partially ordered sets (Bsc thesis Roy Triesscheijn) as I’ve said before the text is in Dutch, but the proofs and attached code should be readable enough. If you’ve got any questions feel free to ask below!
06
Jul 2012
CATEGORY
## Getting the Left, Forward and Back vectors from a View Matrix directly
I was wondering why I had to calculate the forward and left vectors for my arcball camera manually and why these results differed from ViewMatrix.Left and the likes. So I asked at the xna forums and almost immediately Jeremy Walsh pointed me in the right direction. He pointed out to me that view matrices are transposed from a normal matrix (meaning that the rows and columns are switched). To get the right vectors from the view matrix, we have to transpose it again to get the original matrix, however this generates a lot of garbage, so he told me that its better to construct the vectors from the matrix cells themselves.
And so I did, and I’ve packaged them into my neat PositionalMath class (which I might release some day). Here are the methods to get all the information you want from those view matrices, without having to calculate the forward (lookat – position) and crossing that.
```// Because a ViewMatrix is an inverse transposed matrix, viewMatrix.Left is not the real left
// These methods returns the real .Left, .Right, .Up, .Down, .Forward, .Backward
// See: http://forums.xna.com/forums/t/48799.aspx
public static Vector3 ViewMatrixLeft(Matrix viewMatrix)
{
return -ViewMatrixRight(viewMatrix);
}
public static Vector3 ViewMatrixRight(Matrix viewMatrix)
{
return new Vector3(viewMatrix.M11, viewMatrix.M21, viewMatrix.M31);
}
public static Vector3 ViewMatrixUp(Matrix viewMatrix)
{
return new Vector3(viewMatrix.M12, viewMatrix.M22, viewMatrix.M33);
}
public static Vector3 ViewMatrixDown(Matrix viewMatrix)
{
return -ViewMatrixUp(viewMatrix);
}
public static Vector3 ViewMatrixForward(Matrix viewMatrix)
{
return -ViewMatrixBackward(viewMatrix);
}
public static Vector3 ViewMatrixBackward(Matrix viewMatrix)
{
return new Vector3(viewMatrix.M13, viewMatrix.M23, viewMatrix.M33);
}
```
04
Mar 2010
CATEGORY
Blog
|
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https://cot3100su10.wordpress.com/2010/06/20/homework-4/
|
## Homework 4
Homework 4 is due on Thursday, July 1st.
0. Read Chapter 9. Indicating in at most three sentences one or more of the following: the passage in the reading— including its page number—you:
• Found most difficult
• Found most surprising
• Would like to have discussed in the next lecture
1. Show that Dijkstra’s algorithm may not work if edges can have negative weights
2. Show that for any undirected graph with |V| >= 2 nodes there exist two vertices with the same degree.
3. Let G be a graph and v a vertex in G with degree at most half the average degree of the Graph. Show that deleting the vertex v (and all incident edges) does not decrease the average degree of the Graph.
4. Let $G = (V;E)$ be a graph that has at least 5 vertices. The complement of $G$ is a graph $\bar{G} = (V, \bar{E})$ on the same vertices such that two vertices of $\bar{G}$ are adjacent if and only if they are not adjacent in $G$. Show that $G$ or $\bar{G}$ contains a cycle
|
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|
http://codeup.cn/problem.php?id=6110
|
[献花][花圈]
题目描述
Programming Ability Test (PAT) is organized by the College of Computer Science and Technology of Zhejiang University. Each test is supposed to run simultaneously in several places, and the ranklists will be merged immediately after the test. Now it is your job to write a program to correctly merge all the ranklists and generate the final rank.
输入
Each input file contains one test case. For each case, the first line contains a positive number N (<=100), the number of test locations. Then N ranklists follow, each starts with a line containing a positive integer K (<=300), the number of testees, and then K lines containing the registration number (a 13-digit number) and the total score of each testee. All the numbers in a line are separated by a space.
输出
For each test case, first print in one line the total number of testees. Then print the final ranklist in the following format:
registration_number final_rank location_number local_rank
The locations are numbered from 1 to N. The output must be sorted in nondecreasing order of the final ranks. The testees with the same score must have the same rank, and the output must be sorted in nondecreasing order of their registration numbers.
样例输入
2
5
1234567890001 95
1234567890005 100
1234567890003 95
1234567890002 77
1234567890004 85
4
1234567890013 65
1234567890011 25
1234567890014 100
1234567890012 85
样例输出
9
1234567890005 1 1 1
1234567890014 1 2 1
1234567890001 3 1 2
1234567890003 3 1 2
1234567890004 5 1 4
1234567890012 5 2 2
1234567890002 7 1 5
1234567890013 8 2 3
1234567890011 9 2 4
[献花][花圈]
|
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|
http://savannah.nongnu.org/bugs/?41150
|
## bug #41150: Single-letter arguments to math macro are parsed wrongly
Submitted by: None Submitted on: Wed 08 Jan 2014 05:09:31 PM UTC Category: None Severity: 3 - Normal Item Group: None Status: None Privacy: Public Assigned to: None Open/Closed: Open
Add a New Comment (Rich Markup):
## You are not logged in
Wed 08 Jan 2014 05:09:31 PM UTC, original submission:
Adjacent single-letter arguments to a math macro are not parsed correctly in eLyXer 1.2.5 generating HTML output.
This math macro usage, as found in the attached file 'elyxer-bug-single-letter-math-macro-args.lyx':
\global\long\def\mymacro#1#2{(#1,#2)}
$\mymacro BC$
$\mymacro A{\mymacro BC}$
produces HTML output that looks like this:
(BC, #2)
(A, \mymacroBC)
whereas the expected output is:
(B, C)
(A, (B, C))
One work-around is to define the macro using optional arguments: then single-letter arguments are enclosed in brackets, avoiding the parsing problem.
Anonymous
(Note: upload size limit is set to 16384 kB, after insertion of the required escape characters.)
Attach File(s):
Comment:
Attached Files
file #30225: elyxer-bug-single-letter-math-macro-args.lyx added by None (2kB - application/x-lyx)
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Wed 08 Jan 2014 05:09:31 PM UTCNoneAttached File-Added elyxer-bug-single-letter-math-macro-args.lyx, #30225
|
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http://www.physicsforums.com/showthread.php?t=337175
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# Fractions, Exponents, and x :(
by tunaizgood
Tags: exponents, fractions
P: 1 I simply just don't get fractions and exponents i was given this problem: [6x^(4/5)-3x(2/3)]/3x^(1/3) i haven't gotten anywhere and i'm stuck help thanks in advance
Sci Advisor HW Helper PF Gold P: 12,016 What problem? What are you supposed to do? All you have done so far is to present an expression. What are you supposed to do with it? Paint the expression on a subway station, perhaps? (That would be easy, but technically illegal)
Math
Emeritus
Thanks
PF Gold
P: 38,898
Quote by tunaizgood I simply just don't get fractions and exponents i was given this problem: [6x^(4/5)-3x(2/3)]/3x^(1/3)
Is there supposed to be a "^" before the 2/3?
i haven't gotten anywhere and i'm stuck help thanks in advance
So this is
$$\frac{6x^{\frac{4}{5}}- 3x^{\frac{2}{3}}}{3x^{\frac{1}{3}}}$$
and you want to simplify it? I would start by factoring out a "3"
$$\frac{3(2x^{\frac{4}{5}}- x^{\frac{2}{3}})}{3x^{\frac{1}{3}}}$$
$$=\frac{2x^{\frac{4}{5}}- x^{\frac{2}{3}}}{x^{\frac{1}{3}}}$$
Now write the $x^{1/3}$ in the denominator as $x^{-1/3}$ in the numerator and use the "laws of exponents": $x^ax^b= x^{a+b}$
Related Discussions Precalculus Mathematics Homework 13 Calculus & Beyond Homework 3 Precalculus Mathematics Homework 4 General Math 9 General Math 1
|
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https://docs.blender.org/manual/es/dev/compositing/types/input/index.html
|
# Input Nodes¶
Input nodes produce information from some source. For instance, an input could be:
• taken directly from the active camera in a selected scene,
• from a JPG, PNG, etc. file as a static picture,
• a movie clip (such as an image sequence or video),
• or just a color or value.
These nodes generate the information that feeds other nodes. As such, they have no input-connectors; only outputs.
|
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