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http://mathoverflow.net/questions/118793/number-of-maximal-left-ideals | # Number of Maximal Left Ideals
In THIS PROBLEM it is proved that for any non-zero ring $R$ with identity, $R[x]$ has an infinite number of maximal left ideals. Is it possible for an uncountable non-zero ring $R$ with identity, $R[x]$ has only a countable number of maximal left ideals ??
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Generalizing the answer by wccanard: Let $R$ be a commutative ring. Then the kernel of $R[x] \twoheadrightarrow R_{red}[x]$ consists of nilpotent elements, hence this map induces a homeomorphism $\mathrm{Spec}(R_{red}[x]) \cong \mathrm{Spec}(R[x])$. It restricts to a homeomorphism between the subspaces of closed points $\mathrm{Spm}(R_{red}[x]) \cong \mathrm{Spm}(R[x])$. Now take any uncountable $R$ such that $R_{red}$ is a finite field.
Is there an uncountable boolean ring $R$ such that $\mathrm{Spec}(R)$ is countable? This would answer your question, because $\mathrm{Spec}(R[x]) = \coprod_{m \in \mathrm{Spec}(R)} \mathrm{Spec}(R/m[x]) = \coprod_{m \in \mathrm{Spec}(R)} \mathrm{Spec}(\mathbb{F}_2[x])$ is countable. – Martin Brandenburg Jan 13 '13 at 15:36
@Martin: I'm afraid there is no such Boolean algebra. Since maximal ideals are in two-sided correspondence with ultrafilters and if $R$ is a superatomic Boolean algebra then $|Ult(R)| = |R|$ and if $R$ is not superatomic then $|Ult(R)| > 2^{\aleph_0}$. So it seems that there is no uncountable Boolean algebra with only a countable number of ultrafilters. – user30230 Jan 13 '13 at 19:59
Yes. Take your favorite finite field, now form $R$ by adjoining uncountably many new variables each with square equal to zero and product of any two equal to zero (more precisely, let's say any element of $R$ is only allowed to mention finitely many of these variables) and now any maximal ideal will have to contain all of them, so done.
Which is to say, the ideals in $R[x]$ correspond to the ideals in $F[x]$, where $F$ was the finite field. – Allen Knutson Jan 13 '13 at 12:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9361150860786438, "perplexity": 152.93082133035983}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463485.78/warc/CC-MAIN-20150226074103-00140-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/functions-modeling-change-a-preparation-for-calculus-5th-edition/chapter-7-trigonometry-and-periodic-functions-7-3-radians-and-arc-length-exercises-and-problems-for-section-7-3-exercises-and-problems-page-284/3 | ## Functions Modeling Change: A Preparation for Calculus, 5th Edition
$\frac{5\pi}{9}$ rad.
Use the conversion $360^\circ=2\pi \, \textrm{rad.}$ to simplify the expression to $$100^\circ \cdot \frac{2\pi \, \textrm{rad.}}{360^\circ}=\frac{100\pi}{180} \, \textrm{rad.}=\frac{5\pi}{9} \, \textrm{rad.}$$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.847670316696167, "perplexity": 2943.564768317004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540527620.19/warc/CC-MAIN-20191210123634-20191210151634-00342.warc.gz"} |
https://math.hecker.org/ | ## Variance and the sum of squared pairwise differences
The variance $\sigma^2$ of a set of $n$ values $x_1, x_2, ..., x_n$ is usually expressed in terms of squared differences between those values and the mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$ of those values.
$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$
However the sum of squared differences $(x_i - \bar{x})^2$ between the values and the mean can also be expressed in term of the sum of squared pairwise differences $(x_i - x_j)^2$ among the values themselves, without reference to the mean $\bar{x}$.
In particular, we want to show that
$\sum_{i=1}^{n} (x_i - \bar{x})^2 = \frac{1}{2n} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2$.
To get an expression involving $\bar{x}$ we rewrite the squared difference in the righthand sum and then expand the result:
$\sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2 = \sum_{i=1}^{n} \sum_{j=1}^{n} [(x_i - \bar{x}) - (x_j - \bar{x})]^2$
$= \sum_{i=1}^{n} \sum_{j=1}^{n} [(x_i - \bar{x})^2 - 2 (x_i - \bar{x}) (x_j - \bar{x}) + (x_j - \bar{x})^2]$
$= \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x})^2 - 2 \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x}) (x_j - \bar{x}) + \sum_{i=1}^{n} \sum_{j=1}^{n} (x_j - \bar{x})^2$
Since the squared difference in the first term does not depend on $j$, the first term can be rewritten as
$\sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x})^2 = \sum_{i=1}^{n} n (x_i - \bar{x})^2 = n \sum_{i=1}^{n} (x_i - \bar{x})^2$
Since the squared difference in the third term does not depend on $i$, the third term can be rewritten as
$= \sum_{i=1}^{n} \sum_{j=1}^{n} (x_j - \bar{x})^2 = n \sum_{j=1}^{n} (x_j - \bar{x})^2 = n \sum_{i=1}^{n} (x_i - \bar{x})^2$
where in the last step we replaced $j$ as an index with $i$. So the third term is identical to the first term.
We now turn to the second term, $-2 \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x}) (x_j - \bar{x})$. We can bring the difference $(x_i - \bar{x})$ out of the inner sum, since it does not depend on the index $j$. This gives us
$-2 \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x}) (x_j - \bar{x}) = -2 \sum_{i=1}^{n} (x_i - \bar{x}) [\sum_{j=1}^{n} (x_j - \bar{x})]$
The sum $\sum_{j=1}^{n} (x_j - \bar{x})$ can then be rewritten as
$\sum_{j=1}^{n} (x_j - \bar{x}) = \sum_{j=1}^{n} x_j - \sum_{j=1}^{n} \bar{x}$
$= \sum_{j=1}^{n} x_j - n \bar{x}$
But we have $\bar{x} = \frac{1}{n} \sum_{j=1}^{n} x_j$ by definition, so we then have
$\sum_{j=1}^{n} (x_j - \bar{x}) = \sum_{j=1}^{n} x_j - n \bar{x} = n \bar{x} - n \bar{x} = 0$
We can then substitute this result into the second term as follows:
$-2 \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x}) (x_j - \bar{x}) = -2 \sum_{i=1}^{n} (x_i - \bar{x}) [\sum_{j=1}^{n} (x_j - \bar{x})]$
$= -2 \sum_{i=1}^{n} (x_i - \bar{x}) \cdot 0 = -2 \sum_{i=1}^{n} 0 = 0$
Now that we know the value of all three terms we have
$\sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2$
$= \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x})^2 - 2 \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - \bar{x}) (x_j - \bar{x}) + \sum_{i=1}^{n} \sum_{j=1}^{n} (x_j - \bar{x})^2$
$= n \sum_{i=1}^{n} (x_i - \bar{x})^2 + 0 + n \sum_{i=1}^{n} (x_i - \bar{x})^2$
$= 2n \sum_{i=1}^{n} (x_i - \bar{x})^2$
so that
$\sum_{i=1}^{n} (x_i - \bar{x})^2 = \frac{1}{2n} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2$
which is what we set out to prove.
However, we can further simplify this identity. Since $(x_i - x_j) = 0$ when $i = j$ and $(x_i - x_j)^2 = (x_j - x_i)^2$, we can consider only differences when $i < j$ (i.e., elements above the diagonal, if we consider the pairwise comparisons to form a matrix):
$\sum_{i=1}^{n} (x_i - \bar{x})^2 = \frac{1}{2n} \sum_{i=1}^{n} \sum_{j=1}^{n} (x_i - x_j)^2$
$= \frac{1}{2n} [\sum_{i < j} (x_i - x_j)^2 + \sum_{i = j} (x_i - x_j)^2 + \sum_{i > j} (x_i - x_j)^2]$
$\frac{1}{2n} [\sum_{i < j} (x_i - x_j)^2 + 0 + \sum_{i < j} (x_i - x_j)^2]$
$\frac{1}{2n} [2 \sum_{i < j} (x_i - x_j)^2] = \frac{1}{n} \sum_{i < j} (x_i - x_j)^2$
From the definition of $\sigma^2$ we then have
$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$
$= \frac{1}{n} [\frac{1}{n} \sum_{i < j} (x_i - x_j)^2]$
$= \frac{1}{n^2} \sum_{i < j} (x_i - x_j)^2$
Posted in Uncategorized | Leave a comment
## All length-preserving matrices are unitary
I recently read the (excellent) online resource Quantum Computing for the Very Curious by Andy Matuschak and Michael Nielsen. Upon reading the proof that all length-preserving matrices are unitary and trying it out myself, I came to believe that there is an error in the proof as written, specifically with trying to show that off-diagonal entries in $M^\dagger M$ are zero if $M$ is length-preserving.
Using the identity $|| M \left|\psi\right> ||^2 = \left<\psi\right| M^\dagger M \left|\psi\right>$, a suitable choice of $\left|\psi\right> = \left|e_j\right> + \left|e_k\right>$ with $j \ne k$, and the fact that $M$ is length-preserving, Nielsen first shows that $(M^\dagger M)_{jk} + (M^\dagger M)_{kj} = 0$ for $j \ne k$.
He then goes on to write “But what if we’d done something slightly different, and instead of using $\left|\psi\right> = \left|e_j\right> + \left|e_k\right>$ we’d used $\left|\psi\right> = \left|e_j\right> - \left|e_k\right>$? … I won’t explicitly go through the steps – you can do that yourself – but if you do go through them you end up with the equation: $(M^\dagger M)_{jk} - (M^\dagger M)_{kj} = 0$.”
I was an undergraduate physics and math major, but either I never worked with bra-ket notation and Hermitian conjugates or I’ve forgotten whatever I knew about them. In any case in working through this I could not get the same result as Nielsen; I simply ended up once again proving that $(M^\dagger M)_{jk} + (M^\dagger M)_{kj} = 0$.
After some thought and experimentation I concluded that the key is to choose $\left|\psi\right> = \left|e_j\right> + i\left|e_k\right>$. Below is my (possibly mistaken!) attempt at a correct proof that all length-preserving matrices are unitary.
Proof: Let $M$ be a length-preserving matrix such that for any vector $\left|\psi\right>$ we have $|| M \left|\psi\right> || = || \left|\psi\right> ||$. We wish to show that $M$ is unitary, i.e., $M^\dagger M = I$.
We first show that the diagonal elements of $M^\dagger M$, or $(M^\dagger M)_{jj}$, are equal to 1.
To do this we start with the unit vectors $\left|e_j\right>$ and $\left|e_k\right>$ with 1 in positions $j$ and $k$ respectively, and 0 otherwise. The product $M^\dagger M \left|e_k\right>$ is then the $k$th column of $M^\dagger M$, and $\left$ is the $jk$th entry of $M^\dagger M$ or $(M^\dagger M)_{jk}$.
From the general identity $\left<\psi\right| M^\dagger M \left|\psi\right> = || M \left|\psi\right> ||^2$ we also have $\left = || M \left|e_j\right> ||^2$. But since $M$ is length-preserving we have $|| M \left|e_j\right> ||^2 = || \left|e_j\right> ||^2 = 1^2 = 1$ since $\left|e_j\right>$ is a unit vector.
We thus have $(M^\dagger M)_{jj} = \left = || M \left|e_j\right> ||^2 = 1$. So all diagonal entries of $M^\dagger M$ are 1.
We next show that the non-diagonal elements of $M^\dagger M$, or $(M^\dagger M)_{jk}$ with $j \ne k$, are equal to zero.
Let $\left|\psi\right> = \left|e_j\right> + \left|e_k\right>$ with $j \ne k$. Since $M$ is length-preserving we have
$|| M \left|\psi\right> ||^2 = || \left|\psi\right> ||^2 = || \left|e_j\right> + \left|e_k\right> ||^2 = 1^2 + 1^2 = 2$
We also have $|| M \left|\psi\right> ||^2 = \left<\psi\right| M^\dagger M \left|\psi\right>$ where $\left<\psi\right| = \left|\psi\right>^\dagger = (\left|e_j\right> + \left|e_k\right>)^\dagger$. From the definition of the dagger operation and the fact that the nonzero entries of $\left|e_j\right>$ and $\left|e_k\right>$ have no imaginary parts we have $(\left|e_j\right> + \left|e_k\right>)^\dagger = \left.
We then have
$|| M \left|\psi\right> ||^2 = \left<\psi\right| M^\dagger M \left|\psi\right>$
$= \left|\psi\right>^\dagger M^\dagger M \left|\psi\right>$
$= (\left|e_j\right> + \left|e_k\right>)^\dagger M^\dagger M (\left|e_j\right> + \left|e_k\right>)$
$= (\left + \left|e_k\right>)$
$= \left + \left + \left + \left$
$= (M^\dagger M)_{jj} + (M^\dagger M)_{jk} + (M^\dagger M)_{kj} + (M^\dagger M)_{kk}$
$= 2 + (M^\dagger M)_{jk} + (M^\dagger M)_{kj}$
since we previously showed that all diagonal entries of $M^\dagger M$ are 1.
Since $|| M \left|\psi\right> ||^2 = 2$ and also $|| M \left|\psi\right> ||^2 = 2 + (M^\dagger M)_{jk} + (M^\dagger M)_{kj}$ we thus have $(M^\dagger M)_{jk} + (M^\dagger M)_{kj} = 0$ for $j \ne k$.
Now let $\left|\psi\right> = \left|e_j\right> + i\left|e_k\right>$ with $j \ne k$. Again we have $|| M \left|\psi\right> ||^2 = || \left|\psi\right> ||^2$ since $M$ is length-preserving, so that
$|| M \left|\psi\right> ||^2 = || \left|\psi\right> ||^2 = || \left|e_j\right> + i\left|e_k\right> ||^2$
$= (\left|e_j\right> + i\left|e_k\right>)^\dagger (\left|e_j\right> + i\left|e_k\right>)$
Since $i\left|e_k\right>$ has an imaginary part for its (single) nonzero entry, in performing the dagger operation and taking complex conjugates we obtain $(\left|e_j\right> + i\left|e_k\right>)^\dagger = \left. We thus have
$|| M \left|\psi\right> ||^2 = (\left|e_j\right> + i\left|e_k\right>)^\dagger (\left|e_j\right> + i\left|e_k\right>)$
$= (\left + i\left|e_k\right>)$
$= \left + \left - i \left - i \left$
$= \left + i\left - i \left - i^2\left$
$= \left + i\left - i\left + \left$
$= 1^2 + i\cdot 0 - i\cdot 0 + 1^2 = 2$
We also have
$|| M \left|\psi\right> ||^2 = \left<\psi\right| M^\dagger M \left|\psi\right>$
$= \left|\psi\right>^\dagger M^\dagger M \left|\psi\right>$
$= (\left|e_j\right> + i\left|e_k\right>)^\dagger M^\dagger M (\left|e_j\right> + i\left|e_k\right>)$
$= (\left + i\left|e_k\right>)$
$= \left + \left - i\left - i\left$
$= \left + i\left - i\left - i^2\left$
$= (M^\dagger M)_{jj} + i(M^\dagger M)_{jk} - i(M^\dagger M)_{kj} + (M^\dagger M)_{kk}$
$= 2 + i\left((M^\dagger M)_{jk} - (M^\dagger M)_{kj}\right)$
Since $|| M \left|\psi\right> ||^2 = 2$ we have $2 = 2 + i\left((M^\dagger M)_{jk} - (M^\dagger M)_{kj}\right)$ or $0 = i\left((M^\dagger M)_{jk} - (M^\dagger M)_{kj}\right)$ so that $(M^\dagger M)_{jk} - (M^\dagger M)_{kj} = 0$.
But we showed above that $(M^\dagger M)_{jk} + (M^\dagger M)_{kj} = 0$. Adding the two equations the terms for $(M^\dagger M)_{kj}$ cancel out and we get $(M^\dagger M)_{jk} = 0$ for $j \ne k$. So all nondiagonal entries of $M^\dagger M$ are equal to zero.
Since all diagonal entries of $M^\dagger M$ are equal to 1 and all nondiagonal entries of $M^\dagger M$ are equal to zero, we have $M^\dagger M = I$ and thus the matrix $M$ is unitary.
Since we assumed $M$ was a length-preserving matrix we have thus shown that all length-preserving matrices are unitary.
Posted in Uncategorized | 4 Comments
## Linear Algebra and Its Applications, Exercise 3.4.28
Exercise 3.4.28. Given the plane $x_1 + x_2 + x_3 = 0$ and the following vectors
$\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} \qquad \begin{bmatrix} 0 \\ 1 \\ -1 \end{bmatrix} \qquad \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}$
in the plane, find an orthonormal basis for the subspace represented by the plane. Report the dimension of the subspace and the number of nonzero vectors produced by Gram-Schmidt orthogonalization.
Answer: We start with the vector $a_1 = (1, -1, 0)$ and normalize it to create $q_1$:
$\|a_1\|^2 = 1^2 + (-1)^2 + 0^2 = 1 + 1 = 2$
$q_1 = a_1/\|a_1\| = \frac{1}{\sqrt{2}} a_1 = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \end{bmatrix}$
We then take the second vector $a_2 = (0, 1, -1)$ and create a second orthogonal vector $a_2'$ by subtracting from $a_2$ its projection on $q_1$:
$a_2' = a_2 - (q_1^Ta_2)q_1$
$= a_2 - \left[ \frac{1}{\sqrt{2}} \cdot 0 + (-\frac{1}{\sqrt{2}}) \cdot 1 + 0 \cdot (-1) \right]q_1 = a_2 - (-\frac{1}{\sqrt{2}})q_1 = a_2 + \frac{1}{\sqrt{2}}q_1$
$= \begin{bmatrix} 0 \\ 1 \\ -1 \end{bmatrix} + \frac{1}{\sqrt{2}} \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ -1 \end{bmatrix} + \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 0 \end{bmatrix} = \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -1 \end{bmatrix}$
We then normalize $a_2'$ to create $q_2$:
$\|a_2'\|^2 = (\frac{1}{2})^2 + (\frac{1}{2})^2 + (-1)^2 = \frac{1}{4} + \frac{1}{4} + 1 = \frac{3}{2}$
$q_2 = a_2'/\|a_2'\| = a_2'/\sqrt{\frac{3}{2}} = \frac{\sqrt{2}}{\sqrt{3}} \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -1 \end{bmatrix} = \begin{bmatrix} \frac{\sqrt{2}}{2\sqrt{3}} \\ \frac{\sqrt{2}}{2\sqrt{3}} \\ -\frac{\sqrt{2}}{\sqrt{3}} \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \end{bmatrix}$
Finally, we take the third vector $a_3 = (1, 0, -1)$ and attempt to create another orthogonal vector $a_3'$ by subtracting from $a_3$ its projections on $q_1$ and $q_2$:
$a_3' = a_3 - (q_1^Ta_3)q_1 - (q_2^Ta_3)q_2$
$= a_3 - \left[ \frac{1}{\sqrt{2}} \cdot 1 + (-\frac{1}{\sqrt{2}}) \cdot 0 + 0 \cdot (-1) \right]q_1- \left[ \frac{1}{\sqrt{6}} \cdot 1 + \frac{1}{\sqrt{6}} \cdot 0 + (-\frac{2}{\sqrt{6}}) \cdot (-1) \right] q_2$
$= a_3 - \frac{1}{\sqrt{2}}q_1 - \frac{3}{\sqrt{6}}q_2 = \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} - \frac{1}{\sqrt{2}} \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \end{bmatrix} - \frac{3}{\sqrt{6}} \begin{bmatrix} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \end{bmatrix}$
$= \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} - \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 0 \end{bmatrix} - \begin{bmatrix} \frac{3}{6} \\ \frac{3}{6} \\ -\frac{6}{6} \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} - \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 0 \end{bmatrix} - \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -1 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$
Since $a_3' = 0$ we cannot create a third orthogonal vector to $q_1$ and $q_2$. The vectors
$q_1 = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \end{bmatrix} \qquad q_2 = \begin{bmatrix} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \end{bmatrix}$
are an orthonormal basis for the subspace, and the dimension of the subspace is 2.
(In hindsight we could have predicted this result by inspecting the original vectors $a_1$, $a_2$, and $a_3$ and noticing that $a_3 = a_1 + a_2$. Thus only $a_1$ and $a_2$ were linearly independent, $a_3$ being linearly dependent on the first two vectors, so that only two orthonormal basis vectors could be created from the three vectors given.)
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in linear algebra | | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.27
Exercise 3.4.27. Given the subspace spanned by the three vectors
$a_1 = \begin{bmatrix} 1 \\ -1 \\ 0 \\ 0 \end{bmatrix} \qquad a_2 = \begin{bmatrix} 0 \\ 1 \\ -1 \\ 0 \end{bmatrix} \qquad a_3 = \begin{bmatrix} 0 \\ 0 \\ 1 \\ -1 \end{bmatrix}$
find vectors $q_1$, $q_2$, and $q_3$ that form an orthonormal basis for the subspace.
Answer: We can save some time by noting that $a_1$ and $a_3$ are already orthogonal. We can normalize these two vectors to create $q_1$ and $q_3$:
$\|a_1\|^2 = 1^2 + (-1)^2 + 0^2 + 0^2 = 1 + 1 = 2$
$q_1 = a_1/\|a_1\| = \frac{1}{\sqrt{2}} a_1 = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \\ 0 \end{bmatrix}$
$\|a_3\|^2 = 0^2 + 0^2 + 1^2 + (-1)^2 = 1 + 1 = 2$
$q_3 = a_3/\|a_3\| = \frac{1}{\sqrt{2}} a_3 = \begin{bmatrix} 0 \\ 0 \\ \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \end{bmatrix}$
We can then compute a third orthogonal vector $a_2'$ by subtracting from $a_2$ its projections on $q_1$ and $q_3$:
$a_2' = a_2 - (q_1^Ta_2)q_1 - (q_3^Ta_2)q_3$
$= a_2 - \left[ \frac{1}{\sqrt{2}} \cdot 0 + (-\frac{1}{\sqrt{2}}) \cdot 1 + 0 \cdot (-1) + 0 \cdot 0 \right]q_1 - \left[ 0 \cdot 0 + 0 \cdot 1 + \frac{1}{\sqrt{2}} \cdot (-1) + (-\frac{1}{\sqrt{2}}) \cdot 0 \right]q_3$
$= a_2 - (-\frac{1}{\sqrt{2}})q_1 - (-\frac{1}{\sqrt{2}})q_3 = a_2 + \frac{1}{\sqrt{2}}q_1 + \frac{1}{\sqrt{2}}q_3$
$= \begin{bmatrix} 0 \\ 1 \\ -1 \\ 0 \end{bmatrix} + \frac{1}{\sqrt{2}} \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \\ 0 \end{bmatrix} + \frac{1}{\sqrt{2}} \begin{bmatrix} 0 \\ 0 \\ \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ -1 \\ 0 \end{bmatrix} + \begin{bmatrix} \frac{1}{2} \\ -\frac{1}{2} \\ 0 \\ 0 \end{bmatrix} + \begin{bmatrix} 0 \\ 0 \\ \frac{1}{2} \\ -\frac{1}{2} \end{bmatrix} = \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix}$
Finally, we normalize $a_2'$ to create $q_2$:
$\|a_2'\|^2 = (\frac{1}{2})^2 + (\frac{1}{2})^2 + (-\frac{1}{2})^2 + (-\frac{1}{2})^2 = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = 1$
$q_2 = a_2'/\|a_2'\| = a_2' = \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix}$
An orthonormal basis for the space is therefore
$q_1 = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \\ 0 \\ 0 \end{bmatrix} \qquad q_2 = \begin{bmatrix} \frac{1}{2} \\ \frac{1}{2} \\ -\frac{1}{2} \\ -\frac{1}{2} \end{bmatrix} \qquad q_3 = \begin{bmatrix} 0 \\ 0 \\ \frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}} \end{bmatrix}$
(It’s worth noting that the solution for this exercise on page 480 is different than the solution given above. That’s presumably because we computed the orthonormal vectors in the order $q_1$, $q_3$, $q_2$ rather than the standard order $q_1$, $q_2$, $q_3$, taking advantage of the fact that the original vectors $a_1$ and $a_3$ were already orthogonal. Recall that a basis set is not unique, so it is possible to have different orthonormal bases for the same subspace.)
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in linear algebra | | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.26
Exercise 3.4.26. In the Gram-Schmidt orthogonalization process the third component $c'$ is computed as $c' = c - (q_1^Tc)q_1 - (q_2^Tc)q_2$. Verify that $c'$ is orthogonal to both $q_1$ and $q_2$.
Answer: Taking the dot product of $q_1$ and $c'$ we have
$q_1^Tc' = q_1^T \left[ c - (q_1^Tc)q_1 - (q_2^Tc)q_2 \right] = q_1^Tc - q_1^T(q_1^Tc)q_1 - q_1^T(q_2^Tc)q_2$
Since $q_1^Tc$ and $q_2^Tc$ are scalars and $q_1$ and $q_2$ are orthonormal we then have
$q_1^Tc' = q_1^Tc - q_1^T(q_1^Tc)q_1 - q_1^T(q_2^Tc)q_2 = q_1^Tc - (q_1^Tc)q_1^Tq_1 - (q_2^Tc)q_1^Tq_2$
$= q_1^Tc - (q_1^Tc) \cdot 1 - (q_2^Tc) \cdot 0 = q_1^Tc - q_1^Tc = 0$
So $c'$ is orthogonal to $q_1$.
Taking the dot product of $q_2$ and $c'$ we have
$q_2^Tc' = q_2^T \left[ c - (q_1^Tc)q_1 - (q_2^Tc)q_2 \right] = q_2^Tc - q_2^T(q_1^Tc)q_1 - q_2^T(q_2^Tc)q_2$
$= q_1^Tc - (q_1^Tc)q_1^Tq_1 - (q_2^Tc)q_1^Tq_2 = q_2^Tc - q_2^Tc = 0$
So $c'$ is also orthogonal to $q_2$.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in linear algebra | | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.25
Exercise 3.4.25. Given $y = x^2$ over the interval $-1 \le x \le 1$ what is the closest line $C + Dx$ to the parabola formed by $y$?
Answer: This amounts to finding a least-squares solution to the equation $\begin{bmatrix} 1&x \end{bmatrix} \begin{bmatrix} C \\ D \end{bmatrix} = y$, where the entries 1, $x$, and $y = x^2$ are understood as functions of $x$ over the interval -1 to 1 (as opposed to being scalar values).
Interpreting the traditional least squares equation $A^TAx = A^Tb$ in this context, here the matrix $A = \begin{bmatrix} 1&x \end{bmatrix}$ and we have
$A^TA = \begin{bmatrix} 1 \\ x \end{bmatrix} \begin{bmatrix} 1&x \end{bmatrix} = \begin{bmatrix} (1, 1)&(1, x) \\ (x, 1)&(x, x) \end{bmatrix}$
where the entries of $A^TA$ are the dot products of the functions, i.e., the integrals of their products over the interval -1 to 1.
We then have
$(1, 1) = \int_{-1}^1 1 \cdot 1 \;\mathrm{d}x = 2$
$(1, x) = (x, 1) = \int_{-1}^1 1 \cdot x \;\mathrm{d}x = \left( \frac{1}{2}x^2 \right) \;\big|_{-1}^1 = \frac{1}{2} \cdot 1^2 - \frac{1}{2} \cdot (-1)^2 = \frac{1}{2} - \frac{1}{2} = 0$
$(x, x) = \int_{-1}^1 x^2 \;\mathrm{d}x = \left( \frac{1}{3}x^3 \right) \;\big|_{-1}^1 = \frac{1}{3} \cdot 1^3 - \frac{1}{3} \cdot (-1)^3 = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$
so that
$A^TA = \begin{bmatrix} (1, 1)&(1, x) \\ (x, 1)&(x, x) \end{bmatrix} = \begin{bmatrix} 2&0 \\ 0&\frac{2}{3} \end{bmatrix}$
Continuing the interpretation of the least squares equation $A^TAx = A^Tb$ in this context, the role of $b$ is played by the function $y = x^2$, and we have
$A^Ty = \begin{bmatrix} 1 \\ x \end{bmatrix} x^2 = \begin{bmatrix} (1,x^2) \\ (x, x^2) \end{bmatrix}$
where again the entries are dot products of the functions. From above we have
$(1, x^2) = \int_{-1}^1 1 \cdot x^2 \;\mathrm{d}x = \frac{2}{3}$
and from previous exercises we have
$(x, x^2) = \int_{-1}^1 x \cdot x^2 \;\mathrm{d}x = \int_{-1}^1 x^3 \;\mathrm{d}x = 0$
so that
$A^Ty = \begin{bmatrix} \frac{2}{3} \\ 0 \end{bmatrix}$
To get the least squares solution $\bar{C} + \bar{D}x$ we then have
$\begin{bmatrix} 2&0 \\ 0&\frac{2}{3} \end{bmatrix} \begin{bmatrix} \bar{C} \\ \bar{D} \end{bmatrix} = \begin{bmatrix} \frac{2}{3} \\ 0 \end{bmatrix}$
From the second equation we have $\bar{D} = 0$. From the first equation we have $2\bar{C} = \frac{2}{3}$ or $C = \frac{1}{3}$.
The line of best fit to the parabola $y = x^2$ over the interval $-1 \le x \le 1$ is therefore the horizontal line with $y$-intercept of $\frac{1}{3}$.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in linear algebra | Tagged , | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.24
Exercise 3.4.24. As discussed on page 178, the first three Legendre polynomials are 1, $x$, and $x^2 - \frac{1}{3}$. Find the next Legendre polynomial; it will be a cubic polynomial defined for $-1 \le x \le 1$ and will be orthogonal to the first three Legendre polynomials.
Answer: The process of finding the fourth Legendre poloynomial is essentially an application of Gram-Schmidt orthogonalization. The first three polynomials are
$v_1 = 1 \qquad v_2 = x \qquad v_3 = x^2 - \frac{1}{3}$
We can find the fourth Legendre polynomial by starting with $x^3$ and subtracting off the projections of $x_3$ on the first three polynomials:
$v_4 = x^3 - \frac{(v_1, x^3)}{(v_1, v_1)}v_1 - \frac{(v_2, x^3)}{(v_2, v_2)}v_2 - \frac{(v_3, x^3)}{(v_3, v_3)}v_3$
$= \frac{(1, x^3)}{(1, 1)}\cdot 1 - \frac{(x, x^3)}{(x, x)}x - \frac{(x^2-\frac{1}{3}, x^3)}{(x^2-\frac{1}{3}, x^2-\frac{1}{3})}(x^2-\frac{1}{3})$
For the first term we have
$(1, x^3) = \int_{-1}^1 1 \cdot x^3 \;\mathrm{d}x = \int_{-1}^1 x^3 \;\mathrm{d}x = 0$
so that the first term $\frac{(v_1, x^3)}{(v_1, v_1)}v_1$ does not appear in the expression for $v_4$.
The third term $\frac{(v_3, x^3)}{(v_3, v_3)}v_3$ drops out for the same reason: its numerator is
$(x^2-\frac{1}{3}, x^3) = \int_{-1}^1 (x^2 - \frac{1}{3}) x^3 \;\mathrm{d}x$
$= \int_{-1}^1 x^5 \;\mathrm{d}x - \frac{1}{3} \int_{-1}^1 x^3 \;\mathrm{d}x = 0 - \frac{1}{3} \cdot 0 = 0$
That leaves the second term $\frac{(v_2, x^3)}{(v_2, v_2)}v_2$ with numerator of
$(x, x^3) = \int_{-1}^1 x \cdot x^3 \;\mathrm{d}x = \int_{-1}^1 x^4 \;\mathrm{d}x$
$= \left( \frac{1}{5} x^5 \right) \;\big|_{-1}^1 = \frac{1}{5} \cdot 1^5 - \frac{1}{5} \cdot (-1)^5 = \frac{1}{5} - (-\frac{1}{5}) = \frac{2}{5}$
and denominator
$(x, x) = \int_{-1}^1 x^2 \;\mathrm{d}x = \left( \frac{1}{3}x^3 \right) \;\big|_{-1}^1 = \frac{1}{3} \cdot 1^3 - \frac{1}{3} \cdot (-1)^3 = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$
We then have
$v_4 = x^3 - \left[ \frac{2}{5}/\frac{2}{3} \right] x = x^3 - \frac{3}{5}x$
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
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## Linear Algebra and Its Applications, Exercise 3.4.23
Exercise 3.4.23. Given the step function $y$ with $y(x) = 1$ for $0 \le x \le \pi$ and $y(x) = 0$ for $\pi < x < 2\pi$, find the following Fourier coefficients:
$a_0 = \frac{(y, 1)}{(1, 1)} \qquad a_1 = \frac{(y, \cos x)}{(\cos x, \cos x)} \qquad b_1 = \frac{(y, \sin x)}{(\sin x, \sin x)}$
Answer: For $a_0$ the numerator is
$(y, 1) = \int_0^{2\pi} y(x) \cdot 1 \;\mathrm{d}x = \int_0^{\pi} 1 \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \;\mathrm{d}x = \pi$
and the denominator is
$(1, 1) = \int_0^{2\pi} 1^2 \;\mathrm{d}x = 2\pi$
so that $a_0 = \frac{\pi}{2\pi} = \frac{1}{2}$.
For $a_1$ the numerator is
$(y, \cos x) = \int_0^{2\pi} y(x) \cos x \;\mathrm{d}x = \int_0^{\pi} 1 \cdot \cos x \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \cdot \cos x \;\mathrm{d}x$
$= \int_0^{\pi} \cos x = \sin x \;\big|_0^{\pi} = 0 - 0 = 0$
so that $a_1 = 0$.
For $b_1$ the numerator is
$(y, \sin x) = \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x = \int_0^{\pi} 1 \cdot \sin x \;\mathrm{d}x + \int_{\pi}^{2\pi} 0 \cdot \sin x \;\mathrm{d}x$
$= \int_0^{\pi} \sin x = (-\cos x) \;\big|_0^{\pi} = -(-1) - (-1) = 1 + 1 = 2$
and the denominator is
$(\sin x, \sin x) = \int_0^{2\pi} \sin^2 x \;\mathrm{d}x = \left[ \frac{1}{2}x - \frac{1}{4} \sin 2x \right] \;\big|_0^{2\pi}$
$= \left[ \frac{1}{2}\cdot(2\pi) - \frac{1}{4} \sin 2\pi \right] - \left[ \frac{1}{2} \cdot 0 - \frac{1}{4} \sin 2 \cdot 0 \right] = \pi - \frac{1}{4} \cdot 0 - 0 + \frac{1}{4} \cdot 0 = \pi$
so that $b_1 = \frac{2}{\pi}$.
So we have $a_0 = \frac{1}{2}$, $a_1 = 0$, and $b_1 = \frac{2}{\pi}$.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in linear algebra | Tagged , | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.22
Exercise 3.4.22. Given an arbitrary function $y$ find the coefficient $b_1$ that minimizes the quantity
$\|b_1\sin x - y\|^2 = \int_0^{2\pi} (b_1\sin x - y(x))^2 \;\mathrm{d}x$
(Use the method of setting the derivative to zero.) How does this value of $b_1$ compare with the Fourier coefficient $b_1$? What is $b_1$ if $y(x) = \cos x$?
Answer: We are looking for a value of $b_1$ that minimizes the expression on the right, so we need to differentiate with respect to $b_1$. Expanding the right-hand side of the equation above, we have
$\int_0^{2\pi} (b_1\sin x - y(x))^2 \;\mathrm{d}x = \int_0^{2\pi} [b_1^2\sin^2 x - 2b_1y(x)\sin x + y(x)^2] \;\mathrm{d}x$
$= \int_0^{2\pi} b_1^2\sin^2 x \;\mathrm{d}x - 2 \int_0^{2\pi} b_1y(x)\sin x \;\mathrm{d}x + \int_0^{2\pi} y(x)^2 \;\mathrm{d}x$
Since $b_1$ is not dependent on $x$ we can pull it out of the integral, so that
$\int_0^{2\pi} (b_1\sin x - y(x))^2 \;\mathrm{d}x = b_1^2 \int_0^{2\pi} \sin^2 x \;\mathrm{d}x - 2b_1 \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x + \int_0^{2\pi} y(x)^2 \;\mathrm{d}x$
Differentiating with respect to $b_1$ we have
$\frac{\mathrm{d}}{\mathrm{d}b_1} \int_0^{2\pi} (b_1\sin x - y(x))^2 \;\mathrm{d}x$
$\frac{\mathrm{d}}{\mathrm{d}b_1} \left[ b_1^2 \int_0^{2\pi} \sin^2 x \;\mathrm{d}x - 2b_1 \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x + \int_0^{2\pi} y(x)^2 \;\mathrm{d}x \right]$
$= 2b_1 \int_0^{2\pi} \sin^2 x \;\mathrm{d}x - 2 \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x$
Equating the derivative to zero gives us
$2b_1 \int_0^{2\pi} \sin^2 x \;\mathrm{d}x = 2 \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x$
or
$b_1 = \left( \int_0^{2\pi} y(x) \sin x \;\mathrm{d}x \right) / \left( \int_0^{2\pi} \sin^2 x \;\mathrm{d}x \right)$
Note that this is identical to the expression for the Fourier coefficient $b_1$ on page 178; the numerator is the dot product of $y(x)$ with $\sin x$ and the denominator is the dot product of $\sin x$ with itself.
If $y(x) = \cos x$ then the numerator of $b_1$ becomes
$\int_0^{2\pi} \cos x \sin x \;\mathrm{d}x = 0$
since $\cos x$ and $\sin x$ are orthogonal, and we therefore have $b_1 = 0$.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
Posted in Uncategorized | Leave a comment
## Linear Algebra and Its Applications, Exercise 3.4.21
Exercise 3.4.21. Given the function $f(x) = \sin 2x$ on the interval $-\pi \le x \le \pi$, what is the closest function $a \cos x + b \sin x$ to $f$? What is the closest line $c + dx$ to $f$?
Answer: To find the closest function $a \cos x + b \sin x$ to the function $f(x) = \sin 2x$ we first project $f$ onto the function $\cos x$ on the given interval to obtain $a$, and then project $f$ onto $\sin x$ to obtain $b$.
We project $f$ onto $\cos x$ by taking the dot product of $f$ with $\cos x$ and then normalizing by dividing by the dot product of $\cos x$ with itself:
$a = (f, \cos x)/(\cos x, \cos x)$
The numerator is
$(f, \cos x) = \int_{-\pi}^{\pi} f(x) \cos x \;\mathrm{d}x = \int_{-\pi}^{\pi} \sin 2x \cos x \;\mathrm{d}x$
$= 2 \int_{-\pi}^{\pi} \sin x \cos^2 x \;\mathrm{d}x$
where we used the trigonometric identity $\sin 2\theta = \sin \theta \cos \theta$.
To integrate we substitute the variable $u = \cos x$ so that $\mathrm{d}u = -\sin x \;\mathrm{d}x$. We then have
$\int \sin x \cos^2 x \;\mathrm{d}x = -\int \cos^2 x (-\sin x) \;\mathrm{d}x$
$-\int u^2 \;\mathrm{d}u = -\frac{1}{3}u^3 = -\frac{1}{3} \cos^3 x$
We then have
$(f, \cos x) = 2 \int_{-\pi}^{\pi} \sin x \cos^2 x \;\mathrm{d}x = 2 (-\frac{1}{3} \cos^3 x) \;\big|_{-\pi}^{\pi}$
$= -\frac{2}{3} \cos^3 \pi - [-\frac{2}{3} \cos^3 (-\pi)] = -\frac{2}{3} (-1)^3 - [-\frac{2}{3} (-1)^3]$
$= -\frac{2}{3} \cdot (-1) - [-\frac{2}{3} \cdot (-1)] = \frac{2}{3} - \frac{2}{3} = 0$
Since the numerator in the expression for $a$ is zero, we have $a = 0$.
(Note that we do not need to calculate the denominator in the expression for $a$. We know it must be positive, and thus the quotient is defined. See below for a sketch of a proof of this.)
We next project $f$ onto $\sin x$ by taking the dot product of $f$ with $\sin x$ and then normalizing by dividing by the dot product of $\sin x$ with itself:
$a = (f, \sin x)/(\sin x, \sin x)$
The numerator is
$(f, \sin x) = \int_{-\pi}^{\pi} f(x) \sin x \;\mathrm{d}x = \int_{-\pi}^{\pi} \sin 2x \sin x \;\mathrm{d}x$
$= 2 \int_{-\pi}^{\pi} \sin^2 x \cos x \;\mathrm{d}x$
where we used the trigonometric identity $\sin 2\theta = \sin \theta \cos \theta$.
To integrate we substitute the variable $u = \sin x$ so that $\mathrm{d}u = \cos x \;\mathrm{d}x$. We then have
$\int \sin^2 x \cos x \;\mathrm{d}x = \int u^2 \;\mathrm{d}u = \frac{1}{3}u^3 = \frac{1}{3} \sin^3 x$
We then have
$(f, \sin x) = 2 \int_{-\pi}^{\pi} \sin^2 x \cos x \;\mathrm{d}x = 2 (\frac{1}{3} \sin^3 x) \;\big|_{-\pi}^{\pi}$
$= \frac{2}{3} \sin^3 \pi - \frac{2}{3} \sin^3 (-\pi) = \frac{2}{3} (0)^3 - \frac{2}{3} (0)^3$
$= 0 - 0 = 0$
Since the numerator in the expression for $b$ is zero, we have $b = 0$. (Again, we are guaranteed that the denominator is positive and the quotient defined.)
So the closest function $a \cos x + b \sin x$ to $f(x) = \sin 2x$ is $0 \cdot \cos x + 0 \cdot \sin x = 0$.
To find the closest function $c + dx$ to the function $f(x) = \sin 2x$ we first project $f$ onto the constant function with the value 1 on the given interval to obtain $c$, and then project $f$ onto the function $x$ to obtain $d$.
We project $f$ onto the constant function with value 1 by taking the dot product of $f$ with 1 and then normalizing by dividing by the dot product of 1 with itself:
$c = (f, 1)/(1, 1)$
The numerator is
$(f, 1) = \int_{-\pi}^{\pi} f(x) \cdot 1 \;\mathrm{d}x = \int_{-\pi}^{\pi} \sin 2x \;\mathrm{d}x$
To integrate we substitute the variable $u = 2x$ so that $\mathrm{d}u = 2 \;\mathrm{d}x$. We then have
$\int \sin 2x \;\mathrm{d}x = \int \frac{1}{2} \sin 2x \cdot 2 \;\mathrm{d}x$
$= \frac{1}{2} \int \sin u \;\mathrm{d}u = \frac{1}{2}(-\cos u) = -\frac{1}{2} \cos 2x$
We then have
$(f, 1) = \int_{-\pi}^{\pi} \sin 2x \;\mathrm{d}x = -\frac{1}{2} \cos 2x \;\big|_{-\pi}^{\pi}$
$= -\frac{1}{2} \cos 2\pi - (-\frac{1}{2} \cos (-2\pi) = -\frac{1}{2} (1)^3 - (-\frac{1}{2} (1)^3$
$= -\frac{1}{2} + \frac{1}{2}= 0$
Since the numerator in the expression for $c = (f, 1)/(1, 1)$ is zero we have $c = 0$. (Recall that the denominator is guaranteed to be positive.)
We project $f$ onto the function $x$ by taking the dot product of $f$ with $x$ and then normalizing by dividing by the dot product of $x$ with itself:
$d = (f, x)/(x, x)$
The numerator is
$(f, x) = \int_{-\pi}^{\pi} f(x) \cdot x \;\mathrm{d}x = \int_{-\pi}^{\pi} x \sin 2x \;\mathrm{d}x$
To integrate this we use integration by parts, taking advantage of the formula $\int u \;\mathrm{d}v = uv - \int v \;\mathrm{d}u$. (The following is adapted from a post on socratic.org.) We let $\mathrm{d}v = \sin 2x \;\mathrm{d}x$ and $u = x$. Then $\mathrm{d}u$ is simply $\mathrm{d}x$, and $v = -\frac{1}{2} \cos 2x$ (the integrand of $\sin 2x$, as discussed above).
We then have
$\int x \sin x \;\mathrm{d}x = \int u \;\mathrm{d}v = uv - \int v \;\mathrm{d}u$
$= x (-\frac{1}{2} \cos 2x) - \int (-\frac{1}{2} \cos 2x) \;\mathrm{d}x$
$= -\frac{1}{2} x \cos 2x + \frac{1}{2} \int \cos 2x \;\mathrm{d}x$
The second integral we can evaluate by substituting $w = 2x$ and $\mathrm{d}w = 2 \;\mathrm{d}x$ so that
$\int \cos 2x \;\mathrm{d}x = \frac{1}{2} \int \cos w \;\mathrm{d}w = \frac{1}{2} \sin w = \frac{1}{2} \sin 2x$
Substituting for the second integral above we then have
$\int x \sin x \;\mathrm{d}x = -\frac{1}{2} x \cos 2x + \frac{1}{2} \int \cos 2x \;\mathrm{d}x = -\frac{1}{2} x \cos 2x + \frac{1}{2} (\frac{1}{2} \sin 2x)$
$= -\frac{1}{2} x \cos 2x + \frac{1}{4} \sin 2x$
We then have
$(f, x) = \int_{-\pi}^{\pi} x \sin 2x \;\mathrm{d}x = -\frac{1}{2} x \cos 2x \;\big|_{-\pi}^{\pi} + \frac{1}{4} \sin 2x \;\big|_{-\pi}^{\pi}$
$= -\frac{1}{2} \pi \cos 2\pi - (-\frac{1}{2} (-\pi) \cos (-2\pi) + \frac{1}{4} \sin 2\pi - \frac{1}{4} \sin 2(-\pi)$
$= -\frac{1}{2} \pi \cdot 1 + \frac{1}{2} (-\pi) \cdot 1 + \frac{1}{4} \cdot 0 - \frac{1}{4} \cdot 0 = -\frac{\pi}{2} - \frac{\pi}{2}= -\pi$
The denominator in the expression for $d$ is
$(x, x) = \int_{-\pi}^{\pi} x^2 \;\mathrm{d}x = \frac{1}{3} x^3 \;\big|_{-\pi}^{\pi}$
$= \frac{1}{3} \pi^3 - \frac{1}{3} (-\pi)^3 = \frac{2}{3} \pi^3$
We then have
$d = (f, x)/(x, x) = -\pi / (\frac{2}{3} \pi^3) = -\frac{3}{2\pi^2}$
The straight line $c + dx$ closest to the function $\sin 2x$ is thus the line $-\frac{3}{2\pi^2} x$.
ADDENDUM: Suppose that $g$ is a continuous function defined on the interval $[a, b]$ and $g(t) \ne 0$ for some $a \le t \le b$. Then we want to show that the inner product $(g, g) > 0$.
The basic idea of the proof is as follows: The function $g^2$ is always nonnegative, and thus its integral over the interval $[a, b]$ is nonnegative as well. If $g(t)$ is nonzero for some $a \le t \le b$ then since $g$ is continuous $g$ will also be nonzero for some interval $[c, d]$ that includes $t$, with $a \le c < d \le b$. This implies that the integral of $g^2$ over that subinterval $[c, d]$ will be positive.
But we also have $\int_a^b g(x)^2 \;\mathrm{d}x \ge \int_c^d g(x)^2 \;\mathrm{d}x$ since $g(x)^2 \ge 0$ and $[c, d]$ is contained within $[a, b]$. So if $\int_c^d g(x)^2 \;\mathrm{d}x > 0$ then we also have $\int_a^b g(x)^2 \;\mathrm{d}x > 0$ and the inner product $(g, g)$ is positive.
NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.
If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.
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https://www.science.gov/topicpages/r/radio+emission+dendrites.html | #### Sample records for radio emission dendrites
NASA Technical Reports Server (NTRS)
Goldman, M. V.; Smith, D. F.
1981-01-01
Active areas of both observational and theoretical research in which rapid progress is being made are discussed. These include: (1) the dynamic spectrum or frequency versus time plot; (2) physical mechanisms in the development of various types of bursts; (3) microwave type 1, 2, 3, and moving type 4 bursts; (4) bursts caused by trapped electrons; (5) physics of type 3bursts; (6) the physics of type 2 bursts and their related shocks; (7) the physics of both stationary and moving traps and associated type 1 and moving type 4 bursts; and (8) the status of the field of solar radio emission.
2. Radio emission in Mercury magnetosphere
Varela, J.; Reville, V.; Brun, A. S.; Pantellini, F.; Zarka, P.
2016-10-01
Context. Active stars possess magnetized wind that has a direct impact on planets that can lead to radio emission. Mercury is a good test case to study the effect of the solar wind and interplanetary magnetic field (IMF) on radio emission driven in the planet magnetosphere. Such studies could be used as proxies to characterize the magnetic field topology and intensity of exoplanets. Aims: The aim of this study is to quantify the radio emission in the Hermean magnetosphere. Methods: We use the magnetohydrodynamic code PLUTO in spherical coordinates with an axisymmetric multipolar expansion for the Hermean magnetic field, to analyze the effect of the IMF orientation and intensity, as well as the hydrodynamic parameters of the solar wind (velocity, density and temperature), on the net power dissipated on the Hermean day and night side. We apply the formalism derived by Zarka et al. (2001, Astrophys. Space Sci., 277, 293), Zarka (2007, Planet. Space Sci., 55, 598) to infer the radio emission level from the net dissipated power. We perform a set of simulations with different hydrodynamic parameters of the solar wind, IMF orientations and intensities, that allow us to calculate the dissipated power distribution and infer the existence of radio emission hot spots on the planet day side, and to calculate the integrated radio emission of the Hermean magnetosphere. Results: The obtained radio emission distribution of dissipated power is determined by the IMF orientation (associated with the reconnection regions in the magnetosphere), although the radio emission strength is dependent on the IMF intensity and solar wind hydro parameters. The calculated total radio emission level is in agreement with the one estimated in Zarka et al. (2001, Astrophys. Space Sci., 277, 293) , between 5 × 105 and 2 × 106 W.
3. Radio Emission from Binary Stars
Hjellming, R.; Murdin, P.
2000-11-01
Stellar radio emission is most common in double star systems where each star provides something essential in producing the large amounts of radio radiation needed for it to be detectable by RADIO TELESCOPES. They transfer mass, supply energy or, when one of the stars is a NEUTRON STAR or BLACK HOLE, have the strong gravitational fields needed for the energetic particles and magnetic fields needed...
4. Radio emission from binary stars
NASA Technical Reports Server (NTRS)
Dulk, G. A.
1986-01-01
This paper reviews the radio emission from binary star systems - the emission processes that occur, the characteristics of the binary systems inferred from the radio observations, and the reasons for the activity. Several classes of binary stars are described including those with two main sequence stars, those with one normal star and a white dwarf, and those containing a neutron star or a black hole.
SciTech Connect
Weiler, Kurt W.; Panagia, Nino; Sramek, Richard A.; Van Dyk, Schuyler D.; Stockdale, Christopher J.; Kelley, Matthew T.
2009-05-03
Study of radio supernovae over the past 27 years includes more than three dozen detected objects and more than 150 upper limits. From this work it is possible to identify classes of radio properties, demonstrate conformance to and deviations from existing models, estimate the density and structure of the circumstellar material and, by inference, the evolution of the presupernova stellar wind, and reveal the last stages of stellar evolution before explosion. It is also possible to detect ionized hydrogen along the line of sight, to demonstrate binary properties of the presupernova stellar system, and to detect dumpiness of the circumstellar material.
6. Radio emission from binary stars
NASA Technical Reports Server (NTRS)
Dulk, George A.
1986-01-01
Radio emission from binary star systems; characteristics of the binary systems inferred from the radio observations; and the reasons for the activity are reviewed. Binary stars with two main sequence stars, with one normal star and a white dwarf, and those containing a neutron star or a black hole are described. Energy may be directly available as matter falls into the potential well of a compact object. Electromagnetic induction effects may occur due to relative motions of magnetic fields and matter. By enforcing rapid rotation, binaries can induce strong dynamo action and hence generate free energy in the form of intense, complex, evolving magnetic fields. Whatever the source of energy, the observations at radio and X-ray wavelengths demonstrate that electrons are accelerated to high energies (mildly relativistic and, ultrarelativistic). Observed or inferred radio brightness temperatures range up to 10 to the 15th power K or more, implying coherent emission for sources brighter than 10 billion K.
7. Venus - Global surface radio emissivity
NASA Technical Reports Server (NTRS)
Ford, P. G.; Pettengill, G. H.
1983-01-01
Observations of thermal radio emission from the surface of Venus, made by the Pioneer Venus radar mapper at a wavelength of 17 cm, show variations that are dominated by changes in surface emissivity. The regions of lowest emissivity (0.54 + or - 0.05 for the highland areas of Aphrodite Terra and Theia Mons) correspond closely to regions of high radar reflectivity reported earlier. These results support the inference of inclusions of material with high electrical conductivity in the surface rock of these areas.
8. Radio emission from supernova remnants
Dubner, Gloria; Giacani, Elsa
2015-09-01
The explosion of a supernova releases almost instantaneously about 10^{51} ergs of mechanic energy, changing irreversibly the physical and chemical properties of large regions in the galaxies. The stellar ejecta, the nebula resulting from the powerful shock waves, and sometimes a compact stellar remnant, constitute a supernova remnant (SNR). They can radiate their energy across the whole electromagnetic spectrum, but the great majority are radio sources. Almost 70 years after the first detection of radio emission coming from an SNR, great progress has been achieved in the comprehension of their physical characteristics and evolution. We review the present knowledge of different aspects of radio remnants, focusing on sources of the Milky Way and the Magellanic Clouds, where the SNRs can be spatially resolved. We present a brief overview of theoretical background, analyze morphology and polarization properties, and review and critically discuss different methods applied to determine the radio spectrum and distances. The consequences of the interaction between the SNR shocks and the surrounding medium are examined, including the question of whether SNRs can trigger the formation of new stars. Cases of multispectral comparison are presented. A section is devoted to reviewing recent results of radio SNRs in the Magellanic Clouds, with particular emphasis on the radio properties of SN 1987A, an ideal laboratory to investigate dynamical evolution of an SNR in near real time. The review concludes with a summary of issues on radio SNRs that deserve further study, and analysis of the prospects for future research with the latest-generation radio telescopes.
9. Nature of Coherent Radio Emission from Pulsars
Mitra, Dipanjan
2017-09-01
The pulsar radio emission originates from regions below 10% of the light cylinder radius. This requires a mechanism where coherent emission is excited in relativistic pair plasma with frequency ν _{cr} which is below the plasma frequency ν_{°} i.e. ν _{cr} < ν_{°}. A possible model for the emission mechanism is charged bunches (charged solitons) moving relativistically along the curved open dipolar magnetic field lines capable of exciting coherent curvature radio emission. In this article, we review the results from high quality observations in conjunction with theoretical models to unravel the nature of coherent curvature radio emission in pulsars.
10. Radio emission in peculiar galaxies
NASA Technical Reports Server (NTRS)
Demellorabaca, Dulia F.; Abraham, Zulema
1990-01-01
11. Radio Continuum Emission from FS CMa Stars
Rodríguez, L. F.; Báez-Rubio, A.; Miroshnichenko, A. S.
2012-04-01
The FS CMa stars exhibit bright optical emission-line spectra and strong IR excesses. Very little is known of their radio characteristics. We analyzed archive Very Large Array data to search for radio continuum emission in a sample of them. There are good quality data for seven of the ~40 known FS CMa stars. Of these seven stars, five turn out to have associated radio emission. Two of these stars, CI Cam and MWC 300, have been previously reported in the literature as radio emitters. We present and briefly discuss the radio detection of the other three sources: FS CMa (the prototype of the class), AS 381, and MWC 922. The radio emission is most probably of a free-free nature but additional observations are required to better characterize it.
12. Radio emissions from RHESSI TGFs
Mezentsev, Andrey; Østgaard, Nikolai; Gjesteland, Thomas; Albrechtsen, Kjetil; Cummer, Steven
2016-04-01
The discovery of bursts of energetic photons coming out to space from the Earth's atmosphere, referred to as terrsetrial gamma-ray flashes (TGFs), has stimulated research activity investigating different aspects of the TGF generation and accompanying processes. Two models of the TGF production are nowadays competing to explain the observations of the TGFs and related phenomena. One of the models involves the feedback mechanism enhancing the production rate of the runaway electrons in the ambient electric field of a thundercloud. Another model considers runaway electrons accelerated in the strong local electric field in front of the upward propagating negative leader of the +IC. We performed a detailed analysis of RHESSI TGFs detected between August 2004 and September 2015. It was reported that the RHESSI satellite clock has a systematic error of ˜ 1.8 ms, but the exact value remained unknown, also it was unclear if this systematic clock error is changing with time or not. We compared RHESSI TGFs with the world wide lightning location network (WWLLN) database and found the distribution of the time delays between the TGF peak times and associated WWLLN detections. This distribution allowed us to find the value of the RHESSI systematic clock offset with the microsecond accuracy level. Also we found that this offset experienced two changes: in August 2005 and in October 2013, which was confirmed by two independent ways. We found that in case of double TGFs WWLLN detection corresponds to the second TGF of the pair. VLF magnetic field recordings from the Duke University also attribute radio sferics to the second TGF, exhibiting no detectable radio emission during the first TGFs of the TGF pairs. We have proposed a possible scenario that is consistent with the observations. This scenario supports the leader-based model of the TGF generation. Spectral characteristics of 77 sferics recorded by the Duke University VLF sensors and related to the RHEESI TGFs show that maximal
13. Models of Uranium continuum radio emission
NASA Technical Reports Server (NTRS)
Romig, Joseph H.; Evans, David R.; Sawyer, Constance B.; Schweitzer, Andrea E.; Warwick, James W.
1987-01-01
Uranium continuum radio emission detected by the Voyager 2 Planetary Radio Astronomy experiment during the January 1986 encounter is considered. The continuum emissions comprised four components (equatorial emissions, anomaly emissions, strong nightside emissions, and weak nightside emissions) associated with different sources. The equatorial emissions appeared most prominently during the days before closest approach and extended from 40 kHz or below to about 120 kHz. The anomaly emissions were seen about 12 hours before closest approach and extended to about 250 kHz. The agreement found between Miranda's phase and strong radio emission at 20.4 kHz, just after closest approach, suggests intense dynamic activity on the Miranda L shell.
14. Non-thermal radio emission from Saturn
NASA Technical Reports Server (NTRS)
Warwick, J. W.
1978-01-01
Direct, strong evidence for non-thermal radio emission from Saturn exists in the hectometric data observed by Imp 6. The planet has been tentatively identified as a decametric source, but the most sensitive and most recent data fail to confirm this. At metric or decimetric wavelengths Saturn has no non-thermal emission like Jupiter's synchrotron sources. Finally, a comparative study of Earth and Jupiter radio emissions suggests lightning discharges.
15. Prompt Radio Emission from Gamma Ray Bursts
Gotthardt, Noelle
2010-02-01
Gamma-ray bursts have been observed, but these enigmatic objects are yet unexplained. These short duration events are undoubtedly due to high-energy events. Fading optical emission and even radio emission has been observed from such events, but prompt radio emission from these events would be very useful in pinning down the physics of the bursts, the nature of the progenitor object,and possibly the medium in which it occurs. If these phenomena occur at large redshifts, there is the possibility that the observations could probe the Epoch of Reionization, or the intergalactic medium. A number of models have been proposed to explain the gamma-ray bursts, ranging from compact object mergers, to maser-like coherent emission. These models are not well constrained by current observations. Prompt radio emission may be detected by a transient radio array. I will discuss a planned search for such signals by the Eight-meter-wavelength Transient Array (ETA). )
16. Solar emission levels at low radio frequencies
NASA Technical Reports Server (NTRS)
Erickson, W. C.
1990-01-01
Solar radio emission could seriously interfere with observations made by a low frequency (1 to 10 MHz) array in space. International Sun-Earth Explorer (ISEE-3) radio data were used to determine solar emission level. The results indicate that solar emission should seriously disturb less than ten percent of the data, even during the years of solar maximum. Thus it appears that solar emission should not cause a disastrous loss of data. The information needed to design procedures to excise solar interference from the data produced by any low-frequency array is provided.
17. Radio emissions and the heliospheric termination shock
NASA Technical Reports Server (NTRS)
Zank, G. P.; Cairns, I. H.; Donohue, D. J.; Matthaeus, W. H.
1994-01-01
With the Voyager spacecrafts' discovery of low-frequency radio emissions from the depths of the outer heliosphere has come the realization that the boundaries between our heliosphere and the local interstellar medium have been detected. A model is presented here that can account for the observed radio emissions, based upon a termination shock modified by the dynamical effect of galactic and anomalous cosmic rays. Frequency and time domain properties of both continuum and transient radio events are explained, and new estimates for the distance to the termination shock (approximately 60-70 astronomical units) and the heliopause (less than or approximately 90 AU) are given.
18. Transient pulsed radio emission from a magnetar
Camilo, Fernando; Ransom, Scott M.; Halpern, Jules P.; Reynolds, John; Helfand, David J.; Zimmerman, Neil; Sarkissian, John
2006-08-01
Anomalous X-ray pulsars (AXPs) are slowly rotating neutron stars with very bright and highly variable X-ray emission that are believed to be powered by ultra-strong magnetic fields of >1014 G, according to the magnetar' model. The radio pulsations that have been observed from more than 1,700 neutron stars with weaker magnetic fields have never been detected from any of the dozen known magnetars. The X-ray pulsar XTE J1810 - 197 was revealed (in 2003) as the first AXP with transient emission when its luminosity increased 100-fold from the quiescent level; a coincident radio source of unknown origin was detected one year later. Here we show that XTE J1810 - 197 emits bright, narrow, highly linearly polarized radio pulses, observed at every rotation, thereby establishing that magnetars can be radio pulsars. There is no evidence of radio emission before the 2003 X-ray outburst (unlike ordinary pulsars, which emit radio pulses all the time), and the flux varies from day to day. The flux at all radio frequencies is approximately equal-and at >20GHz XTE J1810 - 197 is currently the brightest neutron star known. These observations link magnetars to ordinary radio pulsars, rule out alternative accretion models for AXPs, and provide a new window into the coronae of magnetars.
19. Transient pulsed radio emission from a magnetar.
PubMed
Camilo, Fernando; Ransom, Scott M; Halpern, Jules P; Reynolds, John; Helfand, David J; Zimmerman, Neil; Sarkissian, John
2006-08-24
20. Optical emission in the radio lobes of radio galaxies. II - New observations of 21 radio lobes
Crane, P.; Tyson, J. A.; Saslaw, W. C.
1983-02-01
The authors report new identifications of optical emission associated with the radio lobes of double radio galaxies. Optical emission is present in the outer radio structure of the sources 3C 219, 3C 244.1, 3C 247, 3C 252, 3C 268.2, 3C 321, 3C 319, 3C 337, and possibly in 3C 330. The authors have not found emission to the detection limit of V ≡ 24 in the sources 3C 79, 3C 173.1, 3C 223, 3C 325, and 3C 381. Of the 21 separate sources in optical studies of extended lobes of radio galaxies reported to date, 16 radio sources observed so far show significant optical emission within one or both lobes, while in 11 of these the optical object is within 2arcsec of the radio peak.
1. Nonthermal Radio Emission and the HR Diagram
NASA Technical Reports Server (NTRS)
Gibson, D. M.
1985-01-01
Perhaps the most reliable indicator of non-radiative heating/momentum in a stellar atmosphere is the presence of nonthermal radio emission. To date, 77 normal stellar objects have been detected and identified as nonthermal sources. These stellar objects are tabulated herein. It is apparent that non-thermal radio emission is not ubiquitous across the HR diagram. This is clearly the case for the single stars; it is not as clear for the binaries unless the radio emission is associated with their late-type components. Choosing to make this association, the single stars and the late-type components are plotted together. The following picture emerges: (1) there are four locations on the HR diagram where non-thermal radio stars are found; (2) the peak incoherent 5 GHz luminosities show a suprisingly small range for stars within each class; (3) the fraction of stellar energy that escapes as radio emission can be estimated by comparing the integrated maximum radio luminosity to the bolometric luminosity; (4) there are no apparent differences in L sub R between binaries with two cool components, binaries with one hot and one cool component, and single stars for classes C and D; and (5) The late-type stars (classes B, C, and D) are located in parts of the HR diagram where there is reason to suspect that the surfaces of the stars are being braked with respect to their interiors.
2. Nonthermal Radio Emission and the HR Diagram
NASA Technical Reports Server (NTRS)
Gibson, D. M.
1985-01-01
Perhaps the most reliable indicator of non-radiative heating/momentum in a stellar atmosphere is the presence of nonthermal radio emission. To date, 77 normal stellar objects have been detected and identified as nonthermal sources. These stellar objects are tabulated herein. It is apparent that non-thermal radio emission is not ubiquitous across the HR diagram. This is clearly the case for the single stars; it is not as clear for the binaries unless the radio emission is associated with their late-type components. Choosing to make this association, the single stars and the late-type components are plotted together. The following picture emerges: (1) there are four locations on the HR diagram where non-thermal radio stars are found; (2) the peak incoherent 5 GHz luminosities show a suprisingly small range for stars within each class; (3) the fraction of stellar energy that escapes as radio emission can be estimated by comparing the integrated maximum radio luminosity to the bolometric luminosity; (4) there are no apparent differences in L sub R between binaries with two cool components, binaries with one hot and one cool component, and single stars for classes C and D; and (5) The late-type stars (classes B, C, and D) are located in parts of the HR diagram where there is reason to suspect that the surfaces of the stars are being braked with respect to their interiors.
3. Characterising Radio Emissions in Cosmic Filaments
Miller, R. O.
2014-02-01
A growing number of radio studies probe galaxy clusters into the low-power regime in which star formation is the dominant source of radio emission. However, at the time of writing no comparably deep observations have focused exclusively on the radio populations of cosmic filaments. This thesis describes the ATCA 2.1 GHz observations and subsequent analysis of two such regions - labelled Zone 1 (between clusters A3158 and A3125/A3128) and Zone 2 (between A3135 and A3145) - in the Horologium-Reticulum Supercluster (HRS). Source count profiles of both populations are discussed and a radio luminosity function for Zone 1 is generated. While the source counts of Zone 2 appear to be consistent with expected values, Zone 1 exhibits an excess of counts across a wide flux range (1 mJy< S_1.4 < 200 mJy). An excess in radio activity at the lower extent of this range (log P_1.4 < 22.5; within the SF-dominated regime) is also suggested by the radio luminosity function for that region, and brief colour analysis suggests that such an excess is indeed predominantly associated with a starforming population. The differences between the two filamentary zones is attributed to cosmic variation. The regions are both small (~ 1 degree square), and are significantly separated in the HRS. Further radio observations of filaments are required and the results combined into a larger sample size in order to arrive at a generalised model filamentary population.
4. Possible radio emission mechanism for pulsars
NASA Technical Reports Server (NTRS)
Kovalev, Y. A.
1979-01-01
A mathematical model is presented and discussed as a possible mechanism to describe radio emission from pulsars. The model determines that the magnetic field in the neutron proton electron (npe) layer of a neutron star results from a quasistationary eddy current of superconducting and normal protons relative to normal electrons, which generates radio emission by the Josephson effect. The radiation propagates in the magnetically active medium, from the optically thick npe layer to the magnetosphere through breaks in the crust. As a result, hot radio spots form on the surface of the star, and a radiation pattern forms near the magnetic poles, the cross section of which gives the observed pulse structure. Due to the specific properties of the mechanism, variations of the quasistationary current are converted to amplitude frequency variations of the radiation spectrum. Variations of the fine structure of the spectrum pulse amplitude and spectral index, as well as their correlation are discussed.
5. Radio emission from the Ganymede-Jupiter interaction and consequence for radio emissions from exoplanets
Zarka, Philippe; Soares-Marques, Manilo; Louis, Corentin; Ryabov, Vladimir; Lamy, Laurent; Echer, Ezequiel; Cecconi, Baptiste; Hess, Sébastien; Coffre, Andrée; Denis, Laurent
2017-05-01
Analysis of a catalog of 26 years of radio decameter observations from Jupiter in Nançay (France) allowed us to detect unambiguously the radio emissions resulting from the Ganymede-Jupiter interaction. The duration and power of the 189 events detected suggest sporadic reconnection with an average radio power released in the Ganymede-Jupiter decameter emission 15 times smaller than in the Io-Jupiter one. This compares well with the ratio of the magnetic power (Poynting flux) dissipated at the Ganymede-Jupiter and Io-Jupiter interactions, confirming the radio-magnetic Bode's law of Zarka et al. (2001), that serves as a basis for predicting exoplanetary radio emissions. This result improves our understanding of the interaction between a magnetized flow and an obstacle, the general paradigm of star-planet plasma interactions.
6. Radio emissions from double RHESSI TGFs
Mezentsev, Andrew; Østgaard, Nikolai; Gjesteland, Thomas; Albrechtsen, Kjetil; Lehtinen, Nikolai; Marisaldi, Martino; Smith, David; Cummer, Steven
2016-07-01
A detailed analysis of Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) terrestrial gamma ray flashes (TGFs) is performed in association with World Wide Lightning Location Network (WWLLN) sources and very low frequency (VLF) sferics recorded at Duke University. RHESSI clock offset is evaluated and found to experience changes on the 5 August 2005 and 21 October 2013, based on the analysis of TGF-WWLLN matches. The clock offsets were found for all three periods of observations with standard deviations less than 100 μs. This result opens the possibility for the precise comparative analyses of RHESSI TGFs with the other types of data (WWLLN, radio measurements, etc.) In case of multiple-peak TGFs, WWLLN detections are observed to be simultaneous with the last TGF peak for all 16 cases of multipeak RHESSI TGFs simultaneous with WWLLN sources. VLF magnetic field sferics were recorded for two of these 16 events at Duke University. These radio measurements also attribute VLF sferics to the second peak of the double TGFs, exhibiting no detectable radio emission during the first TGF peak. Possible scenarios explaining these observations are proposed. Double (multipeak) TGFs could help to distinguish between the VLF radio emission radiated by the recoil currents in the +IC leader channel and the VLF emission from the TGF producing electrons.
7. Cross-Correlations in Quasar Radio Emission
Nefedyev, Yuri; Panischev, Oleg; Demin, Sergey
The main factors forming the complex evolution of the accretive astrophysical systems are nonlinearity, intermittency, nonstationarity and also collective phenomena. To discover the dynamic processes in these objects and to detain understanding their properties we need to use all the applicable analyzing methods. Here we use the Flicker-Noise Spectroscopy (FNS) as a phenomenological approach to analyzing and parameterizing the auto- and cross-correlations in time series of astrophysical objects dynamics. As an example we consider the quasar flux radio spectral density at frequencies 2.7 GHz and 8.1 GHz. Data have been observed by Dr. N. Tanizuka (Laboratory for Complex Systems Analysis, Osaka Prefecture University) in a period of 1979 to 1988 (3 309 days). According to mental habits quasar is a very energetic and distant active galactic nucleus containing a supermassive black hole by size 10-10,000 times the Schwarzschild radius. The quasar is powered by an accretion disc around the black hole. The accretion disc material layers, moving around the black hole, are under the influence of gravitational and frictional forces. It results in raising the high temperature and arising the resonant and collective phenomena reflected in quasar emission dynamics. Radio emission dynamics of the quasar 0215p015 is characterized by three quasi-periodic processes, which are prevalent in considering dynamics. By contrast the 1641p399's emission dynamics have not any distinguish processes. It means the presence of high intermittency in accretive modes. The second difference moment allows comparing the degree of manifesting of resonant and chaotic components in initial time series of the quasar radio emission. The comparative analysis shows the dominating of chaotic part of 1641p399's dynamics whereas the radio emission of 0215p015 has the predominance of resonant component. Analyzing the collective features of the quasar radio emission intensity demonstrates the significant
8. DIFFUSE RADIO EMISSION IN ABELL 754
SciTech Connect
Kale, Ruta; Dwarakanath, K. S. E-mail: [email protected]
2009-07-10
We present a low-frequency study of the diffuse radio emission in the galaxy cluster A754. We present a new 150 MHz image of the galaxy cluster A754 made with the Giant Metrewave Radio Telescope and discuss the detection of four diffuse features. We compare the 150 MHz image with the images at 74, 330, and 1363 MHz; one new diffuse feature is detected. The flux density upper limits at 330 and 1363 MHz imply a synchrotron spectral index, {alpha}>2 (S {proportional_to} {nu}{sup -{alpha}}), for the new feature. The 'west relic' detected at 74 MHz is not detected at 150 MHz and is thus consistent with its nondetection at 1363 MHz and 330 MHz. Integrated spectra of all the diffuse features are presented. The fourth diffuse feature is located along the proposed merger axis in A754 and 0.7 Mpc away from the peak of X-ray emission; we refer to it as a relic. We have made use of the framework of the adiabatic compression model to obtain spectra. We show that the spectrum of the fourth diffuse feature is consistent with that of a cocoon of a radio galaxy lurking for about 9 x 10{sup 7} yr; no shock compression is required. The other three diffuse emission have spectra steeper than 1.5 and could be cocoons lurking for longer time. We discuss other possibilities such as shocks and turbulent reacceleration being responsible for the diffuse emission in A754.
9. Models of Neptune's smooth recurrent radio emission
NASA Technical Reports Server (NTRS)
Sawyer, Constance
1993-01-01
The quantitative response of the Planetary Radio Astronomy (PRA) instrument to a wave with polarization ellipse of arbitrary shape and orientation, arriving at the antennas from any direction, can be determined. This capability is used to model the time variation of intensity and circular polarization over a range of radio frequencies for proposed radio-source locations and emission characteristics at Neptune. At frequencies below 400 kHz the observed variation of intensity, polarization, and phase are closely simulated in an offset tilted dipole magnetic field by conjugate sources at midlatitude with filled emission cones. The phase of emission at higher frequencies is reproduced by sources at lower latitude. Modeled wide-cone emission does not reach the spacecraft at the observed phase nor have the polarization sense observed before closest approach. Source-surface maps of apparent polarization for the period before closest approach when instrumental response is especially sensitive to source location is presented. The method is capable of extension to more realistic models of the magnetic field.
10. Radio Emissions from the Outer Heliosphere
NASA Technical Reports Server (NTRS)
Gurnett, D. A.; Kurth, W. S.
1996-01-01
For nearly fifteen years the Voyager 1 and 2 spacecraft have been detecting an unusual radio emission in the outer heliosphere in the frequency range from about 2 to 3 kHz. Two major events have been observed, the first in 1983-84 and the second in 1992-93. In both cases the onset of the radio emission occurred about 400 days after a period of intense solar activity, the first in mid-July 1982, and the second in May-June 1991. These two periods of solar activity produced the two deepest cosmic ray Forbush decreases ever observed. Forbush decreases are indicative of a system of strong shocks and associated disturbances propagating outward through the heliosphere. The radio emission is believed to have been produced when this system of shocks and disturbances interacted with one of the outer boundaries of the heliosphere, most likely in the vicinity of the the heliopause. The emission is believed to be generated by the shock-driven Langmuir-wave mode conversion mechanism, which produces radiation at the plasma frequency (f(sub p)) and at twice the plasma frequency (2f(sub p)). From the 400-day travel time and the known speed of the shocks, the distance to the interaction region can be computed, and is estimated to be in the range from about 110 to 160 AU.
11. The search for exomoon radio emissions
Noyola, Joaquin P.
The field of exoplanet detection has seen many new developments since the discovery of the first exoplanet. Observational surveys by the NASA Kepler Mission and several other instrument have led to the confirmation of over 1900 exoplanets, and several thousands of exoplanet potential candidates. All this progress, however, has yet to provide the first confirmed exomoon. Since all previous attempts to discover exomoons have failed, a novel method to detect them is proposed in this dissertation, which describes development of the method and its applications to select the best exomoon candidates for observational searches. The main goal of these searches is to verify the validity and effectiveness of the method, and discover the first exomoon by using the world largest and most suitable radio telescopes. The discovery of first exomoon would begin a new era of exploratory research in exoplanetary systems. The idea that exomoons can be discovered with radio telescopes was proposed by Noyola, Satyal and Musielak et al. (2014), who suggested that the interaction between Io and the Jovian magnetosphere could also be found in exoplanet-exomoon pairs, and the resulting radio emissions could be used to directly detect these systems. The main results of the original study obtained for single prograde exomoons are also described in this dissertation, which in addition extends the previous study to multiple exomoon systems, as well as retrograde orbits. The main objective of these studies is to identify the best exomoon candidates for detection by chosen radio telescopes. One such candidates, Epsilon Eridani b, was selected and observed by the Giant Metre Radio Telescope (GMRT) in India. The preliminary results of these observations do not show any expected radio emission from the chosen systems. Thus, implementation of several important improvements to the method is discussed in details in this dissertation.
12. Analysis and Modeling of Jovian Radio Emissions Observed by Galileo
NASA Technical Reports Server (NTRS)
Menietti, J. D.
2003-01-01
Our studies of Jovian radio emission have resulted in the publication of five papers in refereed journals, with three additional papers in progress. The topics of these papers include the study of narrow-band kilometric radio emission; the apparent control of radio emission by Callisto; quasi-periodic radio emission; hectometric attenuation lanes and their relationship to Io volcanic activity; and modeling of HOM attenuation lanes using ray tracing. A further study of the control of radio emission by Jovian satellites is currently in progress. Abstracts of each of these papers are contained in the Appendix. A list of the publication titles are also included.
13. Analysis and Modeling of Jovian Radio Emissions Observed by Galileo
NASA Technical Reports Server (NTRS)
Menietti, J. D.
2003-01-01
Our studies of Jovian radio emission have resulted in the publication of five papers in refereed journals, with three additional papers in progress. The topics of these papers include the study of narrow-band kilometric radio emission; the apparent control of radio emission by Callisto; quasi-periodic radio emission; hectometric attenuation lanes and their relationship to Io volcanic activity; and modeling of HOM attenuation lanes using ray tracing. A further study of the control of radio emission by Jovian satellites is currently in progress. Abstracts of each of these papers are contained in the Appendix. A list of the publication titles are also included.
NASA Technical Reports Server (NTRS)
Kogut, A.; Fixsen, D. J.; Levin, S. M.; Limon, M.; Lubin, P. M.; Mirel, P.; Seiffert, M.; Singal, J.; Villela, T.; Wollack, E.; Wuensche, C. A.
2010-01-01
We use absolutely calibrated data from the Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE 2) flight in July 2006 to model Galactic emission at frequencies 3, 8, and 10 GHz. The spatial structure in the data is consistent with a superposition of free-free and synchrotron emission. Emission with spatial morphology traced by the Haslam 408 MHz survey has spectral index beta_synch = -2.5 +/- 0.1, with free-free emission contributing 0.10 +/- 0.01 of the total Galactic plane emission in the lowest ARCADE 2 band at 3.15 GHz. We estimate the total Galactic emission toward the polar caps using either a simple plane-parallel model with csc|b| dependence or a model of high-latitude radio emission traced by the COBE/FIRAS map of CII emission. Both methods are consistent with a single power-law over the frequency range 22 MHz to 10 GHz, with total Galactic emission towards the north polar cap T_Gal = 0.498 +/- 0.028 K and spectral index beta = -2.55 +/- 0.03 at reference frequency 0.31 GHz. The well calibrated ARCADE 2 maps provide a new test for spinning dust emission, based on the integrated intensity of emission from the Galactic plane instead of cross-correlations with the thermal dust spatial morphology. The Galactic plane intensity measured by ARCADE 2 is fainter than predicted by models without spinning dust, and is consistent with spinning dust contributing 0.4 +/- 0.1 of the Galactic plane emission at 23 GHz.
15. Polarization model applied to Uranian radio emission
Sawyer, C. B.; Neal, K. L.; Warwick, J. W.
1991-04-01
The total power and the degree of circular polarization as measured by the Planetary Radio Astronomy experiments on the Voyager spacecraft are modeled. For a source near the electron cyclotron frequency, the degree of circular polarization is determined by the angle between the wave vector and the field. It is shown that the observed strong circular polarization of Uranian smooth low-frequency (SLF) can be modeled as emission that is beamed along the direction of the magnetic field in a filled cone. The main observational constraints of SLF emission from Uranus are met by conjugate sources at about 21 deg from the magnetic equator.
16. Coronal Mass Ejections and Solar Radio Emissions
NASA Technical Reports Server (NTRS)
Gopalswamy, Nat
2010-01-01
Coronal mass ejections (CMEs) have important connections to various types of radio emissions from the Sun. The persistent noise storm radiation (type I storm at metric wavelengths, type III storms at longer wavelengths) can be clearly interrupted by the occurrence of a CME in the active region that produces the storm. Sometimes the noise storm completely disappears and other times, it reappears in the active region. Long-lasting type III bursts are associated with CME eruption, thought to be due to the reconnection process taking place beneath the erupting CME. Type II bursts are indicative of electron acceleration in the CME-driven shocks and hence considered to be the direct response of the CME propagation in the corona and interplanetary medium. Finally type IV bursts indicate large-scale post-eruption arcades containing trapped electrons that produce radio emission. This paper summarizes some key results that connect CMEs to various types of radio emission and what we can learn about particle acceleration in the corona) and interplanetary medium. Particular emphasis will be placed on type If bursts because of their connection to interplanetary shocks detected in situ.
17. Radio emission from RS CVn binary systems
SciTech Connect
Doiron, D.J.
1984-01-01
The RS CVn binary stellar systems UX Ari, HR 1099, AR Lac, HR 5110, II Peg, lambda And, and SZ Psc were investigated by use of radio interferometry during the period from July 1982 through August 1983. Interferometry took two forms: Very Large Array (VLA) observations and Very Long Baseline Interferometry (VLBI). The VLA observations determined the characteristic polarization and flux behavior of the centimeter wavelength radio emission. The observed spectral index was near zero during quiescent periods, rising to between 0.5 and 1.0 during active periods. No net linear polarization is observed to a limit of 1.7%. This is expected since the Faraday depth of thermal electrons deduced from x-ray observations is approx. 10/sup 5/. Circular polarization is observed to be less than 20% at all frequencies often with a helicity reversal between 1.6 GHz and 5 GHz. The VLBI observations have shown that the brightness temperatures are often T/sub B/ approx.> 10/sup 10/ /sup 0/K and size sources smaller than or comparable to the overall size of the binary system. These data are consistent with incoherent gyrosynchrotron emission from mildly relativistic electrons which are optically thick to their own radiation at 1.6 GHz and optically thin at 5 GHz and above. The spectral behavior suggests that the radio emission is due to a power-law distribution of electrons.
18. Coronal Mass Ejections and Solar Radio Emissions
NASA Technical Reports Server (NTRS)
Gopalswamy, Nat
2010-01-01
Coronal mass ejections (CMEs) have important connections to various types of radio emissions from the Sun. The persistent noise storm radiation (type I storm at metric wavelengths, type III storms at longer wavelengths) can be clearly interrupted by the occurrence of a CME in the active region that produces the storm. Sometimes the noise storm completely disappears and other times, it reappears in the active region. Long-lasting type III bursts are associated with CME eruption, thought to be due to the reconnection process taking place beneath the erupting CME. Type II bursts are indicative of electron acceleration in the CME-driven shocks and hence considered to be the direct response of the CME propagation in the corona and interplanetary medium. Finally type IV bursts indicate large-scale post-eruption arcades containing trapped electrons that produce radio emission. This paper summarizes some key results that connect CMEs to various types of radio emission and what we can learn about particle acceleration in the corona) and interplanetary medium. Particular emphasis will be placed on type If bursts because of their connection to interplanetary shocks detected in situ.
19. Smooth radio emission and a new emission at Neptune
NASA Technical Reports Server (NTRS)
Sawyer, C.; Warwick, J. W.; Romig, J. H.
1990-01-01
The Planetary Radio Astronomy (PRA) experiment Warwick et al., (1977) on the spacecraft Voyager 2 observed three types of smooth emission: (1) numerous recurrent episodes are modeled by filled emission cones from midlatitude conjugate sources; (2) an 'equatorial' feature seen soon after closest approach includes electron cyclotron harmonic emission above the upper hybrid resonance, as well as smooth recurrent emission, its strange appearance is a result of rapid change in Voyager's magnetic latitude and; (3) unique 'high-latitude' emission is seen near closest approach during Voyager's single excursion to high north (+) magnetic latitude when fc, the electron cyclotron frequency at the spacecraft, lies in the observable range. The stronger component covers a broad band of frequencies above 2fc; its sensitivity to magnetic field identifies it as extraordinary (X) mode. The weaker component extends smoothly through f = fc and is identified as ordinary (O) mode. At each frequency f the observed sense of polarization reverses when f = 2fc.
20. DETECTION OF RADIO EMISSION FROM FIREBALLS
SciTech Connect
Obenberger, K. S.; Taylor, G. B.; Dowell, J.; Henning, P. A.; Schinzel, F. K.; Stovall, K.; Hartman, J. M.; Ellingson, S. W.; Helmboldt, J. F.; Wilson, T. L.; Kavic, M.; Simonetti, J. H.
2014-06-20
We present the findings from the Prototype All-Sky Imager, a back end correlator of the first station of the Long Wavelength Array, which has recorded over 11,000 hr of all-sky images at frequencies between 25 and 75 MHz. In a search of this data for radio transients, we have found 49 long-duration (10 s of seconds) transients. Ten of these transients correlate both spatially and temporally with large meteors (fireballs), and their signatures suggest that fireballs emit a previously undiscovered low frequency, non-thermal pulse. This emission provides a new probe into the physics of meteors and identifies a new form of naturally occurring radio transient foreground.
1. Radio Cerenkov Emission from UHE Neutrinos
Ekers, Ron; Phillips, Chris; Protheroe, Ray; McFadden, Rebecca; James, Clancy; Roberts, Paul
2008-10-01
Some cosmic ray nuclei have energies equivalent to that of a fast-moving tennis ball. Our Galaxy is too small to produce them, and as they travel through the Universe they loose energy in collisions with microwave background radiation. So where do they come from? The neutrinos hold the key. They are produced in these collisions but interact so weakly that huge detectors are needed. We propose to use the moon as our detector by looking for the coherent Cerenkov radio emission from neutrino induced cascades in lunar regolith (sandy surface layer). The neutrino interaction produces a nanosecond pulse peaking between 1-2GHz.
2. Radio Cerenkov Emission from UHE Neutrinos
Ekers, Ron; Phillips, Chris; Protheroe, Ray; Bhat, Ramesh; McFadden, Rebecca; James, Clancy; Roberts, Paul; Tingay, Steven
2007-10-01
Some cosmic ray nuclei have energies equivalent to that of a fast-moving tennis ball. Our Galaxy is too small to produce them, and as they travel through the Universe they loose energy in collisions with microwave background radiation. So where do they come from? The neutrinos hold the key. They are produced in these collisions but interact so weakly that huge detectors are needed. We propose to use the moon as our detector by looking for the coherent Cerenkov radio emission from neutrino induced cascades in lunar regolith (sandy surface layer). The neutrino interaction produces a nanosecond pulse peaking between 1-2GHz.
3. Radio Cerenkov Emission from UHE Neutrinos
Ekers, Ron; Phillips, Chris; Protheroe, Ray; McFadden, Rebecca; James, Clancy; Roberts, Paul
2008-04-01
Some cosmic ray nuclei have energies equivalent to that of a fast-moving tennis ball. Our Galaxy is too small to produce them, and as they travel through the Universe they loose energy in collisions with microwave background radiation. So where do they come from? The neutrinos hold the key. They are produced in these collisions but interact so weakly that huge detectors are needed. We propose to use the moon as our detector by looking for the coherent Cerenkov radio emission from neutrino induced cascades in lunar regolith (sandy surface layer). The neutrino interaction produces a nanosecond pulse peaking between 1-2GHz.
4. Radio Cerenkov Emission from UHE Neutrinos
Ekers, Ron; Jones, David; Protheroe, Ray; Bhat, Ramesh; McFadden, Rebecca; James, Clancy; Roberts, Paul; Tingay, Steven
2007-04-01
Some cosmic ray nuclei have energies equivalent to that of a fast-moving tennis ball. Our Galaxy is too small to produce them, and as they travel through the Universe they loose energy in collisions with microwave background radiation. So where do they come from? The neutrinos hold the key. They are produced in these collisions but interact so weakly that huge detectors are needed. We propose to use the moon as our detector by looking for the coherent Cerenkov radio emission from neutrino induced cascades in lunar regolith (sandy surface layer). The neutrino interaction produces a nanosecond pulse peaking between 1-2GHz.
5. Radio triangulation - mapping the 3D position of the solar radio emission
Magdalenic, Jasmina
2016-04-01
6. Source characteristics of Jovian hectometric radio emissions
NASA Technical Reports Server (NTRS)
Reiner, M. J.; Fainberg, J.; Stone, R. G.
1993-01-01
Direct confirmation that low-frequency Jovian hectometric (HOM) radio emissions centered near 0 deg central meridian longitude consist of distinct, oppositely polarized northern and southern beams has been achieved using data from the Unified Radio and Plasma Wave (URAP) experiment on the Ulysses spacecraft during the Ulysses-Jupiter encounter in early February 1992. Distinct northern and southern beams were observed in the frequency range from approximately 300 kHz to 1 MHz for at least eight Jovian rotations during the Ulysses inbound pass at distances from 100 to 40 R(sub j). The radiation from the two magnetic hemispheres was measured from different Jovigraphic longitudes and magnetic (or centrifugal) latitudes. Observed temporal variations in the radio intensities, with time scales on the order of 30 min, may result either from longitudinal variations of the HOM sources or from longitudinal density variations in the Io plasma torus. Using the URAP direction-finding capabilities and assuming a tilted dipole planetary magnetic field model, the three-dimensional HOM source locations, the L shell through these source locations, and the beam opening angles were independently deduced. The HOM sources were found to originate at approximately 3 R(sub j) and on low L shells (L approximately 4 to 6), with beam opening angles ranging from 10 to 50 deg.
7. Properties and geometry of radio pulsar emission
Smits, Johannes Martinus
2006-10-01
This thesis consists of a number of studies on the radio emission of pulsars. The central topics are polarisation and multi frequency observations, which both lead to important information on the geometry of the emission. The first chapter introduces different aspects of pulsars that are related to the research that has been done in this thesis. In particular it deals with different aspects concerning the geometry of pulsar emission. Chapter 2 is about the nature of the radio emission. It shows the result of an attempt to confirm and expand on work that has been published by Jenet et al. (2001) on the detection of coherence in pulsar radiation. From an analysis of high time resolution observations, we found that the detection of coherence is consistent with the effects of interstellar scintillation. In chapter 3 a study is carried out on the orthogonal polarisation mode behaviour as a function of frequency of 18 pulsars. By making the assumption that the radiation consists of two 100% polarised completely orthogonal superposed modes, both modes could be separated In chapter 4 PSR B0031-07 is studied at two frequencies using two observations that were carried out simultaneously. It is shown that from the three known drift modes, only one drift mode is seen at high frequency. Based on this result we suggest a geometrical model in which different modes are emitted in concentric rings around the magnetic axis, with each mode having a different radius. The fifth chapter follows the suggestions made in chapter 4 to create a geometrical model of PSR B0031-07 for two of the drift modes. The results can be used to limit the possible geometries of PSR B0031-07. The final chapter consists of documentation of software that was written in C and utilised for this thesis for handling and analysing data files in the EPN format
8. Planetary and stellar auroral magnetospheric radio emission
Speirs, David; Cairns, Robert A.; Bingham, Robert; Kellett, Barry J.; McConville, Sandra L.; Gillespie, Karen M.; Vorgul, Irena; Phelps, Alan D. R.; Cross, Adrian W.; Ronald, Kevin
2012-10-01
A variety of astrophysical radio emissions have been identified to date in association with non-uniform magnetic fields and accelerated particle streams [1]. Such sources are spectrally well defined and for the planetary cases [1,2] show a high degree of extraordinary (X-mode) polarisation within the source region. It is now widely accepted that these emissions are generated by an electron cyclotron-maser instability driven by a horseshoe shaped electron velocity distribution. Although the generation mechanism is well established, a satisfactory explanation does not yet exist for the observed field aligned beaming of the radiation out-with the source region [2]. In the current context, the results of PiC simulations will be presented investigating the spatial growth of the horseshoe-maser instability in an unbounded interaction geometry, with a view to studying the wave vector of emission, spectral properties and RF conversion efficiency. In particular, the potential for backward-wave coupling is investigated as a viable precursor to a model of upward refraction and field-aligned beaming of the radiation [3].[4pt] [1] A.P. Zarka, Advances in Space Research, 12, pp. 99 (1992).[0pt] [2] R.E. Ergun et al., Astrophys. J., 538, pp. 456 (2000)[0pt] [3] J.D. Menietti et al., J. Geophys. Res., 116, A12219 (2011).
9. Radio Cerenkov Emission from UHE neutrinos
Ekers, Ron; Jones, David; Protheroe, Ray; Bhat, Ramesh; McFadden, Rebecca; Tingay, Steven
2006-10-01
Some cosmic ray nuclei have energies equivalent to that of a fast-moving tennis ball. Our Galaxy is too small to produce them, and as they travel through the Universe they loose energy in collisions with microwave background radiation. So where do they come from? The neutrinos hold the key. They are produced in these collisions but interact so weakly that huge detectors are needed. We propose to use the moon as our detector by looking for the coherent Cerenkov radio emission from neutrino induced cascades in lunar regolith (sandy surface layer). The neutrino interaction produces a nanosec pulse peaking between 1-3GHz. This proposal is for time to test two of the parallel techniques we are developing to detect these neutrinos.
10. A multidisciplinary study of planetary, solar and astrophysical radio emissions
NASA Technical Reports Server (NTRS)
Gurnett, D. A.; Calvert, W.; Fielder, R.; Goertz, C.; Grabbe, C.; Kurth, W.; Mutel, R.; Sheerin, J.; Mellott, M.; Spangler, S.
1986-01-01
Combination of the related fields of planetary, solar, and astrophysical radio emissions was attempted in order to more fully understand the radio emission processes. Topics addressed include: remote sensing of astrophysical plasma turbulence; Alfven waves; astrophysical shock waves; surface waves; very long base interferometry results; very large array observations; solar magnetic flux; and magnetohydrodynamic waves as a tool for solar corona diagnostics.
11. Extended optical-emission-line gas in powerful radio galaxies
SciTech Connect
Baum, S.A.
1987-01-01
12. Phenomenology of Neptune's radio emissions observed by the Voyager planetary radio astronomy experiment
NASA Technical Reports Server (NTRS)
Pedersen, B. M.; Lecacheux, A.; Zarka, P.; Aubier, M. G.; Kaiser, M. L.; Desch, M. D.
1992-01-01
The Neptune flyby in 1989 added a new planet to the known number of magnetized planets generating nonthermal radio emissions. We review the Neptunian radio emission morphology as observed by the planetary radio astronomy experiment on board Voyager 2 during a few weeks before and after closest approach. We present the characteristics of the two observed recurrent main components of the Neptunian kilometric radiation, i.e., the 'smooth' and the 'bursty' emissions, and we describe the many specific features of the radio spectrum during closest approach.
13. Solar system radio emissions studies with the largest low-frequency radio telescopes
Zakharenko, V.; Konovalenko, A.; Litvinenko, G.; Kolyadin, V.; Zarka, P.; Mylostna, K.; Vasylieva, I.; Griessmeier, J.-M.; Sidorchuk, M.; Rucker, H.; Fischer, G.; Cecconi, B.; Coffre, A.; Denis, L.; Shevchenko, V.; Nikolaenko, V.
2014-04-01
We describe the trends and tasks in the field of lowfrequency studies of radio emission from the Solar system's objects. The world's largest decameter radio telescopes UTR-2 and URAN have a unique combination of sensitivity and time/frequency resolution parameters, providing the capability of the most detailed studies of various types of solar and planetary emissions.
14. Radio Emission from Saturn's Rings: Polarization
Molnar, L. A.; Dunn, D. E.
2002-09-01
We are pursuing a systematic program of observing and modeling the radio emission from Saturn's rings over a range of wavelengths and ring inclinations. In our earlier reports we have presented a number total intensity maps along with results from our Monte Carlo radiative transfer code, simrings. This has been a fruitful test of particle spatial distribution within the rings: in particular evidence of wake structure in the A ring and of a near monolayer in the C ring. In this contribution we present our first maps of polarized intensity. Such observations offer independent information about the nature of the ring particles. In particular, Grossman (Ph.D. thesis, 1990) showed that the orientation of the position angle of the polarization of the rings is in direct conflict with the predictions of Mie scattering. We will present several polarized maps, discuss some of the subtleties of producing such maps (in particular the tradeoff between angular resolution and reliable intensities), and suggest possible approaches for modeling of the polarized emission. This work was supported in part by a grant from Research Corporation.
15. Neptune's non-thermal radio emissions - Phenomenology and source locations
NASA Technical Reports Server (NTRS)
Rabl, Gerald K. F.; Ladreiter, H.-P.; Rucker, Helmut O.; Kaiser, Michael L.
1992-01-01
During the inbound and the outbound leg of Voyager 2's encounter with Neptune, the Planetary Radio Astronomy (PRA) experiment aboard the spacecraft detected short radio bursts at frequencies within the range of about 500-1300 kHz, and broad-banded smoothly varying emission patterns within the frequency range from about 40-800 kHz. Both emissions can be described in terms of a period of 16.1 hours determining Neptune's rotation period. Furthermore, just near closest approach, a narrow-banded smoothly varying radio component was observed occurring between 600 and 800 kHz. After giving a brief overview about some general characteristics of Neptune's nonthermal radio emission, the source locations of Neptune's emission components are determined, using an offset tilted dipole model for Neptune's magnetic field. Assuming that the emission originates near the electron gyrofrequency a geometrical beaming model is developed in order to fit the observed emission episodes.
16. Radio emission and the forbidden line region of Seyfert galaxies
SciTech Connect
1981-01-01
17. Amalthea's Modulation of Jovian Decametric Radio Emission
Arkhypov, Oleksiy V.
2006-08-01
Institute of Radio Astronomy, National Academy of Sciences of Ukraine, Kharkiv, Ukraine Amalthea is the largest body after Galilean satellites near Jupiter. An anomaly in Jovian synchrotron radiation has been found just on the Amalthea magnetic shell (de Pater, Schulz & Brecht 1997). It has been suggested that Amalthea's motion through Jupiter's magnetic field induces Alfvén or whistler wings or electrostatic high-frequency waves which lead to the pitch angle scattering. It is reasonable to search for another effect of these processes: magnetospheric inhomogeneities which could be found via scattering of Jovian decametric radio emission (DAM). Such scattering on field-aligned inhomogeneities in the Io plasma torus is known as "modulation lanes" in DAM dynamic spectra. To search for analogous Amalthea's modulation, the positions and frequency drift of about 600 lanes are measured on the UFRO spectra of DAM. The special 3D algorithm is used for localization of field-aligned magnetospheric inhomogeneities by the frequency drift of modulation lanes. It is found that about 4% of the lanes are clustered near Amalthea's magnetic shell. There are two such clusters near longitudes of 123°≤λ[III]≤140° and 284°≤λ[III]≤305°, which coincide with the regions of maximum compression of fresh plasma due to rotating magnetic field of Jupiter (where ∂(B^2)/∂λ[III]) is maximal). The Amalthea modulation could explain the enigmatic "hf-lanes" (Genova, Aubier & Lecacheux 1981). The found magnetospheric formations are a new argument for the ice nature of Amalthea which has the density less than that of water (Anderson et al. 2005). Anderson J.D. et al. 2005, Science, 308, 5726, pp. 1291-1293. de Pater I., Schulz M., Brecht S.H. 1997, J. Geophys. Res., 102, A10, pp. 22043-22064. Genova F., Aubier M.G., Lecacheux A. 1981, Astron. and Astrophys. 104, 2, pp. 229-239.
18. Solar wind control of Jupiter's hectometric radio emission
NASA Technical Reports Server (NTRS)
Barrow, C. H.; Desch, M. D.
1989-01-01
Radio, plasma, and magnetic field data obtained by Voyager 1 and Voyager 2 were used to examine the manner in which the Jovian hectometric radio emission (HOM) is controlled by the solar wind. Using the method of superposed epochs, it was found that the higher energy HOM is correlated with the IMF as well as with the solar wind density and pressure. However, unlike the Io-independent decametric radio emission (Non-Io DAM), the HOM displayed no correlation with the solar wind velocity, although this radio component appear to be also influenced by the IMF. The results suggest separate HOM amd Non-Io DAM sources.
19. Detection of radio emission from GX9+1.
NASA Technical Reports Server (NTRS)
Zaumen, W.; Murthy, G. T.; Rappaport, S.; Hjellming, R. M.; Wade, C. M.
1972-01-01
Detection of a variable radio source in association with the X-ray source GX9+1, using the NRAO three-element interferometer at frequencies of 2695 and 8085 MHz. This radio source appears unresolved at all spacings, and must therefore be smaller than 1 arc sec. Two other celestial X-ray sources, GX349+2 and GX340+0 were also observed for radio emission during the same period of observations of GX9+1. These two sources should be good candidates for radio emission.
20. RADIO AND GAMMA-RAY PULSED EMISSION FROM MILLISECOND PULSARS
SciTech Connect
Du, Y. J.; Chen, D.; Qiao, G. J.
2013-01-20
Pulsed {gamma}-ray emission from millisecond pulsars (MSPs) has been detected by the sensitive Fermi space telescope, which sheds light on studies of the emission region and its mechanism. In particular, the specific patterns of radio and {gamma}-ray emission from PSR J0101-6422 challenge the popular pulsar models, e.g., outer gap and two-pole caustic models. Using the three-dimensional annular gap model, we have jointly simulated radio and {gamma}-ray light curves for three representative MSPs (PSR J0034-0534, PSR J0101-6422, and PSR J0437-4715) with distinct radio phase lags, and present the best simulated results for these MSPs, particularly for PSR J0101-6422 with complex radio and {gamma}-ray pulse profiles, and for PSR J0437-4715 with a radio interpulse. We have found that both the {gamma}-ray and radio emission originate from the annular gap region located in only one magnetic pole, and the radio emission region is not primarily lower than the {gamma}-ray region in most cases. In addition, the annular gap model with a small magnetic inclination angle instead of an 'orthogonal rotator' can account for the MSPs' radio interpulse with a large phase separation from the main pulse. The annular gap model is a self-consistent model not only for young pulsars but also MSPs, and multi-wavelength light curves can be fundamentally explained using this model.
1. On the proposed triggering of Jovian radio emissions
NASA Technical Reports Server (NTRS)
Desch, M. D.; Kaiser, M. L.
1985-01-01
Calvert (1985) has proposed that a solar type III radio bursts can trigger the onset of certain Jovian hectometer wavelength emissions. It is shown, using the data obtained by the Voyager Planetary Radio Astronomy experiment, that this triggering hypothesis is not supported statistically. Furthermore, the causality of this proposed triggering is questioned because much of the Jovian hectometer emission is due to a quasi-continuous radio source rotating, in lighthouse fashion, with Jupiter. Thus, an observed 'onset' of emission is simply a function of the observer's position in local time around Jupiter.
2. Neptune radio emission in dipole and multipole magnetic fields
NASA Technical Reports Server (NTRS)
Sawyer, C. B.; King, N. V.; Romig, J. H.; Warwick, J. W.
1995-01-01
We study Neptune's smooth radio emission in two ways: we simulate the observations and we then consider the radio effects of Neptune's magnetic multipoles. A procedure to deduce the characteristics of radio sources observed by the Planetary Radio Astronomy experiment minimizes limiting assumptions and maximizes use of the data, including quantitative measurement of circular polarization. Study of specific sources simulates time variation of intensity and apparent polarization of their integrated emission over an extended time period. The method is applied to Neptune smooth recurrent emission (SRE). Time series are modeled with both broad and beamed emission patterns, and at two frequencies which exhibit different time variation of polarization. These dipole-based results are overturned by consideration of more complex models of Neptune's magnetic field. Any smooth emission from the anticipated auroral radio source is weak and briefly observed. Dominant SRE originates complex fields at midlatitude. Possible SRE source locations overlap that of 'high-latitude' emission (HLE) between +(out) and -(in) quadrupoles. This is the first identification of multipolar magnetic structure with a major source of planetary radio emission.
3. Fast Radio Bursts’ Emission Mechanism: Implication from Localization
Lyutikov, Maxim
2017-03-01
We argue that the localization of the repeating fast radio bursts (FRBs) at ˜1 Gpc excludes a rotationally powered type of radio emission (e.g., analogs of Crab’s giant pulses coming from very young energetic pulsars) as the origin of FRBs.
4. Analysis of Jovian decamteric data: Study of radio emission mechanisms
NASA Technical Reports Server (NTRS)
Staelin, D. H.; Rosenkranz, P. W.; Arias, T. A.; Garnavich, P. N.; Hammerschlag, R.
1986-01-01
This research effort involved careful examination of Jovian radio emission data below 40 MHz, with emphasis on the informative observations of the Planetary Radio Astronomy experiment (PRA) on the Voyager 1 and 2 spacecraft. The work is divided into three sections, decametric arcs, decametric V bursts, and hectometric modulated spectral activity (MSA).
NASA Technical Reports Server (NTRS)
Dudnik, A. V.; Zaljubovsky, I. I.; Kartashev, V. M.; Lasarev, A. V.; Shmatko, E. S.
1985-01-01
During the period of low solar activity at sunrise the effect of sporadic high frequency near Earth space radio emission was experimentally discovered at middle latitudes. The possible mechanism of its origin is discussed.
6. Evidence for solar wind control of Saturn radio emission
NASA Technical Reports Server (NTRS)
Desch, M. D.
1982-01-01
Using data collected by the Voyager 1 and 2 spacecraft in 1980 and 1981, strong evidence is presented for a direct correlation between variations in the solar wind at Saturn and the level of activity of Saturn's nonthermal radio emission. Correlation coefficients of 57 to 58% are reached at lag times of 0 to 1 days between the arrival at Saturn of high pressure solar wind streams and the onset of increased radio emission. The radio emission exhibits a long-term periodicity of 25 days, identical to the periodicity seen in the solar wind at this time and consistent with the solar rotation period. The energy coupling efficiency between the solar wind with the Saturn radio emission is estimated and compared with that for Earth.
7. Satellite Emission Radio Interferometric Earth Surveying (SERIES). [astrometry
NASA Technical Reports Server (NTRS)
Macdoran, P. F.
1980-01-01
Existing satellite radio emissions of the global positioning system were exploited as a resource for cost effective high accuracy geodetic measurements. System applications were directed toward crustal dynamics and earthquake research.
8. Voyager detection of nonthermal radio emission from Saturn
NASA Technical Reports Server (NTRS)
Kaiser, M. L.; Desch, M. D.; Warwick, J. W.; Pearce, J. B.
1980-01-01
The detection of bursts of nonthermal radio noise from Saturn by the planetary radio astonomy experiment onboard the Voyager spacecraft is discussed. The emissions occur near 200 kHz with a peak flux density comparable to higher frequency Jovian emissions. The radiation is right-hand polarized and is most likely emitted in the extraordinary magnetoionic mode from Saturn's northern hemisphere. Modulation is apparent in the data which is consistent with a planetary rotation period of 10 hr 39.9 min.
9. The Arecibo Reconnaissance of Radio Emission from Nearby Extrasolar Planets
Route, Matthew; Wolszczan, Alex
2014-11-01
10. Measurement of radio emission from extensive air showers with LOPES
Hörandel, J. R.; Apel, W. D.; Arteaga, J. C.; Asch, T.; Badea, F.; Bähren, L.; Bekk, K.; Bertaina, M.; Biermann, P. L.; Blümer, J.; Bozdog, H.; Brancus, I. M.; Brüggemann, M.; Buchholz, P.; Buitink, S.; Cantoni, E.; Chiavassa, A.; Cossavella, F.; Daumiller, K.; de Souza, V.; di Pierro, F.; Doll, P.; Ender, M.; Engel, R.; Falcke, H.; Finger, M.; Fuhrmann, D.; Gemmeke, H.; Ghia, P. L.; Glasstetter, R.; Grupen, C.; Haungs, A.; Heck, D.; Horneffer, A.; Huege, T.; Isar, P. G.; Kampert, K.-H.; Kang, D.; Kickelbick, D.; Krömer, O.; Kuijpers, J.; Lafebre, S.; Link, K.; Łuczak, P.; Ludwig, M.; Mathes, H. J.; Mayer, H. J.; Melissas, M.; Mitrica, B.; Morello, C.; Navarra, G.; Nehls, S.; Nigl, A.; Oehlschläger, J.; Over, S.; Palmieri, N.; Petcu, M.; Pierog, T.; Rautenberg, J.; Rebel, H.; Roth, M.; Saftoiu, A.; Schieler, H.; Schmidt, A.; Schröder, F.; Sima, O.; Singh, K.; Toma, G.; Trinchero, G. C.; Ulrich, H.; Weindl, A.; Wochele, J.; Wommer, M.; Zabierowski, J.; Zensus, J. A.
2011-02-01
A new method is explored to detect extensive air showers: the measurement of radio waves emitted during the propagation of the electromagnetic shower component in the magnetic field of the Earth. Recent results of the pioneering experiment LOPES are discussed. It registers radio signals in the frequency range between 40 and 80 MHz. The intensity of the measured radio emission is investigated as a function of different shower parameters, such as shower energy, angle of incidence, and distance to shower axis. In addition, new antenna types are developed in the framework of LOPESstar and new methods are explored to realize a radio self-trigger algorithm in real time.
11. Possible radio-emission signatures of exoplanets
Budding, E.; Slee, O. B.; Johnston-Hollitt, M.
2015-03-01
A brief review of possibly detectable radio-effects from exoplanets is presented. Previous observations may show relevant effects, when appropriate theory is taken into account. Pointers to contemporary and future lines of investigation are also presented.
SciTech Connect
Miller, B. P.; Brandt, W. N.; Schneider, D. P.; Wu Jianfeng; Gibson, R. R.; Steffen, A. T. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
2011-01-01
13. Evidence that the AGN dominates the radio emission in z ˜ 1 radio-quiet quasars
White, Sarah V.; Jarvis, Matt J.; Kalfountzou, Eleni; Hardcastle, Martin J.; Verma, Aprajita; Cao Orjales, José M.; Stevens, Jason
2017-06-01
In order to understand the role of radio-quiet quasars (RQQs) in galaxy evolution, we must determine the relative levels of accretion and star-formation activity within these objects. Previous work at low radio flux densities has shown that accretion makes a significant contribution to the total radio emission, in contrast with other quasar studies that suggest star formation dominates. To investigate, we use 70 RQQs from the Spitzer-Herschel Active Galaxy Survey. These quasars are all at z ˜ 1, thereby minimizing evolutionary effects, and have been selected to span a factor of ˜100 in optical luminosity, so that the luminosity dependence of their properties can be studied. We have imaged the sample using the Karl G. Jansky Very Large Array (JVLA), whose high sensitivity results in 35 RQQs being detected above 2σ. This radio data set is combined with far-infrared luminosities derived from grey-body fitting to Herschel photometry. By exploiting the far-infrared-radio correlation observed for star-forming galaxies, and comparing two independent estimates of the star-formation rate, we show that star formation alone is not sufficient to explain the total radio emission. Considering RQQs above a 2σ detection level in both the radio and the far-infrared, 92 per cent are accretion dominated, and the accretion process accounts for 80 per cent of the radio luminosity when summed across the objects. The radio emission connected with accretion appears to be correlated with the optical luminosity of the RQQ, whilst a weaker luminosity dependence is evident for the radio emission connected with star formation.
14. Radio emission of air showers with extremely high energy measured by the Yakutsk Radio Array
Knurenko, S. P.; Petrov, Z. E.; Petrov, I. S.
2017-09-01
The Yakutsk Array is designed to study cosmic rays at energy 1015 -1020 eV . It consists several independent arrays that register charged particles, muons with energy E ≥ 1 GeV , Cherenkov light and radio emission. The paper presents a technical description of the Yakutsk Radio Array and some preliminary results obtained from measurements of radio emission at 30-35 MHz frequency induced by air shower particles with energy ε ≥ 1 ·1017 eV . The data obtained at the Yakutsk array in 1986-1989 (first set of measurements) and 2009-2014 (new set of measurements). Based on the obtained results we determined: Lateral distribution function (LDF) of air showers radio emission with energy ≥1017 eV . Radio emission amplitude empirical connection with air shower energy. Determination of depth of maximum by ratio of amplitude at different distances from the shower axis. For the first time, at the Yakutsk array radio emission from the air shower with energy >1019 eV was registered including the shower with the highest energy ever registered at the Yakutsk array with energy ∼ 2 ·1020 eV .
15. ON THE ORIGIN OF RADIO EMISSION FROM MAGNETARS
SciTech Connect
Szary, Andrzej; Melikidze, George I.; Gil, Janusz
2015-02-10
16. Spontaneous Radio Frequency Emissions from Natural Aurora. Chapter 4
NASA Technical Reports Server (NTRS)
LaBelle, J.
2009-01-01
At high latitudes, suitably sensitive radio experiments tuned below 5 MHz detect up to three types of spontaneous radio emissions from the Earth s ionosphere. In recent years, ground-based and rocket-borne experiments have provided strong evidence for theoretical explanations of the generation mechanism of some of these emissions, but others remain unexplained. Achieving a thorough understanding of these ionospheric emissions, accessible to ground-based experiments, will not only bring a deeper understanding of Earth s radio environment and the interactions between waves and particles in the ionosphere but also shed light on similar spontaneous emissions occurring elsewhere in Earth s environment as well as other planetary and stellar atmospheres.
17. Terrestrial structured radio emissions occurring close to the equatorial regions
Boudjada, Mohammed Y.; Galopeau, Patrick H. M.; Sawas, Sami; Berthelier, Jean-Jacques
2015-04-01
We study the occurrence of terrestrial radio emissions observed by the electric field experiment (ICE) onboard DEMETER micro-satellite. We principally consider the ICE observations recorded in the HF frequency range between 10 kHz and 3.175 MHz. A dynamic spectrum is recorded each half-orbit with a time and frequency resolutions, respectively, in the order of 3.25 kHz and 2.048 sec. The terrestrial structured radio emission is found to occur when the satellite is approaching the equatorial region of the Earth. It appears as a structured narrow band 'continuum' with a positive or negative low frequency drift rate, less than 1 kHz/s. The bandwidth is, on average, of about 30 kHz. We derive from our investigation the beam and the probable location of the emission source. We discuss the origin of this terrestrial radio emission and its dependence, or not, on the solar and geomagnetic activities.
18. NUclei of GAlaxies. V. Radio emission in 7 NUGA sources
Krips, M.; Eckart, A.; Krichbaum, T. P.; Pott, J.-U.; Leon, S.; Neri, R.; García-Burillo, S.; Combes, F.; Boone, F.; Baker, A. J.; Tacconi, L. J.; Schinnerer, E.; Hunt, L. K.
2007-03-01
We present high angular resolution radio snap-shot observations of seven nearby low-luminosity active galaxies (LLAGN) from the NUclei of GAlaxies (NUGA) survey. The observations were conducted with MERLIN and EVN/VLBI at 18 cm and 6 cm. At all observed angular resolutions and frequencies, we find indications for extended emission in about ~40% of the sources, consistent with the decrease of flux with increasing angular resolution. The extended components resemble jet emission in a majority of cases, consistent with the optically thin synchrotron emission implied by their steep spectra. We consider the compact 6 cm EVN/VLBI radio emission of our sources in the context of the "fundamental plane" that previous LLAGN studies identified within the three-dimensional parameter space of radio luminosity, X-ray luminosity, and black hole mass. We demonstrate, using NGC 7217 and NGC 1068 as particular examples, that high-resolution, multi-epoch radio observations offer useful information about the origin of offsets from the fundamental plane. EVN: The European VLBI Network is a joint facility of European, Chinese, South African and other radio astronomy institutes funded by their national research councils. MERLIN is a national facility operated by the University of Manchester on behalf of PPARC. VLBI including the VLBA: The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
NASA Technical Reports Server (NTRS)
Polletta, M.; Courvoisier, T. J.-L.; Wilkes, B. J.; Hooper, E. J.
2000-01-01
Continuum observations at radio, millimeter, infrared and soft X-ray energies are presented for a sample of 22 quasars, consisting of flat and steep spectrum radio loud, radio intermediate and radio quiet objects. The primary observational distinctions, among the different kinds of quasars in the radio and IR energy domains are studied using large observational datasets provided by ISOPHOT on board the Infrared Space Observatory, by the IRAM interferometer, by the sub-millimetre array SCUBA on JCMT, and by the European Southern Observatory (ESO) facilities IRAC1 on the 2.2 m telescope and SEST. The spectral energy distributions of all quasars from radio to IR energies are analyzed and modeled with non-thermal and thermal spectral components. The dominant mechanism emitting in the far/mid-IR is thermal dust emission in all quasars, with the exception of flat spectrum radio loud quasars for which the presence of thermal IR emission remains rather uncertain, since it is difficult to separate it from the bright non-thermal component. The dust is predominantly heated by the optical/ultraviolet radiation emitted from the external components of the AGN. A starburst contributes to the IR emission at different levels, but always less than the AGN (<= 27%). The distribution of temperatures, sizes, masses, and luminosities of the emitting dust are independent of the quasar type.
NASA Technical Reports Server (NTRS)
Polletta, M.; Courvoisier, T. J.-L.; Wilkes, B. J.; Hooper, E. J.
2000-01-01
Continuum observations at radio, millimeter, infrared and soft X-ray energies are presented for a sample of 22 quasars, consisting of flat and steep spectrum radio loud, radio intermediate and radio quiet objects. The primary observational distinctions, among the different kinds of quasars in the radio and IR energy domains are studied using large observational datasets provided by ISOPHOT on board the Infrared Space Observatory, by the IRAM interferometer, by the sub-millimetre array SCUBA on JCMT, and by the European Southern Observatory (ESO) facilities IRAC1 on the 2.2 m telescope and SEST. The spectral energy distributions of all quasars from radio to IR energies are analyzed and modeled with non-thermal and thermal spectral components. The dominant mechanism emitting in the far/mid-IR is thermal dust emission in all quasars, with the exception of flat spectrum radio loud quasars for which the presence of thermal IR emission remains rather uncertain, since it is difficult to separate it from the bright non-thermal component. The dust is predominantly heated by the optical/ultraviolet radiation emitted from the external components of the AGN. A starburst contributes to the IR emission at different levels, but always less than the AGN (<= 27%). The distribution of temperatures, sizes, masses, and luminosities of the emitting dust are independent of the quasar type.
1. Coronal and interplanetary Type 2 radio emission
Cane, H. V.
1987-09-01
Several observations suggest that the disturbances which generate coronal (meter wavelength) type II radio bursts are not driven by coronal mass ejections (CMEs). A new analysis using a large sample of metric radio bursts and associated soft X-ray events provides further support for the original hypothesis that type II-producing disturbances are blast waves generated at the time of impulsive energy release in flares. Interplanetary (IP) shocks, however, are closely associated with CMEs. The shocks responsible for IP type II events (observed at kilometer wavelengths) are associated with the most energetic CMEs.
2. VLA Detects Unexplained Radio Emission From Three Brown Dwarfs
2005-01-01
3. Radio emission of the sun at millimeter wavelengths
Nagnibeda, V. G.; Piotrovich, V. V.
This review article deals with the radio emission originating from different solar atmospheric regions - the quiet solar atmosphere, active regions and solar flares. All experimental data of the quiet Sun brightness temperature at the region of 0.1 - 20 mm wavelength are summarized. The quiet Sun brightness distributions across the disk and values of the solar radio radius are reviewed. The properties of the sources of sunspot-associated active region emission and radio brightness depression associated with Hα-filaments are considered in comparison with observations at centimetre and optical domains. The observational properties of millimetre wave bursts and their correlations with similar phenomena at other domains are reviewed. Special reference is devoted to nearly 100% correlation impulsive radio bursts with hard X-ray bursts. Existence of the fine temporal structure containing many spikes with time scales up to 10 ms as well as observations of quasi-periodic millisecond oscillations are discussed.
4. Jupiter's decametric radio emission - A nice problem of optics
Lecacheux, A.; Meyer-Vernet, N.; Daigne, G.
1981-02-01
We show that the spectral and temporal 'nested arcs' pattern of the Jovian decametric radio-dynamic spectrum can be interpreted as due solely to the diffraction of a radio-source by a phase changing plasma structure, located permanently in Jupiter's magnetosphere and rotating with the planet. This entirely new approach of the phenomenon explains in a simple way many observational features not understood so far. It allows to reinterpret the observations, thus yielding new constraints on the physics of the emission.
5. Voyager detection of nonthermal radio emission from Saturn
NASA Technical Reports Server (NTRS)
Kaiser, M. L.; Desch, M. D.; Warwick, J. W.; Pearce, J. B.
1980-01-01
The planetary radio astronomy experiment on board the Voyager spacecraft has detected bursts of nonthermal radio noise from Saturn occurring near 200 kilohertz, with a peak flux density comparable to higher frequency Jovian emissions. The radiation is right-hand polarized and is most likely emitted in the extraordinary magnetoionic mode from Saturn's northern hemisphere. Modulation that is consistent with a planetary rotation period of 10 hours 39.9 minutes is apparent in the data.
6. Radio emission from rapidly-rotating cool giant stars
NASA Technical Reports Server (NTRS)
Drake, Stephen A.; Walter, Frederick M.; Florkowski, David R.
1990-01-01
The results of a VLA program are reported to examine the radio continuum emission from 11 rapidly-rotating cool giant stars, all of which were originally believed to be single stars. Six of the 11 stars were detected as radio sources, including FK Com and HR 9024, for which there exist multifrequency observations. HD 199178, UZ Lib (now known to be a binary system), and HD 82558, for which there is only 6-cm data. The radio properties of these stars are compared with those of the active, rapidly rotating evolved stars found in the RS CVn binary systems.
7. Observations of the Solar Continuum Radio Emission at Decameter Wavelengths
Brazhenko, Anatoliy I.; Mel'Nik, Valentin N.; Konovalenko, Alexander A.; Abranin, Edward P.; Dorovskyy, Vladimir V.; Vashchishin, Rostislav V.; Frantzusenko, Anatoly V.; Rucker, Helmut O.
2010-01-01
Results of study of the continuum radio emission of the Sun in the decameter range are presented. Observations were carried out with radio telescope URAN-2 in summer months in 2008-2009. Radio fluxes at frequencies 20 MHz and 25 MHz in frequency band 250 kHz were obtained during the time, when there were no active regions on the solar disk. Their average values for two years were 670 Jy and 850 Jy at frequencies 20 MHz and 25 MHz correspondingly. These fluxes are in agreement with high frequency values.
8. Satellite emission radio interferometric earth surveying series - GPS geodetic system
NASA Technical Reports Server (NTRS)
Macdoran, P. F.
1979-01-01
A concept called SERIES (satellite emissions radio interferometric earth surveying) which makes use of GPS (global positioning system) radio transmissions without any satellite modifications, is described. Through the use of very long baseline interferometry (VLBI) and its calibration methods, 0.5 to 3 cm three dimensional baseline accuracy can be achieved over distances of 2 to 200 km respectively, with only 2 hours of on-site data acquisition. Attention is given to such areas as: the radio flux equivalent of GPS transmissions, synthesized delay precision, transmission and frequency subsystem requirements, tropospheric and ionospheric errors. Applications covered include geodesy and seismic tectonics.
9. A model for radio emission from solar coronal shocks
SciTech Connect
Zhao, G. Q.; Chen, L.; Wu, D. J.
2014-05-01
Solar coronal shocks are very common phenomena in the solar atmosphere and are believed to be the drivers of solar type II radio bursts. However, the microphysical nature of these emissions is still an open question. This paper proposes that electron cyclotron maser (ECM) emission is responsible for the generation of radiation from the coronal shocks. In the present model, an energetic ion beam accelerated by the shock first excites the Alfvén wave (AW), then the excited AW leads to the formation of a density-depleted duct along the foreshock boundary of the shock. In this density-depleted duct, the energetic electron beam produced via the shock acceleration can effectively excite radio emission by ECM instability. Our results show that this model may potentially be applied to solar type II radio bursts.
10. Analysis of Uranian radio emissions, Uranus Data Analysis Program (UDAP)
NASA Technical Reports Server (NTRS)
Calvert, W.
1991-01-01
Progress under this grant has included identifying certain new radio emission components and determining the source location of both these and the two major Uranian radio emission (the SHF and bursty components) by a unique new statistical minimization technique. This new source location technique has subsequently also been applied at Neptune, with considerable success. New radio spectrograms have been prepared to clarify the behavior of such emissions, using both the usual 48-second, log-averaged data and the original 6-second PRA data, the latter showing a number of interesting new features. Also, a plasmasphere was discovered at Uranus, auroral plasma cavities were discovered at both Uranus and Neptune, and it was found that the currently-accepted rotation period for Uranus is in error by a small amount.
11. Probing the radio emission from air showers with polarization measurements
Aab, A.; Abreu, P.; Aglietta, M.; Ahlers, M.; Ahn, E. J.; Albuquerque, I. F. M.; Allekotte, I.; Allen, J.; Allison, P.; Almela, A.; Alvarez Castillo, J.; Alvarez-Muñiz, J.; Alves Batista, R.; Ambrosio, M.; Aminaei, A.; Anchordoqui, L.; Andringa, S.; Antičić, T.; Aramo, C.; Arqueros, F.; Asorey, H.; Assis, P.; Aublin, J.; Ave, M.; Avenier, M.; Avila, G.; Badescu, A. M.; Barber, K. B.; Bardenet, R.; Bäuml, J.; Baus, C.; Beatty, J. J.; Becker, K. H.; Bellido, J. A.; BenZvi, S.; Berat, C.; Bertou, X.; Biermann, P. L.; Billoir, P.; Blanco, F.; Blanco, M.; Bleve, C.; Blümer, H.; Boháčová, M.; Boncioli, D.; Bonifazi, C.; Bonino, R.; Borodai, N.; Brack, J.; Brancus, I.; Brogueira, P.; Brown, W. C.; Buchholz, P.; Bueno, A.; Buscemi, M.; Caballero-Mora, K. S.; Caccianiga, B.; Caccianiga, L.; Candusso, M.; Caramete, L.; Caruso, R.; Castellina, A.; Cataldi, G.; Cazon, L.; Cester, R.; Cheng, S. H.; Chiavassa, A.; Chinellato, J. A.; Chudoba, J.; Cilmo, M.; Clay, R. W.; Cocciolo, G.; Colalillo, R.; Collica, L.; Coluccia, M. R.; Conceição, R.; Contreras, F.; Cooper, M. J.; Coutu, S.; Covault, C. E.; Criss, A.; Cronin, J.; Curutiu, A.; Dallier, R.; Daniel, B.; Dasso, S.; Daumiller, K.; Dawson, B. R.; de Almeida, R. M.; De Domenico, M.; de Jong, S. J.; De La Vega, G.; de Mello Junior, W. J. M.; de Mello Neto, J. R. T.; De Mitri, I.; de Souza, V.; de Vries, K. D.; del Peral, L.; Deligny, O.; Dembinski, H.; Dhital, N.; Di Giulio, C.; Di Matteo, A.; Diaz, J. C.; Díaz Castro, M. L.; Diep, P. N.; Diogo, F.; Dobrigkeit, C.; Docters, W.; D'Olivo, J. C.; Dong, P. N.; Dorofeev, A.; dos Anjos, J. C.; Dova, M. T.; Ebr, J.; Engel, R.; Erdmann, M.; Escobar, C. O.; Espadanal, J.; Etchegoyen, A.; Facal San Luis, P.; Falcke, H.; Fang, K.; Farrar, G.; Fauth, A. C.; Fazzini, N.; Ferguson, A. P.; Fick, B.; Figueira, J. M.; Filevich, A.; Filipčič, A.; Foerster, N.; Fox, B. D.; Fracchiolla, C. E.; Fraenkel, E. D.; Fratu, O.; Fröhlich, U.; Fuchs, B.; Gaior, R.; Gamarra, R. F.; Gambetta, S.; García, B.; Garcia Roca, S. T.; Garcia-Gamez, D.; Garcia-Pinto, D.; Garilli, G.; Gascon Bravo, A.; Gemmeke, H.; Ghia, P. L.; Giammarchi, M.; Giller, M.; Gitto, J.; Glaser, C.; Glass, H.; Gomez Albarracin, F.; Gómez Berisso, M.; Gómez Vitale, P. F.; Gonçalves, P.; Gonzalez, J. G.; Gookin, B.; Gorgi, A.; Gorham, P.; Gouffon, P.; Grebe, S.; Griffith, N.; Grillo, A. F.; Grubb, T. D.; Guardincerri, Y.; Guarino, F.; Guedes, G. P.; Hansen, P.; Harari, D.; Harrison, T. A.; Harton, J. L.; Haungs, A.; Hebbeker, T.; Heck, D.; Herve, A. E.; Hill, G. C.; Hojvat, C.; Hollon, N.; Holt, E.; Homola, P.; Hörandel, J. R.; Horvath, P.; Hrabovský, M.; Huber, D.; Huege, T.; Insolia, A.; Isar, P. G.; Jansen, S.; Jarne, C.; Josebachuili, M.; Kadija, K.; Kambeitz, O.; Kampert, K. H.; Karhan, P.; Kasper, P.; Katkov, I.; Kégl, B.; Keilhauer, B.; Keivani, A.; Kemp, E.; Kieckhafer, R. M.; Klages, H. O.; Kleifges, M.; Kleinfeller, J.; Knapp, J.; Krause, R.; Krohm, N.; Krömer, O.; Kruppke-Hansen, D.; Kuempel, D.; Kunka, N.; La Rosa, G.; LaHurd, D.; Latronico, L.; Lauer, R.; Lauscher, M.; Lautridou, P.; Le Coz, S.; Leão, M. S. A. B.; Lebrun, D.; Lebrun, P.; Leigui de Oliveira, M. A.; Letessier-Selvon, A.; Lhenry-Yvon, I.; Link, K.; López, R.; Lopez Agüera, A.; Louedec, K.; Lozano Bahilo, J.; Lu, L.; Lucero, A.; Ludwig, M.; Lyberis, H.; Maccarone, M. C.; Malacari, M.; Maldera, S.; Maller, J.; Mandat, D.; Mantsch, P.; Mariazzi, A. G.; Marin, V.; Mariş, I. C.; Marquez Falcon, H. R.; Marsella, G.; Martello, D.; Martin, L.; Martinez, H.; Martínez Bravo, O.; Martraire, D.; Masías Meza, J. J.; Mathes, H. J.; Matthews, J.; Matthews, J. A. J.; Matthiae, G.; Maurel, D.; Maurizio, D.; Mayotte, E.; Mazur, P. O.; Medina, C.; Medina-Tanco, G.; Melissas, M.; Melo, D.; Menichetti, E.; Menshikov, A.; Messina, S.; Meyhandan, R.; Mićanović, S.; Micheletti, M. I.; Middendorf, L.; Minaya, I. A.; Miramonti, L.; Mitrica, B.; Molina-Bueno, L.; Mollerach, S.; Monasor, M.; Monnier Ragaigne, D.; Montanet, F.; Morales, B.; Morello, C.; Moreno, J. C.; Mostafá, M.; Moura, C. A.; Muller, M. A.; Müller, G.; Münchmeyer, M.; Mussa, R.; Navarra, G.; Navarro, J. L.; Navas, S.; Necesal, P.; Nellen, L.; Nelles, A.; Neuser, J.; Nhung, P. T.; Niechciol, M.; Niemietz, L.; Niggemann, T.; Nitz, D.; Nosek, D.; Nožka, L.; Oehlschläger, J.; Olinto, A.; Oliveira, M.; Ortiz, M.; Pacheco, N.; Pakk Selmi-Dei, D.; Palatka, M.; Pallotta, J.; Palmieri, N.; Parente, G.; Parra, A.; Pastor, S.; Paul, T.; Pech, M.; PeÂķala, J.; Pelayo, R.; Pepe, I. M.; Perrone, L.; Pesce, R.; Petermann, E.; Petrera, S.; Petrolini, A.; Petrov, Y.; Piegaia, R.; Pierog, T.; Pieroni, P.; Pimenta, M.; Pirronello, V.; Platino, M.; Plum, M.; Pontz, M.; Porcelli, A.; Preda, T.; Privitera, P.; Prouza, M.; Quel, E. J.; Querchfeld, S.; Quinn, S.; Rautenberg, J.; Ravel, O.; Ravignani, D.; Revenu, B.; Ridky, J.; Riggi, S.; Risse, M.; Ristori, P.; Rivera, H.; Rizi, V.; Roberts, J.; Rodrigues de Carvalho, W.; Rodriguez Cabo, I.; Rodriguez Fernandez, G.; Rodriguez Martino, J.; Rodriguez Rojo, J.; Rodríguez-Frías, M. D.; Ros, G.; Rosado, J.; Rossler, T.; Roth, M.; Rouillé-d'Orfeuil, B.; Roulet, E.; Rovero, A. C.; Rühle, C.; Saffi, S. J.; Saftoiu, A.; Salamida, F.; Salazar, H.; Salesa Greus, F.; Salina, G.; Sánchez, F.; Sanchez-Lucas, P.; Santo, C. E.; Santos, E.; Santos, E. M.; Sarazin, F.; Sarkar, B.; Sarmento, R.; Sato, R.; Scharf, N.; Scherini, V.; Schieler, H.; Schiffer, P.; Schmidt, A.; Scholten, O.; Schoorlemmer, H.; Schovánek, P.; Schröder, F. G.; Schulz, A.; Schulz, J.; Sciutto, S. J.; Scuderi, M.; Segreto, A.; Settimo, M.; Shadkam, A.; Shellard, R. C.; Sidelnik, I.; Sigl, G.; Sima, O.; Śmiałkowski, A.; Šmída, R.; Snow, G. R.; Sommers, P.; Sorokin, J.; Spinka, H.; Squartini, R.; Srivastava, Y. N.; Stanič, S.; Stapleton, J.; Stasielak, J.; Stephan, M.; Straub, M.; Stutz, A.; Suarez, F.; Suomijärvi, T.; Supanitsky, A. D.; Šuša, T.; Sutherland, M. S.; Swain, J.; Szadkowski, Z.; Szuba, M.; Tapia, A.; Tartare, M.; Taşcǎu, O.; Thao, N. T.; Tiffenberg, J.; Timmermans, C.; Tkaczyk, W.; Todero Peixoto, C. J.; Toma, G.; Tomankova, L.; Tomé, B.; Tonachini, A.; Torralba Elipe, G.; Torres Machado, D.; Travnicek, P.; Tridapalli, D. B.; Trovato, E.; Tueros, M.; Ulrich, R.; Unger, M.; Valdés Galicia, J. F.; Valiño, I.; Valore, L.; van Aar, G.; van den Berg, A. M.; van Velzen, S.; van Vliet, A.; Varela, E.; Vargas Cárdenas, B.; Varner, G.; Vázquez, J. R.; Vázquez, R. A.; Veberič, D.; Verzi, V.; Vicha, J.; Videla, M.; Villaseñor, L.; Wahlberg, H.; Wahrlich, P.; Wainberg, O.; Walz, D.; Watson, A. A.; Weber, M.; Weidenhaupt, K.; Weindl, A.; Werner, F.; Westerhoff, S.; Whelan, B. J.; Widom, A.; Wieczorek, G.; Wiencke, L.; Wilczyńska, B.; Wilczyński, H.; Will, M.; Williams, C.; Winchen, T.; Wundheiler, B.; Wykes, S.; Yamamoto, T.; Yapici, T.; Younk, P.; Yuan, G.; Yushkov, A.; Zamorano, B.; Zas, E.; Zavrtanik, D.; Zavrtanik, M.; Zaw, I.; Zepeda, A.; Zhou, J.; Zhu, Y.; Zimbres Silva, M.; Ziolkowski, M.; Pierre Auger Collaboration
2014-03-01
The emission of radio waves from air showers has been attributed to the so-called geomagnetic emission process. At frequencies around 50 MHz this process leads to coherent radiation which can be observed with rather simple setups. The direction of the electric field induced by this emission process depends only on the local magnetic field vector and on the incoming direction of the air shower. We report on measurements of the electric field vector where, in addition to this geomagnetic component, another component has been observed that cannot be described by the geomagnetic emission process. The data provide strong evidence that the other electric field component is polarized radially with respect to the shower axis, in agreement with predictions made by Askaryan who described radio emission from particle showers due to a negative charge excess in the front of the shower. Our results are compared to calculations which include the radiation mechanism induced by this charge-excess process.
12. First detection of radio emission from a dwarf nova
NASA Technical Reports Server (NTRS)
Benz, A. O.; Fuerst, E.; Kiplinger, A. L.
1983-01-01
The detection of 4.75 GHz radio emissions from a white dwarf star in SU UMa is reported, and the source of the emission is discussed. The emission was discovered during a survey of six dwarf stars with a double horn receiver system. SU UMa was successfully scanned 123 times, with each scan comprising 31 3-sec integrations 30 arcsec apart. Average fluxes for each beam position were calculated, as was the X ray emission of 7.6 x 10 to the 54th/cu cm in the 0.1-4.5 keV band. The small mass outflow projected for the object indicates a source of suprathermal electrons for the radio emissions A cyclotron maser instability is suggested as the mechanism, and future measurements to detect circular polarization as proof of a coherent source are indicated.
13. An Interpretation of Banded Magnetospheric Radio Emissions
NASA Technical Reports Server (NTRS)
Benson, Robert F.; Osherovich, V. A.; Fainberg, J.; Vinas, A. F.; Ruppert, D. R.; Vondrak, Richard R. (Technical Monitor)
2000-01-01
Recently-published Active Magnetospheric Particle Tracer Explorer/Isothermal Remanent Magnetization (AMPTE/IRM) banded magnetospheric emissions, commonly referred to as '(n + 1/2)f(sub ce)' emissions where f(sub ce) is the electron gyrofrequency, are analyzed by treating them as analogous to sounder-stimulated ionospheric emissions. We show that both individual AMPTE/IRM spectra of magnetospheric banded emissions, and a statistically-derived spectra observed over the two-year lifetime of the mission, can be interpreted in a self-consistent manner. The analysis, which predicts all spectral peaks within 4% of the observed peaks, interprets the higher-frequency emissions as due to low group-velocity Bernstein-mode waves and the lower-frequency emissions as eigen modes of cylindrical-electromagnetic-plasma-oscillations. The demarcation between these two classes of emissions is the electron plasma frequency f(sub pe), where an emission is often observed. This f(sub pe), emission is not necessarily the strongest. None of the observed banded emissions were attributed to the upper-hybrid frequency. We present Alouette-2 and ISIS-1 plasma-resonance data, and model electron temperature (T(sub e)) values, to support the argument that the frequency-spectrum of ionospheric sounder-stimulated emissions is not strongly temperature dependent and thus that the interpretation of these emissions in the ionosphere is relevant to other plasmas (such as the magnetosphere) where N(sub e) and T(sub e) can be quite different but where the ratio f(sub pe)/f(sub ce) is identical.
SciTech Connect
Osten, Rachel A.; Phan-Bao, N.; Hawley, Suzanne L.; Reid, I. Neill; Ojha, Roopesh E-mail: [email protected] E-mail: [email protected]
2009-08-01
15. 3D modelling of stellar auroral radio emission
Leto, P.; Trigilio, C.; Buemi, C. S.; Umana, G.; Ingallinera, A.; Cerrigone, L.
2016-06-01
16. Detection of exomoons through observation of radio emissions
SciTech Connect
Noyola, J. P.; Satyal, S.; Musielak, Z. E. E-mail: [email protected]
2014-08-10
In the Jupiter-Io system, the moon's motion produces currents along the field lines that connect it to Jupiter's polar regions. The currents generate and modulate radio emissions along their paths via the electron-cyclotron maser instability. Based on this process, we suggest that such modulation of planetary radio emissions may reveal the presence of exomoons around giant planets in exoplanetary systems. A model explaining the modulation mechanism in the Jupiter-Io system is extrapolated and used to define criteria for exomoon detectability. A cautiously optimistic scenario of the possible detection of such exomoons around Epsilon Eridani b and Gliese 876 b is provided.
17. Radio Emission by Particles Accelerated in Pulsar Magnetosphere
Thomas, R. M. C.; Gangadhara, R. T.
2003-03-01
We present a relativistic model of pulsar radio emission by plasma accelerated along the rotating magnetic field lines projected on to a 2D plane perpendicular to the rotation axis. We have derived the expression for the trajectory of a particle, and estimated the spectrum of radio emission by the plasma bunches. We used the parameters given in the paper by Peyman and Gangadhara (2002). Further the analystical expressions for the Stokes parameters are derived, and compared them with the observed profiles. The one sense of circular polarization, observed in many pulsars, can be explained in the light of our model.
18. Fine spectral structures in Jovian decametric radio emission observed by ground-based radio telescope.
Panchenko, M.; Brazhenko, A. I.; Shaposhnikov, V. E.; Konovalenko, A. A.; Rucker, H. O.
2014-04-01
Jupiter with the largest planetary magnetosphere in the solar system emits intense coherent non-thermal radio emission in a wide frequency range. This emission is a result of a complicated interaction between the dynamic Jovian magnetosphere and energetic particles supplying the free energy from planetary rotation and the interaction between Jupiter and the Galilean moons. Decametric radio emission (DAM) is the strongest component of Jovian radiation observed in a frequency range from few MHz up to 40 MHz. This emission is generated via cyclotron maser mechanism in sources located along Jovian magnetic field lines. Depending on the time scales the Jovian DAMexhibits different complex spectral structures. We present the observations of the Jovian decametric radio emission using the large ground-based radio telescope URAN- 2 (Poltava, Ukraine) operated in the decametric frequency range. This telescope is one of the largest low frequency telescopes in Europe equipped with high performance digital radio spectrometers. The antenna array of URAN-2 consists of 512 crossed dipoles with an effective area of 28 000m2 and beam pattern size of 3.5 x 7 deg. (at 25 MHz). The instrument enables continuous observations of the Jovian radio during long period of times. Jovian DAM was observed continuously since Sep. 2012 (depending on Jupiter visibility) with relatively high time-frequency resolution (4 kHz - 100ms) in the broad frequency range (8-32MHz). We have detected a big amount of the fine spectral structures in the dynamic spectra of DAM such as trains of S-bursts, quasi-continuous narrowband emission, narrow-band splitting events and zebra stripe-like patterns. We analyzed mainly the fine structures associated with non-Io controlled DAM. We discuss how the observed narrowband structures which most probably are related to the propagation of the decametric radiation in the Jupiter's ionosphere can be used to study the plasma parameters in the inner Jovian magnetosphere.
19. Discussing the processes constraining the Jovian synchrotron radio emission's features
Santos-Costa, Daniel; Bolton, Scott J.
2008-03-01
20. Kiloparsec-scale radio emission in Seyfert and LINER galaxies
2015-01-01
1. Radio Emissions from Plasma with Electron Kappa-Distributions
Fleishman, G. D.; Kuznetsov, A. A.
2015-12-01
Gregory Fleishman (New Jersey Institute of Technology, Newark, USA)Alexey Kuznetsov (Institute of Solar-Terrestrial Physics, Irkutsk, Russia), Currently there is a concern about the ability of the classical thermal (Maxwellian) distribution to describe quasisteady-state plasma in the solar atmosphere, including active regions. In particular, other distributions have been proposed to better fit observations, for example, kappa-distributions. If present, these distributions will generate radio emissions with different observable properties compared with the classical gyroresonance (GR) or free-free emission, which implies a way of remotely detecting these kappa distributions in the radio observations. Here we present analytically derived GR and free-free emissivities and absorption coefficients for the kappa-distribution, and discuss their properties, which are in fact remarkably different from the classical Maxwellian plasma. In particular, the radio brightness temperature from a gyrolayer increases with the optical depth τ for kappa-distribution. This property has a remarkable consequence allowing a straightforward observational test: the GR radio emission from the non-Maxwellian distributions is supposed to be noticeably polarized even in the optically thick case, where the emission would have strictly zero polarization in the case of Maxwellian plasma. This offers a way of remote probing the plasma distribution in astrophysical sources, including solar active regions as a vivid example. In this report, we present analytical formulae and computer codes to calculate the emission parameters. We simulate the gyroresonance emission under the conditions typical of the solar active regions and compare the results for different electron distributions. We discuss the implications of our findings for interpretation of radio observations. This work was supported in part by NSF grants AGS-1250374 and AGS-1262772, NASA grant NNX14AC87G to New Jersey Institute of Technology
2. Mean and extreme radio properties of quasars and the origin of radio emission
SciTech Connect
Kratzer, Rachael M.; Richards, Gordon T.
2015-02-01
3. Neptune radio emission - Predictions based on planetary scaling laws
NASA Technical Reports Server (NTRS)
Desch, Michael D.
1988-01-01
In this paper a prediction is advanced concerning Neptune's low-frequency radio emission based on the radiometric Bode's law for radio planets in combination with the magnetostrophic scaling law for magnetized planets. The total emitted radio power is predicted to be about 1.6 x 10 to the 7th W, very nearly the same as that predicted and observed for Uranus. Possible emission spectral shapes, based on Saturn and earth-like models, are shown. Using these models, the radio emission frequency range is predicted to extend from approximately 100 to just over 1000 kHz, with a spectral peak between 350 and 500 kHz. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the planetary radio astronomy experiment onboard the Voyager spacecraft sometime between 45 and 90 days before closest approach. This detection is likely to represent the first direct evidence of a Neptune magnetic field. Possible implications for Neptune's magnetosphere with regard to the time of first detection are discussed.
4. LOPES - Detecting Radio Emission from Cosmic Ray Air Showers
Horneffer, A.; Falcke, H.; Kampert, K. H.
2002-06-01
High energy cosmic rays, hitting the Earth's atmosphere, produce large amounts of secondary particles in an extensive air shower (EAS). Radio pulses from these air showers were measured during the late 1960ies and early 1970ies. Mainly due to difficulties with radio interference these measurements ceased in the late 1970ies. LOFAR (Low Frequency Array), the new digital radio interferometer under development, will work in the frequency range of interest for air showers. To test this new technology we are building a ''LOFAR Prototype Station'' (LOPES). This will operate in conjunction with an existing air shower array (KASCADE in Karlsruhe) to clarify the nature and properties of radio emission from air showers and develop the software to use LOFAR as a cosmic ray detector.
5. CURVATURE-DRIFT INSTABILITY FAILS TO GENERATE PULSAR RADIO EMISSION
SciTech Connect
Kaganovich, Alexander; Lyubarsky, Yuri
2010-10-01
The curvature-drift instability has long been considered as a viable mechanism for pulsar radio emission. We reconsidered this mechanism by finding an explicit solution describing the propagation of short electromagnetic waves in a plasma flow along curved magnetic field lines. We show that even though the waves could be amplified, the amplification factor remains very close to unity; therefore, this mechanism is unable to generate high brightness temperature emission from initial weak fluctuations.
6. Rotational modulation of Saturn's auroral radio emissions
Lamy, L.
2011-10-01
Among the persistent questions raised by the existence of a rotational modulation of the Saturn Kilometric Radiation (SKR), the origin of the variability of the 10.8 hours SKR period at a 1% level over weeks to years remains intriguing. While its short-term fluctuations (20-30 days) have been related to the variations of the solar wind speed, its long-term fluctuations (months to years) were proposed to be triggered by Enceladus mass-loading and/or seasonal variations. This situation has become even more complicated since the recent identification of two separated periods at 10.8h and 10.6h, each varying with time, corresponding to SKR sources located in the southern (S) and the northern (N) hemispheres, respectively. Here, six years of Cassini continuous radio measurements have been used to derive long-term radio periods and phase systems separately for each hemisphere 1. The S phase has then been used to investigate the S SKR rotational modulation (see Figure 1), shown to be consistent with an intrinsically rotating phenomenon, in contrast with the early Voyager picture, but in agreement with the diurnal modulation observed in other kronian auroral phenomena.
7. The radio/optical emission in 3C 33 south
Rudnick, L.; Saslaw, W. C.; Crane, P.; Tyson, J. A.
1981-06-01
The southern lobe of 3C 33 has been observed with the Very Large Array at wave lengths of 6 cm and 2 cm and resolutions 1 arcsec. The results clearly demonstrate a physical association between the radio source and the optical patch found by Simkin (1978). The spectral index shows that the optical emission could be the synchrotron tail of the radio radiation, provided that the lobe is continually supplied with relativistic particles with gamma not less than 10 to the 6th. If thermal gas is responsible for the optical emission, these radio polarization observations show that it must be well separated from the relativistic material. The ionization and thermal balance of any thermal gas pose a number of interesting problems. Several critical observations for future work are identified.
8. Multi-Spacecraft Observations of Saturn Kilometric Radio Emission
NASA Technical Reports Server (NTRS)
MacDowall, R. J.; Hess, R. A.
2011-01-01
Saturn kilometric radiation (SKR) is the auroral radio emission of Saturn, which has been observed by Voyager 1 & 2, Cassini, and Ulysses. Ulysses is able to detect the intense intervals of SKR from distances up to 10 AU, because of its long antennas (72 m tip-to-tip) and sensitive radio receivers. Studies of SKR by A. Lecacheux gave the surprising result that the periodicity of SKR varied with time; it was not locked to a planetary rotation of Saturn. This result has been confirmed by Cassini radio observations. Here, we compare Ulysses and Cassini observations of SKR to constrain a mode! for the SKR emission geometry. SpecifIcally, we examine the question - are the brighter sources of 5KR fixed in Saturn longitude or local time? The results have significant consequences for our understanding of SKR and its varying periodicity
9. Radio Observation of the Electromagnetic Emission from Warm Clouds.
PubMed
Sartor, J D
1964-02-28
Microdischarges observable at 30 and 50 Mcy/sec appear from within cumulus clouds in an early stage of their development whether the temperatures within the clouds are above or below 0 degrees C. Laboratory observations of radio emission from colliding drops may provide information on the physics of clouds in the atmospheres of this and other planets.
10. Second Harmonic Hectometric Radio Emission at Jupiter
NASA Technical Reports Server (NTRS)
Menietti, J. D.; Gurnett, D. A.; Groene, J. B.
1998-01-01
Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io-L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.
11. Second Harmonic Hectometric Radio Emission at Jupiter
NASA Technical Reports Server (NTRS)
Menietti, J. D.; Gurnett, D. A.; Groene, J. B.
1998-01-01
Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.
12. Second Harmonic Hectometric Radio Emission at Jupiter
NASA Technical Reports Server (NTRS)
Menietti, J. D.; Gurnett, D. A.; Groene, J. B.
1998-01-01
Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.
13. Second Harmonic Hectometric Radio Emission at Jupiter
NASA Technical Reports Server (NTRS)
Menietti, J. D.; Gurnett, D. A.; Groene, J. B.
1998-01-01
Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io-L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.
14. Gamma ray emission from radio pulsars
NASA Technical Reports Server (NTRS)
Romani, Roger W.
1994-01-01
While the proposed research received partial funding under this grant, during the term of support substantial progress was made on the development of a new model for the emission of gamma-rays from isolated rotation-powered pulsars. In phase one of the work, we showed how a modified version of the 'outer gap' model of pulsar emission could reproduce the double peaked profiles seen in CGRO pulsar observations. This work also demonstrated the spectrum of gap radiation varies significantly with position in the magnetosphere, and produced approximate computations of the emission from outer magnetosphere gap zones, including primary curvature radiation, gamma - gamma pair production and synchrotron radiation and inverse Compton scattering by the resulting secondary particles. This work was followed in phase two by a more complete treatment of the geometry of the radiation zone, and improved connections with observations at other wavelengths.
15. Galileo Direction Finding of Jovian Radio Emissions
NASA Technical Reports Server (NTRS)
Menietti, J. D.
1998-01-01
The Galileo spacecraft, in orbit about Jupiter, has observed distinct spin modulation of plasma wave emissions near the Ganymede (G1 and G2) encounters in the frequency range from about 100 kHz to approximately 6 MHz. Assuming circularly polarized, transverse electromagnetic radiation, we have used the spin modulation of the sweep-frequency receivers of the electric dipole antenna over many spins to estimate the source location in the spin plane of the spacecraft. Hectometric (HOM) and decametric (DAM) emission is observed by Galileo as a general and continuous background with frequent bursts that last tens of minutes and can be separated by minutes or hours. We have analyzed HOM and DAM emissions observed near Jupiter just after the GI and G2 encounters, including two HOM/DAM "arc" signatures observed after the G2 encounter. These latter appear to be low-frequency extensions of DAM arcs, with source regions along either the Io or the Ganymede flux tube. While the uncertainties associated with the data analysis do not allow a precise source location, the HOM/DAM emission observed near the G1 and G2 encounters is consistent with a gyroresonant source region, but it is necessary to require refraction due to the Io torus to understand the results. To explain emission from apparent source regions above a gyroresonant source region, wave refraction from asymmetries in the Io plasma torus that extend along magnetic field lines is postulated. Alternatively, if such torus density asymmetries do not exist, emission with sources above a gyroresonant source region would require another free-energy source such as energetic plasma beams in the presence of density gradients or temperature anisotropies.
16. Galileo Direction Finding of Jovian Radio Emissions
NASA Technical Reports Server (NTRS)
Menietti, J. D.
1998-01-01
The Galileo spacecraft, in orbit about Jupiter, has observed distinct spin modulation of plasma wave emissions near the Ganymede (G1 and G2) encounters in the frequency range from about 100 kHz to approximately 6 MHz. Assuming circularly polarized, transverse electromagnetic radiation, we have used the spin modulation of the sweep-frequency receivers of the electric dipole antenna over many spins to estimate the source location in the spin plane of the spacecraft. Hectometric (HOM) and decametric (DAM) emission is observed by Galileo as a general and continuous background with frequent bursts that last tens of minutes and can be separated by minutes or hours. We have analyzed HOM and DAM emissions observed near Jupiter just after the GI and G2 encounters, including two HOM/DAM "arc" signatures observed after the G2 encounter. These latter appear to be low-frequency extensions of DAM arcs, with source regions along either the Io or the Ganymede flux tube. While the uncertainties associated with the data analysis do not allow a precise source location, the HOM/DAM emission observed near the G1 and G2 encounters is consistent with a gyroresonant source region, but it is necessary to require refraction due to the Io torus to understand the results. To explain emission from apparent source regions above a gyroresonant source region, wave refraction from asymmetries in the Io plasma torus that extend along magnetic field lines is postulated. Alternatively, if such torus density asymmetries do not exist, emission with sources above a gyroresonant source region would require another free-energy source such as energetic plasma beams in the presence of density gradients or temperature anisotropies.
17. On the Evolution of the Cores of Radio Sources and Their Extended Radio Emission
Yuan, Zunli; Wang, Jiancheng
2012-01-01
The work in this paper aims at determining the evolution and possible co-evolution of radio-loud active galactic nuclei (AGNs) and their cores via their radio luminosity functions (i.e., total and core RLFs, respectively). Using a large combined sample of 1063 radio-loud AGNs selected at low radio frequency, we investigate the RLF at 408 MHz of steep-spectrum radio sources. Our results support a luminosity-dependent evolution. Using core flux density data of the complete sample 3CRR, we investigate the core RLF at 5.0 GHz. Based on the combined sample with incomplete core flux data, we also estimate the core RLF using a modified factor of completeness. Both results are consistent and show that the comoving number density of radio cores displays a persistent decline with redshift, implying a negative density evolution. We find that the core RLF is obviously different from the total RLF at the 408 MHz band which is mainly contributed by extended lobes, implying that the cores and extended lobes could not be co-evolving at radio emission.
18. Quasar feedback and the origin of radio emission in radio-quiet quasars
Zakamska, Nadia L.; Greene, Jenny E.
2014-07-01
We analyse Sloan Digital Sky Survey spectra of 568 obscured luminous quasars. The [O III] λ5007 Å emission line shows blueshifts and blue excess, indicating that some of the narrow-line gas is undergoing an organized outflow. The velocity width containing 90 per cent of line power ranges from 370 to 4780 km s-1, suggesting outflow velocities up to ˜2000 km s-1, and is strongly correlated with the radio luminosity among the radio-quiet quasars. We propose that radio emission in radio-quiet quasars is due to relativistic particles accelerated in the shocks within the quasar-driven outflows; star formation in quasar hosts is insufficient to explain the observed radio emission. The median radio luminosity of the sample of νLν[1.4 GHz] = 1040 erg s-1 suggests a median kinetic luminosity of the quasar-driven wind of Lwind = 3 × 1044 erg s-1, or about 4 per cent of the estimated median bolometric luminosity Lbol = 8 × 1045 erg s-1. Furthermore, the velocity width of [O III] is positively correlated with mid-infrared luminosity, which suggests that outflows are ultimately driven by the radiative output of the quasar. Emission lines characteristic of shocks in quasi-neutral medium increase with the velocity of the outflow, which we take as evidence of quasar-driven winds propagating into the interstellar medium of the host galaxy. Quasar feedback appears to operate above the threshold luminosity of Lbol ˜ 3 × 1045 erg s-1.
19. High-resolution radio emission from RCW 49/Westerlund 2
Benaglia, P.; Koribalski, B.; Peri, C. S.; Martí, J.; Sánchez-Sutil, J. R.; Dougherty, S. M.; Noriega-Crespo, A.
2013-11-01
Aims: The HII region RCW 49 and its ionizing cluster form an extensive, complex region that has been widely studied at infrared (IR) and optical wavelengths. The Molonglo 843 MHz and Australia Telescope Compact Array data at 1.4 and 2.4 GHz showed two shells. Recent high-resolution IR imaging revealed a complex dust structure and ongoing star formation. New high-bandwidth and high-resolution data of the RCW 49 field have been obtained to survey the radio emission at arcsec scale and investigate the small-scale features and nature of the HII region. Methods: Radio observations were collected with the new 2-GHz bandwidth receivers and the CABB correlator of the Australia Telescope Compact Array [ATCA], at 5.5 and 9.0 GHz. In addition, archival observations at 1.4 and 2.4 GHz have been re-reduced and re-analyzed in conjunction with observations in the optical, IR, X-ray, and gamma-ray regimes. Results: The new 2-GHz bandwidth data result in the most detailed radio continuum images of RCW 49 to date. The radio emission closely mimics the near-IR emission observed by Spitzer, showing pillars and filaments. The brightest continuum emission comes from the region known as the bridge. The overall flattish spectral index is typically consistent with a free-free emission mechanism. However, hints of nonthermal components are also present in the bridge. An interesting jet-like structure surrounded by a bubble feature whose nature is still unclear has been discovered close to the Westerlund 2 core. Two apparent bow shocks and a number of discrete sources have been detected as well in the surroundings of RCW 49. In addition, we also report on and discuss the possible detection of a hydrogen recombination line. Conclusions: The radio results support an association between the cm continuum and molecular emission. The detection of the radio recombination line kinematically favors a RCW 49 distance of 6-7 kpc. If the negative spectral indices measured at the bridge should be
20. Periodic bursts of Jovian non-Io decametric radio emission
PubMed Central
Panchenko, M.; Rucker, H.O.; Farrell, W.M.
2013-01-01
During the years 2000–2011 the radio instruments onboard Cassini, Wind and STEREO spacecraft have recorded a large amount of the Jovian decametric radio emission (DAM). In this paper we report on the analysis of the new type of Jovian periodic radio bursts recently revealed in the decametric frequency range. These bursts, which are non-Io component of DAM, are characterized by a strong periodic reoccurrence over several Jovian days with a period ≈1.5% longer than the rotation rate of the planet's magnetosphere (System III). The bursts are typically observed between 4 and 12 MHz and their occurrence probability has been found to be significantly higher in the sector of Jovian Central Meridian Longitude between 300° and 60° (via 360°). The stereoscopic multispacecraft observations have shown that the radio sources of the periodic bursts radiate in a non-axisymmetric hollow cone-like pattern and sub-corotate with Jupiter remaining active during several planet's rotations. The occurrence of the periodic non-Io DAM bursts is strongly correlated with pulses of the solar wind ram pressure at Jupiter. Moreover the periodic bursts exhibit a tendency to occur in groups every ∼25 days. The polarization measurements have shown that the periodic bursts are right hand polarized radio emission associated with the Northern magnetic hemisphere of Jupiter. We suggest that periodic non-Io DAM bursts may be connected with the interchange instability in Io plasma torus triggered by the solar wind. PMID:23585696
1. Periodic bursts of Jovian non-Io decametric radio emission
Panchenko, M.; Rucker, H. O.; Farrell, W. M.
2013-03-01
During the years 2000-2011 the radio instruments onboard Cassini, Wind and STEREO spacecraft have recorded a large amount of the Jovian decametric radio emission (DAM). In this paper we report on the analysis of the new type of Jovian periodic radio bursts recently revealed in the decametric frequency range. These bursts, which are non-Io component of DAM, are characterized by a strong periodic reoccurrence over several Jovian days with a period ≈1.5% longer than the rotation rate of the planet's magnetosphere (System III). The bursts are typically observed between 4 and 12 MHz and their occurrence probability has been found to be significantly higher in the sector of Jovian Central Meridian Longitude between 300° and 60° (via 360°). The stereoscopic multispacecraft observations have shown that the radio sources of the periodic bursts radiate in a non-axisymmetric hollow cone-like pattern and sub-corotate with Jupiter remaining active during several planet's rotations. The occurrence of the periodic non-Io DAM bursts is strongly correlated with pulses of the solar wind ram pressure at Jupiter. Moreover the periodic bursts exhibit a tendency to occur in groups every ∼25 days. The polarization measurements have shown that the periodic bursts are right hand polarized radio emission associated with the Northern magnetic hemisphere of Jupiter. We suggest that periodic non-Io DAM bursts may be connected with the interchange instability in Io plasma torus triggered by the solar wind.
2. Periodic Bursts of Jovian Non-Io Decametric Radio Emission
NASA Technical Reports Server (NTRS)
Panchenko, M.; Rucker, H O.; Farrell, W. M.
2013-01-01
During the years 2000-2011 the radio instruments onboard Cassini, Wind and STEREO spacecraft have Recorded a large amount of the Jovian decametric radio emission (DAM). In this paper we report on the analysis of the new type of Jovian periodic radio bursts recently revealed in the decametric frequency range. These bursts, which are non-Io component of DAM, are characterized by a strong periodic reoccurrence over several Jovian days with a period approx. = 1:5% longer than the rotation rate of the planet's magnetosphere (System III). The bursts are typically observed between 4 and 12 MHz and their occurrence probability has been found to be significantly higher in the sector of Jovian Central Meridian Longitude between 300 deg. and 60 deg. (via 360 deg.). The stereoscopic multispacecraft observations have shown that the radio sources of the periodic bursts radiate in a non-axisymmetric hollow cone-like pattern and sub-corotate with Jupiter remaining active during several planet's rotations. The occurrence of the periodic non-Io DAM bursts is strongly correlated with pulses of the solar wind ram pressure at Jupiter. Moreover the periodic bursts exhibit a tendency to occur in groups every approx. 25 days. The polarization measurements have shown that the periodic bursts are right hand polarized radio emission associated with the Northern magnetic hemisphere of Jupiter. We suggest that periodic non-Io DAM bursts may be connected with the interchange instability in Io plasma torus triggered by the solar wind.
3. Periodic bursts of Jovian non-Io decametric radio emission.
PubMed
Panchenko, M; Rucker, H O; Farrell, W M
2013-03-01
During the years 2000-2011 the radio instruments onboard Cassini, Wind and STEREO spacecraft have recorded a large amount of the Jovian decametric radio emission (DAM). In this paper we report on the analysis of the new type of Jovian periodic radio bursts recently revealed in the decametric frequency range. These bursts, which are non-Io component of DAM, are characterized by a strong periodic reoccurrence over several Jovian days with a period [Formula: see text] longer than the rotation rate of the planet's magnetosphere (System III). The bursts are typically observed between 4 and 12 MHz and their occurrence probability has been found to be significantly higher in the sector of Jovian Central Meridian Longitude between 300° and 60° (via 360°). The stereoscopic multispacecraft observations have shown that the radio sources of the periodic bursts radiate in a non-axisymmetric hollow cone-like pattern and sub-corotate with Jupiter remaining active during several planet's rotations. The occurrence of the periodic non-Io DAM bursts is strongly correlated with pulses of the solar wind ram pressure at Jupiter. Moreover the periodic bursts exhibit a tendency to occur in groups every [Formula: see text] days. The polarization measurements have shown that the periodic bursts are right hand polarized radio emission associated with the Northern magnetic hemisphere of Jupiter. We suggest that periodic non-Io DAM bursts may be connected with the interchange instability in Io plasma torus triggered by the solar wind.
4. Striated spectral activity in Jovian and Saturnian radio emission
NASA Technical Reports Server (NTRS)
Thieman, James R.; Alexander, Joseph K.; Arias, Tomas A.; Staelin, David H.
1988-01-01
Examination of high time resolution frequency-time spectrograms of radio emission measured near the Voyager 1 and 2 encounters with Jupiter reveals occasional striation patterns within the normally diffuse hectometric radiation. The patterns are characterized by distinctive banded structures of enhanced intensity meandering in frequency over time scales of minutes to tens of minutes. This banded form of striated spectral activity (SSA) has an occurrence probability of the order of 5 percent during the three weeks before and after Jupiter encounters. Plots of single 6-s frequency sweeps often exhibit a slow rise in intensity followed by a sharp drop-off in each band as frequency decreases. Banded SSA is often preceded or followed by chaotic SSA in which banding of the emission becomes discontinuous or unrecognizable, although the intensity modulation is still evident. Although SSA normally occurs in the frequency range of roughly 0.2-1.0 MHz, similar but longer-lasting patterns have been found occasionally in decametric emission above 10 MHz. Analogous modulation has also been observed in the Saturnian radio emission, suggesting that SSA may be a common feature intrinsic to the radio emission at both planets.
5. New observations of the low frequency interplanetary radio emissions
NASA Technical Reports Server (NTRS)
Kurth, W. S.; Gurnett, D. A.
1991-01-01
Recent Voyager 1 observations reveal reoccurrences of the low frequency interplanetary radio emissions. Three of the new events are weak transient events which rise in frequency from the range of 2-2.5 kHz to about 3 kHz with drift rates of approximately 1.5 kHz/year. The first of the transient events begins in mid-1989 and the more recent pair of events both were first detected in late 1991. In addition, there is an apparent onset of a 2-kHz component of the emission beginning near day 70 of 1991. The new transient emissions are barely detectable on Voyager 1 and are below the threshold of detectability on Voyager 2, which is less sensitive than Voyager 1. The new activity provides new opportunities to test various theories of the triggering, generation, and propagation of the outer heliospheric radio emissions and may signal a response of the source of the radio emissions to the increased solar activity associated with the recent peak in the solar cycle.
6. Analysis of Jovian low frequency radio emissions
NASA Technical Reports Server (NTRS)
Gurnett, D. A.
1985-01-01
The density of ions in the Io plasma torus and the scattering of these ions by low frequency electromagnetic emissions detected by Voyager 1 were studied. The ion density profile was investigated using whistler dispersion measurements provided by the Voyager plasma instrument. The scale height and absolute density of H+ ions in the vicinity of the plasma torus were determined by combining the measured plasma densities with the whistler dispersion measurements. A theoretical analysis of the modes of propagation of low frequency electromagnetic emissions in the torus was undertaken. Polarization reversal effects and rough estimates of the ion diffusion coefficient were utilized. Numerical evaluation of the ion diffusion coefficients in the torus were made using the observed Voyager 1 wave intensities. Results show that the observed wave intensities produce significant ion diffusion effects in the ion torus.
7. Theories of radio emissions and plasma waves. [in Jupiter magnetosphere
NASA Technical Reports Server (NTRS)
Goldstein, M. L.; Goertz, C. K.
1983-01-01
The complex region of Jupiter's radio emissions at decameter wavelengths, the so-called DAM, is considered, taking into account the basic theoretical ideas which underly both the older and newer theories and models. Linear theories are examined, giving attention to direct emission mechanisms, parallel propagation, perpendicular propagation, and indirect emission mechanisms. An investigation of nonlinear theories is also conducted. Three-wave interactions are discussed along with decay instabilities, and three-wave up-conversio. Aspects of the Io and plasma torus interaction are studied, and a mechanism by which Io can accelerate electrons is reviewed.
8. Theories of radio emissions and plasma waves. [in Jupiter magnetosphere
NASA Technical Reports Server (NTRS)
Goldstein, M. L.; Goertz, C. K.
1983-01-01
The complex region of Jupiter's radio emissions at decameter wavelengths, the so-called DAM, is considered, taking into account the basic theoretical ideas which underly both the older and newer theories and models. Linear theories are examined, giving attention to direct emission mechanisms, parallel propagation, perpendicular propagation, and indirect emission mechanisms. An investigation of nonlinear theories is also conducted. Three-wave interactions are discussed along with decay instabilities, and three-wave up-conversio. Aspects of the Io and plasma torus interaction are studied, and a mechanism by which Io can accelerate electrons is reviewed.
9. Shocks in nova outflows - II. Synchrotron radio emission
Vlasov, Andrey; Vurm, Indrek; Metzger, Brian D.
2016-11-01
The discovery of GeV gamma-rays from classical novae indicates that shocks and relativistic particle acceleration are energetically key in these events. Further evidence for shocks comes from thermal keV X-ray emission and an early peak in the radio light curve on a time-scale of months with a brightness temperature which is too high to result from freely expanding photoionized gas. Paper I developed a one-dimensional model for the thermal emission from nova shocks. This work concluded that the shock-powered radio peak cannot be thermal if line cooling operates in the post-shock gas at the rate determined by collisional ionization equilibrium. Here we extend this calculation to include non-thermal synchrotron emission. Applying our model to three classical novae, we constrain the amplification of the magnetic field ɛB and the efficiency ɛe of accelerating relativistic electrons of characteristic Lorentz factor γ ˜ 100. If the shocks are radiative (low velocity vsh ≲ 1000 km s-1) and cover a large solid angle of the nova outflow, as likely characterize those producing gamma-rays, then values of ɛe ˜ 0.01-0.1 are required to achieve the peak radio brightness for ɛB = 10-2. Such high efficiencies exclude secondary pairs from pion decay as the source of the radio-emitting particles, instead favouring the direct acceleration of electrons at the shock. If the radio-emitting shocks are instead adiabatic (high velocity), as likely characterize those responsible for the thermal X-rays, then much higher brightness temperatures are possible, allowing the radio-emitting shocks to cover a smaller outflow solid angle.
10. Zebra spectral structures in Jovian decametric radio emissions
Rošker, S.; Panchenko, M.; Rucker, H. O.; Brazhenko, A. I.
2015-10-01
Jupiter with the largest planetary magnetosphere in the solar system emits intense coherent non-thermal radiation in a wide frequency range. This emission is a result of complicated interactions between the dynamic Jovian magnetosphere and energetic particles supplying free energy from planetary rotation and the interaction between Jupiter and the Galilean moon Io. Decametric radio emission (DAM) is the strongest component of Jovian radiation observed in a frequency range from a few MHz up to 40 MHz. Depending on the time scales the Jovian DAM exhibits different complex spectral structures. Recent observations of the Jovian decametric radio emission using the large ground-based radio telescope URAN-2 (Poltava, Ukraine) enabled the detection of fine spectral structures, specifically zebra stripe-like patterns, never reported before in the Jovian decametric wavelength regime (Figure 1). In this presentation we describe and analyse these new observations by investigating the characteristics of the Jovian decametric zebra patterns. On basis of these findings the possible mechanism of wave generation is discussed and in particular the value of the determination of local plasma densities within the Jovian magnetosphere by remote radio sensing is emphasized.
11. Source characteristics of Jovian narrow-band kilometric radio emissions
Reiner, M. J.; Fainberg, J.; Stone, R. G.; Kaiser, M. L.; Desch, M. D.; Manning, R.; Zarka, P.; Pedersen, B.-M.
1993-07-01
New observations of Jovian narrow-band kilometric (nKOM) radio emissions were made by the Unified Radio and Plasma Wave (URAP) experiment on the Ulysses spacecraft during the Ulysses-Jupiter encounter in early February 1992. These observations have demonstrated the unique capability of the URAP instrument for determining both the direction and polarization of nKOM radio sources. An important result is the discovery that nKOM radio emission originates from a number of distinct sources located at different Jovian longitudes and at the inner and outermost regions of the Io plasma torus. These sources have been tracked for several Jovian rotations, yielding their corotational lags, their spatial and temporal evolution, and their radiation characteristics at both low latitudes far from Jupiter and at high latitudes near the planet. Both right-hand and left-hand circularly polarized nKOM sources were observed. The polarizations observed for sources in the outermost regions of the torus seem to favor extraordinary mode emission.
12. No radio emission from SN 2006X after 2 years
Chandra, Poonam; Chevalier, Roger; Patat, Ferdinando
2008-02-01
We observed Type Ia supernova SN 2006X (IAUC 8667) with the VLA for 2 hours in 8.46 GHz band at 2008 Feb 19.47 UT mean time. We did not detect any radio emission, indicating it to be a normal Type Ia supernova. The map rms is 18 uJy and the flux density at the supernova position is 4 +/-18 uJy. We thank VLA staff for making this observation possible. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
13. Virtual observatory tools and amateur radio observations supporting scientific analysis of Jupiter radio emissions
Cecconi, Baptiste; Hess, Sebastien; Le Sidaner, Pierre; Savalle, Renaud; Stéphane, Erard; Coffre, Andrée; Thétas, Emmanuel; André, Nicolas; Génot, Vincent; Thieman, Jim; Typinski, Dave; Sky, Jim; Higgins, Chuck; Imai, Masafumi
2016-04-01
In the frame of the preparation of the NASA/JUNO and ESA/JUICE (Jupiter Icy Moon Explorer) missions, and the development of a planetary sciences virtual observatory (VO), we are proposing a new set of tools directed to data providers as well as users, in order to ease data sharing and discovery. We will focus on ground based planetary radio observations (thus mainly Jupiter radio emissions), trying for instance to enhance the temporal coverage of jovian decametric emission. The data service we will be using is EPN-TAP, a planetary science data access protocol developed by Europlanet-VESPA (Virtual European Solar and Planetary Access). This protocol is derived from IVOA (International Virtual Observatory Alliance) standards. The Jupiter Routine Observations from the Nancay Decameter Array are already shared on the planetary science VO using this protocol, as well as data from the Iitate Low Frquency Radio Antenna, in Japan. Amateur radio data from the RadioJOVE project is also available. The attached figure shows data from those three providers. We will first introduce the VO tools and concepts of interest for the planetary radioastronomy community. We will then present the various data formats now used for such data services, as well as their associated metadata. We will finally show various prototypical tools that make use of this shared datasets.
14. Tracing star formation with non-thermal radio emission
Schober, Jennifer; Schleicher, D. R. G.; Klessen, R. S.
2017-06-01
A key for understanding the evolution of galaxies and in particular their star formation history will be future ultradeep radio surveys. While star formation rates (SFRs) are regularly estimated with phenomenological formulas based on the local FIR-radio correlation, we present here a physically motivated model to relate star formation with radio fluxes. Such a relation holds only in frequency ranges where the flux is dominated by synchrotron emission, as this radiation originates from cosmic rays produced in supernova remnants, therefore reflecting recent star formation. At low frequencies, synchrotron emission can be absorbed by the free-free mechanism. This suppression becomes stronger with increasing number density of the gas, more precisely of the free electrons. We estimate the critical observing frequency below which radio emission is not tracing the SFR, and use the three well-studied local galaxies M51, M82, and Arp 220 as test cases for our model. If the observed galaxy is at high redshift, this critical frequency moves along with other spectral features to lower values in the observing frame. In the absence of systematic evolutionary effects, one would therefore expect that the method can be applied at lower observing frequencies for high-redshift observations. However, in case of a strong increase of the typical gas column densities towards high redshift, the increasing free-free absorption may erase the star formation signatures at low frequencies. At high radio frequencies both, free-free emission and the thermal bump, can dominate the spectrum, also limiting the applicability of this method.
15. Detection of thermal radio emission from a single coronal giant
O'Gorman, E.; Harper, G. M.; Vlemmings, W.
2017-03-01
We report the detection of thermal continuum radio emission from the K0 III coronal giant Pollux (β Gem) with the Karl G. Jansky Very Large Array (VLA). The star was detected at 21 and 9 GHz with flux density values of 150 ± 21 and 43 ± 8 μJy, respectively. We also place a 3σrms upper limit of 23 μJy for the flux density at 3 GHz. We find the stellar disk-averaged brightness temperatures to be approximately 9500, 15 000, and <71 000 K, at 21, 9, and 3 GHz, respectively, which are consistent with the values of the quiet Sun. The emission is most likely dominated by optically thick thermal emission from an upper chromosphere at 21 and 9 GHz. We discuss other possible additional sources of emission at all frequencies and show that there may also be a small contribution from gyroresonance emission above active regions, coronal free-free emission and free-free emission from an optically thin stellar wind, particularly at the lower frequencies. We constrain the maximum mass-loss rate from Pollux to be less than 3.7 × 10-11M⊙ yr-1 (assuming a wind terminal velocity of 215 km s-1), which is about an order of magnitude smaller than previous constraints for coronal giants and is in agreement with existing predictions for the mass-loss rate of Pollux. These are the first detections of thermal radio emission from a single (i.e., non-binary) coronal giant and demonstrate that low activity coronal giants like Pollux have atmospheres at radio frequencies akin to the quiet Sun.
NASA Technical Reports Server (NTRS)
Nguyen, Truong X.; Ely, Jay J.; Williams, Reuben A.; Koppen, Sandra V.; Salud, Maria Theresa P.
2006-01-01
Radiated emissions in aircraft communication and navigation bands are measured from several active radio frequency identification (RFID) tags. The individual tags are different in design and operations. They may also operate in different frequency bands. The process for measuring the emissions is discussed, and includes tag interrogation, reverberation chamber testing, and instrument settings selection. The measurement results are described and compared against aircraft emission limits. In addition, interference path loss for the cargo bays of passenger aircraft is measured. Cargo bay path loss is more appropriate for RFID tags than passenger cabin path loss. The path loss data are reported for several aircraft radio systems on a Boeing 747 and an Airbus A320.
17. Radio triangulation of solar radio emissions associated with the 2012 July 23 CME
Krupar, Vratislav; Kruparova, Oksana; Santolik, Ondrej; Bothmer, Volker; Mrotzek, Niclas; Eastwood, Jonathan P.
2017-04-01
Coronal mass ejections (CMEs) are large-scale eruptions of magnetized plasma that may cause severe geomagnetic storms if Earth directed. The backside CME from 2012 July 23 belongs among historical extreme solar events due to associated solar energetic particle fluxes and the CME-driven shock speed above 2000 kms-1. Here, we focus on analysis of associated interplanetary (IP) radio emissions. The frequency drift of the IP type II burst provides us with a reasonable speed of the CME-driven shock. We have successfully applied a radio direction-finding technique to IP type II and type III bursts observed by the two identical radio receivers aboard the two STEREO spacecraft. The radio triangulation technique allows us to localize radio sources in the IP medium. The obtained locations of the type II and type III bursts are in a very good agreement with the CME direction. We demonstrate the complementarity between radio triangulation and 3D reconstruction techniques for space weather applications.
18. A Search for Radio Emission from Nearby Exoplanets
Maps, Amethyst D.; Bastian, Timothy S.; Beasley, Anthony J.
2017-01-01
Since the discovery of the first extrasolar planet orbiting a main sequence star more than 20 years ago, the study of exoplanets has become a burgeoning field with more than 3300 confirmed extrasolar planets now known. A variety of techniques has been used to discover exoplanets orbiting main sequence stars and to deduce their properties: timing, radial velocities, direct imaging, microlensing, and transits in the optical/IR bands. Absent from this list so far is the detection of exoplanets at radio wavelengths, but not for lack of trying. Searches for radio emission from exoplanets predate their discovery (Winglee et al. 1986) and have continued sporadically to this day. The majority of searches for radio emission from exoplanets has searched for coherent radio emission. It is indeed the case that in our own solar system, all magnetized planets are powerful radio emitters, the likely emission mechanism being the cyclotron maser instability. The outstanding example is Jupiter, which emits 1010-1011 W at decameter wavelengths (frequencies <40 MHz). If there are Jupiter-like planets in other solar systems, many must surely emit CMI radiation. The emitted radiation could be orders of magnitude more intense than Jupiter’s if the interaction between the magnetized planet and the wind from the primary star is stronger than the Sun/Jupiter interaction - due, for example, to a more powerful wind and/or the planet being closer to the star.We have initiated a new search for radio emission from exoplanets, focusing on all known exoplanetary systems within 20 pc - more than 50 systems containing nearly 100 planets using the Jansky Very Large Array (JVLA) in three frequency bands: 1-2 GHz, 2-4 GHz, and 4-8 GHz with a target sensitivity of ~10 microJy. We have completed the 2-4 GHz survey and report our preliminary results, which include the detection of two systems. We discuss whether the emission is from a planet or from the star and the implications of our conclusions for
19. A New Solar Radio Emission Component Observed at Hectometric Wavelengths
Reiner, M.; Kaiser, M.; Fainberg, J.
2003-04-01
From May 17 to 22, 2002 a highly circularly polarized solar radio source was observed by the WAVES receivers on the Wind spacecraft. This unique event, which became quite intense and definite after May 19 and which was observed continuously for 6 days, was characterized by fine frequency structures, 1 to 2 hour amplitude periodicities, and a peaked frequency spectrum. Indeed, this emission has characteristics more typical of planetary emissions than of solar emissions. This is the only such event observed by Wind/WAVES in its 8 years of operation. (The only other example of an event of similar nature may have been observed more than 20 years ago by the ISEE-3 spacecraft.) The direction-finding analysis for this event indicates a relatively small radio source that may lie somewhere between 0.06 and 0.36 AU from the sun. The radiation from this event was very weak at the onset, being nearly an order of magnitude below the galactic background radiation level. It is speculated that this radio event may be a unique hectometric manifestation of a moving type IV burst. The radiation mechanism is unknown--possibilities include plasma emission, gyro-synchrotron, and cyclotron maser.
20. Simultaneous Observation of Jovian Radio Emissions by Cassini and Wind
NASA Technical Reports Server (NTRS)
Kaiser, M. L.; Kurth, W. S.; Hospodarsky, G. B.; Gurnett, D. A.
1999-01-01
During the Cassini instrument checkout interval in January 1999 as the spacecraft was making a distant (0.6 AU) swing by Earth, the radio and plasma wave receiver (RPWS) detected radio emission from the sun, Earth, and Jupiter, the latter including both the hectometric (HOM) and decametric (DAM) components. The WAVES experiment on the Wind spacecraft in orbit near Earth was also making observations of Jupiter at this same time. By combining the RPWS and WAVES data sets, we are able to provide some insight into the instantaneous beaming of Jovian radio emissions. As seen by Jupiter, Cassini and Wind were a few degrees apart during this period, yet the correlation between Jovian DAM arcs observed by the two spacecraft suggests that the beam width is even narrower and does not simultaneously illuminate both. The only earlier spacecraft capable, in principle, of making these observations were Voyager-1 and 2, but their sensitivity to DAM emissions was too limited to reliably measure the instantaneous beaming. The beam width implied by the RPWS-WAVES measurements is approximately the same as the angle through which Jupiter rotates while an arc (at a fixed frequency) is visible. The HOM Jovian emissions, on the other hand, seem similar as observed by RPWS and WAVES, consistent with earlier Wind-Ulysses measurements indicating a somewhat broader beam width.
1. Amalthea's modulation of Jovian decametric radio emission
Arkhypov, O. V.; Rucker, H. O.
2007-08-01
Most modulation lanes in dynamic spectra of Jovian decametric emission (DAM) are formed by radiation scattering on field-aligned inhomogeneities in the Io plasma torus. The positions and frequency drift of hundreds of lanes have been measured on the DAM spectra from UFRO archives. A special 3D algorithm is used for localization of field-aligned magnetospheric inhomogeneities by the frequency drift of modulation lanes. It is found that some lanes are formed near the magnetic shell of the satellite Amalthea mainly at longitudes of 123 to 140 deg. (north; III 1965 system) and 284 to 305 deg. (south). These disturbances coincide with regions of plasma compression by the rotating magnetic field of Jupiter. Such modulations are found at other longitudes too (189 to 236 deg.) with higher sensitivity. Amalthea's plasma torus could be another argument for the ice nature of the satellite, which has a density less than that of water.
2. Amalthea's modulation of Jovian decametric radio emission
Arkhypov, O. V.; Rucker, H. O.
2007-05-01
Most modulation lanes in dynamic spectra of Jovian decametric emission (DAM) are formed by radiation scattering on field-aligned inhomogeneities in the Io plasma torus. The positions and frequency drift of hundreds of lanes have been measured on the DAM spectra from UFRO archives. A special 3D algorithm is used for localization of field-aligned magnetospheric inhomogeneities by the frequency drift of modulation lanes. It is found that some lanes are formed near the magnetic shell of the satellite Amalthea mainly at longitudes of 123°≤λ_III≤140° (north) and 284°≤λ_III≤305° (south). These disturbances coincide with regions of plasma compression by the rotating magnetic field of Jupiter. Such modulations are found at other longitudes too (189° to 236°) with higher sensitivity. Amalthea's plasma torus could be another argument for the ice nature of the satellite, which has a density less than that of water.
3. An Earth-like correspondence between Saturn's auroral features and radio emission.
PubMed
Kurth, W S; Gurnett, D A; Clarke, J T; Zarka, P; Desch, M D; Kaiser, M L; Cecconi, B; Lecacheux, A; Farrell, W M; Galopeau, P; Gérard, J-C; Grodent, D; Prangé, R; Dougherty, M K; Crary, F J
2005-02-17
Saturn is a source of intense kilometre-wavelength radio emissions that are believed to be associated with its polar aurorae, and which provide an important remote diagnostic of its magnetospheric activity. Previous observations implied that the radio emission originated in the polar regions, and indicated a strong correlation with solar wind dynamic pressure. The radio source also appeared to be fixed near local noon and at the latitude of the ultraviolet aurora. There have, however, been no observations relating the radio emissions to detailed auroral structures. Here we report measurements of the radio emissions, which, along with high-resolution images of Saturn's ultraviolet auroral emissions, suggest that although there are differences in the global morphology of the aurorae, Saturn's radio emissions exhibit an Earth-like correspondence between bright auroral features and the radio emissions. This demonstrates the universality of the mechanism that results in emissions near the electron cyclotron frequency narrowly beamed at large angles to the magnetic field.
Malov, I.; Timirkeeva, M.
2017-06-01
Comparison of three pulsar samples — radio pulsars (R), gamma pulsars (γ) and pulsars with emission in both ranges (γ+R) — has been carried out. It was shown that magnetic fields at the light cylinder are two orders of magnitude higher in gamma pulsars (=3.60 - 3.95 G) when compared with radio pulsars (=1 .75 G). Losses of rotation energy in these objects differ much more (log dE/dt=35.37 -35.53 and 32.60, correspondingly). Gamma pulsars form two groups separated in space. The conclusion is made that generation of gamma emission takes place at the light cylinder and can be caused by the synchrotron mechanism.
5. ELECTRON-BEAM-INDUCED RADIO EMISSION FROM ULTRACOOL DWARFS
SciTech Connect
Yu, S.; Doyle, J. G.; Kuznetsov, A.; Hallinan, G.; Antonova, A.; MacKinnon, A. L.; Golden, A.
2012-06-10
We present the numerical simulations for an electron-beam-driven and loss-cone-driven electron-cyclotron maser (ECM) with different plasma parameters and different magnetic field strengths for a relatively small region and short timescale in an attempt to interpret the recent discovered intense radio emission from ultracool dwarfs. We find that a large amount of electromagnetic (EM) field energy can be effectively released from the beam-driven ECM, which rapidly heats the surrounding plasma. A rapidly developed high-energy tail of electrons in velocity space (resulting from the heating process of the ECM) may produce the radio continuum depending on the initial strength of the external magnetic field and the electron beam current. Both significant linear polarization and circular polarization of EM waves can be obtained from the simulations. The spectral energy distributions of the simulated radio waves show that harmonics may appear from 10 to 70{nu}{sub pe} ({nu}{sub pe} is the electron plasma frequency) in the non-relativistic case and from 10 to 600{nu}{sub pe} in the relativistic case, which makes it difficult to find the fundamental cyclotron frequency in the observed radio frequencies. A wide frequency band should therefore be covered by future radio observations.
6. Radio emission from an ultraluminous x-ray source.
PubMed
Kaaret, Philip; Corbel, Stephane; Prestwich, Andrea H; Zezas, Andreas
2003-01-17
The physical nature of ultraluminous x-ray sources is uncertain. Stellar-mass black holes with beamed radiation and intermediate black holes with isotropic radiation are two plausible explanations. We discovered radio emission from an ultraluminous x-ray source in the dwarf irregular galaxy NGC 5408. The x-ray, radio, and optical fluxes as well as the x-ray spectral shape are consistent with beamed relativistic jet emission from an accreting stellar black hole. If confirmed, this would suggest that the ultraluminous x-ray sources may be stellar-mass rather than intermediate-mass black holes. However, interpretation of the source as a jet-producing intermediate-mass black hole cannot be ruled out at this time.
7. Discovery of Circularly Polarized Radio Emission from SS 433.
PubMed
Fender; Rayner; Norris; Sault; Pooley
2000-02-10
We report the discovery of circularly polarized radio emission from the radio-jet X-ray binary SS 433 with the Australia Telescope Compact Array. The flux density spectrum of the circular polarization, clearly detected at four frequencies between 1 and 9 GHz, is of the form V~nu-0.9+/-0.1. Multiple components in the source and a lack of very high spatial resolution do not allow a unique determination of the origin of the circular polarization or of the spectrum of fractional polarization. However, we argue that the emission is likely to arise in the inner regions of the binary, possibly via propagation-induced conversion of linear to circular polarization, and the fractional circular polarization of these regions may be as high as 10%. Observations such as these have the potential to help us investigate the composition, whether pairs or baryonic, of the ejecta from X-ray binaries.
8. Physical Analysis of the Jovian Synchrotron Radio Emission
Santos-Costa, D.; Bolton, S. J.; Levin, S. M.; Thorne, R. M.
2006-12-01
9. Escaping radio emission from pulsars: Possible role of velocity shear
SciTech Connect
Mahajan, S.M. |; Machabeli, G.Z.; Rogava, A.D. |
1997-01-01
It is demonstrated that the velocity shear, intrinsic to the e{sup +}e{sup {minus}} plasma present in the pulsar magnetosphere, can efficiently convert the nonescaping longitudinal Langmuir waves (produced by some kind of a beam or stream instability) into propagating (escaping) electromagnetic waves. It is suggested that this shear induced transformation may be the basic mechanism needed for the eventual generation of the observed pulsar radio emission.
10. Periodic Bursts of Coherent Radio Emission from an Ultracool Dwarf
DTIC Science & Technology
2007-06-15
unidentified cool, dim brown dwarf or extrasolar planet in the solar neighborhood. In particular, the period of 1.28 hr observed for the bursts from...coherent radiation detected from the magnetized planets in our solar system (Zarka 1998; Ergun et al. 2000). However, studies of the electron...maser instability is the mechanism deemed responsible for the coherent radio emission detected from the magnetized planets in our solar system (Zarka 1998
11. Dendrite
NASA Technical Reports Server (NTRS)
2004-01-01
Researchers have found that as melted metals and alloys (combinations of metals) solidify, they can form with different arrangements of atoms, called microstructures. These microstructures depend on the shape of the interface (boundary) between the melted metal and the solid crystal it is forming. There are generally three shapes that the interface can take: planar, or flat; cellular, which looks like the cells of a beehive; and dendritic, which resembles tiny fir trees. Convection at this interface can affect the interface shape and hide the other phenomena (physical events). To reduce the effects of convection, researchers conduct experiments that examine and control conditions at the interface in microgravity. Microgravity also helps in the study of alloys composed of two metals that do not mix. On Earth, the liquid mixtures of these alloys settle into different layers due to gravity. In microgravity, the liquid metals do not settle, and a solid more uniform mixture of both metals can be formed.
12. Radio emission from Supernovae and High Precision Astrometry
Perez-Torres, M. A.
1999-11-01
The present thesis work makes contributions in two scientific fronts: differential astrometry over the largest angular scales ever attempted (approx. 15 arcdegrees) and numerical simulations of radio emission from very young supernovae. In the first part, we describe the results of the use of very-long-baseline interferometry (VLBI) in one experiment designed to measure with very high precision the angular distance between the radio sources 1150+812 (QSO) and 1803+784 (BL Lac). We observed the radio sources on 19 November 1993 using an intercontinental array of radio telescopes, which simultaneously recorded at 2.3 and 8.4 GHz. VLBI differential astrometry is capable, Nature allowing, of yielding source positions with precisions well below the milliarcsecond level. To achieve this precision, we first had to accurately model the rotation of the interferometric fringes via the most precise models of Earth Orientation Parameters (EOP; precession, polar motion and UT1, nutation). With this model, we successfully connected our phase delay data at both frequencies and, using difference astrometric techniques, determined the coordinates of 1803+784 relative to those of 1150+812-within the IERS reference frame--with an standard error of about 0.6 mas in each coordinate. We then corrected for several effects including propagation medium (mainly the atmosphere and ionosphere), and opacity and source-structure effects within the radio sources. We stress that our dual-frequency measurements allowed us to accurately subtract the ionosphere contribution from our data. We also used GPS-based TEC measurements to independently find the ionosphere contribution, and showed that these contributions agree with our dual-frequency measurements within about 2 standard deviations in the less favorables cases (the longest baselines), but are usually well within one standard deviation. Our estimates of the relative positions, whether using dual-frequency-based or GPS-based ionosphere
13. Radio emission from the magnetic equator of Uranus
SciTech Connect
Kaiser, M.L.; Desch, M.D.; Connerney, J.E.P. )
1989-03-01
The major observational characteristics of the smooth, narrow bandwidth component of Uranus' radio emissions are well described by sources radiating near the local electron gyrofrequency, confined to the magnetic equatorial plane and encircling the plant at radial distances of approximately 2 to 3 R{sub v}. The most intense emission appears to be generated in association with the {var epsilon} ring at 2.0 R{sub v} radial distance. The authors infer a cold electron density of {le} 4 cm{sup {minus}3} in this region.
14. The Role of the Jet Emission in Young Radio Sources
Migliori, Giulia
2014-07-01
We investigated the contribution of the jet to the observed high energy emission in a sample of young and compact radio quasars. For the first time, we compared the Fermi-LAT and Chandra observations of the sample to γ-ray and X-ray luminosities predicted assuming a jet synchrotron and inverse Compton radiative model. The simulations performed for a reasonable set of model parameters and assumptions provide constraints on the minimum jet power (Ljet,kin/Ldisk >0.01), on the contribution of the jet to the X-ray emission, and on the particles to magnetic field energy density ratios.
NASA Technical Reports Server (NTRS)
Curtis, S. A.; Desch, M. D.; Kaiser, M. L.
1987-01-01
On the basis of the location of the source field lines of the smooth nightside component of Uranus kilometric radiation, the most likely free energy source is the outer radiation belts. As the terminator sweeps over the magnetic north polar region, precipitation of electrons generated by solar heating of the upper atmosphere and submergence of the electron mirror points deeper in the atmosphere will create a backscattered electron distribution with an enhanced population at large pitch angles. The clocklike radio emission turns out to be a direct consequence of the terminator's control of the emission process.
16. Radio emission from the magnetic equator of Uranus
NASA Technical Reports Server (NTRS)
Kaiser, M. L.; Desch, M. D.; Connerney, J. E. P.
1989-01-01
The major observational characteristics of the smooth, narrow bandwidth component of Uranus' radio emissions are well described by sources radiating near the local electron gyrofrequency, confined to the magnetic equatorial plane and encircling the planet at radial distances of approximately 2 to 3 R(U). The most intense emission appears to be generated in association with the epsilon ring at 2.0 R(U) radial distance. A cold electron density of less than or equal to 4/cu cm are inferred in this region.
17. Fast Radio Bursts with Extended Gamma-Ray Emission?
Murase, Kohta; Mészáros, Peter; Fox, Derek B.
2017-02-01
We consider some general implications of bright γ-ray counterparts to fast radio bursts (FRBs). We show that even if these manifest in only a fraction of FRBs, γ-ray detections with current satellites (including Swift) can provide stringent constraints on cosmological FRB models. If the energy is drawn from the magnetic energy of a compact object such as a magnetized neutron star, the sources should be nearby and be very rare. If the intergalactic medium is responsible for the observed dispersion measure, the required γ-ray energy is comparable to that of the early afterglow or extended emission of short γ-ray bursts. While this can be reconciled with the rotation energy of compact objects, as expected in many merger scenarios, the prompt outflow that yields the γ-rays is too dense for radio waves to escape. Highly relativistic winds launched in a precursor phase, and forming a wind bubble, may avoid the scattering and absorption limits and could yield FRB emission. Largely independent of source models, we show that detectable radio afterglow emission from γ-ray bright FRBs can reasonably be anticipated. Gravitational wave searches can also be expected to provide useful tests.
18. Radio Emission in Atmospheric Air Showers Measured by LOPES-30
SciTech Connect
Isar, P. G.
2008-01-24
When Ultra High Energy Cosmic Rays (UHECR) interact with particles in the Earth's atmosphere, they produce a shower of secondary particles propagating towards the ground. These relativistic particles emit synchrotron radiation in the radio frequency range when passing the Earth's magnetic field. The LOPES (LOFAR Prototype Station) experiment investigates the radio emission from these showers in detail and will pave the way to use this detection technique for large scale applications like in LOFAR (Low Frequency Array) and the Pierre Auger Observatory. The LOPES experiment is co-located and measures in coincidence with the air shower experiment KASCADE-Grande at Forschungszentrum Karlsruhe, Germany. LOPES has an absolute amplitude calibration array of 30 dipole antennas (LOPES-30). After one year of measurements of the single East-West polarization by all 30 antennas, recently, the LOPES-30 set-up was configured to perform dual-polarization measurements. Half of the antennas have been configured for measurements of the North-South polarization. Only by measuring at the same time both, the E-W and N-S polarization components of the radio emission, the geo-synchrotron effect as the dominant emission mechanism in air showers can be verified. The status of the measurements, including the absolute calibration procedure of the dual-polarized antennas as well as analysis of dual-polarized event examples are reported.
19. Detection of 610-MHz radio emission from hot magnetic stars
Chandra, P.; Wade, G. A.; Sundqvist, J. O.; Oberoi, D.; Grunhut, J. H.; ud-Doula, A.; Petit, V.; Cohen, D. H.; Oksala, M. E.; David-Uraz, A.
2015-09-01
We have carried out a study of radio emission from a small sample of magnetic O- and B-type stars using the Giant Metrewave Radio Telescope, with the goal of investigating their magnetospheres at low frequencies. These are the lowest frequency radio measurements ever obtained of hot magnetic stars. The observations were taken at random rotational phases in the 1390 and the 610 MHz bands. Out of the eight stars, we detect five B-type stars in both the 1390 and the 610 MHz bands. The three O-type stars were observed only in the 1390 MHz band, and no detections were obtained. We explain this result as a consequence of free-free absorption by the free-flowing stellar wind exterior to the confined magnetosphere. We also study the variability of individual stars. One star - HD 133880 - exhibits remarkably strong and rapid variability of its low-frequency flux density. We discuss the possibility of this emission being coherent emission as reported for CU Vir by Trigilio et al.
20. RADIO CONTINUUM EMISSION AND WATER MASERS TOWARD CB 54
SciTech Connect
De Gregorio-Monsalvo, Itziar; Gomez, Jose F.; Anglada, Guillem; Suarez, Olga; Torrelles, Jose M.; Kuiper, Thomas B. H.; Patel, Nimesh A.
2009-06-15
We present high angular resolution observations of water masers at 1.3 cm and radio continuum emission at 1.3, 3.6, and 6 cm toward the Bok globule CB 54 using the Very Large Array. At 1.3 cm, with subarcsecond angular resolution, we detect a radio continuum compact source located to the southwest of the globule and spatially coincident with a mid-infrared (mid-IR) embedded object (MIR-b). The spectral index derived between 6 and 1.3 cm ({alpha} = 0.3 {+-} 0.4) is flat, consistent with optically thin free-free emission from ionized gas. We propose the shock-ionization scenario as a viable mechanism for producing the radio continuum emission observed at cm frequencies. Water masers are detected at two different positions separated by 2.''3, and coincide spatially with two mid-IR sources: MIR-b and MIR-c. The association of these mid-IR sources with water masers confirms that they are likely protostars undergoing mass loss, and they are the best candidate as driving sources of the molecular outflows in the region.
1. Prospects for planet detection using pulsed radio emission from UCD's
Mutel, Robert
2017-05-01
Pulsed radio emission from ultra-cool dwarfs is thought to be due to the electron-cyclotron maser instability (ECMI) from mildly relativistic electrons precipitating in large kilogauss magnetic loops above the stellar photosphere. This emission, which highly circularly polarized and highly beamed, may be altered by the presence of close-in planets, and therefore provide a means for inferring the presence of the planet. I will discuss the basic plasma physics of ECMI emission, as well as recent observations of ECMI emission at the Earth, Jupiter, and Saturn. These observations, especially the beaming properties, are highly relevant to predicting whether and how close-in planets can effect ECMI pulses from the parent star.
2. Constraining Substellar Magnetic Dynamos using Auroral Radio Emission
Kao, Melodie; Hallinan, Gregg; Pineda, J. Sebastian; Escala, Ivanna; Burgasser, Adam J.; Stevenson, David J.
2017-01-01
An important outstanding problem in dynamo theory is understanding how magnetic fields are generated and sustained in fully convective stellar objects. A number of models for possible dynamo mechanisms in this regime have been proposed but constraining data on magnetic field strengths and topologies across a wide range of mass, age, rotation rate, and temperature are sorely lacking, particularly in the brown dwarf regime. Detections of highly circularly polarized pulsed radio emission provide our only window into magnetic field measurements for objects in the ultracool brown dwarf regime. However, these detections are very rare; previous radio surveys encompassing ˜60 L6 or later targets have yielded only one detection. We have developed a selection strategy for biasing survey targets based on possible optical and infrared tracers of auroral activity. Using our selection strategy, we previously observed six late L and T dwarfs with the Jansky Very Large Array (VLA) and detected the presence of highly circularly polarized radio emission for five targets. Our initial detections at 4-8 GHz provided the most robust constraints on dynamo theory in this regime, confirming magnetic fields >2.5 kG. To further develop our understanding of magnetic fields in the ultracool brown dwarf mass regime bridging planets and stars, we present constraints on surface magnetic field strengths for two Y-dwarfs as well as higher frequency observations of the previously detected L/T dwarfs corresponding ~3.6 kG fields. By carefully comparing magnetic field measurements derived from auroral radio emission to measurements derived from Zeeman broadening and Zeeman Doppler imaging, we provide tentative evidence that the dynamo operating in this mass regime may be inconsistent with predicted values from currently in vogue models. This suggests that parameters beyond convective flux may influence magnetic field generation in brown dwarfs.
3. Wavelet Based Characterization of Low Radio Frequency Solar Emissions
Suresh, A.; Sharma, R.; Das, S. B.; Oberoi, D.; Pankratius, V.; Lonsdale, C.
2016-12-01
Low-frequency solar radio observations with the Murchison Widefield Array (MWA) have revealed the presence of numerous short-lived, narrow-band weak radio features, even during quiet solar conditions. In their appearance in in the frequency-time plane, they come closest to the solar type III bursts, but with much shorter spectral spans and flux densities, so much so that they are not detectable with the usual swept frequency radio spectrographs. These features occur at rates of many thousand features per hour in the 30.72 MHz MWA bandwidth, and hence necessarily require an automated approach to determine robust statistical estimates of their properties, e.g., distributions of spectral widths, temporal spans, flux densities, slopes in the time-frequency plane and distribution over frequency. To achieve this, a wavelet decomposition approach has been developed for feature recognition and subsequent parameter extraction from the MWA dynamic spectrum. This work builds on earlier work by the members of this team to achieve a reliable flux calibration in a computationally efficient manner. Preliminary results show that the distribution of spectral span of these features peaks around 3 MHz, most of them last for less than two seconds and are characterized by flux densities of about 60% of the background solar emission. In analogy with the solar type III bursts, this non-thermal emission is envisaged to arise via coherent emission processes. There is also an exciting possibility that these features might correspond to radio signatures of nanoflares, hypothesized (Gold, 1964; Parker, 1972) to explain coronal heating.
4. Saturn's Radio Emissions and their Relation to Magnetospheric Dynamics
Jackman, C. M.
With the arrival of the Cassini spacecraft at Saturn in July 2004, there have been quasi-continuous observations of Saturn Kilometric Radiation (SKR) emissions. In this paper we review the response of these emissions to dynamics in Saturn's magnetosphere, driven by factors internal and external to the system. We begin by reviewing solar wind data upstream of Saturn and discuss the link between solar wind compressions and dynamics in Saturn's magnetosphere, evidenced by intensifications and occasional phase changes in the SKR emission. We then review the link between magnetotail reconnection and planetary radio emissions. We begin in the well-sampled magnetotail of Earth and then move to Saturn where exploration of the nightside magnetosphere has revealed evidence of plasmoid-like magnetic structures and other phenomena indicative of the kronian equivalent of terrestrial substorms. In general, there is a good correlation between the timing of reconnection events and enhancements in the SKR emission, coupled with extension of the emission to lower frequencies. We interpret this as growth of the radio source region to higher altitudes along the field lines, stimulated by increased precipitation of energetic electrons into the auroral zones following reconnection. We also comment on the observation that the majority of reconnection events occur at SKR phases where the SKR power would be expected to be rising with time, indicating that reconnection is most likely to occur at a preferred phase. We conclude with a summary of the current knowledge of the link between Saturn's magnetospheric dynamics and SKR emissions, and list a number of open questions to be addressed in the future.
5. Natural radio emission of Jupiter as interferences for radar investigations of the icy satellites of Jupiter
Cecconi, B.; Hess, S.; Hérique, A.; Santovito, M. R.; Santos-Costa, D.; Zarka, P.; Alberti, G.; Blankenship, D.; Bougeret, J. L.; Bruzzone, L.; Kofman, W.
2011-10-01
6. Natural radio emission of Jupiter as interferences for radar investigations of the icy satellites of Jupiter
Cecconi, B.; Hess, S.; Hérique, A.; Santovito, M. R.; Santos-Costa, D.; Zarka, P.; Alberti, G.; Blankenship, D.; Bougeret, J.-L.; Bruzzone, L.; Kofman, W.
2012-02-01
7. Radio emission from the nova-like variable AC Cancri and the symbiotic variable AG Draconis
SciTech Connect
Torbett, M.V.; Campbell, B.
1987-07-01
Radio emission at 6 cm has been detected from the nova-like cataclysmic variable AC Cnc and the symbiotic variable AG Dra. The AC Cnc observation constitutes the first radio detection in this class of objects. The AG Dra source is probably resolved and appears to show asymmetric, extended structure. The radio emission can best be explained by thermal bremsstrahlung. 26 references.
8. Pulsed Radio Emission from PSR J1119-6127 re-activated
Burgay, M.; Possenti, A.; Kerr, M.; Esposito, P.; Rea, N.; Zelati, F. Coti; Israel, G. L.; Johnston, S.
2016-08-01
Prompted by the disappearance of the pulsed radio emission from the known pulsar PSR J1119-6127 (Burgay et al., Atel #9286; Majid et al. Atel #9321), we have undertaken a program at the Parkes radio telescope to investigate any further evolution of the radio emission from the neutron star.
9. Modelling of radio emission from cosmic ray air showers
Ludwig, Marianne
2011-06-01
Cosmic rays entering the Earth's atmosphere induce extensive air showers consisting of up to billions of secondary particles. Among them, a multitude of electrons and positrons are generated. These get deflected in the Earth's magnetic field, creating time-varying transverse currents. Thereby, the air shower emits coherent radiation in the MHz frequency range measured by radio antenna arrays on the ground such as LOPES at the KIT. This detection method provides a possibility to study cosmic rays with energies above 1017 eV. At this time, the radio technique undergoes the change from prototype experiments to large scale application. Thus, a detailed understanding of the radio emission process is needed more than ever. Before starting this work, different models made conflicting predictions on the pulse shape and the amplitude of the radio signal. It turned out that a radiation component caused by the variation of the number of charged particles within the air shower was missed in several models. The Monte Carlo code REAS2 superposing the radiation of the individual air shower electrons and positrons was one of those. At this time, it was not known how to take the missing component into account. For REAS3, we developed and implemented the endpoint formalism, a universal approach, to calculate the radiation from each single particle. For the first time, we achieve a good agreement between REAS3 and MGMR, an independent and completely different simulation approach. In contrast to REAS3, MGMR is based on a macroscopic approach and on parametrisations of the air shower. We studied the differences in the underlying air shower models to explain the remaining deviations. For comparisons with LOPES data, we developed a new method which allows "top-down" simulations of air showers. From this, we developed an air shower selection criterion based on the number of muons measured with KASCADE to take shower-to-shower fluctuations for a single event analysis into account. With
10. RADIO EMISSION FROM RED-GIANT HOT JUPITERS
SciTech Connect
Fujii, Yuka; Spiegel, David S.; Mroczkowski, Tony; Nordhaus, Jason; Zimmerman, Neil T.; Parsons, Aaron R.; Mirbabayi, Mehrdad; Madhusudhan, Nikku
2016-04-01
When planet-hosting stars evolve off the main sequence and go through the red-giant branch, the stars become orders of magnitudes more luminous and, at the same time, lose mass at much higher rates than their main-sequence counterparts. Accordingly, if planetary companions exist around these stars at orbital distances of a few au, they will be heated up to the level of canonical hot Jupiters and also be subjected to a dense stellar wind. Given that magnetized planets interacting with stellar winds emit radio waves, such “Red-Giant Hot Jupiters” (RGHJs) may also be candidate radio emitters. We estimate the spectral auroral radio intensity of RGHJs based on the empirical relation with the stellar wind as well as a proposed scaling for planetary magnetic fields. RGHJs might be intrinsically as bright as or brighter than canonical hot Jupiters and about 100 times brighter than equivalent objects around main-sequence stars. We examine the capabilities of low-frequency radio observatories to detect this emission and find that the signal from an RGHJ may be detectable at distances up to a few hundred parsecs with the Square Kilometer Array.
11. Radio Emission from Red-Giant Hot Jupiters
NASA Technical Reports Server (NTRS)
Fujii, Yuka; Spiegel, David S.; Mroczkowski, Tony; Nordhaus, Jason; Zimmerman, Neil T.; Parsons, Aaron R.; Mirbabayi, Mehrdad; Madhusudhan, Nikku
2016-01-01
When planet-hosting stars evolve off the main sequence and go through the red-giant branch, the stars become orders of magnitudes more luminous and, at the same time, lose mass at much higher rates than their main sequence counterparts. Accordingly, if planetary companions exist around these stars at orbital distances of a few au, they will be heated up to the level of canonical hot Jupiters and also be subjected to a dense stellar wind. Given that magnetized planets interacting with stellar winds emit radio waves, such "Red-Giant Hot Jupiters" (RGHJs) may also be candidate radio emitters. We estimate the spectral auroral radio intensity of RGHJs based on the empirical relation with the stellar wind as well as a proposed scaling for planetary magnetic fields. RGHJs might be intrinsically as bright as or brighter than canonical hot Jupiters and about 100 times brighter than equivalent objects around main-sequence stars. We examine the capabilities of low-frequency radio observatories to detect this emission and find that the signal from an RGHJ may be detectable at distances up to a few hundred parsecs with the Square Kilometer Array.
12. Radio Emission from Red-Giant Hot Jupiters
NASA Technical Reports Server (NTRS)
Fujii, Yuka; Spiegel, David S.; Mroczkowski, Tony; Nordhaus, Jason; Zimmerman, Neil T.; Parsons, Aaron R.; Mirbabayi, Mehrdad; Madhusudhan, Nikku
2016-01-01
When planet-hosting stars evolve off the main sequence and go through the red-giant branch, the stars become orders of magnitudes more luminous and, at the same time, lose mass at much higher rates than their main sequence counterparts. Accordingly, if planetary companions exist around these stars at orbital distances of a few au, they will be heated up to the level of canonical hot Jupiters and also be subjected to a dense stellar wind. Given that magnetized planets interacting with stellar winds emit radio waves, such "Red-Giant Hot Jupiters" (RGHJs) may also be candidate radio emitters. We estimate the spectral auroral radio intensity of RGHJs based on the empirical relation with the stellar wind as well as a proposed scaling for planetary magnetic fields. RGHJs might be intrinsically as bright as or brighter than canonical hot Jupiters and about 100 times brighter than equivalent objects around main-sequence stars. We examine the capabilities of low-frequency radio observatories to detect this emission and find that the signal from an RGHJ may be detectable at distances up to a few hundred parsecs with the Square Kilometer Array.
13. Radio Emission from Red-giant Hot Jupiters
Fujii, Yuka; Spiegel, David S.; Mroczkowski, Tony; Nordhaus, Jason; Zimmerman, Neil T.; Parsons, Aaron R.; Mirbabayi, Mehrdad; Madhusudhan, Nikku
2016-04-01
When planet-hosting stars evolve off the main sequence and go through the red-giant branch, the stars become orders of magnitudes more luminous and, at the same time, lose mass at much higher rates than their main-sequence counterparts. Accordingly, if planetary companions exist around these stars at orbital distances of a few au, they will be heated up to the level of canonical hot Jupiters and also be subjected to a dense stellar wind. Given that magnetized planets interacting with stellar winds emit radio waves, such “Red-Giant Hot Jupiters” (RGHJs) may also be candidate radio emitters. We estimate the spectral auroral radio intensity of RGHJs based on the empirical relation with the stellar wind as well as a proposed scaling for planetary magnetic fields. RGHJs might be intrinsically as bright as or brighter than canonical hot Jupiters and about 100 times brighter than equivalent objects around main-sequence stars. We examine the capabilities of low-frequency radio observatories to detect this emission and find that the signal from an RGHJ may be detectable at distances up to a few hundred parsecs with the Square Kilometer Array.
14. Low-frequency radio emissions in the outer heliosphere
NASA Technical Reports Server (NTRS)
Macek, W. M.; Cairns, I. H.; Kurth, W. S.; Gurnett, D. A.
1991-01-01
Progress is reported toward a model for the 2 and 3 kHz radio waves observed by Voyagers 1 and 2 during the 1983-1987 interval at radial distances from the sun of 17 and 13 AU, respectively. The brightness temperature and range of the volume emissivity for the radiation are calculated, and the results are compared with the characteristics of known radiation at multiples of the plasma frequency. The derived brightness temperatures are used to constrain the source of the Langmuir waves required to generate the observed emission and to rule out certain emission mechanisms. Minimum values of 3-30 micro-V/m are derived for the Langmuir wave electric field intensity and are found to be in reasonable agreement with observed values at planetary bow shocks. Path lengths required for the radiation to reach the observed levels are derived and discussed. The relevance of these ideas to possible direct observations of heliospheric boundaries is addressed.
15. The Lightning and Radio Emission Detector (LRD) instrument
Lanzerotti, L. J.; Rinnert, K.; Dehmel, G.; Gliem, F. O.; Krider, E. P.; Uman, M. A.; Umlauft, G.; Bach, J.
1992-05-01
The Lightning and Radio Emission Detector (LRD) instrument will be carried by the Galileo Probe into Jupiter's atmosphere. The LRD will verify the existence of lightning in the atmosphere and will determine the details of many of its basic characteristics. The instrument, operated in its magnetospheric mode at distances of about 5, 4, 3, and 2 planetary radii from Jupiter's center, will also measure the RF noise spectrum in Jupiter's magnetosphere. The LRD instrument is composed of a ferrite-core radio frequency antenna and two photodiodes mounted behind individual fisheye lenses. The output of the RF antenna is analyzed both separately and in coincidence with the optical signals from the photodiodes. The RF antenna provides data both in the frequency domain (with three narrow-band channels, primarily for deducing the physical properties of distant lightning) and in the time domain with a priority scheme (primarily for determining from individual RF waveforms the physical properties of closeby-lightning).
Melnik, Valentin N.; Konovalenko, Alexander A.; Rucker, Helmut O.; Lecacheux, Alain
2007-08-01
Results of the last observations of solar sporadic radio emission at the UTR-2 radio telescope (Kharkov, Ukraine) at the frequencies 10 - 30 MHz are presented. The use of new backend facilities, the DSP and 60-channel spectrometer, allows us to obtain data with time resolution up to 2 ms and frequency resolution of 12 kHz in the continuous frequency band 12 MHz. Usual Type III bursts, Type IIIb bursts, U- and J-bursts in the decameter range are discussed. Special attention is paid to detection and analysis of Type II bursts and their properties, newly discovered fine time structures of Type III bursts, Type III-like bursts, s-bursts, new observational features of drift pair bursts, and ‘absorption’ bursts.
Mel'Nik, V. N.; Konovalenko, A. A.; Rucker, H. O.; Lecacheux, A.
2006-08-01
Results of the last observations of solar sporadic radio emission on the UTR-2 radio telescope (Kharkov, Ukraine) at the frequencies 10-30MHz are presented. Using of new back-end facilities, the DSP and 60-channel spectrometer, allows obtaining data with time resolution up to 2 ms and frequency resolution 12 kHz in the continuous frequency band 12MHz. Usual Type III bursts, type III-b bursts, U- and J- bursts in the decameter range are discussed. Especial attention is paid to detection and analysis of Type II bursts and their properties, first found fine time structures of Type III bursts, Type III-like bursts, s-bursts, new observational features of drift pair bursts, "absorption" burst.
18. Ground and space observations of medium frequency auroral radio emissions
Broughton, Matthew C.
The auroral zone is a rich source of natural radio emissions that can be observed in space and at ground-level. By studying these waves, scientists can gain insight into the plasma processes that generate them and use the near-Earth space environment as a large-scale plasma physics laboratory. This thesis uses both ground-level and in situ observations to study two kinds of natural radio emissions. First, we report observations of a new kind of auroral radio emission. The waves have frequencies ranging from 1.3-2.2 MHz, bandwidths ranging from 90-272 kHz, and durations ranging from 16-355 s. Spectral analysis of the waveform data has revealed that the emission has a complex combination of at least three kinds of fine structures. For model auroral electron distributions, calculations indicate that Langmuir waves could be excited at frequencies consistent with observations. The remainder of the thesis discusses auroral medium frequency (MF) burst, an impulsive, broadband natural radio emission observed at ground-level within a few minutes of local substorm onset. LaBelle [2011] proposed that MF burst originates as Langmuir/Z-mode waves on the topside of the ionosphere that subsequently mode convert to L-mode waves and propagate to ground-level. Using continuous waveform measurements and combined observations with the Sondrestrom Incoherent Scatter Radar, we have performed two tests of this mechanism. The results of these tests are consistent with the mechanism described in LaBelle [2011]. A survey of 8,624 half-orbits of the DEMETER spacecraft has revealed 68 observations of bursty MF waves. We have compared the wave properties of these waves to those of MF burst and have found that although it is uncertain, the balance of the evidence suggests that the bursty MF waves observed with DEMETER are the same phenomenon as the ground-level MF burst. Finally, we have used numerical simulations to model both the fine structure of MF burst and to estimate the attenuation the
SciTech Connect
Williams, Peter K. G.; Berger, Edo; Zauderer, B. Ashley
2013-04-20
Radio detections of ultracool dwarfs provide insight into their magnetic fields and the dynamos that maintain them, especially at the very bottom of the main sequence, where other activity indicators dramatically weaken. Until recently, radio emission was only detected in the M and L dwarf regimes, but this has changed with the Arecibo detection of rapid polarized flares from the T6.5 dwarf 2MASS J10475385+2124234. Here, we report the detection of quasi-quiescent radio emission from this source at 5.8 GHz using the Karl G. Jansky Very Large Array. The spectral luminosity is L{sub {nu}} = (2.2 {+-} 0.7) Multiplication-Sign 10{sup 12} erg s{sup -1} Hz{sup -1}, a factor of {approx}100 times fainter than the Arecibo flares. Our detection is the lowest luminosity yet achieved for an ultracool dwarf. Although the emission is fully consistent with being steady, unpolarized, and broad band, we find tantalizing hints for variability. We exclude the presence of short-duration flares as seen by Arecibo, although this is not unexpected given estimates of the duty cycle. Follow-up observations of this object will offer the potential to constrain its rotation period, electron density, and the strength and configuration of the magnetic field. Equally important, follow-up observations will address the question of whether the electron cyclotron maser instability, which is thought to produce the flares seen by Arecibo, also operates in the very different parameter regime of the emission we detect, or whether instead this ultracool dwarf exhibits both maser and gyrosynchrotron radiation, potentially originating from substantially different locations.
20. Chromospheric evaporation and decimetric radio emission in solar flares
NASA Technical Reports Server (NTRS)
Aschwanden, Markus J.; Benz, Arnold O.
1995-01-01
We have discovered decimetric signatures of the chromospheric evaporation process. Evidence for the radio detection of chromospheric evaporation is based on the radio-inferred values of (1) the electron density, (2) the propagation speed, and (3) the timing, which are found to be in good agreement with statistical values inferred from the blueshifted Ca XIX soft X-ray line. The physical basis of our model is that free-free absorption of plasma emission is strongly modified by the steep density gradient and the large temperature increase in the upflowing flare plasma. The steplike density increase at the chromospheric evaporation front causes a local discontinuity in the plasma frequency, manifested as almost infinite drift rate in decimetric type III bursts. The large temperature increase of the upflowing plasma considerably reduces the local free-free opacity (due to the T(exp -3/2) dependence) and thus enhances the brightness of radio bursts emitted at the local plasma frequency near the chromospheric evaporation front, while a high-frequency cutoff is expected in the high-density regions behind the front, which can be used to infer the velocity of the upflowing plasma. From model calculations we find strong evidence that decimetric bursts with a slowly drifting high-frequency cutoff are produced by fundamental plasma emission, contrary to the widespread belief that decimetric bursts are preferentially emitted at the harmonic plasma level. We analyze 21 flare episodes from 1991-1993 for which broadband (100-3000 MHz) radio dynamic spectra from Pheonix, hard X-ray data from (BATSE/CGRO) and soft X-ray data from Burst and Transient Source Experiment/Compton Gamma Ray Observatory (GOES) were available.
1. Dark Matter and Synchrotron Emission from Galactic Center Radio Filaments
SciTech Connect
2011-11-10
The inner degrees of the Galactic center contain a large population of filamentary structures observed at radio frequencies. These so-called non-thermal radio filaments (NRFs) trace magnetic field lines and have attracted significant interest due to their hard (S_v ~ -0.1 +/- 0.4) synchrotron emission spectra. The origin of these filaments remains poorly understood. We show that the electrons and positrons created through the annihilations of a relatively light (~5-10 GeV) dark matter particle with the cross section predicted for a simple thermal relic can provide a compelling match to the intensity, spectral shape, and flux variation of the NRFs. Furthermore, the characteristics of the dark matter particle necessary to explain the synchrotron emission from the NRFs is consistent with those required to explain the excess gamma-ray emission observed from the Galactic center by the Fermi-LAT, as well as the direct detection signals observed by CoGeNT and DAMA/LIBRA.
2. DARK MATTER AND SYNCHROTRON EMISSION FROM GALACTIC CENTER RADIO FILAMENTS
SciTech Connect
2011-11-10
The inner degrees of the Galactic center contain a large population of filamentary structures observed at radio frequencies. These so-called non-thermal radio filaments (NRFs) trace magnetic field lines and have attracted significant interest due to their hard (S{sub v} {proportional_to}{nu}{sup -0.1{+-}0.4}) synchrotron emission spectra. The origin of these filaments remains poorly understood. We show that the electrons and positrons created through the annihilations of a relatively light ({approx}5-10 GeV) dark matter particle with the cross section predicted for a simple thermal relic can provide a compelling match to the intensity, spectral shape, and flux variation of the NRFs. Furthermore, the characteristics of the dark matter particle necessary to explain the synchrotron emission from the NRFs are consistent with those required to explain the excess {gamma}-ray emission observed from the Galactic center by the Fermi Large Area Telescope, as well as the direct detection signals observed by CoGeNT and DAMA/LIBRA.
3. STUDY OF CALIBRATION OF SOLAR RADIO SPECTROMETERS AND THE QUIET-SUN RADIO EMISSION
SciTech Connect
Tan, Chengming; Yan, Yihua; Tan, Baolin; Fu, Qijun; Liu, Yuying; Xu, Guirong
2015-07-20
This work presents a systematic investigation of the influence of weather conditions on the calibration errors by using Gaussian fitness, least chi-square linear fitness, and wavelet transform to analyze the calibration coefficients from observations of the Chinese Solar Broadband Radio Spectrometers (at frequency bands of 1.0–2.0 GHz, 2.6–3.8 GHz, and 5.2–7.6 GHz) during 1997–2007. We found that calibration coefficients are influenced by the local air temperature. Considering the temperature correction, the calibration error will reduce by about 10%–20% at 2800 MHz. Based on the above investigation and the calibration corrections, we further study the radio emission of the quiet Sun by using an appropriate hybrid model of the quiet-Sun atmosphere. The results indicate that the numerical flux of the hybrid model is much closer to the observation flux than that of other ones.
4. Auroral radio emission from ultracool dwarfs: a Jovian model
Turnpenney, S.; Nichols, J. D.; Wynn, G. A.; Casewell, S. L.
2017-10-01
A number of fast-rotating ultracool dwarfs (UCDs) emit pulsed coherent radiation, attributed to the electron-cyclotron maser instability, a phenomenon that occurs in the Solar system at planets with strong auroral emission. In this paper, we examine magnetosphere-ionosphere coupling currents in UCDs, adopting processes used in models of Jovian emission. We consider the angular velocity gradient arising from a steady outward flux of angular momentum from an internal plasma source, as analogous to the Jovian main oval current system, as well as the interaction of a rotating magnetosphere with the external medium. Both of these mechanisms are seen in the Solar system to be responsible for the production of radio emission. We present the results of an investigation over a range of relevant plasma and magnetosphere-ionosphere coupling parameters to determine regimes consistent with observed UCD radio luminosities. Both processes are able to explain observed UCD luminosities with ionospheric Pedersen conductances of ˜1-2 mho, either for a closed magnetosphere with a plasma mass outflow rate of ˜105 kg s-1, i.e. a factor of ˜100 larger than that observed at Jupiter's moon Io, or for a dwarf with an open magnetosphere moving through the interstellar medium at ˜50 km s-1 and a plasma mass outflow rate of ˜1000 kg s-1. The radio luminosity resulting from these mechanisms has opposing dependencies on the magnetic field strength, a point that may be used to discriminate between the two models as more data become available.
5. Theory of Type 3 and Type 2 Solar Radio Emissions
NASA Technical Reports Server (NTRS)
Robinson, P. A.; Cairns, I. H.
2000-01-01
The main features of some current theories of type III and type II bursts are outlined. Among the most common solar radio bursts, type III bursts are produced at frequencies of 10 kHz to a few GHz when electron beams are ejected from solar active regions, entering the corona and solar wind at typical speeds of 0.1c. These beams provide energy to generate Langmuir waves via a streaming instability. In the current stochastic-growth theory, Langmuir waves grow in clumps associated with random low-frequency density fluctuations, leading to the observed spiky waves. Nonlinear wave-wave interactions then lead to secondary emission of observable radio waves near the fundamental and harmonic of the plasma frequency. Subsequent scattering processes modify the dynamic radio spectra, while back-reaction of Langmuir waves on the beam causes it to fluctuate about a state of marginal stability. Theories based on these ideas can account for the observed properties of type III bursts, including the in situ waves and the dynamic spectra of the radiation. Type 11 bursts are associated with shock waves propagating through the corona and interplanetary space and radiating from roughly 30 kHz to 1 GHz. Their basic emission mechanisms are believed to be similar to those of type III events and radiation from Earth's foreshock. However, several sub-classes of type II bursts may exist with different source regions and detailed characteristics. Theoretical models for type II bursts are briefly reviewed, focusing on a model with emission from a foreshock region upstream of the shock for which observational evidence has just been reported.
6. Solar radio emissions: 2D full PIC simulations
Pierre, H.; Sgattoni, A.; Briand, C.; Amiranoff, F.; Riconda, C.
2016-12-01
Solar radio emissions are electromagnetic waves observed at the local plasma frequency and/or at twice the plasma frequency. To describe their origin a multi-stage model has been proposed by Ginzburg & Zhelezniakov (1958) and further developed by several authors, which consider a succession of non-linear three-wave interaction processes. Electron beams accelerated by solar flares travel in the interplanetary plasma and provide the free energy for the development of plasma instabilities. The model describes how part of the free energy of these beams can be transformed in a succession of plasma waves and eventually into electromagnetic waves. Following the work of Thurgood & Tsiklauri (2015) we performed several 2D Particle In Cell simulations. The simulations follow the entire set of processes from the electron beam propagation in the background plasma to the generation of the electromagnetic waves in particular the 2ωp emission, including the excitation of the low frequency waves. As suggested by Thurgood & Tsiklauri (2015) it is possible to identify regimes where the radiation emission can be directly linked to the electron beams. Our attention was devoted to estimate the conversion efficiency from electron kinetic energy to the em energy, and the growth rate of the several processes which can be identified. We studied the emission angles of the 2ωpradiation and compared them with the theoretical predictions of Willes et. al. (1995). We also show the role played by some numerical parameters i.e. the size and shape of the simulation box. This work is the first step to prepare laser-plasma experiments. V. L. Ginzburg, V. V. Zhelezniakov On the Possible Mechanisms of Sporadic Solar Radio Emission (Radiation in an Isotropic Plasma) Soviet Astronomy, Vol. 2, p.653 (1958) J. O. Thurgood and D. Tsiklauri Self-consistent particle-in-cell simulations of funda- mental and harmonic plasma radio emission mechanisms. Astronomy & Astrophysics 584, A83 (2015). A. Willes, P
7. Planetary radio emissions from low magnetic latitudes - Observations and theories
Jones, Dyfrig
Recent observations of planetary radiations from low magnetic latitudes are reviewed. At Earth a major source of nonthermal continuum is Terrestrial Myriametric Radiation (TMR) from the equatorial plasmapause and from the magnetopause. The theories proposed for the production of TMR are listed and their predictions are compared with satellite observations. The application of the theories to Jovian Kilometric Radiation (KOM), the radio emission at Jupiter which has been suggested to be the analogue of TMR, is reviewed. The implications of the TMR and KOM results for radiations observed at Saturn and Uranus are briefly considered.
8. Correlation of pulsar radio emission spectrum with peculiarities of particle acceleration in a polar gap
SciTech Connect
Kontorovich, V. M. Flanchik, A. B.
2013-01-15
The analytical expression for the frequency of radio emission intensity maximum in pulsars with free electron emission from the stellar surface has been found. Peculiarities of the electron acceleration in a polar gap are considered. The correlation between the high-frequency cutoff and low-frequency turnover in the radio emission spectrum of pulsars known from observations has been explained.
9. New data of radio emission from three AXPs
Teplykh, Daria
2011-07-01
Anomalous X-ray pulsars (AXPs) are a group of 9 X-ray sources showing periodical pulsation at periods in the 2-12 s range. The main problem is the source of energy, because their X-ray luminosities much higher than can be provided by the rotational kinetic-energy losses. Many attempts have been made to detect radio emission. The first detection of periodical pulsations from the AXP 1E 2259+586 have been made at the frequency 111 MHz by Malofeev (Malofeev et al., 2001, 2005). The second transient AXP XTE J1810-197 and the third AXP candidate 1E1547.0-5408 (Camilo et al., 2006, 2007) have been detected in the large frequency band 0.69-42 GHz. In this report we present new data for three AXPs 1E 2259+586, 4U 0142+61 and XTE J1810-197 at low frequencies. The observations were carried out on two sensitive transit radio telescopes in the range 42-112 MHz. The flux densities and mean pulse profiles, the estimation of the distances and integrated radio luminosities are presented. We used new digital receivers to obtain pulse profiles and dynamic spectra. Comparison with X-ray data shows large differences in the mean pulse widths and luminosities.
10. A Searchlight Beam Model of Jupiter's Decametric Radio Emissions
Imai, K.; Garcia, L.; Reyes, F.; Imai, M.; Thieman, J. R.; Ikuta, M.
2008-12-01
It has long been recognized that there is a marked long-term periodic variation in Jupiter's integrated radio occurrence probability. The period of the variation is on the order of a decade. Carr et al. [1970] showed that such variations are much more closely correlated with Jovicentric declination of the Earth (De). The range of the smoothed variation of De is from approximately +3.3 to -3.3 degrees. This De effect was extensively studied and confirmed by Garcia [1996]. It shows that the occurrence probability of the non-Io-A source is clearly controlled by De at 18, 20, and 22 MHz during the 1957-1994 apparitions. We propose a new model to explain the De effect. This new model shows that the beam structure of Jupiter radio emissions, which has been thought of like a hollow-cone, has a narrow beam like a searchlight, which can be explained by assuming that the three dimensional shape of the radio source expands along the line of the magnetic field. Various computer graphics illustrate the concept of this searchlight beam model.
11. Radio continuum and far-infrared emission of spiral galaxies: Implications of correlations
NASA Technical Reports Server (NTRS)
Rengarajan, T. N.; Iyengar, K. V. K.
1990-01-01
Researchers present a study extending the correlation seen between radio continuum and far-infrared emissions from spiral galaxies to a lower frequency of 408 MHz and also as a function of radio spectral index. The tight correlation seen between the two luminosities is then used to constrain several parameters governing the emissions such as the changes in star formation rate and mass function, frequency of supernovae that are parents of the interstellar electrons and factors governing synchrotron radio emission.
12. Roles Played by Electrostatic Waves in Producing Radio Emissions
NASA Technical Reports Server (NTRS)
Cairns, Iver H.
2000-01-01
Processes in which electromagnetic radiation is produced directly or indirectly via intermediate waves are reviewed. It is shown that strict theoretical constraints exist for electrons to produce nonthermal levels of radiation directly by the Cerenkov or cyclotron resonances. In contrast, indirect emission processes in which intermediary plasma waves are converted into radiation are often favored on general and specific grounds. Four classes of mechanisms involving the conversion of electrostatic waves into radiation are linear mode conversion, hybrid linear/nonlinear mechanisms, nonlinear wave-wave and wave-particle processes, and radiation from localized wave packets. These processes are reviewed theoretically and observational evidence summarized for their occurrence. Strong evidence exists that specific nonlinear wave processes and mode conversion can explain quantitatively phenomena involving type III solar radio bursts and ionospheric emissions. On the other hand, no convincing evidence exists that magnetospheric continuum radiation is produced by mode conversion instead of nonlinear wave processes. Further research on these processes is needed.
13. Is the Enigma of Pulsar Radio Emission Solved?
Gil, Janusz A.; Melikidze, George I.
2011-08-01
An intriguing paper has recently been published claiming that the long-sought Rosetta Stone needed to decipher the nature of pulsar radio emission has been finally identified as the bifurcated features in averaged pulsar profiles. The authors argued that highly symmetric bifurcated features observed in PSR J1012+5307 and other pulsars are produced by a split-fan beams of extraordinary-mode curvature radiation emitted by thin streams of sources conducted by a very narrow bundles of magnetic field lines. We examined the arguments leading to such a profound conclusion and found at least one fatal flaw. Using an elementary pulsar physics we showed that there is not enough energy to power the bifurcated feature in J1012+5307 within a split-fan beams model. If the source streams are indeed so thin that their emission can reveal the signatures of elementary radiation mechanism, then the energy deficit reaches several orders of magnitude.
14. Chromospheric Evaporation and Decimetric Radio Emission in Solar Flares
NASA Technical Reports Server (NTRS)
Aschwanden, Markus J.; Benz, Arnold O.
1995-01-01
We have discovered decimetric signatures of the chromospheric evaporation process. Evidence for the radio detection of chromospheric evaporation is based on the radio-inferred values of (1) the electron density, (2) the propagation speed, and (3) the timing, which are found to be in good agreement with statistical values inferred from the blueshifted Ca xix soft X-ray line. The physical basis of our model is that free-free absorption of plasma emission is strongly modified by the steep density gradient and the large temperature increase in the upflowing flare plasma. The steplike density increase at the chromospheric evaporation front causes a local discontinuity in the plasma frequency, manifested as almost infinite drift rate in decimetric type III bursts. The large temperature increase of the upflowing plasma considerably reduces the local free-free opacity (due to the T-(exp -3/2) dependence) and thus enhances the brightness of radio bursts emitted at the local plasma frequency near the chromospheric evaporation front, while a high-frequency cutoff is expected in the high-density regions behind the front, which can be used to infer the velocity of the upflowing plasma. From model calculations we find strong evidence that decimetric bursts with a slowly drifting high-frequency cutoff are produced by fundamental plasma emission, contrary to the widespread belief that decimetric bursts are preferentially emitted at the harmonic plasma level. We analyzed 21 flare episodes from 1991-1993 for which broadband (100-3000 MHz) radio dynamic spectra from Phoenix, hard X-ray data from BATSE/CGRO, and soft X-ray data from GOES were available. We detected slowly drifting high-frequency cutoffs between 1.1 and 3.0 GHz, with drift rates of -41 +/- 32 MHz/s, extending over time intervals of 24 +/- 23 s. Developing a density model for type III-emitting flare loops based on the statistically observed drift rate of type III bursts by Alvarez & Haddock, we infer velocities of up to
15. Radio emission of sea surface at centimeter wavelengths and is fluctuations
NASA Technical Reports Server (NTRS)
Tseytlin, N. M.; Shutko, A. M.; Zhislin, G. M.
1981-01-01
The eigen thermal radio emission of the sea was examined as well as the agitated surface of the sea when the reflection (scattering) is similar in nature to diffused scattering. The contribution of this emission to the total emission of the sea is practically constant in time, and the time fluctuations of the radio emissions of the sea are basically determined only by a change in the eigen emission of the sea, connected with the agitation.
16. Recent Observations of the Centimeter Radio Emission from the T Tauri System
Johnston, K. J.; Fey, A. L.; Gaume, R. A.; Claussen, M. J.; Hummel, C. A.
2004-08-01
Observations of the centimeter radio emission of T Tau in 2003 June are consistent with the radio source T Tau N being coincident with the optical star (T Tau A) and its radio emission due predominately to a stellar wind. The absolute position of radio source T Tau N shows acceleration in declination, which confirms it is gravitationally bound to T Tau B. The emission from the radio source T Tau S is associated with but may not be coincident with the pre-main-sequence M star (T Tau Bb) in the T Tau B binary. An orbital fit to the IR and radio data, adopting a distance of 140 pc, allows an estimate of the masses of 2.1 and 0.44 Msolar for the T Tau B binary system. The radio emission of T Tau S may be due to magnetic reconnections in the interbinary medium.
17. Tracking the CME-driven shock wave on 2012 March 5 and radio triangulation of associated radio emission
SciTech Connect
Magdalenić, J.; Marqué, C.; Mierla, M.; Zhukov, A. N.; Rodriguez, L.; Krupar, V.; Maksimović, M.; Cecconi, B.
2014-08-20
18. UNRAVELING THE NATURE OF COHERENT PULSAR RADIO EMISSION
SciTech Connect
Mitra, Dipanjan; Gil, Janusz; Melikidze, George I. E-mail: [email protected]
2009-05-10
Forty years have passed since the discovery of pulsars, yet the physical mechanism of their coherent radio emission is a mystery. Recent observational and theoretical studies strongly suggest that the radiation coming out from the pulsar magnetosphere mainly consists of extraordinary waves polarized perpendicular to the planes of pulsar dipolar magnetic field. However, the fundamental question of whether these waves are excited by maser or coherent curvature radiation, remains open. High-quality single-pulse polarimetry is required to distinguish between these two possible mechanisms. Here we showcase such decisive, strong single pulses from 10 pulsars observed with the Giant Meterwave Radio Telescope, showing extremely high linear polarization with the position angle following locally the mean position angle traverse. These pulses, which are relatively free from depolarization, must consist exclusively of a single polarization mode. We associate this mode with the extraordinary wave excited by the coherent curvature radiation. This crucial observational signature enables us to argue, for the first time, in favor of the coherent curvature emission mechanism, excluding the maser mechanism.
19. AURORAL RADIO EMISSION FROM STARS: THE CASE OF CU VIRGINIS
SciTech Connect
Trigilio, Corrado; Leto, Paolo; Umana, Grazia; Buemi, Carla S.; Leone, Francesco
2011-09-20
CU Virginis is a rapidly rotating Magnetic Chemically Peculiar star with at present unique characteristics as a radio emitter. The most intriguing one is the presence of intense, 100% circularly polarized radiation ascribed to a cyclotron maser. Each time the star rotates, this highly beamed emission points two times toward the Earth, like a pulsar. We observed CU Vir in 2010 April with the Expanded Very Large Array in two bands centered at 1450 and 1850 MHz. We covered nearly the whole rotational period, confirming the presence of the two pulses at a flux density up to 20 mJy. Dynamical spectra, obtained with unprecedented spectral and temporal sensitivity, allow us to clearly see the different time delays as a function of frequency. We interpret this behavior as a propagation effect of the radiation inside the stellar magnetosphere. The emerging scenario suggests interesting similarities with the auroral radio emission from planets, in particular with the Auroral Kilometric Radiation from Earth, which originates at few terrestrial radii above the magnetic poles and was only recently discovered to be highly beamed. We conclude that the magnetospheres of CU Vir, Earth, and other planets, maybe also exoplanets, could have similar geometrical and physical characteristics in the regions where the cyclotron maser is generated. In addition, the pulses are perfect 'markers' of the rotation period. This has given us for the first time the possibility to measure with extraordinary accuracy the spin-down of a star on or near the main sequence.
20. Sharing Planetary Radio Emission Dataset in the Virtual Observatory
Cecconi, B.; Hess, S.; Le Sidaner, P.; Coffre, A.; Thetas, E.; andre, N.
2013-12-01
In the double frame of the preparation of the ESA-led JUICE mission and the development of a planetary sciences virtual observatory (VO), we are proposing a new set of tools directed to data providers as well as users, in order to ease data sharing and discovery. We will focus on ground based planetary radio observations (thus mainly Jupiter radio emissions), trying for instance to enhance the temporal coverage of jovian decametric emission. The data service we will be using is EPN-TAP, a planetary science data access protocol developed by Europlanet/IDIS (Integrated and Distributed Information Service). This protocol is derived from IVOA (International Virtual Observatory Alliance) standards. The Jupiter Routine Observations from the Nançay Decameter Array are already shared on the planetary science VO using this protocol. We will first introduce the VO tools and concepts of interest for the planetary radioastronomy community. We will then present the various data formats now used for such data services, as well as their associated metadata. We will finally show various prototypical tools that make use of this shared datasets.
1. In situ observations of medium frequency auroral radio emissions
Broughton, M.; Labelle, J. W.; Pfaff, R. F.; Parrot, M.; Yan, X.; Burchill, J. K.
2013-12-01
The auroral ionosphere is a region rich with plasma waves that can be studied both in space and on the ground. These waves may mediate energy exchange between particle populations and provide information about the local plasma properties and boundaries. Auroral medium frequency (MF) burst is an impulsive radio emission observed at ground-level from 1.3-4.5 MHz that is associated with local substorm onset. There have been two recent reports of impulsive, broadband, MF waves at high latitudes. Burchill and Pfaff [2005] reported observations from the FAST satellite of impulsive, broadband, MF and low frequency (LF) radio waves. Using data from the DEMETER satellite, Parrot et al. [2009] surveyed MF waves caused by lightning. This study did show a high-latitude population of MF waves. We investigate whether the waves observed by these two satellites are related to auroral MF burst. Using FAST satellite burst mode electric field data from high-latitude (> 60 degrees magnetic), low-altitude (< 1000 km) intervals of moderate to large geomagnetic activity (Kp > 3) from 1996-2002, we have found forty-four examples of impulsive MF waves, all of which are associated with impulsive LF waves. Although MF burst and the waves observed by FAST have similar spectral signatures, they have different magnetic local time dependencies, which suggests that they may be unrelated. A study of MF waves observed at high latitude by DEMETER is ongoing. In situ observations of MF burst could provide crucial information about this heretofore unexplained natural radio emission.
2. Polarized radio emission from extensive air showers measured with LOFAR
SciTech Connect
Schellart, P.; Buitink, S.; Corstanje, A.; Enriquez, J.E.; Falcke, H.; Hörandel, J.R.; Krause, M.; Nelles, A.; Rachen, J.P.; Veen, S. ter; Thoudam, S.
2014-10-01
We present LOFAR measurements of radio emission from extensive air showers. We find that this emission is strongly polarized, with a median degree of polarization of nearly 99%, and that the angle between the polarization direction of the electric field and the Lorentz force acting on the particles, depends on the observer location in the shower plane. This can be understood as a superposition of the radially polarized charge-excess emission mechanism, first proposed by Askaryan and the geomagnetic emission mechanism proposed by Kahn and Lerche. We calculate the relative strengths of both contributions, as quantified by the charge-excess fraction, for 163 individual air showers. We find that the measured charge-excess fraction is higher for air showers arriving from closer to the zenith. Furthermore, the measured charge-excess fraction also increases with increasing observer distance from the air shower symmetry axis. The measured values range from (3.3± 1.0)% for very inclined air showers at 25 m to (20.3± 1.3)% for almost vertical showers at 225 m. Both dependencies are in qualitative agreement with theoretical predictions.
3. Rotational modulation of Saturn's radio emissions after equinox
Ye, S.-Y.; Fischer, G.; Kurth, W. S.; Menietti, J. D.; Gurnett, D. A.
2016-12-01
Saturn kilometric radiation (SKR), narrowband emission, and auroral hiss are periodically modulated due to Saturn's rotation, and the periods were found to vary with time. We analyze Cassini observations of Saturn's radio emissions with the main focus on the four years 2012-2015. It is shown that the rotation rates of SKR north and south were different since mid-2012 with SKR north being faster until autumn 2013, followed by a 1 year interval of similar north and south rotation rates and phases, before the northern SKR component finally became slower than the southern SKR in late 2014. The dual rotation rates of 5 kHz narrowband emissions reappeared for slightly longer than 1 year after a long break since equinox. Auroral hiss provides an unambiguous way of tracking the rotation signals from each hemisphere because the whistler mode waves cannot cross the equator. Rotation rates of auroral hiss and narrowband emissions are consistent with each other and those of SKR when they are observed at high latitudes in early 2013. The phase difference between SKR and auroral hiss and the intensity of auroral hiss are local time dependent.
4. Natural radio emission of Jupiter as interferences for radar investigations of the icy satellites of Jupiter
Cecconi, B.; Hess, S.; Herique, A.; Santos-Costa, D.; Santovito, M.; Zarka, P. M.; Alberti, G.; Blankenship, D. D.; Bougeret, J. H.; Bruzzone, L.; Kofman, W. W.
2010-12-01
Hervet, O.; Boisson, C.; Sol, H.
2015-06-01
Ap Lib is one of the rare low-synchrotron-peaked blazars detected so far at TeV energies. This type of source is not properly modelled by standard one-zone leptonic synchrotron self-Compton (SSC) emission scenarios. The aim of this paper is to study the relevance of additional components that should naturally occur in an SSC scenario for a better understanding of the emission mechanisms, especially at very high energies (VHE). We use simultaneous data from a multi-wavelength campaign of the Planck, Swift-UVOT, and Swift-XRT telescopes carried out in February 2010, as well as quasi-simultaneous data of WISE, Fermi, and HESS taken in 2010. The multi-lambda emission of Ap Lib is modelled by a blob-in-jet SSC scenario including the contribution of the base of the VLBI-extended jet, the radiative blob-jet interaction, the accretion disk, and its associated external photon field. We show that signatures of a strong parsec-scale jet and of an accretion disk emission are present in the spectral energy distribution. We can link the observational VLBI jet features from MOJAVE to parameters expected for a VHE-emitting blob accelerated near the jet base. The VHE emission appears to be dominated by the inverse-Compton effect of the blob relativistic electrons interacting with the jet synchrotron radiation. In this scenario, Ap Lib appears as an intermediate source between BL Lac objects and flat-spectrum radio quasars. Ap Lib could be a bright representative of a specific class of blazars, in which the parsec-scale jet luminosity is no more negligible compared to the blob and contributes to the high-energy emission through inverse-Compton processes.
6. Two component model for X-ray emission of radio selected QSO's
NASA Technical Reports Server (NTRS)
Isobe, T.; Feigelson, E. D.; Singh, K. P.; Kembhavi, A.
1986-01-01
Using a large database of radio, optical, and x ray luminosities of AGNs with survival analysis, it was found that the x ray emission of the radio selected quasars has two components. One is related to the optical luminosity and the other is related to the radio luminosity.
7. The role of solar wind reconnection in driving the Neptune radio emission
NASA Technical Reports Server (NTRS)
Desch, M. D.; Farrell, W. M.; Kaiser, M. L.; Lepping, R. P.; Steinberg, J. T.; Villanueva, L. A.
1991-01-01
The only remote diagnostic of conditions within the outer planets' magnetospheres is the highly variable flux of low-frequency radio waves. As at the other radio planets, Neptune radio emission also manifests, on a time scale of days, major intensity fluctuations that are indicative of a solar wind energy-coupling process of some kind. It is found that the merging of interplanetary magnetic field lines with Neptune's magnetosphere is the best predictor of emitted radio energy. By contrast, viscouslike energy coupling processes, such as might be caused by solar wind density or bulk speed fluctuations, are apparently ineffective in driving the radio emission.
8. Local Time Dependence of Jovian Radio Emissions Observed by Galileo
NASA Technical Reports Server (NTRS)
Menietti, J. D.; Gurnett, D. A.; Kurth, W. S.; Groene, J. B.
1999-01-01
Galileo has been in orbit around Jupiter since December 1995. All the orbits are equatorial and elliptical, with apogees between 60 R(sub J) - 142 R(sub J) and perigees from 8 - 12 R(sub J). Since orbit injection, the plasma wave instrument (PWS) has been collecting data over specific intervals of each of the orbits at all local times and a range of different radial distances. We present the results of a survey of the data for the frequency range 300 kHz to 5.6 MHz, which includes the hectometric (HOM) and low-frequency decametric (DAM) emissions. The results indicate that both the HOM and DAM emission are more intense and occur more frequently in the midnight sector of Jupiter. This is in analogy to Earth and consistent with a magnetic substorm source for a portion of the radio emissions in this frequency range. Another peak in the power levels is observed on the Jovian dayside in the local time range 11 hrs < LT < 12 hrs. This peak does not have a terrestrial counterpart. We speculate that this dayside peak may be a result of sampling near perigee, but we cannot rule out the possibility that this is not the case.
9. Analysis of Jovian decametric data: Study of radio emission mechanisms
NASA Technical Reports Server (NTRS)
Staelin, D. H.
1986-01-01
Catalogues of approx. 200 decametric arcs and approx. 200 gaps between arcs were studied, in an effort to reconcile the data with predictions for the model wherein reflections of Io-induced currents each emit in a conical pattern and yield a distinct radio arc. The most recent interpretations of this data suggest that these Io-produced Alfven waves persist for at least one or two passages of Io, and that the emission cone half angles are approx. 40 to 90 deg., varying from arc to arc. Below 1.2 MHz it was discovered that Jupiter emits radiation strongly modulated in frequency with periods of approx. 200 kHz; this quasi-sinusoidal emission (MSA) can shift more than 180 deg. in phase over periods of 6 seconds, although these shifts are usually much smaller. MSA is not strongly correlated with the longitudes of Io or Jupiter, and typically occurs in patches covering approx. 500 kHz or more for periods of a few minutes. Furthermore, this modulation sometimes resembles a train of impulses in frequency with exponential decays toward high frequencies. Comparison of these results with the previous studies of V-shaped S-bursts is suggestive of an emission mechanism.
10. Analysis of Jovian decametric data: Study of radio emission mechanisms
NASA Technical Reports Server (NTRS)
Staelin, D. H.
1986-01-01
Catalogues of approx. 200 decametric arcs and approx. 200 gaps between arcs were studied, in an effort to reconcile the data with predictions for the model wherein reflections of Io-induced currents each emit in a conical pattern and yield a distinct radio arc. The most recent interpretations of this data suggest that these Io-produced Alfven waves persist for at least one or two passages of Io, and that the emission cone half angles are approx. 40 to 90 deg., varying from arc to arc. Below 1.2 MHz it was discovered that Jupiter emits radiation strongly modulated in frequency with periods of approx. 200 kHz; this quasi-sinusoidal emission (MSA) can shift more than 180 deg. in phase over periods of 6 seconds, although these shifts are usually much smaller. MSA is not strongly correlated with the longitudes of Io or Jupiter, and typically occurs in patches covering approx. 500 kHz or more for periods of a few minutes. Furthermore, this modulation sometimes resembles a train of impulses in frequency with exponential decays toward high frequencies. Comparison of these results with the previous studies of V-shaped S-bursts is suggestive of an emission mechanism.
11. On the Variability of Radio Emission from MWC 349
Parihar, Prachi; Bartlett, C.; Pomerantz, B.; Strelnitski, V.
2013-01-01
We analyze the results of 15-year monitoring of millimeter radio emission from MWC 349 in hydrogen recombination α-lines and in continuum made on the 12-m and 10-m radio telescopes of Arizona Radio Observatory (ARO). Both the masing lines and the continuum show large intensity variations, up to a factor of a few, at various time scales, from days to years. Other line parameters vary more moderately. In the best studied double-peaked H30α line, both the width of the peaks and their radial velocities (relative to the systemic velocity) vary within ±10%.The narrowness of the peaks and the rate of their intensity variations indicate that the H30α maser is essentially unsaturated. The observed single case of short-time scale correlated variability of H30α and the optical Hα line (the latter monitored with the Maria Mitchell Obs.’s 24-inch CCD telescope) confirms this conclusion. The changes of the “red” (R) and “blue” (B) peaks correlate but to varying extent, which indicates the presence of both a variable central source of excitation and the independently varying local conditions in the portions of the circumstellar disk where the B and R masers are assumed to arise. The variability pattern and the computer calculations of hydrogen level populations under the putative conditions in the disk allow us to estimate the unsaturated gain of the maser as |τ| ≈ 3±1. The observed anti-correlation of the B and R radial velocities for H30α and H35α lines confirms a common variable central source of excitation and the location of the masers at opposite sides of a (quasi)-Keplerian disk. We acknowledge with gratitude the TAC and the technical staff of ARO for the allocated time and help with the observations. This project was supported by NSF/REU grant AST-0851892 and the Nantucket Maria Mitchell Association.
12. Estimation of emission cone wall thickness of Jupiter's decametric radio emission using stereoscopic STEREO/WAVES observations
Panchenko, M.; Rucker, H. O.
2016-11-01
Aims: Stereoscopic observations by the WAVES instrument onboard two STEREO spacecraft have been used with the aim of estimating wall thickness of an emission cone of Jovian decametric radio emission (DAM). Methods: Stereoscopic observations provided by STEREO-A and -B facilitate unambiguous recognition of the Jovian DAM in observed dynamic spectra as well as identification of its components (Io DAM or non-Io DAM). The dynamic spectra of radio emissions recorded by STEREO/WAVES have been analyzed using the method of cross-correlation of the radio dynamic spectra. Results: Altogether, 139 radio events, in particular 91 Io- and 48 non-Io-related radio events were observed. The averaged width of the emission cone wall for Io-DAM as well as for non-Io DAM is about 1.1° ± 0.2°. These results are in agreement with previous findings.
13. Herringbone bursts associated with type II solar radio emission
NASA Technical Reports Server (NTRS)
Cairns, I. H.; Robinson, R. D.
1987-01-01
Detailed observations of the herringbone (HB) fine structure on type II solar radio bursts are presented. Data from the Culgoora radiospectrograph, radiometer and radioheliograph are analyzed. The characteristic spectral profiles, frequency drift rates and exciter velocities, fluxes, source sizes, brightness temperatures, and polarizations of individual HB bursts are determined. Correlations between individual bursts within the characteristic groups of bursts and the properties of the associated type II bursts are examined. These data are compatible with HB bursts being radiation at multiples of the plasma frequency generated by electron streams accelerated by the type II shock. HB bursts are physically distinct phenomena from type II and type III bursts, differing significantly in emission processes and/or source conditions; this conclusion indicates that many of the presently available theoretical ideas for HB bursts are incorrect.
14. The magnetoionic modes and propagation properties of auroral radio emissions
NASA Technical Reports Server (NTRS)
Calvert, Wynne; Hashimoto, Kozo
1990-01-01
The nature of the magnetoionic wave modes which accompany the aurora is clarified here by a detailed analysis, using multiple techniques, of DE 1 auroral radio observations. All four of the possible magnetoionic wave modes are found to occur, apparently emitted from two different source regions on the same auroral field line. AKR originates primarily in the X mode near the electron cyclotron frequency, and is frequently also accompanied by a weaker O-mode component from the same location. The next most prominent auroral emission is the W-mode auroral hiss originating from altitudes always well below the DE 1 satellite at frequencies below the local cyclotron frequency. The previously reported Z-mode auroral radiation was also detected, but from sources also below the satellite at the poleward edge of the cavity, and not from the expected AKR source at the cyclotron frequency.
15. Solar wind control of Jupiter's decametric radio emission
NASA Technical Reports Server (NTRS)
Barrow, C. H.; Genova, F.; Desch, M. D.
1986-01-01
Observations of the solar wind close to Jupiter are compared with the decametric radio emission (DAM), using data recorded by Voyager 1 and Voyager 2 during 1979. The Non-Io DAM, recorded by both spacecraft and combined using the superposed epoch technique, is found to correlate with the solar wind density and velocity, as well as with the interplanetary magnetic field (IMF) magnitude. In agreement with earlier work using ground-based observations, there are indications that the Non-Io DAM is somehow associated with magnetic sector structure although the precise details of the relationship are still not known and it is not clear if this is a fundamental effect or some secondary effect of intercorrelation.
16. Radio emission signature of Saturn immersions in Jupiter's magnetic tail
NASA Technical Reports Server (NTRS)
Desch, M. D.
1983-01-01
During the interval from about May through August 1981, when Voyager 2 was inbound to Saturn, the Planetary Radio Astronomy instrument measured repeated, dramatic decreases in the intensity of the Saturn Kilometric Radiation (SKR). The emission dropouts averaged two orders of magnitude below mean energy levels and varied from about 1 to 10 Saturn rotations in duration. Comparison with pre-Saturn encounter Voyager 1 observations (June to November, 1980) shows that the SKR dropouts were unique to the Voyager 2 observing interval, consistent with the closer proximity of Saturn to Jupiter's distant magnetotail in 1981. Further, the dropouts occurred on the average at times when Voyager 2 is known to have been within or near Jupiter's magnetic tail.
17. The relationship of storm severity to directionally resolved radio emissions
NASA Technical Reports Server (NTRS)
Johnson, R. O.; Bushman, M. L.; Sherrill, W. M.
1980-01-01
Directionally resolved atmospheric radio frequency emission data were acquired from thunderstorms occurring in the central and southwestern United States. In addition, RF sferic tracking data were obtained from hurricanes and tropical depressions occurring in the Gulf of Mexico. The data were acquired using a crossed baseline phase interferometer operating at a frequency of 2.001 MHz. The received atmospherics were tested for phase linearity across the array, and azimuth/elevation angles of arrival were computed in real time. A histogram analysis of sferic burst count versus azimuth provided lines of bearing to centers of intense electrical activity. Analysis indicates a consistent capability of the phase linear direction finder to detect severe meteorological activity to distances of 2000 km from the receiving site. The technique evidences the ability to discriminate severe storms from nonsevere storms coexistent in large regional scale thunderstorm activity.
18. Analysis of Jovian decametric data: Study of radio emission mechanisms
NASA Technical Reports Server (NTRS)
Staelin, D. H.; Arias, T. A.
1985-01-01
Data gathered by the Voyager 1 and Voyager 2 Planetary Radio Astronomy Experiments (PRA) are unique in many ways including their frequency range, time resolution, polarization information and geometric characteristics. Studies of rapidly varying phenomena have thus far been hampered by paper display techniques which require large amounts of paper to exploit the full PRA time resolution. A software package capable of effectively displaying full 6s resolution PRA dynamic spectra on a high quality video monitor while compensating for the aforementioned variations was developed. The most striking phenomena revealed by the new display techniques is called Modulated Spectral Activity (MSA) because of its appearance in dynamic spectra as a series at least two parallel emission bands which drift back and forth in frequency on time scales of tens of seconds. In an attempt to locate and understand the MSA source mechanism, a catalogue has been compiled of the start and end of all known MSA events.
19. Solar wind control of Jupiter's decametric radio emission
NASA Technical Reports Server (NTRS)
Barrow, C. H.; Genova, F.; Desch, M. D.
1986-01-01
Observations of the solar wind close to Jupiter are compared with the decametric radio emission (DAM), using data recorded by Voyager 1 and Voyager 2 during 1979. The Non-Io DAM, recorded by both spacecraft and combined using the superposed epoch technique, is found to correlate with the solar wind density and velocity, as well as with the interplanetary magnetic field (IMF) magnitude. In agreement with earlier work using ground-based observations, there are indications that the Non-Io DAM is somehow associated with magnetic sector structure although the precise details of the relationship are still not known and it is not clear if this is a fundamental effect or some secondary effect of intercorrelation.
20. On the elliptical polarization of Jupiter's decametric radio emission
NASA Technical Reports Server (NTRS)
Melrose, D. B.; Dulk, G. A.
1991-01-01
The origin of the 100 percent elliptical polarization of Jupiter's decametric radio emission is investigated. The transfer of polarized radiation when coupling of the Stokes parameters is important is studied, and it is found, in agreement with earlier authors, that the density in and near the source region must be so low that the polarization remains fixed along the ray path. The polarization of the cyclotron maser radiation in these circumstances is determined, and it is found that the dispersion relation of the rarefied plasma composed of energetic, anisotropic electrons is like that in the vacuum. It is also found that the growth rate is sufficient to saturate the maser and account for the observed brightness temperature. Possible sources of plasma in and near the source region in Jupiter's inner, polar magnetosphere are considered.
1. Direct evidence for solar wind control of Jupiter's hectometer-wavelength radio emission
NASA Technical Reports Server (NTRS)
Desch, M. D.; Barrow, C. H.
1984-01-01
Observations of the solar wind close to Jupiter, by the Voyager 1 and Voyager 2 spacecraft in 1978 and 1979, are compared with the hectometer wavelength radio emission from the planet. A significant positive correlation is found between variations in the solar wind plasma density at Jupiter and the level of Jovian radio emission output. During the 173-day interval studied for the Voyager 2 data, the radio emission displayed a long term periodicity of about 13 days, identical to that shown by the solar wind density at Jupiter and consistent with the magnetic sector structure association already proposed for groundbased observations of the decameter wavelength emission.
2. LOFAR Search for Magnetospheric Radio Emissions from Exoplanet HD 80606b
Winterhalter, D.; Lazio, J.; Hartman, J.; Majid, W.; Farrell, W. M.; Splitter, L.; Kuiper, T.
2013-05-01
This paper describes observations (LOFAR Cycle 0) targeting magnetospheric radio emission from the exoplanet HD 80606b during a periastron passage. Its orbit is among the most eccentric known, meaning that it is naturally exposed to a wide range of stellar wind strengths, which should modulate its radio emission. Further, the high orbital eccentricity suggests that it is in a state of pseudo-synchronous rotation, leading to a relatively robust estimate of its characteristic emission frequency. It may be among the most promising planets for the direct detection of radio emission.
3. Far-UV Emission Properties of FR1 Radio Galaxies
Danforth, Charles W.; Stocke, John T.; France, Kevin; Begelman, Mitchell C.; Perlman, Eric
2016-11-01
The power mechanism and accretion geometry for low-power FR 1 radio galaxies are poorly understood in comparison to those for Seyfert galaxies and QSOs. In this paper, we use the diagnostic power of the Lyα recombination line observed using the Cosmic Origins Spectrograph (COS) aboard the Hubble Space Telescope (HST) to investigate the accretion flows in three well-known, nearby FR 1s: M87, NGC 4696, and Hydra A. The Lyα emission line’s luminosity, velocity structure, and the limited knowledge of its spatial extent provided by COS are used to assess conditions within a few parsecs of the supermassive black hole in these radio-mode active galactic nuclei. We observe strong Lyα emission in all three objects with total luminosity similar to that seen in BL Lacertae objects. M87 shows a complicated emission-line profile in Lyα, which varies spatially across the COS aperture and possibly temporally over several epochs of observation. In both NGC 4696 and M87, the Lyα luminosities ˜1040 erg s-1 are closely consistent with the observed strength of the ionizing continuum in Case B recombination theory and with the assumption of a near-unity covering factor. It is possible that the Lyα-emitting clouds are ionized largely by beamed radiation associated with the jets. Long-slit UV spectroscopy can be used to test this hypothesis. Hydra A and the several BL Lac objects studied in this and previous papers have Lyα luminosities larger than M87 but their extrapolated, nonthermal continua are so luminous that they overpredict the observed strength of Lyα, a clear indicator of relativistic beaming in our direction. Given their substantial space density (˜4 × 10-3 Mpc-3), the unbeamed Lyman continuum radiation of FR 1s may make a substantial minority contribution (˜10%) to the local UV background if all FR 1s are similar to M87 in ionizing flux level.
4. Simultaneous Radio and UV Observations of Brown Dwarfs: Looking for the UV Counterpart to Auroral Radio Emission
Pineda, J. Sebastian; Hallinan, Gregg; France, Kevin
2017-05-01
The strong rotationally pulsed radio emission observed from some ultracool dwarfs provides strong evidence for the existence of highly accelerated energetic electron beams powered by strong magnetospheric current systems pervading their magnetospheres. These beams precipitate into the cool atmosphere, depositing their energy, and generating a host of multi-wavelength auroral emissions, like Hα. We report on our simultaneous VLA and HST-COS observations of known radio brown dwarfs looking to observe the electronically excited emissions of molecular hydrogen in the far ultraviolet and their relation to known auroral radio emissions. Our monitoring observations of the radio ultracool dwarfs TVLM513-46546 and LSRJ1836+3259 show no strong indications of any FUV emission, despite significant rotational phase coverage over the course of the Hubble orbits. We discuss potential implications of these results for the strength of the auroral electron beams, atmospheric energy deposition and the possibility of significant atmospheric absorption. We use these results to motivate considerations for the ability of future missions like LUVOIR to detect brown dwarf UV auroral emissions.
5. Interstellar matter in early-type galaxies. III - Radio emission and star formation
NASA Technical Reports Server (NTRS)
Walsh, D. E. P.; Knapp, G. R.; Wrobel, J. M.; Kim, D.-W.
1989-01-01
The relationship between the IR and radio luminosity in early-type galaxies is examined using the correlation among spiral galaxies as a diagnostic of the presence of star formation. For ellipticals, the presence of long-wavelength IR emission enhances the probability that the galaxy is a radio source and is also correlated with the strength of that source. These findings are consistent with the idea that active radio nuclei are due to black holes being fueled by accretion of gas. The majority of S0s detected in both radio and far-IR have a similar ratio of IR to radio luminosity as has been found in spirals, and which is considered to be indicative of recent star formation. Sensitive radio limits for several galaxies reveal another substantial population of S0s with moderately strong IR emission unaccompanied by radio power.
6. On the Origin of Intense Radio Emission from the Brown Dwarfs
Zaitsev, V. V.; Stepanov, A. V.
2017-04-01
7. In Vivo Dendritic Cell Tracking Using Fluorescence Lifetime Imaging and Near-Infrared-Emissive Polymersomes
PubMed Central
Christian, Natalie A.; Benencia, Fabian; Milone, Michael C.; Li, Guizhi; Frail, Paul R.; Therien, Michael J.; Coukos, George; Hammer, Daniel A.
2009-01-01
Purpose: Noninvasive in vivo cell-tracking techniques are necessary to advance the field of cellular-based therapeutics as well as to elucidate mechanisms governing in vivo cell biology. Fluorescence is commonly used for in vitro and postmortem biomedical studies but has been limited by autofluorescence at the whole-animal level. Procedures: In this report, we demonstrate the ability of in vivo fluorescent lifetime imaging to remove autofluorescence and thereby enable in vivo dendritic cell tracking in naïve mice. Specifically, we track mature dendritic cells (DCs) labeled internally with near-infrared-emissive polymersomes (NIR-DCs). Results: We establish the ability to detect labeled cells in vivo and image NIR-DC trafficking after both intravenous and subcutaneous delivery. In addition, we demonstrate the longitudinal capacity of this method by characterizing NIR-DC migration kinetics in the popliteal lymph node. Conclusions: This work provides a tool to evaluate dendritic-cell-based immunotherapy and generates novel opportunities for in vivo fluorescence imaging. PMID:19194761
8. Offset, tilted dipole models of Uranian smooth high-frequency radio emission
NASA Technical Reports Server (NTRS)
Schweitzer, Andrea E.; Romig, Joseph H.; Evans, David R.; Sawyer, Constance B.; Warwick, James W.
1990-01-01
The smooth high-frequency (SHF) component of the radio emission detected during the Voyager 2 encounter with Uranus (January 1986) is studied. An offset tilted dipole (OTD) investigation of the SHF emission at L shells is carried out within the range of the bursty source locations. A viable high L shell model is presented. It is suggested that Miranda, which reaches a minimum L shell at L = 5, may be related to the timing of several types of radio emissions.
9. Simultaneous observations of periodic non-Io decametric radio emission by ground radio telescope URAN-2 and STEREO/WAVES
Panchenko, M.; Brazhenko, A. I.; Rucker, H. O.; Frantzusenko, A.; Shaposhnikov, V. E.; Konovalenko, A. A.
2013-09-01
Periodic bursts of the non-Io component of Jovian decametric radio emission (non-Io DAM) is observed as (1) series of arc-like radio bursts with negative frequency drift which reoccur with 1.5% longer period than the Jovian magnetosphere rotation rate, (2) series of bursts with positive frequency drift which reoccur with Jupiter's rotation period and (3) periodic non-arc like radio features [1, 2]. These bursts are typically detected during several Jupiter rotations in decametric frequency range from 4 MHz to 12 - 16 MHz between 300° and 60° of CML. We present simultaneous observations of the periodic non-Io controlled DAM performed by the WAVES radio experiment onboard the two STEREO spacecraft and the groundbased radio telescope URAN-2 (Poltava, Ukraine) operated in the decametric frequency range. URAN-2 with an effective area of about 30000 m2 consists of 512 broadband crossed dipoles and equipped with the high performance digital radio spectrometer with polarization measurement capability. During the observation campaign Sep., 2012 - Apr., 2013 URAN-2 recorded a large amount of Jovian DAM events with the high time-frequency resolution (4 kHz - 100 ms) in a frequency range 8-32 MHz. In the same time the two spatially separated STEREO spacecraft was able to observe DAM in the frequency range up to 16 MHz. The first analysis of the acquired stereoscopic observations is presented. In particular, we show one episode when the periodic non-arc DAM was recorded together with long lasting Jovian narrow band (NB) emissions. These NB emission was observed at the high frequency cutoff of DAM and can be interpreted as propagation of the decametric radiation in the Jovian ionosphere [3]. We discuss the possible relations between the observed NB events and the periodic non-Io controlled Jovian decametric radio emission.
10. Observation of HF radio emission bursts of magnetospheric origin at mid latitudes
Dudnik, O. V.
1999-01-01
Results of the observations of high frequency radio noises of magnetospheric origin at 150 MHz in 1993 are presented. The radio receiving channel for the registration of radio noises at mid latitudes and the method of data processing are described. Perturbations necessary for generation of radio emission are shown to be transported by irregularities of high-speed solar wind streams toward the Earth's magnetosphere. The possible mechanism of radio bursts generation by precipitating energetic electrons from the Earth's radiation belts during the magnetospheric storms is discussed.
11. Radio Emissions Precursors of Impulsive Phase of Solar Flares Recorded by CALLISTO-BR
Fernandes, Francisco; Cunha-Silva, Rafael; Galdino, Marcela; Sodré, Zuleika
2016-07-01
A solar flare consists in an eruptive process and involves a sudden release of energy generated by processes carried on from instabilities in the magnetic configuration at solar atmosphere, generating emissions at different wavelengths. Usually, the pre-flare phase presents an increasing of soft X-ray, ultraviolet and radio emissions. In this work, we present a survey of solar radio emission recorded in metric wavelengths (45 - 250 MHz) by CALLISTO-BR spectrograph, belong to the e-Callisto network, associated with pre-flare phase of solar X-rays flares. A sample of 281 radio emissions was analyzed, and 120 were identified as precursor emissions of X-rays flares. The main results of the statistics can be summarized as: (a) 55% of the precursor radio emissions start less than 60 minutes before the beginning of the associated X-ray flare and about 20% start less than 20 minutes before the X-ray emission; (b) 27% of flares with precursor emissions are classified as B class, 61% of C class, and less than 22% of M class. No precursors radio emissions were associated with X class flare; (c) about 42% of radio precursor emissions are of type III bursts and 33% have complex morphology, as drifting pulsating structures. Analysis of global emission trends recorded during the precursor phase of the C4.8 flare of February 15, 2011 (14:32-14:51 UT) is also presented. The occurrence of radio emission during the pre-impulsive phase of a solar flare suggests the presence of plasma turbulence in the active region, since during the impulsive phase, when the energy is released, occur the heating of the plasma and increasing of soft X-ray emission as identified in the event analyzed. The results are presented and discussed.
12. Mpc-scale diffuse radio emission in two massive cool-core clusters of galaxies
Sommer, Martin W.; Basu, Kaustuv; Intema, Huib; Pacaud, Florian; Bonafede, Annalisa; Babul, Arif; Bertoldi, Frank
2017-04-01
13. The connection between the 15 GHz radio and gamma-ray emission in blazars
Max-Moerbeck, W.; Richards, J. L.; Hovatta, T.; Pavlidou, V.; Pearson, T. J.; Readhead, A. C. S.; King, O. G.; Reeves, R.
2015-03-01
Since mid-2007 we have carried out a dedicated long-term monitoring programme at 15 GHz using the Owens Valley Radio Observatory 40 meter telescope (OVRO 40m). One of the main goals of this programme is to study the relation between the radio and gamma-ray emission in blazars and to use it as a tool to locate the site of high energy emission. Using this large sample of objects we are able to characterize the radio variability, and study the significance of correlations between the radio and gamma-ray bands. We find that the radio variability of many sources can be described using a simple power law power spectral density, and that when taking into account the red-noise characteristics of the light curves, cases with significant correlation are rare. We note that while significant correlations are found in few individual objects, radio variations are most often delayed with respect to the gamma-ray variations. This suggests that the gamma-ray emission originates upstream of the radio emission. Because strong flares in most known gamma-ray-loud blazars are infrequent, longer light curves are required to settle the issue of the strength of radio-gamma cross-correlations and establish confidently possible delays between the two. For this reason continuous multiwavelength monitoring over a longer time period is essential for statistical tests of jet emission models.
ERIC Educational Resources Information Center
Downes, Ann
1986-01-01
ERIC Educational Resources Information Center
Downes, Ann
1986-01-01
16. EMISSION PATTERNS OF SOLAR TYPE III RADIO BURSTS: STEREOSCOPIC OBSERVATIONS
SciTech Connect
Thejappa, G.; Bergamo, M.; MacDowall, R. J. E-mail: [email protected]
2012-02-01
Simultaneous observations of solar type III radio bursts obtained by the STEREO A, B, and WIND spacecraft at low frequencies from different vantage points in the ecliptic plane are used to determine their directivity. The heliolongitudes of the sources of these bursts, estimated at different frequencies by assuming that they are located on the Parker spiral magnetic field lines emerging from the associated active regions into the spherically symmetric solar atmosphere, and the heliolongitudes of the spacecraft are used to estimate the viewing angle, which is the angle between the direction of the magnetic field at the source and the line connecting the source to the spacecraft. The normalized peak intensities at each spacecraft R{sub j} = I{sub j} /{Sigma}I{sub j} (the subscript j corresponds to the spacecraft STEREO A, B, and WIND), which are defined as the directivity factors are determined using the time profiles of the type III bursts. It is shown that the distribution of the viewing angles divides the type III bursts into: (1) bursts emitting into a very narrow cone centered around the tangent to the magnetic field with angular width of {approx}2 Degree-Sign and (2) bursts emitting into a wider cone with angular width spanning from {approx} - 100 Degree-Sign to {approx}100 Degree-Sign . The plots of the directivity factors versus the viewing angles of the sources from all three spacecraft indicate that the type III emissions are very intense along the tangent to the spiral magnetic field lines at the source, and steadily fall as the viewing angles increase to higher values. The comparison of these emission patterns with the computed distributions of the ray trajectories indicate that the intense bursts visible in a narrow range of angles around the magnetic field directions probably are emitted in the fundamental mode, whereas the relatively weaker bursts visible to a wide range of angles are probably emitted in the harmonic mode.
17. Emission Patterns of Solar Type III Radio Bursts: Stereoscopic Observations
NASA Technical Reports Server (NTRS)
Thejappa, G.; MacDowall, R.; Bergamo, M.
2012-01-01
Simultaneous observations of solar type III radio bursts obtained by the STEREO A, B, and WIND spacecraft at low frequencies from different vantage points in the ecliptic plane are used to determine their directivity. The heliolongitudes of the sources of these bursts, estimated at different frequencies by assuming that they are located on the Parker spiral magnetic field lines emerging from the associated active regions into the spherically symmetric solar atmosphere, and the heliolongitudes of the spacecraft are used to estimate the viewing angle, which is the angle between the direction of the magnetic field at the source and the line connecting the source to the spacecraft. The normalized peak intensities at each spacecraft Rj = Ij /[Sigma]Ij (the subscript j corresponds to the spacecraft STEREO A, B, and WIND), which are defined as the directivity factors are determined using the time profiles of the type III bursts. It is shown that the distribution of the viewing angles divides the type III bursts into: (1) bursts emitting into a very narrow cone centered around the tangent to the magnetic field with angular width of approximately 2 deg and (2) bursts emitting into a wider cone with angular width spanning from [approx] -100 deg to approximately 100 deg. The plots of the directivity factors versus the viewing angles of the sources from all three spacecraft indicate that the type III emissions are very intense along the tangent to the spiral magnetic field lines at the source, and steadily fall as the viewing angles increase to higher values. The comparison of these emission patterns with the computed distributions of the ray trajectories indicate that the intense bursts visible in a narrow range of angles around the magnetic field directions probably are emitted in the fundamental mode, whereas the relatively weaker bursts visible to a wide range of angles are probably emitted in the harmonic mode.
18. CONSTRAINING THE VELA PULSAR'S RADIO EMISSION REGION USING NYQUIST-LIMITED SCINTILLATION STATISTICS
SciTech Connect
Johnson, M. D.; Gwinn, C. R.; Demorest, P. E-mail: [email protected]
2012-10-10
Using a novel technique, we achieve {approx}100 picoarcsec resolution and set an upper bound of less than 4 km for the characteristic size of the Vela pulsar's emission region. Specifically, we analyze flux-density statistics of the Vela pulsar at 760 MHz. Because the pulsar exhibits strong diffractive scintillation, these statistics convey information about the spatial extent of the radio emission region. We measure both a characteristic size of the emission region and the emission sizes for individual pulses. Our results imply that the radio emission altitude for the Vela pulsar at this frequency is less than 340 km.
19. Upper limits on gravitational wave emission from 78 radio pulsars
Abbott, B.; Abbott, R.; Adhikari, R.; Agresti, J.; Ajith, P.; Allen, B.; Amin, R.; Anderson, S. B.; Anderson, W. G.; Arain, M.; Araya, M.; Armandula, H.; Ashley, M.; Aston, S.; Aufmuth, P.; Aulbert, C.; Babak, S.; Ballmer, S.; Bantilan, H.; Barish, B. C.; Barker, C.; Barker, D.; Barr, B.; Barriga, P.; Barton, M. A.; Bayer, K.; Belczynski, K.; Betzwieser, J.; Beyersdorf, P. T.; Bhawal, B.; Bilenko, I. A.; Billingsley, G.; Biswas, R.; Black, E.; Blackburn, K.; Blackburn, L.; Blair, D.; Bland, B.; Bogenstahl, J.; Bogue, L.; Bork, R.; Boschi, V.; Bose, S.; Brady, P. R.; Braginsky, V. B.; Brau, J. E.; Brinkmann, M.; Brooks, A.; Brown, D. A.; Bullington, A.; Bunkowski, A.; Buonanno, A.; Burmeister, O.; Busby, D.; Butler, W. E.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Camp, J. B.; Cannizzo, J.; Cannon, K.; Cantley, C. A.; Cao, J.; Cardenas, L.; Carter, K.; Casey, M. M.; Castaldi, G.; Cepeda, C.; Chalkey, E.; Charlton, P.; Chatterji, S.; Chelkowski, S.; Chen, Y.; Chiadini, F.; Chin, D.; Chin, E.; Chow, J.; Christensen, N.; Clark, J.; Cochrane, P.; Cokelaer, T.; Colacino, C. N.; Coldwell, R.; Conte, R.; Cook, D.; Corbitt, T.; Coward, D.; Coyne, D.; Creighton, J. D. E.; Creighton, T. D.; Croce, R. P.; Crooks, D. R. M.; Cruise, A. M.; Cumming, A.; Dalrymple, J.; D'Ambrosio, E.; Danzmann, K.; Davies, G.; Debra, D.; Degallaix, J.; Degree, M.; Demma, T.; Dergachev, V.; Desai, S.; Desalvo, R.; Dhurandhar, S.; Díaz, M.; Dickson, J.; di Credico, A.; Diederichs, G.; Dietz, A.; Doomes, E. E.; Drever, R. W. P.; Dumas, J.-C.; Dupuis, R. J.; Dwyer, J. G.; Ehrens, P.; Espinoza, E.; Etzel, T.; Evans, M.; Evans, T.; Fairhurst, S.; Fan, Y.; Fazi, D.; Fejer, M. M.; Finn, L. S.; Fiumara, V.; Fotopoulos, N.; Franzen, A.; Franzen, K. Y.; Freise, A.; Frey, R.; Fricke, T.; Fritschel, P.; Frolov, V. V.; Fyffe, M.; Galdi, V.; Ganezer, K. S.; Garofoli, J.; Gholami, I.; Giaime, J. A.; Giampanis, S.; Giardina, K. D.; Goda, K.; Goetz, E.; Goggin, L.; González, G.; Gossler, S.; Grant, A.; Gras, S.; Gray, C.; Gray, M.; Greenhalgh, J.; Gretarsson, A. M.; Grosso, R.; Grote, H.; Grunewald, S.; Guenther, M.; Gustafson, R.; Hage, B.; Hammer, D.; Hanna, C.; Hanson, J.; Harms, J.; Harry, G.; Harstad, E.; Hayler, T.; Heefner, J.; Heng, I. S.; Heptonstall, A.; Heurs, M.; Hewitson, M.; Hild, S.; Hirose, E.; Hoak, D.; Hosken, D.; Hough, J.; Howell, E.; Hoyland, D.; Huttner, S. H.; Ingram, D.; Innerhofer, E.; Ito, M.; Itoh, Y.; Ivanov, A.; Jackrel, D.; Johnson, B.; Johnson, W. W.; Jones, D. I.; Jones, G.; Jones, R.; Ju, L.; Kalmus, P.; Kalogera, V.; Kasprzyk, D.; Katsavounidis, E.; Kawabe, K.; Kawamura, S.; Kawazoe, F.; Kells, W.; Keppel, D. G.; Khalili, F. Ya.; Kim, C.; King, P.; Kissel, J. S.; Klimenko, S.; Kokeyama, K.; Kondrashov, V.; Kopparapu, R. K.; Kozak, D.; Krishnan, B.; Kwee, P.; Lam, P. K.; Landry, M.; Lantz, B.; Lazzarini, A.; Lee, B.; Lei, M.; Leiner, J.; Leonhardt, V.; Leonor, I.; Libbrecht, K.; Lindquist, P.; Lockerbie, N. A.; Longo, M.; Lormand, M.; Lubiński, M.; Lück, H.; Machenschalk, B.; Macinnis, M.; Mageswaran, M.; Mailand, K.; Malec, M.; Mandic, V.; Marano, S.; Márka, S.; Markowitz, J.; Maros, E.; Martin, I.; Marx, J. N.; Mason, K.; Matone, L.; Matta, V.; Mavalvala, N.; McCarthy, R.; McClelland, D. E.; McGuire, S. C.; McHugh, M.; McKenzie, K.; McNabb, J. W. C.; McWilliams, S.; Meier, T.; Melissinos, A.; Mendell, G.; Mercer, R. A.; Meshkov, S.; Messaritaki, E.; Messenger, C. J.; Meyers, D.; Mikhailov, E.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Miyakawa, O.; Mohanty, S.; Moreno, G.; Mossavi, K.; Mowlowry, C.; Moylan, A.; Mudge, D.; Mueller, G.; Mukherjee, S.; Müller-Ebhardt, H.; Munch, J.; Murray, P.; Myers, E.; Myers, J.; Nash, T.; Newton, G.; Nishizawa, A.; Nocera, F.; Numata, K.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pan, Y.; Papa, M. A.; Parameshwaraiah, V.; Parameswariah, C.; Patel, P.; Pedraza, M.; Penn, S.; Pierro, V.; Pinto, I. M.; Pitkin, M.; Pletsch, H.; Plissi, M. V.; Postiglione, F.; Prix, R.; Quetschke, V.; Raab, F.; Rabeling, D.; Radkins, H.; Rahkola, R.; Rainer, N.; Rakhmanov, M.; Rawlins, K.; Ray-Majumder, S.; Re, V.; Regimbau, T.; Rehbein, H.; Reid, S.; Reitze, D. H.; Ribichini, L.; Riesen, R.; Riles, K.; Rivera, B.; Robertson, N. A.; Robinson, C.; Robinson, E. L.; Roddy, S.; Rodriguez, A.; Rogan, A. M.; Rollins, J.; Romano, J. D.; Romie, J.; Route, R.; Rowan, S.; Rüdiger, A.; Ruet, L.; Russell, P.; Ryan, K.; Sakata, S.; Samidi, M.; de La Jordana, L. Sancho; Sandberg, V.; Sanders, G. H.; Sannibale, V.; Saraf, S.; Sarin, P.; Sathyaprakash, B. S.; Sato, S.; Saulson, P. R.; Savage, R.; Savov, P.; Sazonov, A.; Schediwy, S.; Schilling, R.; Schnabel, R.; Schofield, R.; Schutz, B. F.; Schwinberg, P.; Scott, S. M.; Searle, A. C.; Sears, B.; Seifert, F.; Sellers, D.; Sengupta, A. S.; Shawhan, P.; Shoemaker, D. H.; Sibley, A.; Sidles, J. A.; Siemens, X.; Sigg, D.; Sinha, S.; Sintes, A. M.; Slagmolen, B. J. J.; Slutsky, J.; Smith, J. R.; Smith, M. R.; Somiya, K.; Strain, K. A.; Strom, D. M.; Stuver, A.; Summerscales, T. Z.; Sun, K.-X.; Sung, M.; Sutton, P. J.; Takahashi, H.; Tanner, D. B.; Tarallo, M.; Taylor, R.; Taylor, R.; Thacker, J.; Thorne, K. A.; Thorne, K. S.; Thüring, A.; Tokmakov, K. V.; Torres, C.; Torrie, C.; Traylor, G.; Trias, M.; Tyler, W.; Ugolini, D.; Ungarelli, C.; Urbanek, K.; Vahlbruch, H.; Vallisneri, M.; van den Broeck, C.; van Putten, M.; Varvella, M.; Vass, S.; Vecchio, A.; Veitch, J.; Veitch, P.; Villar, A.; Vorvick, C.; Vyachanin, S. P.; Waldman, S. J.; Wallace, L.; Ward, H.; Ward, R.; Watts, K.; Webber, D.; Weidner, A.; Weinert, M.; Weinstein, A.; Weiss, R.; Wen, S.; Wette, K.; Whelan, J. T.; Whitbeck, D. M.; Whitcomb, S. E.; Whiting, B. F.; Wiley, S.; Wilkinson, C.; Willems, P. A.; Williams, L.; Willke, B.; Wilmut, I.; Winkler, W.; Wipf, C. C.; Wise, S.; Wiseman, A. G.; Woan, G.; Woods, D.; Wooley, R.; Worden, J.; Wu, W.; Yakushin, I.; Yamamoto, H.; Yan, Z.; Yoshida, S.; Yunes, N.; Zanolin, M.; Zhang, J.; Zhang, L.; Zhao, C.; Zotov, N.; Zucker, M.; Zur Mühlen, H.; Zweizig, J.; Kramer, M.; Lyne, A. G.
2007-08-01
We present upper limits on the gravitational wave emission from 78 radio pulsars based on data from the third and fourth science runs of the LIGO and GEO 600 gravitational wave detectors. The data from both runs have been combined coherently to maximize sensitivity. For the first time, pulsars within binary (or multiple) systems have been included in the search by taking into account the signal modulation due to their orbits. Our upper limits are therefore the first measured for 56 of these pulsars. For the remaining 22, our results improve on previous upper limits by up to a factor of 10. For example, our tightest upper limit on the gravitational strain is 2.6×10-25 for PSR J1603-7202, and the equatorial ellipticity of PSR J2124 3358 is less than 10-6. Furthermore, our strain upper limit for the Crab pulsar is only 2.2 times greater than the fiducial spin-down limit.
20. Predicting radio emission from the newborn hot Jupiter V830 Tauri b and its host star
Vidotto, A. A.; Donati, J.-F.
2017-06-01
1. Variable low-frequency radio emission of the solar system and galactic objects
Konovalenko, Alexander; Kolyadin, Vladimir; Rucker, Helmut; Zakharenko, Vyacheslav; Zarka, Philippe; Griessmeier, Jean-M.; Denis, Loran; Melnik, Valentin; Litvinenko, Galina; Zaitsev, Valerij; Falkovich, Igor; Ulyanov, Oleg; Sidorchuk, Mikhail; Stepkin, Sergej; Stanislavskij, Alexander; Kalinichenko, Nikolaj; Boiko, Nastja; Vasiljiva, Iaroslavna; Mukha, Dmytro; Koval, Artem
2013-04-01
There are many physical processes and propagation effects for the producing the time variable radio emission just at the low frequencies (at the decameter wavelength). The study of this radio emission is the important part of the modern radio astronomy. Strong progress in the development of the radio telescopes, methods and instrumentation allowed to start the corresponding investigations at new quality and quantity levels. It related to the implementation of the world largest UTR-2 radio telescope (effective area is more than 100 000 sq.m) more high sensitive at frequencies less than 30 MHz. During last years many new observations were carried out with this radio telescope and many new effects have been detected for the Sun, planets, interplanetary medium, exoplanets as well as various kinds of the stars.
2. PREDICTION OF TYPE II SOLAR RADIO BURSTS BY THREE-DIMENSIONAL MHD CORONAL MASS EJECTION AND KINETIC RADIO EMISSION SIMULATIONS
SciTech Connect
Schmidt, J. M.; Cairns, Iver H.; Hillan, D. S.
2013-08-20
Type II solar radio bursts are the primary radio emissions generated by shocks and they are linked with impending space weather events at Earth. We simulate type II bursts by combining elaborate three-dimensional MHD simulations of realistic coronal mass ejections (CMEs) at the Sun with an analytic kinetic radiation theory developed recently. The modeling includes initialization with solar magnetic and active region fields reconstructed from magnetograms of the Sun, a flux rope of the initial CME dimensioned with STEREO spacecraft observations, and a solar wind driven with averaged empirical data. We demonstrate impressive accuracy in time, frequency, and intensity for the CME and type II burst observed on 2011 February 15. This implies real understanding of the physical processes involved regarding the radio emission excitation by shocks and supports the near-term development of a capability to predict and track these events for space weather prediction.
3. Coherent Cherenkov radio emission and problems of ultrahigh-energy cosmic ray and neutrino detection
Tsarev, V. A.
2006-08-01
This review is concerned with prospects for employment of coherent Cherenkov radio emission for detecting ultrahigh-energy cosmic rays and neutrinos. Reasons for interest in and problems of studying the ultrahigh-energy particles are summarized. A history of the development of a radio-wave method and its main merits are recalled. Current experiments and proposals based on this method are briefly discussed with emphasize on the most recent Lunar Orbital Radio Detector (LORD) proposal.
4. Search for 150 MHz radio emission from extrasolar planets in the TIFR GMRT Sky Survey
Sirothia, S. K.; Lecavelier des Etangs, A.; Gopal-Krishna; Kantharia, N. G.; Ishwar-Chandra, C. H.
2014-02-01
5. CO emission from radio quiet quasars - New detections support a thermal origin for the FIR emission
Alloin, D.; Barvainis, R.; Gordon, M. A.; Antonucci, R. R. J.
1992-11-01
We report detections of CO emission from the radio quiet quasars and luminous Seyfert 1 galaxies 0050+12, 0157+00, 0232-09, 0838+77, 1353+18, 1434+59, and 1613+65, and upper limits in five others. The observations show the same correlation between CO and FIR luminosity, and between 60-100 micron color temperature and the ratio L(FIR)/M(H2), as has previously been found for luminous IR galaxies. These results support thermal radiation from dust as the far-infrared source rather than synchrotron emission. Because we have observed with two different telescopes, and in two different transitions, we have been able to constrain source sizes in a few objects.
6. An anomalous component of Neptune radio emission - Implications for the auroral zone
NASA Technical Reports Server (NTRS)
Desch, M. D.; Farrell, W. M.; Kaiser, M. L.
1991-01-01
The Voyager planetary radio astronomy experiment detected a bursty, narrow-band radio emission originating in Neptune's magnetosphere. The time of occurrence of nearly all of the episodes of this bursty radio emission can be explained on the basis of a radio source located just above and to the east of the south magnetic offset tilted dipole (OTD) tip (Farrell et al., 1990). However, several episodes of bursty emission do not occur at the usual frequency and planetaray rotation phase for emissions of this type. The occurrences of these rarely seen anomalous episodes are shifted systematically in planetary longitude so as to be consistent with a source of emission to the southwest of the southern magnetic OTD pole. Owing to the proximity of these sources to the magnetic polar region, they are associated with an active auroral region. Therefore, at least from the standpoint of the radio emission, the picture that emerges is of an auroral zone with two emission hot spots approximately diametrically east and west of the south magnetic pole. The possibility of a complete radio-active auroral oval is discussed.
7. Luminescent dendritic cyclometalated iridium(III) polypyridine complexes: synthesis, emission behavior, and biological properties.
PubMed
Zhang, Kenneth Yin; Liu, Hua-Wei; Fong, Tommy Tsz-Him; Chen, Xian-Guang; Lo, Kenneth Kam-Wing
2010-06-21
Luminescent dendritic cyclometalated iridium(III) polypyridine complexes [{Ir(N--C)(2)}(n)(bpy-n)](PF(6))(n) (HN--C = 2-phenylpyridine, Hppy, n = 8 (ppy-8), 4 (ppy-4), 3 (ppy-3); HN--C = 2-phenylquinoline, Hpq, n = 8 (pq-8), 4 (pq-4), 3 (pq-3)) have been designed and synthesized. The properties of these dendrimers have been compared to those of their monomeric counterparts [Ir(N--C)(2)(bpy-1)](PF(6)) (HN--C = Hppy (ppy-1), Hpq (pq-1)). Cyclic voltammetric studies revealed that the iridium(IV/III) oxidation and bpy-based reduction occurred at about +1.24 to +1.29 V and -1.21 to -1.27 V versus SCE, respectively, for all the complexes. The molar absorptivity of the dendritic iridium(III) complexes is approximately proportional to the number of [Ir(N--C)(2)(N--N)] moieties in one complex molecule. However, the emission lifetimes and quantum yields are relatively independent of the number of [Ir(N--C)(2)(N--N)] units, suggesting negligible electronic communications between these units. Upon photoexcitation, the complexes displayed triplet metal-to-ligand charge-transfer ((3)MLCT) (dpi(Ir) --> pi*(bpy-n)) emission. The interaction of these complexes with plasmid DNA has been investigated by agarose gel retardation assays. The results showed that the dendritic iridium(III) complexes, unlike their monomeric counterparts, bound to the plasmid, and the interaction was electrostatic in nature. The lipophilicity of all the complexes has been determined by reversed-phase high-performance liquid chromatography (HPLC). Additionally, the cellular uptake of the complexes by the human cervix epithelioid carcinoma (HeLa) cell line has been examined by inductively coupled plasma mass spectrometry (ICP-MS), laser-scanning confocal microscopy, and flow cytometry. Upon internalization, all the complexes were localized in the perinuclear region, forming very sharp luminescent rings surrounding the nuclei. Interestingly, in addition to these rings, HeLa cells treated with the dendritic
8. Ground-based decameter wavelength observations of the planetary and stellar radio emission
Konovalenko, A. A.; Rucker, H. O.; Lecacheux, A.; Melnik, V. N.; Litvinenko, G. V.; Abranin, E. P.; Falkovich, I. S.
2007-08-01
The studies of the non-thermal radio emission of the magnetized objects (the Sun, planets, exoplanets, active stars, etc.) are the important field of low-frequency radio astronomy and astrophysics. This kind of radio emission mainly relates to transient phenomena and requires for its investigations the high sensitive radio telescopes as well as the special technique and methods. Such investigations represent the significant part of future LOFAR scientific program. But the existing largest instruments (first, the Ukrainian decameter radio telescopes UTR-2, URAN) give the good possibilities for studying. Huge effective area of UTR-2 radio telescope (> 100 000 sq. m), broadband (8 *10E32 MHz), high dynamic range, the electronic steering and multi-beam ON-OFF method implementation allow to reach the sensitivity less than 1Jy, high time and frequency resolution and reliable detection of weak sporadic low-frequency radio emission events. Here we present the main results of the studies of the Sun, Jupiter, Saturn, active stars radio emission as well as outer heliosphere investigation by the scintillation method. Special interest paid to the simultaneous ground-based and space low-frequency experiments with the existing and future space missions (WIND, Cassini, STEREO, etc.). The favourable perspectives of the future investigations are evident from the presented researches.
9. Type II and Type III Radio Emissions and Their Association with Solar Energetic Particles
Richardson, I. G.; Cane, H. V.
2016-12-01
It is well known that CME-driven shocks are a major source of solar energetic particles (SEPs). The solar phenomena associated with high energy SEP increases nearly always include type II radio emissions indicative of the presence of shocks. However, there is also a clear link between particles accelerated in the low corona and type III radio bursts. For the most energetic events the type III emissions extend into or occur after, the flare impulsive phase. Such emission has been named type III-l mainly because the emission is "late". In our work, we have found an excellent correlation between the pattern of radio emissions and the associated particle events. However, various other studies have investigated type III-l emissions and found the association with SEP events to be less compelling. We explore the results of these studies in order to determine why this is the case.
10. Ultraviolet and Radio Emission from the Northern Middle Lobe of Centaurus A
NASA Technical Reports Server (NTRS)
Neff, Susan
2009-01-01
We present deep GALEX ultraviolet (135 - 280 nm) images of the Northern Middle Lobe (NML) of the nearby radio galaxy Centaurus A. We find that the ultraviolet emission appears to have a complex interaction with soft X-ray, H-alpha emission, and radio emission, which should help constrain various models of energy transport in the NML. We also present new 90cm VLA images of the NML. The radio morphology at this wavelength is indicative of a more complex system than either a straightforward flaring jet (Morganti et al. 1999) or a bubble with trailing stem (Saxton et al. 2001). New limits are placed on the lack of radio emission from any corresponding southern counterpart to the NML.
11. Ultraviolet and Radio Emission from the Northern Middle Lobe of Centaurus A
NASA Technical Reports Server (NTRS)
Neff, Susan
2009-01-01
We present deep GALEX ultraviolet (135 - 280 nm) images of the Northern Middle Lobe (NML) of the nearby radio galaxy Centaurus A. We find that the ultraviolet emission appears to have a complex interaction with soft X-ray, H-alpha emission, and radio emission, which should help constrain various models of energy transport in the NML. We also present new 90cm VLA images of the NML. The radio morphology at this wavelength is indicative of a more complex system than either a straightforward flaring jet (Morganti et al. 1999) or a bubble with trailing stem (Saxton et al. 2001). New limits are placed on the lack of radio emission from any corresponding southern counterpart to the NML.
12. Sharing Low Frequency Radio Emissions in the Virtual Observatory: Application for JUNO-Ground-Radio Observations Support.
Cecconi, B.; Savalle, R.; Zarka, P. M.; Anderson, M.; Andre, N.; Coffre, A.; Clarke, T.; Denis, L.; Ebert, R. W.; Erard, S.; Genot, V. N.; Girard, J. N.; Griessmeier, J. M.; Hess, S. L.; Higgins, C. A.; Hobara, Y.; Imai, K.; Imai, M.; Kasaba, Y.; Konovalenko, A. A.; Kumamoto, A.; Kurth, W. S.; Lamy, L.; Le Sidaner, P.; Misawa, H.; Nakajo, T.; Orton, G. S.; Ryabov, V. B.; Sky, J.; Thieman, J.; Tsuchiya, F.; Typinski, D.
2015-12-01
In the frame of the preparation of the NASA/JUNO and ESA/JUICE (Jupiter Icy Moon Explorer) missions, and the development of a planetary sciences virtual observatory (VO), we are proposing a new set of tools directed to data providers as well as users, in order to ease data sharing and discovery. We will focus on ground based planetary radio observations (thus mainly Jupiter radio emissions), trying for instance to enhance the temporal coverage of jovian decametric emission. The data service we will be using is EPN-TAP, a planetary science data access protocol developed by Europlanet-VESPA (Virtual European Solar and Planetary Access). This protocol is derived from IVOA (International Virtual Observatory Alliance) standards. The Jupiter Routine Observations from the Nancay Decameter Array are already shared on the planetary science VO using this protocol, as well as data from the Iitate Low Frquency Radio Antenna, in Japan. Amateur radio data from the RadioJOVE project is also available. The attached figure shows data from those three providers. We will first introduce the VO tools and concepts of interest for the planetary radioastronomy community. We will then present the various data formats now used for such data services, as well as their associated metadata. We will finally show various prototypical tools that make use of this shared datasets.
13. Circular polarization of radio emission from air showers in thunderstorm conditions
Trinh, T. N. G.; Scholten, O.; Bonardi, A.; Buitink, S.; Corstanje, A.; Ebert, U.; Enriquez, J. E.; Falcke, H.; Hörandel, J. R.; Mitra, P.; Mulrey, K.; Nelles, A.; Thoudam, S.; Rachen, J. P.; Rossetto, L.; Rutjes, C.; Schellart, P.; ter Veen, S.; Winchen, T.
2017-03-01
We present measured radio emission from cosmic-ray-induced air showers under thunderstorm conditions. We observe for these events large differences in intensity, linear polarization and circular polarization from the events measured under fair-weather conditions. This can be explained by the effects of atmospheric electric fields in thunderclouds. Therefore, measuring the intensity and polarization of radio emission from cosmic ray extensive air showers during thunderstorm conditions provides a new tool to probe the atmospheric electric fields present in thunderclouds.
14. Observation of radio-wave-induced red hydroxyl emission at low altitude in the ionosphere.
PubMed
Kagan, L M; Nicolls, M J; Kelley, M C; Carlson, H C; Belikovich, V V; Bakhmet'eva, N V; Komrakov, G P; Trondsen, T S; Donovan, E
2005-03-11
We report the discovery of radio-wave-induced red emission of OH Meinel rotation-vibrational bands at 629.79 nm. These are the first measurements of artificial aurora below 100 km. We believe that the 629.79-nm OH emission was due to radio-wave focusing by sporadic ionization clouds near 80-85 km altitude, thus giving a technique to visualize the low-altitude sporadic ionization and providing insight into ionospheric interactions at these low altitudes.
15. Searches for correlated X-ray and radio emission from X-ray burst sources
NASA Technical Reports Server (NTRS)
Johnson, H. M.; Catura, R. C.; Lamb, P. A.; White, N. E.; Sanford, P. W.; Hoffman, J. A.; Lewin, W. H. G.; Jernigan, J. G.
1978-01-01
The NRAO Green Bank interferometer has been used to monitor MXB 1730-335 and MXB 1837+05 during periods when 68 X-ray bursts were detected by X-ray observations. No significant radio emission was detected from these objects, or from MXB 1820-30 and MXB 1906+00, which emitted no bursts throughout the simultaneous observations. The data place upper limits on radio emission from these objects in the 2695 and 8085 MHz bands.
16. Radio-Quiet Quasars in the VIDEO Survey: Evidence for AGN-powered radio emission below 1 mJy
White, Sarah; Jarvis, Matt; Haeussler, Boris; Maddox, Natasha
2015-01-01
Several lines of evidence suggest that the interaction between active galactic nucleus (AGN) activity and star formation is responsible for the co-evolution of black hole mass with galaxy bulge mass. Therefore studying this interplay is crucial to our understanding of galaxy formation and evolution. The new generation of radio surveys are able to play a key role in this area, as both processes produce radio emission.We use a combination of optical and near-infrared photometry to select a sample of 72 quasars from the VISTA Deep Extragalactic Observations (VIDEO) Survey, over 1 deg2. The depth of VIDEO allows us to study very low accretion rates and/or lower-mass black holes. 26% of the candidate quasar sample has been spectroscopically confirmed using the Southern African Large Telescope and the VIMOS VLT Deep Survey. We then use a radio-stacking technique to sample below the nominal flux-density threshold of existing Very Large Array data at 1.4 GHz. In agreement with other work, we show that a power-law fit to the radio number counts is inadequate, with an upturn in the counts being observed at these faint luminosities. Previous authors attribute this to an emergent star-forming population. However, by comparing radio emission from our quasars with that from a control sample of galaxies, we suggest that this emission is predominantly caused by accretion activity. Further support for an AGN origin is provided by a comparison of two independent estimates of star formation rate. These findings have important implications for modelling radio populations below 1 mJy, which is necessary for the development of the Square Kilometre Array.
17. LATE-TIME RADIO EMISSION FROM X-RAY-SELECTED TIDAL DISRUPTION EVENTS
SciTech Connect
Bower, Geoffrey C.; Cenko, S. Bradley; Silverman, Jeffrey M.; Bloom, Joshua S.; Metzger, Brian D.
2013-02-15
We present new observations with the Karl G. Jansky Very Large Array of seven X-ray-selected tidal disruption events (TDEs). The radio observations were carried out between 9 and 22 years after the initial X-ray discovery, and thus probe the late-time formation of relativistic jets and jet interactions with the interstellar medium in these systems. We detect a compact radio source in the nucleus of the galaxy IC 3599 and a compact radio source that is a possible counterpart to RX J1420.4+5334. We find no radio counterparts for five other sources with flux density upper limits between 51 and 200 {mu}Jy (3{sigma}). If the detections truly represent late radio emission associated with a TDE, then our results suggest that a fraction, {approx}> 10%, of X-ray-detected TDEs are accompanied by relativistic jets. We explore several models for producing late radio emission, including interaction of the jet with gas in the circumnuclear environment (blast wave model), and emission from the core of the jet itself. Upper limits on the radio flux density from archival observations suggest that the jet formation may have been delayed for years after the TDE, possibly triggered by the accretion rate dropping below a critical threshold of {approx}10{sup -2}-10{sup -3} M-dot {sub Edd}. The non-detections are also consistent with this scenario; deeper radio observations can determine whether relativistic jets are present in these systems. The emission from RX J1420.4+5334 is also consistent with the predictions of the blast wave model; however, the radio emission from IC 3599 is substantially underluminous, and its spectral slope is too flat, relative to the blast wave model expectations. Future radio monitoring of IC 3599 and RX J1420.4+5334 will help to better constrain the nature of the jets in these systems.
18. The low-frequency radio emission in blazar PKS2155-304
Pandey-Pommier, M.; Sirothia, S.; Chadwick, P.; Martin, J.-M.; Colom, P.; van Driel, W.; Combes, F.; Kharb, P.; Crespeau, P.-J.; Richard, J.; Guiderdoni, B.
2016-12-01
We report radio imaging and monitoring observations in the frequency range 0.235 - 2.7 GHz during the flaring mode of PKS 2155-304, one of the brightest BL Lac objects. The high sensitivity GMRT observations not only reveal extended kpc-scale jet and FRI type lobe morphology in this erstwhile 'extended-core' blazar but also delineate the morphological details, thanks to its arcsec scale resolution. The radio light curve during the end phase of the outburst measured in 2008 shows high variability (8.5%) in the jet emission in the GHz range, compared to the lower core variability (3.2%) seen at the lowest frequencies. The excess of flux density with a very steep spectral index in the MHz range supports the presence of extra diffuse emission at low frequencies. The analysis of multi wavelength (radio/optical/gamma-ray) light curves at different radio frequencies confirms the variability of the core region and agrees with the scenario of high energy emission in gamma-rays due to inverse Compton emission from a collimated relativistic plasma jet followed by synchrotron emission in radio. Clearly, these results give an interesting insight of the jet emission mechanisms in blazars and highlight the importance of studying such objects with low frequency radio interferometers like LOFAR and the SKA and its precursor instruments.
19. A Giant Radio Flare from Cygnus X-3 with Associated Gamma-Ray Emission
NASA Technical Reports Server (NTRS)
Corbel, S.; Dubus, G.; Tomsick, J. A.; Szostek, A.; Corbet, R. H. D.; Miller-Jones, J. C. A.; Richards, J. L.; Pooley, G.; Trushkin, S.; Dubois, R.;
2012-01-01
With frequent flaring activity of its relativistic jets, Cygnus X-3 (Cyg X-3) is one of the most active microquasars and is the only Galactic black hole candidate with confirmed high energy gamma-ray emission, thanks to detections by Fermi/LAT and AGILE. In 2011, Cyg X-3 was observed to transit to a soft X-ray state, which is known to be associated with high-energy gamma-ray emission. We present the results of a multiwavelength campaign covering a quenched state, when radio emission from Cyg X-3 is at its weakest and the X-ray spectrum is very soft. A giant (approx 20 Jy) optically thin radio flare marks the end of the quenched state, accompanied by rising non-thermal hard X-rays. Fermi/LAT observations (E greater than or equal 100 MeV) reveal renewed gamma-ray activity associated with this giant radio flare, suggesting a common origin for all non-thermal components. In addition, current observations unambiguously show that the gamma-ray emission is not exclusively related to the rare giant radio flares. A 3-week period of gamma-ray emission is also detected when Cyg X-3 was weakly flaring in radio, right before transition to the radio quenched state. No gamma rays are observed during the one-month long quenched state, when the radio flux is weakest. Our results suggest transitions into and out of the ultrasoft X-ray (radio quenched) state trigger gamma-ray emission, implying a connection to the accretion process, and also that the gamma-ray activity is related to the level of radio flux (and possibly shock formation), strengthening the connection to the relativistic jets.
20. NASA Astrophysics Data System (ADS)
Rankin, Joanna M.
2017-01-01
With their enormous densities and fields, neutron stars entail some of the most exotic physics in the cosmos. Similarly, the physical mechanisms of pulsar radio emission are no less exotic, and we are only now beginning to understand them. The talk will provide an introduction to the phenomenology of radio pulsar emission and focus on those aspects of the exquisite Arecibo observations that bear on their challenging emission physics.The commonalities of the radio beamforms of most slow pulsars (and some millisecond pulsars) argue strongly that their magnetic fields have a nearly dipolar structure at the height of their radio emission regions. These heights can often be determined by aberration/retardation analyses. Similarly, measurement of the orientation of the polarized radio emission with respect to the emitting magnetic field facilitates identification of the physical(X/O) emission modes and study of the plasma coupling to the electromagnetic radiation.While the physics of primary plasma generation above the pulsar polar cap is only beginning to be understood, it is clear that the radio pulsars we see are able to generate copious amounts of electron-positron plasma in their emission regions. Within the nearly dipolar field structure of these emission regions, the plasma density is near to that of the Goldreich-Julian model, and so the physical conditions in these regions can be accurately estimated.These conditions show that the plasma frequencies in the emission regions are much higher than the frequency of the emitted radiation, such that the plasma couples most easily to the extraordinary mode as observed. Therefore, the only surviving emission mechanism is curvature radiation from charged solitons, produced by the two-stream instability. Such soliton emission has probably been observed directly in the Crab pulsar; however, a physical theory of charged soliton radiation does not yet exist.
1. RFID Transponders' RF Emissions in Aircraft Communication and Navigation Radio Bands
NASA Technical Reports Server (NTRS)
Nguyen, Truong X.; Ely, Jay J.; Koppen Sandra V.; Fersch, Mariatheresa S.
2008-01-01
Radiated emission data in aircraft communication and navigation bands are presented for several active radio frequency identification (RFID) tags. The individual tags are different in design, operation and transmitting frequencies. The process for measuring the tags emissions in a reverberation chamber is discussed. Measurement issues dealing with tag interrogation, low level measurement in the presence of strong transmissions, and tags low duty factors are discussed. The results show strong emissions, far exceeding aircraft emission limits and can be of potential interference risks.
2. Origin and evolution of the radio emission from immediate postoutburst supernovae
NASA Technical Reports Server (NTRS)
Marscher, A. P.; Brown, R. L.
1978-01-01
Several models for the radio emission from immediate postoutburst supernovae are examined under the assumption that the expanding remnant consists of a homogeneously mixed distribution of relativistic particles, magnetic field, and thermal plasma. The evolutionary models are: (1) an adiabatic expansion model; (2) a model incorporating the existence of a central pulsar; and (3) variations on the first two models in which relativistic electrons are accelerated either instantaneously or over an extended period of time and in which ionization, bremsstrahlung, synchrotron, Compton, and expansion losses are explicitly included. The character of the radio emission expected from these models is quite dissimilar. Whereas in adiabatic expansion models the emission is expected to increase slowly and become most intense at high frequencies, in models involving a central pulsar the emission should increase rapidly with a maximum flux density that is the same at all frequencies. The theoretical evolution of the radio emission for each model is compared with observations of SN 1970g.
3. The Influence of The Galilean Satellites on Radio Emissions From The Jovian System
NASA Technical Reports Server (NTRS)
Kurth, W. S.; Gurnett, D. A.; Menietti, J. D.
2000-01-01
4. Wave propagation and earth satellite radio emission studies
NASA Technical Reports Server (NTRS)
Yeh, K. C.; Liu, C. H.; Flaherty, B. J.
1974-01-01
Radio propagation studies of the ionosphere using satellite radio beacons are described. The ionosphere is known as a dispersive, inhomogeneous, irregular and sometimes even nonlinear medium. After traversing through the ionosphere the radio signal bears signatures of these characteristics. A study of these signatures will be helpful in two areas: (1) It will assist in learning the behavior of the medium, in this case the ionosphere. (2) It will provide information of the kind of signal characteristics and statistics to be expected for communication and navigational satellite systems that use the similar geometry.
5. A study of diffuse radio sources and X-ray emission in six massive clusters
Parekh, V.; Dwarakanath, K. S.; Kale, R.; Intema, H.
2017-01-01
6. The birthplace of planetary radio astronomy: The Seneca, Maryland observatory 50 years after Burke and Franklin's Jupiter radio emission discovery.
Garcia, L. N.; Thieman, J. R.; Higgins, C. A.
2004-12-01
Burke and Franklin's discovery of radio emissions from Jupiter in 1955 effectively marked the birth of the field of planetary radio astronomy. The discovery was made near Seneca, Maryland using the Department of Terrestrial Magnetism/Carnegie Institution of Washington's Mills Cross Array. Fifty years later there is very little evidence of this 96-acre X-shaped array of dipoles still in existence, nor evidence of any of the other antennas used at this site. The site, now known as the McKee Besher Wildlife Management Area, is owned by the State of Maryland Department of Natural Resources. Radio Jove, a NASA/GSFC education and public outreach project, will recognize the 50th anniversary of this discovery through an historic reenactment using their receiver and dual-dipole array system. Our search through the DTM/CIW archives, our visit to the site to look for evidence of this array, and other efforts at commemorating this anniversary will be described.
7. Radio Emission from an Electron Shower in a Dielectric in the Presence of a Magnetic Field
Wissel, Stephanie; Belov, Konstantin
2014-03-01
Several new experiments employ the radio technique to detect ultra-high-energy cosmic rays. The dominant component of the radio-frequency radiation arises from synchrotron emission due to the interaction of the cosmic ray's air shower particles with the Earth's magnetic field. Secondary, but non-negligible, radiation arises from the build up of a charge asymmetry in the shower. We present measurements from the SLAC T-510 experiment in which we bombard a polyethylene target (n = 1.5) in a magnetic field (up to a few kiloGauss) with a few GeV electron beam. Antennas in bands ranging between 30-300 MHz and 300-1200 MHz map out the radio emission in bands relevant for ground arrays and balloon-borne experiments such as ANITA. The data presented here serve to calibrate models of radio emission, ZHAires and CoREAS, by providing a suite of controlled, accelerator-based measurements.
8. Shock-powered radio emission from V5589 Sagittarii (Nova Sgr 2012 #1)
Weston, Jennifer H. S.; Sokoloski, J. L.; Chomiuk, Laura; Linford, Justin D.; Nelson, Thomas; Mukai, Koji; Finzell, Tom; Mioduszewski, Amy; Rupen, Michael P.; Walter, Frederick M.
2016-08-01
Since the Fermi discovery of γ-rays from novae, one of the biggest questions in the field has been how novae generate such high-energy emission. Shocks must be a fundamental ingredient. Six months of radio observations of the 2012 Nova V5589 Sgr with the VLA and 15 weeks of X-ray observations with Swift/XRT show that the radio emission consisted of: (1) a shock-powered, non-thermal flare; and (2) weak thermal emission from 10-5 M⊙ of freely expanding, photoionized ejecta. Absorption features in the optical spectrum and the peak optical brightness suggest that V5589 Sgr lies 4 kpc away (3.2-4.6 kpc). The shock-powered flare dominated the radio light curve at low frequencies before day 100. The spectral evolution of the radio flare, its high radio brightness temperature, the presence of unusually hard (kTx > 33 keV) X-rays, and the ratio of radio to X-ray flux near radio maximum all support the conclusions that the flare was shock-powered and non-thermal. Unlike most other novae with strong shock-powered radio emission, V5589 Sgr is not embedded in the wind of a red-giant companion. Based on the similar inclinations and optical line profiles of V5589 Sgr and V959 Mon, we propose that shocks in V5589 Sgr formed from collisions between a slow flow with an equatorial density enhancement and a subsequent faster flow. We speculate that the relatively high speed and low mass of the ejecta led to the unusual radio emission from V5589 Sgr, and perhaps also to the non-detection of γ-rays.
9. Surveying for Exoplanetary Auroral Radio Emission with HERA
Williams, Peter K. G.; Berger, Edo
2017-05-01
HERA, the Hydrogen Epoch of Reionization Array, is a long wavelength radio telescope under construction in South Africa. Although HERA's primary science driver is the search for radio signatures of the Epoch of Reionization, its large collecting area, excellent calibratability, and methodical observing scheme make it a world-class tool for time-domain radio astronomy as well. In particlar, the completed HERA array will be sensitive to auroral radio bursts from planets with auroral powers and magnetic field strengths comparable to (factors of a few larger than) those of Jupiter, assuming a fiducial distance of 10 pc. HERA will log thousands of hours monitoring the stellar systems in its sky footprint, including the 40 systems found within this fiducial horizon. In this talk I will describe the current status of HERA and its future prospects for directly detecting exoplanetary magnetospheres.
10. The radio emission from the ultraluminous far-infrared galaxy NGC 6240
NASA Technical Reports Server (NTRS)
Colbert, Edward J. M.; Wilson, Andrew S.; Bland-Hawthorn, Jonathan
1994-01-01
We present new radio observations of the 'prototypical' ultraluminous far-infrared galaxy NGC 6240, obtained using the Very Large Array (VLA) at lambda = 20 cm in B-configuration and at lambda = 3.6 cm in A-configuration. These data, along with those from four previous VLA observations, are used to perform a comprehensive study of the radio emission from NGC 6240. Approximately 70% (approximately 3 x 10(exp 23) W/Hz) of the total radio power at 20 cm originates from the nuclear region (approximately less than 1.5 kpc), of which half is emitted by two unresolved (R approximately less than 36 pc) cores and half by a diffuse component. The radio spectrum of the nuclear emission is relatively flat (alpha approximately equals 0.6; S(sub nu) proportional to nu(exp -alpha). The supernova rate required to power the diffuse component is consistent with that predicted by the stellar evolution models of Rieke et al. (1985). If the radio emission from the two compact cores is powered by supernova remnants, then either the remnants overlap and form hot bubbles in the cores, or they are very young (approximately less than 100 yr.) Nearly all of the remaining 30% of the total radio power comes from an 'armlike' region extending westward from the nuclear region. The western arm emission has a steep spectrum (alpha approximately equals 1.0), suggestive of aging effects from synchrotron or inverse-Compton losses, and is not correlated with starlight; we suggest that it is synchrotron emission from a shell of material driven by a galactic superwind. Inverse Compton scattering of far-infrared photons in the radio sources is expected to produce an X-ray flux of approximately 2 - 6 x 10(exp -14) ergs/s/sq cm in the 2 - 10 keV band. No significant radio emission is detected from or near the possible ultramassive 'dark core'.
11. The radio emission from the ultraluminous far-infrared galaxy NGC 6240
NASA Technical Reports Server (NTRS)
Colbert, Edward J. M.; Wilson, Andrew S.; Bland-Hawthorn, Jonathan
1994-01-01
We present new radio observations of the 'prototypical' ultraluminous far-infrared galaxy NGC 6240, obtained using the Very Large Array (VLA) at lambda = 20 cm in B-configuration and at lambda = 3.6 cm in A-configuration. These data, along with those from four previous VLA observations, are used to perform a comprehensive study of the radio emission from NGC 6240. Approximately 70% (approximately 3 x 10(exp 23) W/Hz) of the total radio power at 20 cm originates from the nuclear region (approximately less than 1.5 kpc), of which half is emitted by two unresolved (R approximately less than 36 pc) cores and half by a diffuse component. The radio spectrum of the nuclear emission is relatively flat (alpha approximately equals 0.6; S(sub nu) proportional to nu(exp -alpha). The supernova rate required to power the diffuse component is consistent with that predicted by the stellar evolution models of Rieke et al. (1985). If the radio emission from the two compact cores is powered by supernova remnants, then either the remnants overlap and form hot bubbles in the cores, or they are very young (approximately less than 100 yr.) Nearly all of the remaining 30% of the total radio power comes from an 'armlike' region extending westward from the nuclear region. The western arm emission has a steep spectrum (alpha approximately equals 1.0), suggestive of aging effects from synchrotron or inverse-Compton losses, and is not correlated with starlight; we suggest that it is synchrotron emission from a shell of material driven by a galactic superwind. Inverse Compton scattering of far-infrared photons in the radio sources is expected to produce an X-ray flux of approximately 2 - 6 x 10(exp -14) ergs/s/sq cm in the 2 - 10 keV band. No significant radio emission is detected from or near the possible ultramassive 'dark core'.
12. Radio emission from air showers. Comparison of theoretical approaches
Belov, Konstantin
2013-05-01
While the fluorescence and the ground counter techniques for the detection of ultra-high energy cosmic rays (UHECR) were being developed for decades, the interest in the radio detection diminished after the initial experiments in the 1960s. As a result, the fluorescence and the surface array techniques are more mature today, providing more reliable measurements of the primary cosmic particle energy, chemical composition and the inelastic cross-section. The advantages of the radio technique are 100% duty cycle and lower deployment and operational costs. Thus, the radio technique can greatly complement the fluorescence and the ground array detection and can also work independently. With the ANITA balloon detector observing UHECRs and the success of LOPES, CODALEMA and other surface radio detectors, the radio technique received a significant boost in recent years. Reliable Monte Carlo (MC) simulations are needed in order to obtain the energy and other parameters of the primary cosmic ray particle from the radio observations. Several MC techniques, like ZHairesS and the Endpoint Formalism, were proposed in recent years. While they seem to reproduce some of the observed data quite well, there is a divergence between the different approaches under certain conditions. In this work we derive these approaches from Maxwell's equations and prove their identity under certain conditions as well as discuss their applicability to the UHECR air showers and to a proposed experiment at SLAC.
13. Solar Radio Emission as a Prediction Technique for Coronal Mass Ejections' registration
2016-07-01
The concept of solar Coronal Mass Ejections (CMEs) as global phenomenon of solar activity caused by the global magnetohydrodynamic processes is considered commonly accepted. These processes occur in different ranges of emission, primarily in the optical and the microwave emission being generated near the surface of the sun from a total of several thousand kilometers. The usage of radio-astronomical data for CMEs prediction is convenient and promising. Actually, spectral measurements of solar radio emission cover all heights of solar atmosphere, sensitivity and accuracy of measurements make it possible to record even small energy changes. Registration of the radio emission is provided by virtually all-weather ground-based observations, and there is the relative cheapness to obtain the corresponding information due to a developed system of monitoring observations. On the large statistical material there are established regularities of the existence of sporadic radio emission at the initial stage of CMEs' formation and propagation in the lower layers of the solar atmosphere during the time interval from 2-3 days to 2 hours before registration of CMEs on coronagraph. In this report we present the prediction algorithm and scheme of short-term forecasting developed on the base of statistical analysis regularities of solar radio emission data prior to "isolated" solar Coronal Mass Ejections registered in 1998, 2003, 2009-2013.
14. High sensitive observations of the planetary radio emission in decameter wavelength
Litvinenko, Galina; Zakharenko, Vyacheslav; Rucker, Helmut; Konovalenko, Alexander; Shaposhnikov, Vladimir; Zarka, Philippe; Griessmeier, Jean-M.; Fisher, Georg; Vinogradov, Vladimir; Mylostna, Krystyna
2013-04-01
The progress of the ground-based low frequency radio astronomy has opened a new approach to the study of planetary radio emission in the solar system and beyond. This is manifested in the study of the Jupiter (detection of various types of the sporadic emission), of the Saturn (investigation of the electrostatic discharges emission, SED), as well as other planets and exoplanets. High efficiency decameter wavelength radio telescope UTR-2 and modern registration systems (effective area is more than 100 000 sq.m., instant frequency band is 8-33 MHz, dynamic range is about 90 dB, the frequency resolution is about 1 kHz, the temporal resolution is about 1 microsecond) allow for a new observation and detect many interesting phenomena. This includes the detection of superfine time-frequency structures and new types of the modulations effects in the Jovian radio emission, the detection of microsecond scales in the SED emission of the Saturn, and dispersion delay of the SED signals in the interplanetary medium. In addition, the described above method of observation of the planetary signals allowed for the first time to start ground-based searching radio emission from Uranus, Venus, Mars and exoplanets.
15. COMPARATIVE ANALYSIS OF TWO FORMATION SCENARIOS OF BURSTY RADIO EMISSION FROM ULTRACOOL DWARFS
SciTech Connect
Kuznetsov, A. A.; Doyle, J. G.; Yu, S.; Hallinan, G.; Antonova, A.; Golden, A.
2012-02-10
Recently, a number of ultracool dwarfs have been found to produce periodic radio bursts with high brightness temperature and polarization degree; the emission properties are similar to the auroral radio emissions of the magnetized planets of the solar system. We simulate the dynamic spectra of radio emission from ultracool dwarfs. The emission is assumed to be generated due to the electron-cyclotron maser instability. We consider two source models: the emission caused by interaction with a satellite and the emission from a narrow sector of active longitudes; the stellar magnetic field is modeled by a tilted dipole. We have found that for the dwarf TVLM 513-46546, the model of the satellite-induced emission is inconsistent with observations. On the other hand, the model of emission from an active sector is able to reproduce qualitatively the main features of the radio light curves of this dwarf; the magnetic dipole seems to be highly tilted (by about 60 Degree-Sign ) with respect to the rotation axis.
16. Observation of local radio emission associated with type III radio bursts and Langmuir waves
NASA Technical Reports Server (NTRS)
Reiner, M. J.; Stone, R. G.; Fainberg, J.
1992-01-01
The first clear detection of fundamental and harmonic radiation from the type III radio source region is presented. This radiation is characterized by its lack of frequency drift, its short rise and decay times, its relative weakness compared to the remotely observed radiation and its temporal coincidence with observed Langmuir waves. The observations were made with the radio and plasma frequency (URAP) receivers on the Ulysses spacecraft between about 1 and 2 AU from the Sun.
17. Unprecedentedly Strong and Narrow Electromagnetic Emissions Stimulated by High-Frequency Radio Waves in the Ionosphere
SciTech Connect
Norin, L.; Leyser, T. B.; Nordblad, E.; Thide, B.; McCarrick, M.
2009-02-13
Experimental results of secondary electromagnetic radiation, stimulated by high-frequency radio waves irradiating the ionosphere, are reported. We have observed emission peaks, shifted in frequency up to a few tens of Hertz from radio waves transmitted at several megahertz. These emission peaks are by far the strongest spectral features of secondary radiation that have been reported. The emissions are attributed to stimulated Brillouin scattering, long predicted but hitherto never unambiguously identified in high-frequency ionospheric interaction experiments. The experiments were performed at the High-Frequency Active Auroral Research Program (HAARP), Alaska, USA.
18. Unprecedentedly strong and narrow electromagnetic emissions stimulated by high-frequency radio waves in the ionosphere.
PubMed
Norin, L; Leyser, T B; Nordblad, E; Thidé, B; McCarrick, M
2009-02-13
Experimental results of secondary electromagnetic radiation, stimulated by high-frequency radio waves irradiating the ionosphere, are reported. We have observed emission peaks, shifted in frequency up to a few tens of Hertz from radio waves transmitted at several megahertz. These emission peaks are by far the strongest spectral features of secondary radiation that have been reported. The emissions are attributed to stimulated Brillouin scattering, long predicted but hitherto never unambiguously identified in high-frequency ionospheric interaction experiments. The experiments were performed at the High-Frequency Active Auroral Research Program (HAARP), Alaska, USA.
19. Unprecedentedly Strong and Narrow Electromagnetic Emissions Stimulated by High-Frequency Radio Waves in the Ionosphere
Norin, L.; Leyser, T. B.; Nordblad, E.; Thidé, B.; McCarrick, M.
2009-02-01
Experimental results of secondary electromagnetic radiation, stimulated by high-frequency radio waves irradiating the ionosphere, are reported. We have observed emission peaks, shifted in frequency up to a few tens of Hertz from radio waves transmitted at several megahertz. These emission peaks are by far the strongest spectral features of secondary radiation that have been reported. The emissions are attributed to stimulated Brillouin scattering, long predicted but hitherto never unambiguously identified in high-frequency ionospheric interaction experiments. The experiments were performed at the High-Frequency Active Auroral Research Program (HAARP), Alaska, USA.
20. Is lightning a possible source of the radio emission on HAT-P-11b?
Hodosán, G.; Rimmer, P. B.; Helling, Ch.
2016-09-01
Lightning induced radio emission has been observed on Solar system planets. There have been many attempts to observe exoplanets in the radio wavelength, however, no unequivocal detection has been reported. Lecavelier des Etangs et al. carried out radio transit observations of the exoplanet HAT-P-11b, and suggested that a small part of the radio flux can be attributed to the planet. Here, we assume that this signal is real, and study if this radio emission could be caused by lightning with similar energetic properties like in the Solar system. We find that a lightning storm with 3.8 × 106 times larger flash densities than the Earth-storms with the largest lightning activity is needed to produce the observed signal from HAT-P-11b. The optical emission of such thunderstorm would be comparable to that of the host star. We show that HCN produced by lightning chemistry is observable 2-3 yr after the storm, which produces signatures in the L (3.0-4.0 μm) and N (7.5-14.5 μm) infrared bands. We conclude that it is unlikely that the observed radio signal was produced by lightning, however, future, combined radio and infrared observations may lead to lightning detection on planets outside the Solar system.
1. New high-latitude radio emissions detected in Jupiter's magnetosphere using Juno spacecraft observations
Tetrick, Sadie; Kurth, William; Gurnett, Donald; Imai, Masafumi; Hospodarsky, George; Bolton, Scott; Connerney, John; Levin, Steven; Mauk, Barry
2017-04-01
The Juno spacecraft is currently in polar orbit around Jupiter, as of July 5, 2016. As the spacecraft passed over the high latitude regions of Jupiter for the first time on August 27, 2016, the radio and plasma wave instrument detected a new electromagnetic radio emission. This study will investigate the characteristics of this new radio emission and consider the mechanisms by which it is generated. A cross-correlation with an electron beam flux, occurring around the same time as the emission, was performed to help determine the generation mechanism. The emission's polarization and E/cB ratio have been investigated and it was found that the E/cB ratio was near 1 and there was also evidence of field-aligned guiding by density irregularities, indicating signs of ducting along the planetary magnetic field. Arguments for and against each possible mode of propagation are presented.
2. A Study of Nonthermal X-Ray and Radio Emission from the O Star 9 Sgr
NASA Technical Reports Server (NTRS)
Waldron, Wayne L.; Corcoran, Michael F.; Drake, Stephen A.
1999-01-01
The observed X-ray and highly variable nonthermal radio emission from OB stars has eluded explanation for more than 18 years. The most favorable model of X-ray production in these stars (shocks) predicts both nonthermal radio and X-ray emission. The nonthermal X-ray emission should occur above 2 keV and the variability of this X-ray component should also be comparable to the observed radio variability. To test this scenario, we proposed an ASC/VLA monitoring program to observe the OB star, 9 Sgr, a well known nonthermal, variable radio source and a strong X-ray source. We requested 625 ks ASCA observations with a temporal spacing of approximately 4 days which corresponds to the time required for a density disturbance to propagate to the 6 cm radio free-free photosphere. The X-ray observations were coordinated with 5 multi-wavelength VLA observations. These observations represent the first systematic attempt to investigate the relationship between the X-ray and radio emission in OB stars.
3. Multi-parameter Correlation of Jovian Radio Emissions with Solar Wind and Interplanetary Magnetic Field Data
MacDowall, R. J.; Golla, T.; Reiner, M. J.; Farrell, W. M.
2015-12-01
Variability of the numerous varieties of Jovian radio emission has been associated with aspects of solar wind (SW) and interplanetary magnetic field (IMF) parameters outside the magnetosphere. Here we demonstrate multiple-parameter correlations that relate each of several Jovian emissions, including bKOM and quasi-periodic bursts, to the SW and IMF impacting the Jovian magnetosphere. The data used are from the Ulysses spacecraft with radio data from the Unified Radio and Plasma wave (URAP) instrument, which provides high-quality remote radio observations of the Jovian emissions. The URAP observations are correlated with SW and IMF data from the relevant instruments on Ulysses, propagated to the nose of the Jovian magnetosphere with a sophisticated code. Because the aphelion of the Ulysses orbit was at the Jovian distance from the Sun, Ulysses spent ample time near Jupiter in 1991-1992 and 2003-2004, which are the intervals analyzed. Our results can be inverted such that radio observations by a Jovian orbiter, such as Cassini or Juno, are able to identify SW/IMF changes based on the behavior of the radio emissions.
4. Transition radiation model for LF radio emission produced by ultrahigh-energy cosmic rays
Rahman, M.; Boruah, K.
2016-03-01
Wide-band radio emission from cosmic ray-induced extensive air showers is now well established. The electromagnetic component of the extensive air shower, during their propagation through atmosphere, interacts with their surroundings emitting radio pulses which can be detected from the very low frequency to the very high frequency. Conventional detection techniques, although effective, have lower duty cycles and are expensive. The radio method, on the other hand, provides almost 100 % duty cycle after suppressing the radio frequency interferences and is also cost-effective. Correlation studies show that there must be at least two separate mechanisms responsible for radio emission at low and high frequencies. So far, theoretical models based on computer simulations have been successful in explaining the emission at high frequencies. However, at low frequencies, the available theories have been incapable of explaining the observed field strengths as high as 750 μV/m/MHz. In this paper, a mathematical model based on transition radiation is proposed to explain the low-frequency radio emission that uses realistic particle distribution obtained from the Monte Carlo simulation code CORSIKA.
5. Search for Radio Emission from HD80606b: a Highly Eccentric Exoplanet
Knapp, M.; Winterhalter, D.; Lazio, J.; Majid, W.; Kuiper, T.; Farrell, W. M.; Spitler, L.
2014-12-01
Exoplanetary radio emission is a potential goldmine of information about a wider sample of planetary interiors, dynamos, and magnetospheres than our solar system provides. To date, however, radio searches for exoplanetary radio emission have been unsuccessful likely because the observing frequencies are too high. Using the relatively new Low Frequency Array (LOFAR), we present analyses of observations of the highly eccentric Jovian exoplanet HD80606b during five epochs before and after the planet's periastron. All of the gas giants in the solar system, as well as the Earth, exhibit magnetospheric radio emission due to the electron cyclotron maser instability. The power of this emission is modulated by the solar wind intensity. HD80606b is in a highly eccentric (e=0.93) orbit with a 111 day period. As the planet passes from apastron (0.88 AU) to periastron (0.03 AU), it experiences widely varying stellar wind conditions which should lead to variable radio emission with the highest power corresponding to periastron passage. HD80606b has been observed previously with the VLA at 325 MHz and 1425 MHz by Lazio et. al (2010), but LOFAR's lower frequency range (30-75 MHz) and high sensitivity is better suited to Jovian-type radio emissions. The LOFAR observations were made 48 hours and 18 hours pre-periastron, plus 18 and 48 hours post-periastron to capture the predicted strongest emission, and near apastron to provide a baseline level. The data are analyzed for both time-dependent and frequency dependent emission at each of the five observation epochs. This work presents the ongoing analysis of the data. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
6. Source characteristics and locations of hectometric radio emissions from the northern Jovian hemisphere
NASA Technical Reports Server (NTRS)
Reiner, M. J.; Fainberg, J.; Stone, R. G.
1993-01-01
Northern Jovian hectometric (HOM) radio emissions, detected from high Jovian latitudes by the Unified Radio and Plasma Wave experiment on the Ulysses spacecraft, were observed at all Jovian longitudes. This emission was observed to be predominantly right-hand circularly polarized, but some left-hand circular polarization was observed implying the presence of O mode emissions from the northern Jovian hemisphere. Intense HOM emissions, with well-defined directions and polarizations, were often confined to similar longitudinal regions where intense HOM emissions were previously observed at low latitudes. The present analysis confirms that these northern HOM sources lie in the Jovian polar regions on magnetic field lines that pass through the Io plasma torus. The observations may be consistent with emission from either a filled cone beam or a longitudinal distribution of thin hollow cones.
7. Radio emission at the centre of the galaxy cluster Abell 3560: evidence for core sloshing?
Venturi, T.; Rossetti, M.; Bardelli, S.; Giacintucci, S.; Dallacasa, D.; Cornacchia, M.; Kantharia, N. G.
2013-10-01
8. Source location of the smooth high-frequency radio emissions from Uranus
NASA Technical Reports Server (NTRS)
Farrell, W. M.; Calvert, W.
1989-01-01
The source location of the smooth high-frequency radio emissions from Uranus has been determined. Specifically, by fitting the signal dropouts which occurred as Voyager traversed the hollow center of the emission pattern to a symmetrical cone centered on the source magnetic field direction at the cyclotron frequency, a southern-hemisphere (nightside) source was found at approximately 56 deg S, 219 deg W. The half-angle for the hollow portion of the emission pattern was found to be 13 deg.
9. Spectroscopy of emission-line nebulae in powerful radio galaxies - Interpretation
Baum, S. A.; Heckman, T. M.; van Breugel, W.
1992-04-01
Long-slit optical spectra of the emission-line nebulae associated with 21 low-redshift (less than 0.2) radio galaxies are analyzed. Nebulae are classified kinematically into three types: rotators, calm nonrotators, and violent nonrotators; these types are characterized. It is proposed that the rotators have dynamically young disks of gas recently acquired by the radio galaxy in an interaction or merger with a gas-rich galaxy. This is consistent with the data on the morphologies, colors, and stellar dynamics of radio galaxies with strong emission lines. It is inferred from the association of the large-scale gas kinematics with the radio and optical properties of an active galaxy that the angular momentum of the gas which fuels the AGN may be an important parameter in the determinant of how activity is manifest in an AGN.
10. Quantitative prediction of type II solar radio emission from the Sun to 1 AU
Schmidt, J. M.; Cairns, Iver H.
2016-01-01
Coronal mass ejections (CMEs) are frequently associated with shocks and type II solar radio bursts. Despite involving fundamental plasma physics and being the archetype for collective radio emission from shocks, type II bursts have resisted detailed explanation for over 60 years. Between 29 November and 1 December 2013 the two widely separated spacecraft STEREO A and B observed a long lasting, intermittent, type II radio burst from ≈4 MHz to 30 kHz (harmonic), including an intensification when the CME-driven shock reached STEREO A. We demonstrate the first accurate and quantitative simulation of a type II burst from the high corona (near 11 solar radii) to 1 AU for this event with a combination of a data-driven three-dimensional magnetohydrodynamic simulation for the CME and plasma background and an analytic quantitative kinetic model for the radio emission.
11. An Analysis of Interplanetary Solar Radio Emissions Associated with a Coronal Mass Ejection
Krupar, V.; Eastwood, J. P.; Kruparova, O.; Santolik, O.; Soucek, J.; Magdalenić, J.; Vourlidas, A.; Maksimovic, M.; Bonnin, X.; Bothmer, V.; Mrotzek, N.; Pluta, A.; Barnes, D.; Davies, J. A.; Martínez Oliveros, J. C.; Bale, S. D.
2016-05-01
Coronal mass ejections (CMEs) are large-scale eruptions of magnetized plasma that may cause severe geomagnetic storms if Earth directed. Here, we report a rare instance with comprehensive in situ and remote sensing observations of a CME combining white-light, radio, and plasma measurements from four different vantage points. For the first time, we have successfully applied a radio direction-finding technique to an interplanetary type II burst detected by two identical widely separated radio receivers. The derived locations of the type II and type III bursts are in general agreement with the white-light CME reconstruction. We find that the radio emission arises from the flanks of the CME and are most likely associated with the CME-driven shock. Our work demonstrates the complementarity between radio triangulation and 3D reconstruction techniques for space weather applications.
12. Updated modeling of Io and non-Io Radio Auroral Emissions of Jupiter
Louis, C.; Lamy, L.; Zarka, P.; Cecconi, B.; Hess, S.
2015-10-01
The radio auroral emissions produced by the Jupiter's magnetosphere between a few kHz and 40MHz, the most intense of our Solar System, are known since half a century, but they still drive many questions, and their deepened study is one of the main aim of the JUNO missions (arrival in July 2016). Jovian auroral radio emissions are thought to be produced through the Cyclotron Maser Instability (CMI), from non-maxwellian weakly relativistic electrons gyrating along high-latitude magnetic fields lines (Zarka, 1998). These emissions divide in different spectral components, driven or not by the moon Io. The origin and the relationship between kilometric, hectometric and decametric non-Io emissions in particular remains poorly understood. To investigate these emissions, we simulated numerical dynamic spectra with the most recent version of the ExPRES code - Exoplanetary and Planetary Radio Emission Simulator, available at http://maser.obspm.fr - already used to successfully model Io decametric and Saturn's kilometric arcshaped emissions (Hess et al., 2008, Lamy et al., 2008) and predict exoplanetary radio emissions (Hess et al., 2011). Such simulations bring direct constraints on the locus of active magnetic field lines and on the nature of CMI-unstable electrons (Hess et al., submitted). We validated the new theoretical calculation of the beaming angle used by ExPRES, which now includes refraction at the source. We then built updated simulations of Io and non-Io emissions which were compared to the radio observations acquired by the Cassini spacecraft (Jupiter flyby in 2000) and the Nançay decameter array (routines observations of Jupiter).
13. On Using Solar Radio Emission to Probe Interiors of Asteroids and Comets
Winebrenner, D. P.; Gary, D. E.; Sahr, J. D.; Asphaug, E. I.
2015-12-01
Asteroids, comets and other primitive solar system bodies are key sources of information on the early solar system, on volatiles and organics delivered to the terrestrial planets, and on processes of planetary formation now observed in operation around other stars. Whether asteroids (in various size classes) are rubble piles or monolithic, and whether any porosity or internal voids contain volatiles, are first-order questions for understanding the delivery of volatiles to the early Earth, and for assessing impact hazards. Information on bulk composition aids discrimination between types and origins of primitive bodies, .e.g., the degree of aqueous alteration and bound-water content of carbonaceous chondrite bodies, and the volatile mass fraction of comets. Radar and radio methods can provide direct information on bulk composition, micro- and macro-porosity, body-scale internal structure, and on whether voids in rocky materials are volatile- or vacuum-filled. Such methods therefore figure prominently in current missions to primitive bodies (e.g., CONSERT) and in a variety of proposed missions. Radio transmitters necessary for conventional methods, however, add considerably to spacecraft mass and power requirements. Moreover, at many wavelengths most useful for radio sounding, powerful radio emission from the Sun strongly interferes with conventional signals. Here we present initial results from an investigation of how solar radio emission could serve as a natural resource for probing interiors of primitive bodies, rather than as interference. We briefly review methods for using stochastic radio illumination (aka noise radar methods), and illustrate the characteristics of solar radio emission relevant to mission design (e.g., observed intervals between emission events of specified intensity for different points in the solar cycle). We then discuss methods for selecting and interpreting observations in terms of interior properties, for bodies is different size classes
14. ON THE ORIGIN OF THE RADIO EMISSION OF Sw 1644+57
SciTech Connect
Barniol Duran, Rodolfo; Piran, Tsvi E-mail: [email protected]
2013-06-20
15. Study of Extragalactic Sources with Extended Radio Emission
Jamrozy, M.; Klein, U.; Mack, K.-H.
Galaxies (and quasars) hosting active galactic nuclei (AGN) are usually powerful radio sources which produce jets and extended radio emitting regions (lobes) of plasma. There is a huge range from less than 100 pc up to few Mpc in linear extent of the radio galaxies (RGs). RGs with sizes over more than one Mpc represent the biggest single objects in the Universe. The most extreme of those is 3C236 which has a projected linear size of 4.2 Mpc (H0 =71 km s-1 Mpc-1, Ω = 1). Another example of a giant radio galaxy (GRG) B0503-286 is shown in Fig. 1. The very large angular sizes (up to several dozens of arcminutes) of GRGs on the sky give an excellent opportunity to study the nature of AGNs and provide important constraints on the evolution of galaxies. Because of their sizes and luminosities GRGs have significant influence on the intergalactic medium (IGM). The total energy delivered into the IGM by the twin jets of a GRG is about 1054 J, which is a significant fraction of the gravitational energy released during the formation of a supermassive black hole in the centre of an AGN's parent galaxy. On the other hand, GRGs possess low equipartition magnetic field strengths and energy densities of their cocoons. This matches the statement of Colgate & Li [1] who affirm that for most radio sources located in a low-density environment only a small fraction of the magnetic energy is dissipated in the form of synchrotron radiation while the bulk of the magnetic energy is deposited in the walls and voids of the Universe. Kronberg et al. [2] suggest that the magnetic energy which originates from AGN outflows and which is stored in the intergalactic magnetic field has a major influence on the evolution of galaxies and visible structure formation on scales of up to ~ 1Mpc.
16. RADIO MONITORING OF THE PERIODICALLY VARIABLE IR SOURCE LRLL 54361: NO DIRECT CORRELATION BETWEEN THE RADIO AND IR EMISSIONS
SciTech Connect
Forbrich, Jan; Rodríguez, Luis F.; Palau, Aina; Zapata, Luis A.; Muzerolle, James; Gutermuth, Robert A.
2015-11-20
LRLL 54361 is an infrared source located in the star-forming region IC 348 SW. Remarkably, its infrared luminosity increases by a factor of 10 over roughly one week every 25.34 days. To understand the origin of these remarkable periodic variations, we obtained sensitive 3.3 cm JVLA radio continuum observations of LRLL 54361 and its surroundings in six different epochs: three of them during the IR-on state and three during the IR-off state. The radio source associated with LRLL 54361 remained steady and did not show a correlation with the IR variations. We suggest that the IR is tracing the results of fast (with a timescale of days) pulsed accretion from an unseen binary companion, while the radio traces an ionized outflow with an extent of ∼100 AU that smooths out the variability over a period of the order of a year. The average flux density measured in these 2014 observations, 27 ± 5 μJy, is about a factor of two less than that measured about 1.5 years before, 53 ± 11 μJy, suggesting that variability in the radio is present, but over larger timescales than in the IR. We discuss other sources in the field, in particular two infrared/X-ray stars that show rapidly varying gyrosynchrotron emission.
17. Control of Jupiter's radio emission and aurorae by the solar wind.
PubMed
Gurnett, D A; Kurth, W S; Hospodarsky, G B; Persoon, A M; Zarka, P; Lecacheux, A; Bolton, S J; Desch, M D; Farrell, W M; Kaiser, M L; Ladreiter, H-P; Rucker, H O; Galopeau, P; Louarn, P; Young, D T; Pryor, W R; Dougherty, M K
2002-02-28
Radio emissions from Jupiter provided the first evidence that this giant planet has a strong magnetic field and a large magnetosphere. Jupiter also has polar aurorae, which are similar in many respects to Earth's aurorae. The radio emissions are believed to be generated along the high-latitude magnetic field lines by the same electrons that produce the aurorae, and both the radio emission in the hectometric frequency range and the aurorae vary considerably. The origin of the variability, however, has been poorly understood. Here we report simultaneous observations using the Cassini and Galileo spacecraft of hectometric radio emissions and extreme ultraviolet auroral emissions from Jupiter. Our results show that both of these emissions are triggered by interplanetary shocks propagating outward from the Sun. When such a shock arrives at Jupiter, it seems to cause a major compression and reconfiguration of the magnetosphere, which produces strong electric fields and therefore electron acceleration along the auroral field lines, similar to the processes that occur during geomagnetic storms at the Earth.
18. Gamma-ray Burst Reverse Shock Emission in Early Radio Afterglows
Resmi, Lekshmi; Zhang, Bing
2016-07-01
Reverse shock (RS) emission from gamma-ray bursts is an important tool in investigating the nature of the ejecta from the central engine. If the magnetization of the ejecta is not high enough to suppress the RS, a strong RS emission component, usually peaking in the optical/IR band early on, would provide an important contribution to early afterglow light curve. In the radio band, synchrotron self-absorption may suppress early RS emission and also delay the RS peak time. In this paper, we calculate the self-absorbed RS emission in the radio band under different dynamical conditions. In particular, we stress that the RS radio emission is subject to self-absorption in both RSs and forward shocks (FSs). We calculate the ratio between the RS to FS flux at the RS peak time for different frequencies, which is a measure of the detectability of the RS emission component. We then constrain the range of physical parameters for a detectable RS, in particular the role of magnetization. We notice that unlike optical RS emission which is enhanced by moderate magnetization, moderately magnetized ejecta do not necessarily produce a brighter radio RS due to the self-absorption effect. For typical parameters, the RS emission component would not be detectable below 1 GHz unless the medium density is very low (e.g., n < 10-3 cm-3 for the interstellar medium and A * < 5 × 10-4 for wind). These predictions can be tested using the afterglow observations from current and upcoming radio facilities such as the Karl G. Jansky Very Large Array, the Low-Frequency Array, the Five Hundred Meter Aperture Spherical Telescope, and the Square Kilometer Array.
19. Auroral medium frequency burst radio emission associated with the 23 March 2007 THEMIS study substorm
Bunch, N. L.; Labelle, J.; Weatherwax, A. T.; Hughes, J. M.
2008-01-01
Auroral medium frequency (MF) burst is an impulsive auroral radio emission associated with substorm onset detected by ground-based instruments between 1.3 and 4.5 MHz. On 23 March 2007 an MF burst emission was detected by the Dartmouth radio interferometer located near Toolik Lake, Alaska. This emission temporally coincides with the onset of the 23 March 2007 Time History of Events and Macroscale Interactions during Substorms (THEMIS) study substorm. Directions of arrival computed using the Dartmouth radio interferometer for this event also coincide spatially with the location of the expanding auroral arcs to the south observed by the all-sky imager at Fort Yukon, Alaska. This observation represents the first example of a direction of arrival measurement for MF burst. It strongly supports the association of MF burst with intense auroral arcs accompanying substorm onset. The direction of arrival of the MF burst is consistent with the direction to the eastern edge of the substorm onset location determined by multiple data sets during this substorm and suggests that location of MF burst radio emissions may be an effective method of locating substorm onsets, much as radio atmospherics are used to locate lightning.
20. Bright radio emission from an ultraluminous stellar-mass microquasar in M 31.
PubMed
Middleton, Matthew J; Miller-Jones, James C A; Markoff, Sera; Fender, Rob; Henze, Martin; Hurley-Walker, Natasha; Scaife, Anna M M; Roberts, Timothy P; Walton, Dominic; Carpenter, John; Macquart, Jean-Pierre; Bower, Geoffrey C; Gurwell, Mark; Pietsch, Wolfgang; Haberl, Frank; Harris, Jonathan; Daniel, Michael; Miah, Junayd; Done, Chris; Morgan, John S; Dickinson, Hugh; Charles, Phil; Burwitz, Vadim; Della Valle, Massimo; Freyberg, Michael; Greiner, Jochen; Hernanz, Margarita; Hartmann, Dieter H; Hatzidimitriou, Despina; Riffeser, Arno; Sala, Gloria; Seitz, Stella; Reig, Pablo; Rau, Arne; Orio, Marina; Titterington, David; Grainge, Keith
2013-01-10
A subset of ultraluminous X-ray sources (those with luminosities of less than 10(40) erg s(-1); ref. 1) are thought to be powered by the accretion of gas onto black holes with masses of ∼5-20M cicled dot, probably by means of an accretion disk. The X-ray and radio emission are coupled in such Galactic sources; the radio emission originates in a relativistic jet thought to be launched from the innermost regions near the black hole, with the most powerful emission occurring when the rate of infalling matter approaches a theoretical maximum (the Eddington limit). Only four such maximal sources are known in the Milky Way, and the absorption of soft X-rays in the interstellar medium hinders the determination of the causal sequence of events that leads to the ejection of the jet. Here we report radio and X-ray observations of a bright new X-ray source in the nearby galaxy M 31, whose peak luminosity exceeded 10(39) erg s(-1). The radio luminosity is extremely high and shows variability on a timescale of tens of minutes, arguing that the source is highly compact and powered by accretion close to the Eddington limit onto a black hole of stellar mass. Continued radio and X-ray monitoring of such sources should reveal the causal relationship between the accretion flow and the powerful jet emission.
1. Time-scales of close-in exoplanet radio emission variability
See, V.; Jardine, M.; Fares, R.; Donati, J.-F.; Moutou, C.
2015-07-01
We investigate the variability of exoplanetary radio emission using stellar magnetic maps and 3D field extrapolation techniques. We use a sample of hot Jupiter hosting stars, focusing on the HD 179949, HD 189733 and τ Boo systems. Our results indicate two time-scales over which radio emission variability may occur at magnetized hot Jupiters. The first is the synodic period of the star-planet system. The origin of variability on this time-scale is the relative motion between the planet and the interplanetary plasma that is corotating with the host star. The second time-scale is the length of the magnetic cycle. Variability on this time-scale is caused by evolution of the stellar field. At these systems, the magnitude of planetary radio emission is anticorrelated with the angular separation between the subplanetary point and the nearest magnetic pole. For the special case of τ Boo b, whose orbital period is tidally locked to the rotation period of its host star, variability only occurs on the time-scale of the magnetic cycle. The lack of radio variability on the synodic period at τ Boo b is not predicted by previous radio emission models, which do not account for the co-rotation of the interplanetary plasma at small distances from the star.
2. Drifting tadpoles'' in wavelet spectra of decimetric radio emission of fiber bursts
Mészárosová, H.; Karlický, M.; Rybák, J.; Jiřička, K.
2009-08-01
3. Simulation of radio emission from air showers in atmospheric electric fields
SciTech Connect
Buitink, S.; Huege, T.; Falcke, H; Kuijpers, J.
2010-02-25
We study the effect of atmospheric electric fields on the radio pulse emitted by cos- mic ray air showers. Under fair weather conditions the dominant part of the radio emission is driven by the geomagnetic field. When the shower charges are accelerated and deflected in an electric field additional radiation is emitted. We simulate this effect with the Monte Carlo code REAS2, using CORSIKA-simulated showers as input. In both codes a routine has been implemented that treats the effect of the electric field on the shower particles. We find that the radio pulse is significantly altered in background fields of the order of ~100 V/cm and higher. Practically, this means that air showers passing through thunderstorms emit radio pulses that are not a reliable measure for the shower energy. Under other weather circumstances significant electric field effects are expected to occur rarely, but nimbostratus clouds can harbor fields that are large enough. In general, the contribution of the electric field to the radio pulse has polarization properties that are different from the geomagnetic pulse. In order to filter out radio pulses that have been affected by electric field effects, radio air shower experiments should keep weatherinformation and perform full polarization measurements of the radio signal.
4. Sampling Studies Of Quasars, Radio-loud Galaxies, & Radio-quiet Galaxies -- Searching For The Cause Of Radio Emission
Coldwell, G.; Salois, Amee; Soechting, I.; Smith, M.
2011-01-01
Comparing the environments of Radio-Loud Galaxies, Radio-Quiet Galaxies, and Quasars offers an opportunity to study the evolution of these objects. Our samples have been carefully chosen from Data Release 7 of the Sloan Digital Sky Survey, which also includes samples studied in the FIRST survey, and have been cut to determine the best possible results. Our study includes three samples. The Quasar sample currently contains 69 objects, the Radio-Loud Galaxy (RLG) sample has 1,335 objects, and the Radio-Quiet Galaxy (RQG) sample contains 2,436 objects (any updates will be given at the meeting). A number of trims were made to produce (smaller) samples with characteristics suited for precise results. By comparing the environments of these three samples we will be able to see any similarities or differences between them. If similarities are detected it suggests that the central object has evolved according to 'nature' - in an isolated manner with little environmental feedback, which may or may not have an effect on its evolution, as supposed by Coldwell et al. (2009). If differences are detected it suggests that the central object has evolved according to nurture’ and that the environment may have played an important role in the development of their properties. We employ similar procedures used by Coldwell et al. (2009) in their study of blue and red AGNs. Upon the completion of an accurate sample, future work will be pursued studying a number of properties of the environments including studies of: the stellar masses, star formation rates, sersic morphologies, as well as densities and ages of the environments.
5. The influence of eclipses in the stellar radio emission
2017-10-01
Here we simulate the shape of a planetary transit observed at radio wavelengths. The simulations use a light curve of the K4 star HAT-P-11 and its hot Jupiter companion as proxy. From the HAT-P-11 optical light curve, a prominent spot was identified (1.10 R P and 0.6 I C ). On the radio regime, the limb brighting of 30% was simulated by a quadratic function, and the active region was assumed to have the same size of the optical spot. Considering that the planet size is 6.35% of the the stellar radius, for the quiet star regions the transit depth is smaller than 0.5%, however, this value can increase to ~2% when covering an active region with 5.0 times the quiet star brightness temperature.
6. Observations of the solar radio emission with the Callisto spectrometer
Monstein, Kh. A.; Lesovoy, S. V.; Maslov, A. I.
2009-12-01
In the framework of the program for setting the Callisto spectrometer network into operation, the spectral measurements were carried out at the sites of spectrometer locations in India and Russia in winter 2006. The results achieved at Badary, the site where the Siberian Solar Radio Telescope (SSRT) is located, are presented. The measurements were performed using a broadband log-periodic antenna connected to the Callisto spectrometer developed at the Institute of Astronomy (Zurich). The results of these measurements should explain whether spectral studies at frequencies below 1 GHz can be performed using such antennas or new antennas should be developed. The presented results are compared with the similar results obtained in Switzerland in the frequency intervals of interest for radio astronomy. Concerning electromagnetic noise, Badary is a better site for observing the Sun in the 50-800 MHz frequency range as compared to observatories in Switzerland.
7. Radio emission evolution of nonstationary sources in the Hedgehog model
NASA Technical Reports Server (NTRS)
Kovalev, Y. A.; Mikhaylutsa, V. P.
1980-01-01
Correlations are obtained for numerical calculation of flux F sub v and polarized radiation intensity of a cloud of arbitrary geometry, consisting of ultrarelativistic electrons that dissipate in a radial magnetic field of the nucleus at a random angle to the observer. It is possible that some of the variable extragalactic objects that were previously described by the Shklovskiy model are young formations in the examined model. Radio astronomical observations would permit a determination of their distance, age, and lifetime.
8. Searching towards the Galactic Centre region for pulsed radio emission
Toomey, Lawrence; Johnston, Simon; Hobbs, George; Bhat, Ramesh; Shannon, Ryan
2014-10-01
A search of archival Parkes survey data has uncovered a source similar to that of a radio pulsar, however the detection DM indicates that it may be either the closest pulsar ever discovered, or simply a case of mistaken identity and is in fact an RFI event that closely mimics that of a pulsar signal. We would like to propose a grid search of the location of this source, at 3 available frequency bands, in order to determine its nature.
9. Search of the radio emission from flare stars at decameter wavelengths
Boiko, A. I.; Konovalenko, A. A.; Koliadin, V. L.; Melnik, V. N.
2012-11-01
Observations of the two M-dwarf flare stars (AD Leonis and EV Lacertae), which were carried out with the radio telescope UTR-2 (Kharkiv, Ukraine) in the range of 16.5-33 MHz, are presented. 167 events of radio emission from AD Leo and 73 events from EV Lac were detected in the period of 2010-2011. These events were considered as stellar emission in ON-OFF regime of observations. The morphology of the probable events in the form of bursts from flare stars is considered and frequency drift rates, durations and fluxes of the bursts are analysed.
Hjellming, Robert M.
The state of knowledge on continuum radio emission from the stars is considered. Fundamental radio emission process and stellar radiative transfer are reviewed, and solar radio emission is examined. Flare stars and active binaries are addressed, and stellar winds and cataclysmic variables are considered. Radio-emitting X-ray binaries are discussed.
11. Detection of Nonthermal Radio Emission from a Polar coronal mass ejection
Gopalswamy, Nat; Reiner, Mike J.; Makela, Pertti; Yashiro, Seiji; Akiyama, Sachiko
2016-07-01
12. Detection of fundamental and harmonic type III radio emission and the associated Langmuir waves at the source region
NASA Technical Reports Server (NTRS)
Reiner, M. J.; Stone, R. G.; Fainberg, J.
1992-01-01
Type III radio emission generated in the vicinity of the Ulysses spacecraft has been detected at both the fundamental and harmonic of the local plasma frequency. The observations represent the first clear evidence of locally generated type III radio emission. This local emission shows no evidence of frequency drift, exhibits a relatively short rise time, is less intense than the observed remotely generated radio emission, and is temporally correlated with observed in situ Langmuir waves. The observations were made with the unified radio astronomy and wave (URAP) experiment on the Ulysses spacecraft between 1990 November 4 and 1991 April 30, as it traveled from 1 to 3 AU from the sun. During this time period many thousands of bursts were observed. However, only three examples of local emission and associated Langmuir waves were identified. This supports previous suggestions that type III radio emission is generated in localized regions of the interplanetary medium, rather than uniformly along the extent of the electron exciter beam.
13. The ATLAS3D Project - XXXI. Nuclear radio emission in nearby early-type galaxies
Nyland, Kristina; Young, Lisa M.; Wrobel, Joan M.; Sarzi, Marc; Morganti, Raffaella; Alatalo, Katherine; Blitz, Leo; Bournaud, Frédéric; Bureau, Martin; Cappellari, Michele; Crocker, Alison F.; Davies, Roger L.; Davis, Timothy A.; de Zeeuw, P. T.; Duc, Pierre-Alain; Emsellem, Eric; Khochfar, Sadegh; Krajnović, Davor; Kuntschner, Harald; McDermid, Richard M.; Naab, Thorsten; Oosterloo, Tom; Scott, Nicholas; Serra, Paolo; Weijmans, Anne-Marie
2016-05-01
We present the results of a high-resolution, 5 GHz, Karl G. Jansky Very Large Array study of the nuclear radio emission in a representative subset of the ATLAS3D survey of early-type galaxies (ETGs). We find that 51 ± 4 per cent of the ETGs in our sample contain nuclear radio emission with luminosities as low as 1018 W Hz-1. Most of the nuclear radio sources have compact (≲25-110 pc) morphologies, although ˜10 per cent display multicomponent core+jet or extended jet/lobe structures. Based on the radio continuum properties, as well as optical emission line diagnostics and the nuclear X-ray properties, we conclude that the majority of the central 5 GHz sources detected in the ATLAS3D galaxies are associated with the presence of an active galactic nucleus (AGN). However, even at subarcsecond spatial resolution, the nuclear radio emission in some cases appears to arise from low-level nuclear star formation rather than an AGN, particularly when molecular gas and a young central stellar population is present. This is in contrast to popular assumptions in the literature that the presence of a compact, unresolved, nuclear radio continuum source universally signifies the presence of an AGN. Additionally, we examine the relationships between the 5 GHz luminosity and various galaxy properties including the molecular gas mass and - for the first time - the global kinematic state. We discuss implications for the growth, triggering, and fuelling of radio AGNs, as well as AGN-driven feedback in the continued evolution of nearby ETGs.
14. Heliospheric 2-3 kHz radio emissions and their relationship to large Forbush decreases
NASA Technical Reports Server (NTRS)
Gurnett, D. A.; Kurth, W. S.
1995-01-01
Two intense heliospheric 2-3 kHz radio emission events have been observed by Voyagers 1 and 2, the first in 1983-84 and the second in 1992-93. These radio emission events occurred about 400 days after large Forbush decreases in mid-1982 and mid-1991. Since Forbush decreases are indicative of a strong interplanetary shock propagating outward through the heliosphere, this temporal relationship provides strong evidence that the radio emissions are triggered by the interaction of a shock with one of the outer boundaries of the heliosphere. From the travel time and the known speed of the shock, the distance to the interaction region can be estimated and is well beyond 100 AU. At this great distance the plasma frequency at the terminal shock (100 to 200 Hz) is believed to be too small to explain the observed emission frequencies, which extend up to 3.6 kHz. For this reason, we have proposed that the interaction takes place at or near the heliopause, where remote sensing measurements show that the plasma frequency is in a suitable range (approximately 3 kHz) for explaining the radio emission. From the travel time and shock propagation speed, the radial distance to the heliopause has been calculated for various candidate solar events. After taking into account the likely deceleration of the shock, the heliopause is estimated to be in the range from about 110 to 160 AU.
15. Correlated spin-down rates and radio emission in PSR B1859+07
Perera, B. B. P.; Stappers, B. W.; Weltevrede, P.; Lyne, A. G.; Rankin, J. M.
2016-01-01
We study the spin-down changes of PSR B1859+07 over a period of more than 28 years of radio observation. We identify that the time derivative of the rotational frequency (ν) varies quasi-periodically with a period of ˜350 d, switching mainly between two spin-down states. The profile shape of the pulsar is correlated with the ν˙ variation, producing two slightly different profile shapes corresponding to high- and low-ν˙ states. In addition to these two normal emission states, we confirm the occasional flare-state of the pulsar, in which the emission appears early in spin phase compared to that of the common normal emission. The profile of the flare-state is significantly different from that of the two normal emission states. The correlation analysis further shows that the flare-state is not directly linked with the ν˙ changes. With a simple emission beam model, we estimate the emission altitude of the normal emission to be 240 km, and explain the origin of the flare-state as an emission height variation from the leading edge of the beam. We also argue that the emission of these states can be explained with a partially active beam model. In this scenario, the trailing portion of the radio beam is usually active and the normal emission is produced. The flare-state occurs when the leading edge of the beam becomes active while the trailing part is being blocked. This model estimates a fixed emission altitude of 360 km. However, the cause of the flare-state (i.e. the emission height variation, or the time-dependent activity across the radio beam) is not easily explained.
16. Simultaneous observations of solar sporadic radio emission by the radio telescopes UTR-2, URAN-2 and NDA within the frequency range 8-42 MHz
Melnik, V.; Konovalenko, A.; Brazhenko, A.; Briand, C.; Dorovskyy, V.; Zarka, P.; Denis, L.; Bulatzen, V.; Frantzusenko, A.; Rucker, H.; Stanislavskyy, A.
2012-09-01
From 25 June till 12 August 2011 sporadic solar radio emission was observed simultaneously by three separate radio telescopes: UTR-2 (Kharkov, Ukraine), URAN-2 (Poltava, Ukraine) and NDA (Nancay, France). During these observations some interesting phenomena were observed. Some of them are discussed in this paper.
17. Beamed and Unbeamed X-Ray Emission in FR1 Radio Galaxies
NASA Technical Reports Server (NTRS)
Worrall, Diana M.
2000-01-01
The research exploited ROSAT's sensitivity, together with its spatial and spectral resolution, to separate X-ray emission components in the sources. Prior to ROSAT, the dominant X-ray emission mechanism in radio galaxies as a class was unclear, with correlations between the X-ray and radio emission used on one hand to argue for a nuclear origin for the X-rays, and on the other hand for a thermal origin. Our observations (normally between 10 and 25 ks in length) routinely detected the target sources, and demonstrated that both resolved (thermal) and unresolved X-ray emission are typically present. Highlights of our work included two of the first detections of high-power radio galaxies at high redshift, 3C 280 and 3C 220.1. When combined with the work of two other groups, we find that of the 38 radio galaxies at z > 0.6 in the 3CRR sample, 12 were observed in ROSAT pointed observations and 9 were detected with the four most significant detections exhibiting source extent, including 3C 280 and 3C 220.1. Moreover, we discovered extended emission around five 3CRR quasars at redshift greater than about 0.4, one of which is at z > 0.6. Unification predicts that the X-ray environments of powerful radio galaxies and quasars should be similar, and our results show that powerful radio sources are finding some of the highest-redshift X-ray clusters known to date, pointing to deep gravitational potential wells early in the Universe.
18. Detection of Radio Emission from the Hyperactive L Dwarf 2MASS J13153094-2649513AB
Burgasser, Adam J.; Melis, Carl; Zauderer, B. Ashley; Berger, Edo
2013-01-01
We report the detection of radio emission from the unusually active L5e + T7 binary 2MASS J13153094-2649513AB made with the Australian Telescope Compact Array. Observations at 5.5 GHz reveal an unresolved source with a continuum flux of 370 ± 50 μJy, corresponding to a radio luminosity of L rad = νL ν = (9 ± 3)×1023 erg s-1 and log10 L rad/L bol = -5.44 ± 0.22. No detection is made at 9.0 GHz to a 5σ limit of 290 μJy, consistent with a power-law spectrum S νvpropν-α with α >~ 0.5. The emission is quiescent, with no evidence of variability or bursts over three hours of observation, and no measurable polarization (V/I < 34%). 2MASS J1315-2649AB is one of the most radio-luminous ultracool dwarfs detected in quiescent emission to date, comparable in strength to other cool sources detected in outburst. Its detection indicates no decline in radio flux through the mid-L dwarfs. It is unique among L dwarfs in having strong and persistent Hα and radio emission, indicating the coexistence of a cool, neutral photosphere (low electron density) and a highly active chromosphere (high electron density and active heating). These traits, coupled with the system's mature age and substellar secondary, make 2MASS J1315-2649AB an important test for proposed radio emission mechanisms in ultracool dwarfs.
19. THE CONNECTION BETWEEN THE RADIO JET AND THE GAMMA-RAY EMISSION IN THE RADIO GALAXY 3C 120
SciTech Connect
Casadio, Carolina; Gómez, José L.; Grandi, Paola; Jorstad, Svetlana G.; Marscher, Alan P.; Lister, Matthew L.; Kovalev, Yuri Y.; Pushkarev, Alexander B.
2015-08-01
We present the analysis of the radio jet evolution of the radio galaxy 3C 120 during a period of prolonged γ-ray activity detected by the Fermi satellite between 2012 December and 2014 October. We find a clear connection between the γ-ray and radio emission, such that every period of γ-ray activity is accompanied by the flaring of the millimeter very long baseline interferometry (VLBI) core and subsequent ejection of a new superluminal component. However, not all ejections of components are associated with γ-ray events detectable by Fermi. Clear γ-ray detections are obtained only when components are moving in a direction closer to our line of sight. This suggests that the observed γ-ray emission depends not only on the interaction of moving components with the millimeter VLBI core, but also on their orientation with respect to the observer. Timing of the γ-ray detections and ejection of superluminal components locate the γ-ray production to within ∼0.13 pc from the millimeter VLBI core, which was previously estimated to lie about 0.24 pc from the central black hole. This corresponds to about twice the estimated extension of the broad line region, limiting the external photon field and therefore suggesting synchrotron self Compton as the most probable mechanism for the production of the γ-ray emission. Alternatively, the interaction of components with the jet sheath can provide the necessary photon field to produced the observed γ-rays by Compton scattering.
20. Effects of exomoon’s magnetic field on generation of radio emissions
Griffith, John; Noyola, Joaquin; Satyal, Suman; Musielak, Zdzislaw E.
2017-01-01
In the recent work by Noyola et al. (2014, 2016), a novel technique of detection of exomoons through the radio emissions produced by the magnetic field interactions between exoplanet-exomoon pair is emulated based upon the processes occurring in the Jupiter-Io system. Their calculations have shown that the radio signal from the distant extra-solar planetary systems is detectable by current technology provided that the systems emanating the radio waves are relatively closer, have some form of atmosphere, and have larger exomoons. In this work, we explore the effect of exomoon’s magnetic field on the radio emission processes by considering a hypothetical magnetic exomoon and re-calculating the resulting radio flux. Then, a limit to the exomoon’s magnetic field is proposed based on the signal amplification versus the dampening effect the magnetic field induces on the secondary conditions such as the containment of ions within the exomoon’s magnetic field and the effect of the plasma torus density that co-orbits with the moon. The energy from the exomoon’s magnetic field is expected to amplify the radio signal, hence increasing the probability of detection of the first exomoons.
1. Discovery of radio emission from the brown dwarf LP944-20.
PubMed
Berger, E; Ball, S; Becker, K M; Clarke, M; Frail, D A; Fukuda, T A; Hoffman, I M; Mellon, R; Momjian, E; Murphy, N W; Teng, S H; Woodruff, T; Zauderer, B A; Zavala, R T
2001-03-15
Brown dwarfs are not massive enough to sustain thermonuclear fusion of hydrogen at their centres, but are distinguished from gas-giant planets by their ability to burn deuterium. Brown dwarfs older than approximately 10 Myr are expected to possess short-lived magnetic fields and to emit radio and X-rays only very weakly from their coronae. An X-ray flare was recently detected on the brown dwarf LP944-20, whereas previous searches for optical activity (and one X-ray search) yielded negative results. Here we report the discovery of quiescent and flaring radio emission from LP944-20, with luminosities several orders of magnitude larger than predicted by the empirical relation between the X-ray and radio luminosities that has been found for many types of stars. Interpreting the radio data within the context of synchrotron emission, we show that LP944-20 has an unusually weak magnetic field in comparison to active M-dwarf stars, which might explain the previous null optical and X-ray results, as well as the strength of the radio emissions compared to those at X-ray wavelengths.
2. Oscillation of solar radio emission at coronal acoustic cut-off frequency
Pylaev, O. S.; Zaqarashvili, T. V.; Brazhenko, A. I.; Melnik, V. N.; Hanslmeier, A.; Panchenko, M.
2017-05-01
Recent SECCHI COR2 observations on board STEREO-A spacecraft have detected density structures at a distance of 2.5-15 R0 propagating with periodicity of about 90 min. The observations show that the density structures probably formed in the lower corona. We used the large Ukrainian radio telescope URAN-2 to observe type IV radio bursts in the frequency range of 8-32 MHz during the time interval of 08:15-11:00 UT on August 1, 2011. Radio emission in this frequency range originated at the distance of 1.5-2.5 R0 according to the Baumbach-Allen density model of the solar corona. Morlet wavelet analysis showed the periodicity of 80 min in radio emission intensity at all frequencies, which demonstrates that there are quasi-periodic variations of coronal density at all heights. The observed periodicity corresponds to the acoustic cut-off frequency of stratified corona at a temperature of 1 MK. We suggest that continuous perturbations of the coronal base in the form of jets/explosive events generate acoustic pulses, which propagate upwards and leave the wake behind oscillating at the coronal cut-off frequency. This wake may transform into recurrent shocks due to the density decrease with height, which leads to the observed periodicity in the radio emission. The recurrent shocks may trigger quasi-periodic magnetic reconnection in helmet streamers, where the opposite field lines merge and consequently may generate periodic density structures observed in the solar wind.
3. THE UBIQUITOUS RADIO CONTINUUM EMISSION FROM THE MOST MASSIVE EARLY-TYPE GALAXIES
SciTech Connect
Brown, Michael J. I.; Jannuzi, Buell T.; Floyd, David J. E.; Mould, Jeremy R.
2011-04-20
We have measured the radio continuum emission of 396 early-type galaxies brighter than K = 9, using 1.4 GHz imagery from the NRAO Very Large Array Sky Survey, Green Bank 300 ft Telescope, and 64 m Parkes Radio Telescope. For M{sub K} < -24 early-type galaxies, the distribution of radio powers at fixed absolute magnitude spans four orders of magnitude and the median radio power is proportional to K-band luminosity to the power 2.78 {+-} 0.16. The measured flux densities of M{sub K} < -25.5 early-type galaxies are greater than zero in all cases. It is thus highly likely that the most massive galaxies always host an active galactic nucleus or have recently undergone star formation.
4. Radio emission of energetic cosmic ray air showers: Polarization measurements with LOPES
Lopes Collaboration; Isar, P. G.; Apel, W. D.; Arteaga, J. C.; Asch, T.; Auffenberg, J.; Badea, F.; Bähren, L.; Bekk, K.; Bertaina, M.; Biermann, P. L.; Blümer, J.; Bozdog, H.; Brancus, I. M.; Brüggemann, M.; Buchholz, P.; Buitink, S.; Cantoni, E.; Chiavassa, A.; Cossavella, F.; Daumiller, K.; de Souza, V.; di Pierro, F.; Doll, P.; Engel, R.; Falcke, H.; Finger, M.; Fuhrmann, D.; Gemmeke, H.; Ghia, P. L.; Glasstetter, R.; Grupen, C.; Haungs, A.; Heck, D.; Hörandel, J. R.; Horneffer, A.; Huang, X.; Huege, T.; Kampert, K.-H.; Kang, D.; Kickelbick, D.; Kolotaev, Y.; Krömer, O.; Kuijpers, J.; Lafebre, S.; Łuczak, P.; Mathes, H. J.; Mayer, H. J.; Milke, J.; Mitrica, B.; Morello, C.; Navarra, G.; Nehls, S.; Nigl, A.; Oehlschläger, J.; Over, S.; Petcu, M.; Pierog, T.; Rautenberg, J.; Rebel, H.; Roth, M.; Saftoiu, A.; Schieler, H.; Schmidt, A.; Schröder, F.; Sima, O.; Singh, K.; Stümpert, M.; Toma, G.; Trinchero, G. C.; Ulrich, H.; Walkowiak, W.; Weindl, A.; Wochele, J.; Wommer, M.; Zabierowski, J.; Zensus, J. A.; LOPES Collaboration
2009-06-01
LOPES is a radio antenna array co-located with the Karlsruhe Shower Core and Array DEtector, KASCADE-Grande in Forschungszentrum Karlsruhe, Germany, which provides well-calibrated trigger information and air shower parameters for primary energies up to 10eV. By the end of 2006, the radio antennas were re-configured to perform polarization measurements of the radio signal of cosmic ray air showers, recording in the same time both, the East-West and North-South polarization directions of the radio emission. The main goal of these measurements is to reconstruct the polarization characteristics of the emitted signal. This will allow a detailed comparison with theoretical predictions. The current status of these measurements is reported here.
5. The Relationship Between Solar Radio and Hard X-Ray Emission
NASA Technical Reports Server (NTRS)
White, S. M.; Benz, A. O.; Christe, S.; Farnik, F.; Kundu, M. R.; Mann, G.; Ning, Z.; Raulin, J.-P.; Silva-Valio, A. V. R.; Saint-Hilaire, P.; Vilmer, N.; Warmuth, A.
2011-01-01
This review discusses the complementary relationship between radio and hard Xray observations of the Sun using primarily results from the era of the Reuven Ramaty High Energy Solar Spectroscopic Imager satellite. A primary focus of joint radio and hard X-ray studies of solar flares uses observations of nonthermal gyrosynchrotron emission at radio wavelengths and bremsstrahlung hard X-rays to study the properties of electrons accelerated in the main flare site, since it is well established that these two emissions show very similar temporal behavior. A quantitative prescription is given for comparing the electron energy distributions derived separately from the two wavelength ranges: this is an important application with the potential for measuring the magnetic field strength in the flaring region, and reveals significant differences between the electrons in different energy ranges. Examples of the use of simultaneous data from the two wavelength ranges to derive physical conditions are then discussed, including the case of microflares, and the comparison of images at radio and hard X-ray wavelengths is presented. There have been puzzling results obtained from observations of solar flares at millimeter and submillimeter wavelengths, and the comparison of these results with corresponding hard X-ray data is presented. Finally, the review discusses the association of hard X-ray releases with radio emission at decimeter and meter wavelengths, which is dominated by plasma emission (at lower frequencies) and electron cyclotron maser emission (at higher frequencies), both coherent emission mechanisms that require small numbers of energetic electrons. These comparisons show broad general associations but detailed correspondence remains more elusive.
6. Aperture synthesis observations of solar and stellar radio emission
Bastian, Timothy Stephen
1987-06-01
The results of observations using the Very Large Array are presented in three major sections. The first discusses maximum entropy-type image reconstruction techniques that were applied. Both single disk and interferometer data were used to generate full disk images of the sun at a wavelength of approximately 21 cm. Using a set of six such images obtained during the sun's decline from sunspot maximum to minimum, a number of previously unreported phenomena were noted. Among these: (1) a systematic decrease in quiet sun's brightness temperature as it declined to minimum; (2) a systematic decrease in the sun's radius at 21 cm; and (3) evidence for the evolution of polar coronal holes during the course of the solar cycle. The observed variation, though not noted previously at radio wavelengths, is entirely consistent with white light K coronagraph data. The results reported here explain the conflicting nature of a number of past observations. The second section presents the results of a long term survey of magnetic cataclysmic variables (CVs). Cataclysmic variables are close binary systems which contain a white dwarf accreting mass from a late-type secondary, typically a dwarf of spectral type G, K, or M. The third section presents new results on flare stars in the solar neighborhood and in the Pleiades. Of the nearly 170 sources found in the Pleiades' fields, all but two were determined to be extragalactic. Neither of the two stellar radio sources is a known flare star or a Pleiades member.
7. A giant radio flare from Cygnus X-3 with associated γ-ray emission: The 2011 radio and γ-ray flare of Cyg X-3
SciTech Connect
Corbel, S.; Dubus, G.; Tomsick, J. A.; Szostek, A.; Corbet, R. H. D.; Miller-Jones, J. C. A.; Richards, J. L.; Pooley, G.; Trushkin, S.; Dubois, R.; Hill, A. B.; Kerr, M.; Max-Moerbeck, W.; Readhead, A. C. S.; Bodaghee, A.; Tudose, V.; Parent, D.; Wilms, J.; Pottschmidt, K.
2012-04-10
With frequent flaring activity of its relativistic jets, Cygnus X-3 (Cyg X-3) is one of the most active microquasars and is the only Galactic black hole candidate with confirmed high-energy γ-ray emission, thanks to detections by Fermi Large Area Telescope (Fermi/LAT) and AGILE. In 2011, we observed Cyg X-3 in order to transit to a soft X-ray state, which is known to be associated with high-energy γ-ray emission. We present the results of a multiwavelength campaign covering a quenched state, when radio emission from Cyg X-3 is at its weakest and the X-ray spectrum is very soft. A giant (~20 Jy) optically thin radio flare marks the end of the quenched state, accompanied by rising non-thermal hard X-rays. Fermi/LAT observations (E≥ 100 MeV) reveal renewed γ-ray activity associated with this giant radio flare, suggesting a common origin for all non-thermal components. In addition, current observations unambiguously show that the γ-ray emission is not exclusively related to the rare giant radio flares. A three-week period of γ-ray emission is also detected when Cyg X-3 was weakly flaring in radio, right before transition to the radio quenched state. There were no γ-rays observed during the ~1-month long quenched state, when the radio flux is weakest. These results suggest transitions into and out of the ultrasoft X-ray (radio-quenched) state trigger γ-ray emission, implying a connection to the accretion process, and also that the γ-ray activity is related to the level of radio flux (and possibly shock formation), strengthening the connection to the relativistic jets.
8. A giant radio flare from Cygnus X-3 with associated γ-ray emission: The 2011 radio and γ-ray flare of Cyg X-3
DOE PAGES
Corbel, S.; Dubus, G.; Tomsick, J. A.; ...
2012-04-10
With frequent flaring activity of its relativistic jets, Cygnus X-3 (Cyg X-3) is one of the most active microquasars and is the only Galactic black hole candidate with confirmed high-energy γ-ray emission, thanks to detections by Fermi Large Area Telescope (Fermi/LAT) and AGILE. In 2011, we observed Cyg X-3 in order to transit to a soft X-ray state, which is known to be associated with high-energy γ-ray emission. We present the results of a multiwavelength campaign covering a quenched state, when radio emission from Cyg X-3 is at its weakest and the X-ray spectrum is very soft. A giant (~20more » Jy) optically thin radio flare marks the end of the quenched state, accompanied by rising non-thermal hard X-rays. Fermi/LAT observations (E≥ 100 MeV) reveal renewed γ-ray activity associated with this giant radio flare, suggesting a common origin for all non-thermal components. In addition, current observations unambiguously show that the γ-ray emission is not exclusively related to the rare giant radio flares. A three-week period of γ-ray emission is also detected when Cyg X-3 was weakly flaring in radio, right before transition to the radio quenched state. There were no γ-rays observed during the ~1-month long quenched state, when the radio flux is weakest. These results suggest transitions into and out of the ultrasoft X-ray (radio-quenched) state trigger γ-ray emission, implying a connection to the accretion process, and also that the γ-ray activity is related to the level of radio flux (and possibly shock formation), strengthening the connection to the relativistic jets.« less
9. Cassini and Wind Stereoscopic Observations of Jovian Non-Thermal Radio Emissions
NASA Technical Reports Server (NTRS)
Kaiser, Michael L.; Kurth, W. S.; Hospodarsky, G. B.; Gurnett, D. A.; Zarka, P.
1999-01-01
During two intervals in 1999, simultaneous observations of Jupiter's decametric and hectometric radio emissions were made with the Cassini radio and plasma wave instrument (RPWS) and the radio and plasma wave instrument (WAVES) on the Wind spacecraft in Earth orbit. During January, the Jovian longitude difference between the two spacecraft was about 5 deg, whereas for the August-September Earth flyby of Cassini, the angle ranged from 0 deg to about 2.5 deg. With these separations, the instantaneous widths of the walls of the hollow conical radiation beams of some of the decametric arcs were measured suggesting that the typical width is approximately 2 deg. The conical beams seem to move at Io's revolution rate rather than with Jupiter's rotation rate. Additionally, some of the non-arc emissions have very narrow and quite peculiar beamwidths.
10. Relationship between the bursts in solar local sources of centimeter radio emission.
Golubchina, O. A.
The author presents results of synchronous observations of local sources of solar radio emission at wavelengths 2.3 cm and 4.5 cm. The sources were observed with the RATAN-600 radio telescope by the relay method in February 1980 and July 1981. The author demonstrates that the synchronous brightenings of solar local sources actually exist even when the sources are 105km apart. They were recorded in virtually all cases of radio bursts of different kinds: 3 s, 5 s, 8 s, 28 PRF, 31 ABS, 45 s, 20 GRF, 21 GRF, 30 PBI. They are observed, as a rule, during the enhancement of soft X-ray emission. The lower limit of disturbing agent velocity ranges from 2×103 to 12×103km/s. The synchronous brightenings of local sources are more frequent than sympathetic bursts, and this invalidates the opinion that they are exotic phenomena.
11. ORIGIN OF ELECTRON CYCLOTRON MASER INDUCED RADIO EMISSIONS AT ULTRACOOL DWARFS: MAGNETOSPHERE-IONOSPHERE COUPLING CURRENTS
SciTech Connect
Nichols, J. D.; Burleigh, M. R.; Casewell, S. L.; Cowley, S. W. H.; Wynn, G. A.; Clarke, J. T.; West, A. A.
2012-11-20
A number of ultracool dwarfs emit circularly polarized radio waves generated by the electron cyclotron maser instability. In the solar system such radio is emitted from regions of strong auroral magnetic-field-aligned currents. We thus apply ideas developed for Jupiter's magnetosphere, being a well-studied rotationally dominated analog in our solar system, to the case of fast-rotating UCDs. We explain the properties of the radio emission from UCDs by showing that it would arise from the electric currents resulting from an angular velocity shear in the fast-rotating magnetic field and plasma, i.e., by an extremely powerful analog of the process that causes Jupiter's auroras. Such a velocity gradient indicates that these bodies interact significantly with their space environment, resulting in intense auroral emissions. These results strongly suggest that auroras occur on bodies outside our solar system.
12. The Absence of Radio Emission from the Globular Cluster G1
Miller-Jones, J. C. A.; Wrobel, J. M.; Sivakoff, G. R.; Heinke, C. O.; Miller, R. E.; Plotkin, R. M.; Di Stefano, R.; Greene, J. E.; Ho, L. C.; Joseph, T. D.; Kong, A. K. H.; Maccarone, T. J.
2012-08-01
The detections of both X-ray and radio emission from the cluster G1 in M31 have provided strong support for existing dynamical evidence for an intermediate-mass black hole (IMBH) of mass (1.8 ± 0.5) × 104 M ⊙ at the cluster center. However, given the relatively low significance and astrometric accuracy of the radio detection, and the non-simultaneity of the X-ray and radio measurements, this identification required further confirmation. Here we present deep, high angular resolution, strictly simultaneous X-ray and radio observations of G1. While the X-ray emission (L X = 1.74+0.53 -0.44 × 1036 (d/750 kpc)2 erg s-1 in the 0.5-10 keV band) remained fully consistent with previous observations, we detected no radio emission from the cluster center down to a 3σ upper limit of 4.7 μJy beam-1. Our favored explanation for the previous radio detection is flaring activity from a black hole low-mass X-ray binary (LMXB). We performed a new regression of the "Fundamental Plane" of black hole activity, valid for determining black hole mass from radio and X-ray observations of sub-Eddington black holes, finding log M BH = (1.638 ± 0.070)log L R - (1.136 ± 0.077)log L X - (6.863 ± 0.790), with an empirically determined uncertainty of 0.44 dex. This constrains the mass of the X-ray source in G1, if a black hole, to be <9.7 × 103 M ⊙ at 95% confidence, suggesting that it is a persistent LMXB. This annuls what was previously the most convincing evidence from radiation for an IMBH in the Local Group, though the evidence for an IMBH in G1 from velocity dispersion measurements remains unaffected by these results.
13. The influence of circumnuclear environment on the radio emission from TDE jets
Generozov, A.; Mimica, P.; Metzger, B. D.; Stone, N. C.; Giannios, D.; Aloy, M. A.
2017-01-01
Dozens of stellar tidal disruption events (TDEs) have been identified at optical, UV and X-ray wavelengths. A small fraction of these, most notably Swift J1644+57, produce radio synchrotron emission, consistent with a powerful, relativistic jet shocking the surrounding circumnuclear gas. The dearth of similar non-thermal radio emission in the majority of TDEs may imply that powerful jet formation is intrinsically rare, or that the conditions in galactic nuclei are typically unfavourable for producing a detectable signal. Here we explore the latter possibility by constraining the radial profile of the gas density encountered by a TDE jet using a one-dimensional model for the circumnuclear medium which includes mass and energy input from a stellar population. Near the jet Sedov radius of 1018 cm, we find gas densities in the range of n18 ˜ 0.1-1000 cm-3 across a wide range of plausible star formation histories. Using one- and two-dimensional relativistic hydrodynamical simulations, we calculate the synchrotron radio light curves of TDE jets (as viewed both on and off-axis) across the allowed range of density profiles. We find that bright radio emission would be produced across the plausible range of nuclear gas densities by jets as powerful as Swift J1644+57, and we quantify the relationship between the radio luminosity and jet energy. We use existing radio detections and upper limits to constrain the energy distribution of TDE jets. Radio follow-up observations several months to several years after the TDE candidate will strongly constrain the energetics of any relativistic flow.
14. Study of sub-auroral radio emissions observed by ICE experiment onboard DEMETER satellite
Boudjada, M. Y.; Galopeau, P. H. M.; Mogilevski, M. M.; Sawas, S.; Blecki, J.; Berthelier, J. J.; Voller, W.
2012-04-01
We report on the terrestrial kilometric and hectometric radio emissions recorded by the DEMETER/ICE (Instrument Champ Electrique) experiment. This instrument measures the electric field components of electromagnetic and electrostatic waves in the frequency range from DC to 3.25 MHz. Despite the limited satellite invariant latitude (data acquisition below about 65°), specific events have been observed, close to the sub-auroral region, in the frequency range from 100 kHz to about 1 MHz. This range covers the well-known auroral kilometric radiation (AKR), the terrestrial kilometric continuum, and the sub-auroral terrestrial emission at higher frequency up to 3 MHz. The high spectral capability of the experiment leads us to distinguish between the bursty and the continuum emissions. Selected events have been found to principally occur in the late evening and early morning sectors of the magnetosphere (22 MLT - 02 MLT) but others have been observed on the dayside. Our first results are compared to previous radio observations performed on board INTERBALL-1 (Kuril'chik et al, Cosmic Research, 43, 2005) and GEOTAIL (Hashimoto et al., JGR, 104, 1999) satellites. We also discuss the common and different features of the Earth and Jovian radio emissions. We emphasis on the observational parameters: the occurrence probability, the emission beam and the spectral emission types. We show that the physical interpretation of the auroral phenomena needs a good knowledge of the geometric configuration of the source and observer and the reception system (antenna beam and receivers).
15. Analysis of Saturnian planetary rotation following the knowledge on Jovian radio emission
Boudjada, Mohammed Y.; Galopeau, Patrick H. M.; Sawas, Sami; Lammer, Helmut
2017-04-01
We report on the Saturnian Radio Emission (SRE) recorded at Saturn by the Cassini Radio and Plasma Wave Science experiment (RPWS). We attempt to estimate the planetary rotation by applying the spectral method previously considered for the Jupiter radio emissions. This technique consists to distinguish between the spectral patterns occurring during one full Jovian rotation. Hence symmetrical features act around the axis of the planetary magnetic field due to the hollow cone beam. Therefore arc shapes appear with different orientations, i.e. vertex-early and -late arcs. This spectral 'symmetry' is fortified by the inclination between the geographical and the magnetic axes. The Saturnian radio emissions exhibit more spectral complexity because both axes (.i.e. magnetic and geographic) are quasi-aligned. Arc shapes are not frequently observed as in the case of Jupiter. We illustrate in our analysis that there is possibility to separate between Saturnian planetary rotations. Their occurrences are compared to the classic technique based on the variation of the Saturnian Kilometric Radiation (SKR) versus the sub-solar phase and the observation time (Kurth et al., JGR, 113, 2008). We discuss and we show that in several cases the planetary rotation accuracy is less than few minutes when combining both methods. We emphasize on spectral features by showing that the SRE and the SKR exhibit similar planetary rotation despite a difference in the emission frequency range.
16. Lateral distribution of radio emission and its dependence on air shower longitudinal development
SciTech Connect
Kalmykov, Nikolai N.; Konstantinov, Andrey A. E-mail: [email protected]
2012-12-01
The lateral distribution function (LDF) of radio emission from an extensive air shower is considered as the basic signature sensitive to the shower longitudinal development and, as a consequence, to the mass of a primary cosmic ray's particle that initiated a given shower. The peculiarities in the LDF's structure as well as their sensitivity to the height of shower maximum are investigated and explained.
17. Sporadic radio emission connected with a definite manifestation of solar activity in the near Earth space
NASA Technical Reports Server (NTRS)
Dudnic, A. V.; Zaljubovski, I. I.; Kartashev, V. M.; Shmatko, E. S.
1985-01-01
Sporadic radio emission of near Earth space at the frequency of 38 MHz is shown to appear in the event of a rapid development of instabilities in the ionospheric plasma. The instabilities are generated due to primary ionospheric disturbances occurring under the influence of solar chromospheric flares.
18. Young Stars and Non-Stella Emission in the Aligned Radio Galaxy 3C 256
NASA Technical Reports Server (NTRS)
Eisenhardt, P.; Simpson, C.; Armus, L.; Chokshi, A.; Dicksinson, M.; Djorgovski, S.; Elston, R.; Jannuzi, B.; McCarthy, P.; Pahre, M.;
1999-01-01
We present ground-based images of the z=1.824 radio galaxy 3C 256 in the standard BVRIJHK filters and an interference filter centered at 8800 A, a Hubble Space Telescope image in a filter dominated by Ly alpha emission (F336W), and spectra covering rest-frame wavelengths from Ly alpha to [O III} lambda 5007.
19. SciTech Connect
Dicken, D.; Axon, D.; Robinson, A.; Kharb, P.; Tadhunter, C.; Morganti, R. E-mail: [email protected] E-mail: [email protected]
2010-10-20
We present Spitzer photometric data for a complete sample of 19 low-redshift (z< 0.1) 3CRR radio galaxies as part of our efforts to understand the origin of the prodigious mid- to far-infrared (MFIR) emission from radio-loud active galactic nuclei (AGNs). Our results show a correlation between AGN power (indicated by [O III]{lambda}5007 emission line luminosity) and 24 {mu}m luminosity. This result is consistent with the 24 {mu}m thermal emission originating from warm dust heated directly by AGN illumination. Applying the same correlation test for 70 {mu}m luminosity against [O III] luminosity we find this relation to suffer from increased scatter compared to that of 24 {mu}m. In line with our results for the higher-radio-frequency-selected 2 Jy sample, we are able to show that much of this increased scatter is due to heating by starbursts that boost the far-infrared emission at 70 {mu}m in a minority of objects (17%-35%). Overall this study supports previous work indicating AGN illumination as the dominant heating mechanism for MFIR emitting dust in the majority of low-to-intermediate redshift radio galaxies (0.03 < z < 0.7), with the advantage of strong statistical evidence. However, we find evidence that the low-redshift broad-line objects (z < 0.1) are distinct in terms of their positions on the MFIR versus [O III] correlations.
20. VizieR Online Data Catalog: Jupiter decametric radio emissions over 26 years (Marques+, 2017)
Marques, M. S.; Zarka, P.; Echer, E.; Ryabov, V. B.; Alves, M. V.; Denis, L.; Coffre, A.
2017-05-01
We provide two files ('obs.dat' and 'em.dat') where the classification of decametric radio emission from Jupiter observed by Nancay Decametric Array during 26-years was done. The data is associated with the dynamic spectrums that you can access at https://www.obs-nancay.fr/ (Instruments/Decameter Array/Data availability/) (2 data files).
1. A parametric study of the propagation of auroral radio emissions through auroral cavities
Gautier, A.; Hess, S.; Cecconi, B.; Zarka, P. M.
2013-12-01
Auroral Kilometric Radiation is the radio counterpart of the Earth's auroral radiations, observed in a large domain of wavelength, from Infrared to UV and obviously in visible. It is generated at high latitude (~70°), mostly along the nightside magnetic field lines connecting to the Earth's magnetospheric tail. In-situ observations by numerous spacecraft show that the radio sources are embedded inside depleted cavities. The auroral cavities contain a hot tenuous plasma (ne~1 cm-3, Te~5 keV) in a strong ambient magnetic field (fp/fc < 0.1). The mechanism of emission, the Cyclotron Maser Instability (CMI), predicts an intense X mode emission near gyromagnetic frequency preferentially perpendicular to the local magnetic field. But as the radio waves are generated inside a depleted cavity, they are refracted. The apparent beaming of the source is different from that predicted by the CMI. The characteristics of the apparent beaming of the source outside of the cavity depends on several geometrical and physical parameters of the surrounding medium, as well as the frequency of the radio wave. A ray tracing code (ARTEMIS-P), which computes the trajectories of electromagnetic waves in magnetized plasma, is use to compute the path of radio ray from the source inside the hot tenuous plasma of the cavity to the outside. We model a cylindrical plasma cavity characterized by a few parameters (width, edge and parallel gradients) and we study the effect of the cavity geometry on the beaming of AKR for several frequencies. We draw conclusions about the deterministic nature of the beaming angle of the radio emissions generated in cavities. We then extend our study to emissions from giant planets.
2. Correlated variations of UV and radio emissions during an outstanding Jovian auroral event
NASA Technical Reports Server (NTRS)
Prange, R.; Zarka, P.; Ballester, G. E.; Livengood, T. A.; Denis, L.; Carr, T.; Reyes, F.; Bame, S. J.; Moos, H. W.
1993-01-01
An exceptional Jovian aurora was detected in the FUV on December 21, 1990, by means of Vilspa and Goddard Space Flight Center (GFSC) International Ultraviolet Explorer (IUE) observations. This event included intensification by a factor of three between December 20 and 21, leading to the brightest aurora identified in the IUE data analyzed, and, in the north, to a shift of the emission peak towards larger longitudes. The Jovian radio emission simultaneously recorded at decameter wavelengths in Nancay also exhibits significant changes, from a weak and short-duration emission on December 20 to a very intense one, lasting several hours, on December 21. Confirmation of this intense radio event is also found in the observations at the University of Florida on December 21. The emissions are identified as right-handed Io-independent 'A' (or 'non Io-A') components from the northern hemisphere. The radio source region deduced from the Nancay observations lies, for both days, close to the UV peak emission, exhibiting in particular a similar shift of the source region toward larger longitudes from one day to the next. A significant broadening of the radio source was also observed and it is shown that on both days, the extent of the radio source closely followed the longitude range for which the UV brightness exceeds a given threshold. The correlated variations, both in intensity and longitude, strongly suggest that a common cause triggered the variation of the UV and radio emissions during this exceptional event. On one hand, the variation of the UV aurora could possibly be interpreted according to the Prange and Elkhamsi (1991) model of diffuse multicomponent auroral precipitation (electron and ion): it would arise from an increase in the precipitation rate of ions together with an inward shift of their precipitation locus from L approximately equal 10 to L approximately equal 6. On the other hand, the analysis of Ulysses observations in the upstream solar wind suggests that
3. Weathering the Largest Storms in the Universe : Understanding environmental effects on extended radio emission in clusters
Dehghan, S.
2014-05-01
4. Physical properties of conventional explosives deduced from radio frequency emissions
SciTech Connect
Harlin, Jeremiah D; Nemzek, Robert
2008-01-01
Los Alamos National Laboratory collected broadband radio frequency (RF) electric field change measurements from multiple detonations of high explosives (HE). Three types of HE were used: small cylinders of flake TNT, solid TNT, and PBX-9501. Low frequency signals (<80 MHz) were shot-to-shot repeatable and occurred within the first 100 {mu} s at measured amplitudes of about 2 V m{sup -1} at 35 m distance. High frequency signals (>290 MHz) occurred later, were an order of magnitude lower in signal strength, and were not repeatable. There is a positive correlation between the maximum electric field change and the shock velocity of the HE. The amount of free charge produced in the explosion estimated from the first RF pulse is between 10 and 150 {mu} C. This implies a weakly ionized plasma with temperatures between 2600 and 2900 K.
5. The evolution of the radio emission from Kepler's Supernova remnant
NASA Technical Reports Server (NTRS)
Dickel, John R.; Sault, Robert; Arendt, Richard G.; Korista, Kirk T.; Matsui, Yutaka
1988-01-01
High-resolution radio maps of Kepler's Supernova remnant (SNR) using all four arrays of the VLA have been obtained at wavelengths of 20 and 6 cm. They show the complete structure of the remnant; all features are resolved with sizes greater than about 2 arcsec, and the relative brightness of the smooth component near the center is about 1/4 the brightness of the rim. The results have been compared with earlier more limited data to measure changes in the remnant over a four-year time span. The SNR is expanding with a mean rate of R proportional to t exp 0.50 with considerable variations around the shell. Values range from R proportional to t exp 0.35 on the bright northern rim to R proportional to t exp 0.65 on the eastern part of the shell. The measurements are consistent with expansion into a variable circumstellar medium.
6. The Absence of Radio Emission from the Globular Cluster G1
Wrobel, J. M.; Miller-Jones, J. C. A.; Heinke, C. O.; Sivakoff, G. R.; Miller, R. E.; Di Stefano, R.; Kong, A. K. H.; Greene, J. E.; Ho, L. C.
2012-01-01
7. Diffuse radio emission in/around the Coma cluster: beyond simple accretion
Brown, Shea; Rudnick, Lawrence
2011-03-01
We report on new 1.41-GHz Green Bank Telescope (GBT) and 352-MHz Westerbork Synthesis Radio Telescope observations of the Coma cluster and its environs. At 1.41 GHz, we tentatively detect an extension to the Coma cluster radio relic source 1253+275 which makes its total extent ˜2 Mpc. This extended relic is linearly polarized as seen in our GBT data, the NRAO VLA Sky Survey, and archival images, strengthening a shock interpretation. The extended relic borders a previously undetected 'wall' of galaxies in the infall region of the Coma cluster. We suggest that the radio relic is an infall shock, as opposed to the outgoing merger shocks believed responsible for other radio relics. We also find a sharp edge, or 'front', on the western side of the 352-MHz radio halo. This front is coincident with a similar discontinuity in the X-ray surface brightness and temperature in its southern half, suggesting a primary shock-acceleration origin for the local synchrotron emitting electrons. The northern half of the synchrotron front is less well correlated with the X-ray properties, perhaps due to projection effects. We confirm the global pixel-to-pixel power-law correlation between the 352-MHz radio brightness and X-ray brightness with a slope that is inconsistent with predictions of either primary shock acceleration or secondary production of relativistic electrons in giant radio haloes, but is allowable in the framework of the turbulent re-acceleration of relic plasma. The failure of these first-order models and the need for a more comprehensive view of the intracluster medium energization are also highlighted by the very different shapes of the diffuse radio and X-ray emission. We note the puzzling correspondence between the shape of the brighter regions of the radio halo and the surface mass density derived from weak lensing.
8. Radio emission observed by Galileo in the inner Jovian magnetosphere during orbit A-34
Menietti, J. Douglas; Gurnett, Donald A.; Groene, Joseph B.
2005-10-01
The Galileo spacecraft encountered the inner magnetosphere of Jupiter on its way to a flyby of Amalthea on November 5, 2002. During this encounter, the spacecraft observed distinct spin modulation of plasma wave emissions. The modulations occurred in the frequency range from a few hundred hertz to a few hundred kilohertz and probably include at least two distinct wave modes. Assuming transverse EM radiation, we have used the swept-frequency receivers of the electric dipole antenna to determine the direction to the source of these emissions. Additionally, with knowledge of the magnetic field some constraints are placed on the wave mode of the emission based on a comparative analysis of the wave power versus spin phase of the different emissions. The emission appears in several bands separated by attenuation lanes. The analysis indicates that the lanes are probably due to blockage of the freely propagating emission by high density regions of the Io torus near the magnetic equator. Radio emission at lower frequencies (<40 kHz) appears to emanate from sources at high latitude and is not attenuated. Emission at f>80kHz is consistent with O-mode and Z-mode. Lower frequency emissions could be a mixture of O-mode, Z-mode and whistler mode. Emission for f<5kHz shows bands that are similar to upper hybrid resonance bands observed near the terrestrial plasmapause, and also elsewhere in Jovian magnetosphere. Based on the observations and knowledge of similar terrestrial emissions, we hypothesize that radio emission results from mode conversion near the strong density gradient of the inner radius of the cold plasma torus, similar to the generation of nKOM and continuum emission observed in the outer Jovian magnetosphere and in the terrestrial magnetosphere from source regions near the plasmapause.
9. Comparative analysis of theories of zebra-pattern in solar radio emission
Zlotnik, E.
2007-08-01
Strong and weak aspects of different theories of fine structure on solar radio emission dynamic spectra observed as several or numerous quasi- equidistant bands of enhanced and reduced radiation (zebra-pattern) are discussed. Most of works proposing zebra-pattern interpretation is based on plasma mechanism of radio emission generation which consists of exciting plasma (electrostatic) waves and their succeeding transformation into electromagnetic emission. Plasma waves arise due to kinetic or hydrodynamic instability at the upper hybrid frequencies (at the levels of double plasma resonance in a distributed source) or at the electron gyrofrequency harmonics (Bernstein modes in a compact source with quasi-uniform magnetic field). The reason for the instability is occurrence of a number of electrons with nonequilibrium distribution over velocities perpendicular to magnetic field. Radio emission escaping from the source is a result of nonlinear coalescence of plasma waves with low frequency or high frequency waves which does not break the harmonic character of spectrum. A significant number of works is devoted to considering whistlers as a main reason for occurring stripes in emission and absorption on dynamic spectra. Whistlers are also believed to be excited by a group of nonequilibrium electrons, and then some nonlinear processes including whistler interaction result in specific frequency spectrum with enhanced and reduced radiation stripes. An alternative theory of zebra-pattern origin suggests the presence of a compact source with trapped plasma waves in the corona. The trapped waves in a confined space easily provide discrete spectrum. One more interpretation is based on special effects that may occur when radio waves are propagating through non-uniform coronal plasma: the alternate bright and dark stripes on dynamic spectra are supposed to be a result of radio wave interference or diffraction on some periodical structure in the solar corona. All suggested
10. Searching the Nearest Stars for Exoplanetary Radio Emission: VLA and LOFAR Observations
Knapp, Mary; Winterhalter, Daniel; Lazio, Joseph
2016-10-01
Six of the eight solar system planets and one moon (Ganymede) exhibit present-day dynamo magnetic fields. To date, however, there are no conclusive detections of exoplanetary magnetic fields. Low frequency radio emission via the cyclotron maser instability (CMI) from interactions between a planet and the solar/stellar wind is the most direct means of detecting and characterizing planetary/exoplanetary magnetic fields. We have undertaken a survey of the very nearest stars in low frequency radio (30 MHz - 4 GHz) in order to search for yet-undiscovered planets. The closest stars are chosen in order to reduce the attenuation of the magnetospheric radio signal by distance dilution, thereby increasing the chances of making a detection if a planet with a strong magnetic field is present. The VLA telescope (P-band: 230-470 MHz, L-band: 1-2 GHz, S-band: 2-4 GHz) and LOFAR telescope (LBA: 30-75 MHz) have been used to conduct this survey.This work focuses on VLA and LOFAR observations of an M-dwarf binary system: GJ 725. We present upper limits on radio flux as a function of frequency. Since the peak emission frequency of CMI-type emission is the local plasma frequency in the emission region, the peak frequency of planetary radio emission is a direct proxy for the magnetic field strength of the planet. Our spectral irradiance upper limits therefore represent upper limits on the magnetic field strengths of any planets in the GJ 725 system.Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
11. RADIO EMISSION FROM SN 1994I IN NGC 5194 (M 51): THE BEST-STUDIED TYPE Ib/c RADIO SUPERNOVA
SciTech Connect
Weiler, Kurt W.; Panagia, Nino; Stockdale, Christopher; Rupen, Michael; Sramek, Richard A.; Williams, Christopher L. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
2011-10-20
We present the results of detailed monitoring of the radio emission from the Type Ic supernova SN 1994I from three days after optical discovery on 1994 March 31 until eight years later at age 2927 days on 2002 April 5. The data were mainly obtained using the Very Large Array at the five wavelengths of {lambda}{lambda}1.3, 2.0, 3.6, 6.2, and 21 cm and from the Cambridge 5 km Ryle Telescope at {lambda}2.0 cm. Two additional measurements were obtained at millimeter wavelengths. This data set represents the most complete, multifrequency radio observations ever obtained for a Type Ib/c supernova. The radio emission evolves regularly in both time and frequency and is well described by established supernova emission/absorption models. It is the first radio supernova with sufficient data to show that it is clearly dominated by the effects of synchrotron self-absorption at early times.
12. Interplanetary radio storms. II - Emission levels and solar wind speed in the range 0.05-0.8 AU
Bougeret, J.-L.; Fainberg, J.; Stone, R. G.
1984-12-01
Storms of interplanetary type III radio bursts (IP storms) are commonly observed in the interplanetary medium by the ISEE-3 radio instrument. This instrument has the capability of accurately determining the arrival direction of the radio emission. At each observing frequency, the storm radio sources are tracked as they cross the line-of-sight to the sun. Using a simple model, the emission levels are determined at a number of radio frequencies for four separate storms. The IP storm radiation is found to occur in regions of enhanced density at levels of 0.05 to 0.8 AU. The density in these enhancements falls off faster than R(-2). The solar wind speed in the storm region is also measured. The analysis is consistent with steady conditions in the storm region during a few days around the III storm burst radio emission at the harmonic of the local plasma frequency.
13. Interplanetary radio storms. II - Emission levels and solar wind speed in the range 0.05-0.8 AU
NASA Technical Reports Server (NTRS)
Bougeret, J.-L.; Fainberg, J.; Stone, R. G.
1984-01-01
Storms of interplanetary type III radio bursts (IP storms) are commonly observed in the interplanetary medium by the ISEE-3 radio instrument. This instrument has the capability of accurately determining the arrival direction of the radio emission. At each observing frequency, the storm radio sources are tracked as they cross the line-of-sight to the sun. Using a simple model, the emission levels are determined at a number of radio frequencies for four separate storms. The IP storm radiation is found to occur in regions of enhanced density at levels of 0.05 to 0.8 AU. The density in these enhancements falls off faster than R(-2). The solar wind speed in the storm region is also measured. The analysis is consistent with steady conditions in the storm region during a few days around the III storm burst radio emission at the harmonic of the local plasma frequency.
14. Probing Atmospheric Electric Fields through Radio Emission from Cosmic-Ray-Induced Air Showers
Scholten, Olaf; Trinh, Gia; Buitink, Stijn; Corstanje, Arthur; Ebert, Ute; Enriquez, Emilio; Falcke, Heino; Hoerandel, Joerg; Nelles, Anna; Schellart, Pim; Rachen, Joerg; Rutjes, Casper; ter Veen, Sander; Rossetto, Laura; Thoudam, Satyendra
2016-04-01
Energetic cosmic rays impinging on the atmosphere create a particle avalanche called an extensive air shower. In the leading plasma of this shower electric currents are induced that generate coherent radio wave emission that has been detected with LOFAR, a large and dense array of simple radio antennas primarily developed for radio-astronomy observations. Our measurements are performed in the 30-80 MHz frequency band. For fair weather conditions the observations are in excellent agreement with model calculations. However, for air showers measured under thunderstorm conditions we observe large differences in the intensity and polarization patterns from the predictions of fair weather models. We will show that the linear as well as the circular polarization of the radio waves carry clear information on the magnitude and orientation of the electric fields at different heights in the thunderstorm clouds. We will show that from the measured data at LOFAR the thunderstorm electric fields can be reconstructed. We thus have established the measurement of radio emission from extensive air showers induced by cosmic rays as a new tool to probe the atmospheric electric fields present in thunderclouds in a non-intrusive way. In part this presentation is based on the work: P. Schellart et al., Phys. Rev. Lett. 114, 165001 (2015).
15. A study of halo and relic radio emission in merging clusters using the Murchison Widefield Array
George, L. T.; Dwarakanath, K. S.; Johnston-Hollitt, M.; Intema, H. T.; Hurley-Walker, N.; Bell, M. E.; Callingham, J. R.; For, Bi-Qing; Gaensler, B.; Hancock, P. J.; Hindson, L.; Kapińska, A. D.; Lenc, E.; McKinley, B.; Morgan, J.; Offringa, A.; Procopio, P.; Staveley-Smith, L.; Wayth, R. B.; Wu, Chen; Zheng, Q.
2017-05-01
We have studied radio haloes and relics in nine merging galaxy clusters using the Murchison Widefield Array (MWA). The images used for this study were obtained from the GaLactic and Extragalactic All-sky MWA (GLEAM) Survey which was carried out at five frequencies, viz. 88, 118, 154, 188 and 215 MHz. We detect diffuse radio emission in eight of these clusters. We have estimated the spectra of haloes and relics in these clusters over the frequency range 80-1400 MHz; the first such attempt to estimate their spectra at low frequencies. The spectra follow a power law with a mean value of α = -1.13 ± 0.21 for haloes and α = -1.2 ± 0.19 for relics, where S ∝ να. We reclassify two of the cluster sources as radio galaxies. The low-frequency spectra are thus an independent means of confirming the nature of cluster sources. Five of the nine clusters host radio haloes. For the remaining four clusters, we place upper limits on the radio powers of possible haloes in them. These upper limits are a factor of 2-20 below those expected from the LX-P1.4 relation. These limits are the lowest ever obtained and the implications of these limits to the hadronic model of halo emission are discussed.
16. A study of halo and relic radio emission in merging clusters using the Murchison Widefield Array
George, L. T.; Dwarakanath, K. S.; Johnston-Hollitt, M.; Intema, H. T.; Hurley-Walker, N.; Bell, M. E.; Callingham, J. R.; For, Bi-Qing; Gaensler, B.; Hancock, P. J.; Hindson, L.; Kapińska, A. D.; Lenc, E.; McKinley, B.; Morgan, J.; Offringa, A.; Procopio, P.; Staveley-Smith, L.; Wayth, R. B.; Wu, Chen; Zheng, Q.
2017-01-01
We have studied radio haloes and relics in nine merging galaxy clusters using the Murchison Widefield Array (MWA). The images used for this study were obtained from the GaLactic and Extragalactic All-sky MWA (GLEAM) Survey which was carried out at 5 frequencies, viz. 88, 118, 154, 188 and 215 MHz. We detect diffuse radio emission in 8 of these clusters. We have estimated the spectra of haloes and relics in these clusters over the frequency range 80 - 1400 MHz; the first such attempt to estimate their spectra at low frequencies. The spectra follow a power law with a mean value of α = -1.13 ± 0.21 for haloes and α = -1.2 ± 0.19 for relics where, S∝να. We reclassify two of the cluster sources as radio galaxies. The low frequency spectra are thus an independent means of confirming the nature of cluster sources. Five of the nine clusters host radio haloes. For the remaining four clusters, we place upper limits on the radio powers of possible haloes in them. These upper limits are a factor of 2 - 20 below those expected from the LX - P1.4 relation. These limits are the lowest ever obtained and the implications of these limits to the hadronic model of halo emission are discussed.
17. Testing the Young Neutron Star Scenario with Persistent Radio Emission Associated with FRB 121102
Kashiyama, Kazumi; Murase, Kohta
2017-04-01
Recently a repeating fast radio burst (FRB) 121102 has been confirmed to be an extragalactic event and a persistent radio counterpart has been identified. While other possibilities are not ruled out, the emission properties are broadly consistent with Murase et al. that theoretically proposed quasi-steady radio emission as a counterpart of both FRBs and pulsar-driven supernovae. Here, we constrain the model parameters of such a young neutron star scenario for FRB 121102. If the associated supernova has a conventional ejecta mass of M ej ≳ a few M ⊙, a neutron star with an age of t age ∼ 10–100 years, an initial spin period of P i ≲ a few ms, and a dipole magnetic field of B dip ≲ a few × 1013 G can be compatible with the observations. However, in this case, the magnetically powered scenario may be favored as an FRB energy source because of the efficiency problem in the rotation-powered scenario. On the other hand, if the associated supernova is an ultra-stripped one or the neutron star is born by the accretion-induced collapse with M ej ∼ 0.1 M ⊙, a younger neutron star with t age ∼ 1–10 years can be the persistent radio source and might produce FRBs with the spin-down power. These possibilities can be distinguished by the decline rate of the quasi-steady radio counterpart.
18. Electron plasma oscillations associated with type 3 radio emissions and solar electrons
NASA Technical Reports Server (NTRS)
Gurnett, D. A.; Frank, L. A.
1975-01-01
An extensive study of the IMP-6 and IMP-8 plasma and radio wave data was performed to try to find electron plasma oscillations associated with type III radio noise bursts and low-energy solar electrons. It is shown that electron plasma oscillations are seldom observed in association with solar electron events and type III radio bursts at 1.0 AU. For the one case in which electron plasma oscillations are definitely produced by the electrons ejected by the solar flare the electric field strength is relatively small. Electromagnetic radiation, believed to be similar to the type III radio emission, is observed coming from the region of the more intense electron plasma oscillations upstream. Quantitative calculations of the rate of conversion of the plasma oscillation energy to electromagnetic radiation are presented for plasma oscillations excited by both solar electrons and electrons from the bow shock. These calculations show that neither the type III radio emissions nor the radiation from upstream of the bow shock can be adequately explained by a current theory for the coupling of electron plasma oscillations to electromagnetic radiation.
19. A search for extended radio emission from selected compact galaxy groups
Nikiel-Wroczyński, B.; Urbanik, M.; Soida, M.; Beck, R.; Bomans, D. J.
2017-07-01
Context. Studies on compact galaxy groups have led to the conclusion that a plenitude of phenomena take place in between galaxies that form them. However, radio data on these objects are extremely scarce and not much is known concerning the existence and role of the magnetic field in intergalactic space. Aims: We aim to study a small sample of galaxy groups that look promising as possible sources of intergalactic magnetic fields; for example data from radio surveys suggest that most of the radio emission is due to extended, diffuse structures in and out of the galaxies. Methods: We used the Effelsberg 100 m radio telescope at 4.85 GHz and NRAO VLA Sky Survey (NVSS) data at 1.40 GHz. After subtraction of compact sources we analysed the maps searching for diffuse, intergalactic radio emission. Spectral index and magnetic field properties were derived. Results: Intergalactic magnetic fields exist in groups HCG 15 and HCG 60, whereas there are no signs of them in HCG 68. There are also hints of an intergalactic bridge in HCG 44 at 4.85 GHz. Conclusions: Intergalactic magnetic fields exist in galaxy groups and their energy density may be comparable to the thermal (X-ray) density, suggesting an important role of the magnetic field in the intra-group medium, wherever it is detected.
20. Long-period dynamic spectrograms of low-frequency interplanetary radio emissions
NASA Technical Reports Server (NTRS)
Kurth, W. S.; Gurnett, D. A.; Scarf, F. L.; Poynter, R. L.
1987-01-01
Dynamic spectrograms of the low-frequency interplanetary radio emissions as observed by Voyagers 1 and 2 from 1983 through mid-1986 are reported. The radio emissions were observed to be most intense in the latter portion of 1983 at 3 kHz but have also been detected at 2 kHz. The emission has been present almost continuously at either 2 or 3 kHz since late 1983. The spectrograms presented herein show that the phenomenon appears almost identically as observed by the two spacecraft separated by more than 10 AU, at least at the higher frequency. One feature revealed by the dynamic spectrograms which had not been noticed previously is a gradual rise in frequency of the 3-kHz component following the onset of the late 1983 event. These new observations reinforce the conclusion that the low-frequency emissions are freely propagating radio waves, but the two-component spectral structure implies that the previous model of emission at twice the plasma frequency at the inner heliosphere shock is inadequate to fully account for the observations. Either an additional source region or an additional source mechanism is suggested.
1. Steep-Spectrum Radio Emission from the Low-Mass Active Galactic Nucleus GH 10
Wrobel, J. M.; Greene, J. E.; Ho, L. C.; Ulvestad, J. S.
2008-10-01
GH 10 is a broad-lined active galactic nucleus (AGN) energized by a black hole of mass 800,000 M⊙. It was the only object detected by Greene et al. in their Very Large Array (VLA) survey of 19 low-mass AGNs discovered by Greene & Ho. New VLA imaging at 1.4, 4.9, and 8.5 GHz reveals that GH 10's emission has an extent of less than 320 pc, has an optically thin synchrotron spectrum with a spectral index α = - 0.76 +/- 0.05 (Sν propto ν+ α), is less than 11% linearly polarized, and is steady—although poorly sampled—on timescales of weeks and years. Circumnuclear star formation cannot dominate the radio emission, because the high inferred star formation rate, 18 M⊙ yr-1, is inconsistent with the rate of less than 2 M⊙ yr-1 derived from narrow Hα and [O II] λ3727 emission. Instead, the radio emission must be mainly energized by the low-mass black hole. GH 10's radio properties match those of the steep-spectrum cores of Palomar Seyfert galaxies, suggesting that, like those galaxies, the emission is outflow-driven. Because GH 10 is radiating close to its Eddington limit, it may be a local analog of the starting conditions, or seeds, for supermassive black holes. Future imaging of GH 10 at higher linear resolution thus offers an opportunity to study the relative roles of radiative versus kinetic feedback during black hole growth.
2. Radio Emission from particle cascades in the presence of a magnetic field
Mulrey, Katharine
2015-04-01
Geomagnetic radiation from air showers is an attractive technique for detecting ultra-high energy cosmic rays. Macroscopic and microscopic models have been developed which qualitatively agreed with field observations. A controlled laboratory experiment at the SLAC National Accelerator Laboratory (SLAC) was designed to test these models. The experiment measures the radio frequency emission from cascades of secondary particles in a dense dielectric medium in the presence of a magnetic field. The cascades were induced by a ~ 4.5 GeV electron beam in a polyethylene target placed in magnetic fields up to +/-1000 G. The radio emission beam pattern was sampled in horizontal and vertical polarizations by multiple antennas with a total frequency band of 30-3000 MHz. The emission was found to be in good agreement with model predictions, including a Cerenkov-like beam pattern and linear scaling with magnetic field. Katharine Mulrey for the T-510 Collaboration.
3. Long-term changes in Jovian synchrotron radio emission - Intrinsic variations or effects of viewing geometry?
Hood, L. L.
1993-04-01
Possible causes of the observed long-term variation of Jovian synchrotron radio emission, including both intrinsic changes in the Jovian radiation belts and apparent changes due to variations in the Jovigraphic declination of the earth, DE, are investigated. An increase in diffusion rate with other parameters held constant results in an inward displacement of the peak emission radial distance that is not observed. Effects of viewing geometry changes are examined. The possible importance of such effects is suggested by a correlation between the total decimetric radio flux and DE, which varies between -3.3 and +3.3 deg during one Jovian orbital period. Because the Jovian central meridian longitudes where the magnetic latitude passes through zero during a given Jovian rotation change substantially with DE and since significant longitudinal asymmetries exist in both the volume emissivity and the latitudinal profile of the beam, the total intensity should be at least a partial function of D sub E.
4. Radio detection of formaldehyde emission from Comet Halley
NASA Technical Reports Server (NTRS)
Snyder, Lewis E.; Palmer, Patrick; De Pater, Imke
1989-01-01
The J(K-1 K1) = -1(11) -10(10) transition of H2CO was detected in emission at 4829.659 MHz from Comet Halley. The H2CO emission line had a peak intensity of 2.66 + or - 0.78 mJy/beam with a small blueshift of -0.76 + or - 0.40 km/s, which is consistent with the anisotropic outgassing of the nucleus in the solar direction found for other cometary species. Data analysis suggests that cometary H2CO was produced from an extended source in the coma as well as directly from the nucleus and that it was not refrigerated as in interstellar dark nebulae. The derived H2CO production rate of 1.5 x 10 to the 28th molecules/s is obtained which is consistent with observational and theoretical findings.
5. Source location of the smooth high-frequency radio emissions from Uranus
SciTech Connect
Farrell, W.M.; Calvert, W. )
1989-05-01
The source location of the smooth high-frequency (SHF) radio emissions from Uranus has been determined using a technique differing from those applied previously. Specifically, by fitting the signal dropouts which occurred as Voyager traversed the hollow center for the emission pattern to a symmetrical cone centered on the source magnetic field direction at the cyclotron frequency, a southern-hemisphere (nightside) source was found at approximately 56{degree} S, 219{degree} W. The half-angle for the hollow portion of the emission pattern was found to be 13{degree}.
6. Synoptic observations of Jupiter's radio emissions - Average statistical properties observed by Voyager
NASA Technical Reports Server (NTRS)
Alexander, J. K.; Carr, T. D.; Thieman, J. R.; Schauble, J. J.; Riddle, A. C.
1981-01-01
Observations of Jupiter's low-frequency radio emissions collected over one-month intervals before and after each Voyager encounter are analyzed to provide a synoptic view of the average statistical properties of the emissions. Compilations of occurrence probability, average power flux density, and average sense of circular polarization are given as a function of central meridian longitude, phase of Io, and frequency. The results are then compared with ground-based observations. The necessary geometric conditions and preferred polarization sense for Io-related decametric emission observed by Voyager from above both the dayside and nightside hemispheres are found to be basically the same as those observed in earth-based studies.
7. Recent Observations of the Very Low Frequency Interplanetary Radio Emission.
DTIC Science & Technology
1986-08-01
fluctuations. Finally, we would like to take advantage of the Voyager 2 Uranus Observatory Phase during which wideband data were available on...seen by both Voyagers even though the spacecraft are separated by large distances. Finally, the Uranus encounter provided an opportunity to track the...from Voyager 2 as it j approached. Uranus . ( Uranus closest approach occured on day 24 of 1986.) Notice the emission at 3.4 kHz decreases smoothly in
8. Non-thermal radio emission from colliding flows in classical nova V1723 Aql
Weston, Jennifer H. S.; Sokoloski, J. L.; Metzger, Brian D.; Zheng, Yong; Chomiuk, Laura; Krauss, Miriam I.; Linford, Justin D.; Nelson, Thomas; Mioduszewski, Amy J.; Rupen, Michael P.; Finzell, Tom; Mukai, Koji
2016-03-01
The importance of shocks in nova explosions has been highlighted by Fermi's discovery of γ-ray-producing novae. Over three years of multiband Very Large Array radio observations of the 2010 nova V1723 Aql show that shocks between fast and slow flows within the ejecta led to the acceleration of particles and the production of synchrotron radiation. Soon after the start of the eruption, shocks in the ejecta produced an unexpected radio flare, resulting in a multipeaked radio light curve. The emission eventually became consistent with an expanding thermal remnant with mass 2 × 10-4 M⊙ and temperature 104 K. However, during the first two months, the ≳106 K brightness temperature at low frequencies was too high to be due to thermal emission from the small amount of X-ray-producing shock-heated gas. Radio imaging showed structures with velocities of 400 km s-1 (d/6 kpc) in the plane of the sky, perpendicular to a more elongated 1500 km s-1 (d/6 kpc) flow. The morpho-kinematic structure of the ejecta from V1723 Aql appears similar to nova V959 Mon, where collisions between a slow torus and a faster flow collimated the fast flow and gave rise to γ-ray-producing shocks. Optical spectroscopy and X-ray observations of V1723 Aql during the radio flare are consistent with this picture. Our observations support the idea that shocks in novae occur when a fast flow collides with a slow collimating torus. Such shocks could be responsible for hard X-ray emission, γ-ray production, and double-peaked radio light curves from some classical novae.
9. Non-thermal radio emission from O-type stars. V. 9 Sagittarii
Blomme, R.; Volpi, D.
2014-01-01
10. MODELING OF GYROSYNCHROTRON RADIO EMISSION PULSATIONS PRODUCED BY MAGNETOHYDRODYNAMIC LOOP OSCILLATIONS IN SOLAR FLARES
SciTech Connect
Mossessian, George; Fleishman, Gregory D.
2012-04-01
A quantitative study of the observable radio signatures of the sausage, kink, and torsional magnetohydrodynamic (MHD) oscillation modes in flaring coronal loops is performed. Considering first non-zero order effect of these various MHD oscillation modes on the radio source parameters such as magnetic field, line of sight, plasma density and temperature, electron distribution function, and the source dimensions, we compute time-dependent radio emission (spectra and light curves). The radio light curves (of both flux density and degree of polarization) at all considered radio frequencies are then quantified in both time domain (via computation of the full modulation amplitude as a function of frequency) and in Fourier domain (oscillation spectra, phases, and partial modulation amplitude) to form the signatures specific to a particular oscillation mode and/or source parameter regime. We found that the parameter regime and the involved MHD mode can indeed be distinguished using the quantitative measures derived in the modeling. We apply the developed approach to analyze radio burst recorded by Owens Valley Solar Array and report possible detection of the sausage mode oscillation in one (partly occulted) flare and kink or torsional oscillations in another flare.
11. Aborted jets and the X-ray emission of radio-quiet AGNs
Ghisellini, G.; Haardt, F.; Matt, G.
2004-01-01
We propose that radio-quiet quasars and Seyfert galaxies have central black holes powering outflows and jets which propagate only for a short distance, because the velocity of the ejected material is smaller than the escape velocity. We call them aborted" jets. If the central engine works intermittently, blobs of material may be produced, which can reach a maximum radial distance and then fall back, colliding with the blobs produced later and still moving outwards. These collisions dissipate the bulk kinetic energy of the blobs by heating the plasma, and can be responsible (entirely or at least in part) for the generation of the high energy emission in radio-quiet objects. This is alternative to the more conventional scenario in which the X-ray spectrum of radio-quiet sources originates in a hot (and possibly patchy) corona above the accretion disk. In the latter case the ultimate source of energy of the emission of both the disk and the corona is accretion. Here we instead propose that the high energy emission is powered also by the extraction of the rotational energy of the black hole (and possibly of the disk). By means of Montecarlo simulations we calculate the time dependent spectra and light curves, and discuss their relevance to the X-ray spectra in radio-quiet AGNs and galactic black hole sources. In particular, we show that time variability and spectra are similar to those observed in Narrow Line Seyfert 1 galaxies.
12. On altitude structure of centimeter-wave radio emission of solar active regions
Bogod, V. M.; Yasnov, L. V.
2013-07-01
A method is presented for the direct measurement of the heights of the radio emission of solar active regions when they are located at the limb in order to reconstruct the vertical structure of the magnetic field in solar active regions. The method involves an analysis of radio source positions in the scans based on high frequency resolution one-dimensional centimeter-wave measurements performed on the RATAN-600 radio telescope. Radio sources are difficult to identify at many frequencies when observed at the limb at zero position angle because of abrupt signal variations at the solar limb. To eliminate edge effects on the scan, special observing periods are used (near vernal and autumnal equinoxes), when the source at the limb is located far from the scan edge because of the large position angle of the Sun. As a result of these observations, the spectra of relative heights are constructed for a number of sources for the period from 2007 through 2012. Source heights are shown to generally increase with wavelength. The height difference between the 5 and 2 cm emission is equal to 5.2 ± 2.0 Mm, and the corresponding height difference between the 8 and 2 cm emission is equal to 9.6 ± 3.0 Mm. It is shown that such characteristics can be obtained for a field generated by a dipole submerged under the photosphere at a depth of 17 Mm irrespective of the possible reduction of relative altitudes to absolute altitudes.
13. Radio emission and mass loss rate limits of four young solar-type stars
Fichtinger, Bibiana; Güdel, Manuel; Mutel, Robert L.; Hallinan, Gregg; Gaidos, Eric; Skinner, Stephen L.; Lynch, Christene; Gayley, Kenneth G.
2017-03-01
Aims: Observations of free-free continuum radio emission of four young main-sequence solar-type stars (EK Dra, π1 UMa, χ1 Ori, and κ1 Cet) are studied to detect stellar winds or at least to place upper limits on their thermal radio emission, which is dominated by the ionized wind. The stars in our sample are members of The Sun in Time programme and cover ages of 0.1-0.65 Gyr on the main-sequence. They are similar in magnetic activity to the Sun and thus are excellent proxies for representing the young Sun. Upper limits on mass loss rates for this sample of stars are calculated using their observational radio emission. Our aim is to re-examine the faint young Sun paradox by assuming that the young Sun was more massive in its past, and hence to find a possible solution for this famous problem. Methods: The observations of our sample are performed with the Karl G. Jansky Very Large Array (VLA) with excellent sensitivity, using the C-band receiver from 4-8 GHz and the Ku-band from 12-18 GHz. Atacama Large Millimeter/Submillitmeter Array (ALMA) observations are performed at 100 GHz. The Common Astronomy Software Application (CASA) package is used for the data preparation, reduction, calibration, and imaging. For the estimation of the mass loss limits, spherically symmetric winds and stationary, anisotropic, ionized winds are assumed. We compare our results to 1) mass loss rate estimates of theoretical rotational evolution models; and 2) to results of the indirect technique of determining mass loss rates: Lyman-α absorption. Results: We are able to derive the most stringent direct upper limits on mass loss so far from radio observations. Two objects, EK Dra and χ1 Ori, are detected at 6 and 14 GHz down to an excellent noise level. These stars are very active and additional radio emission identified as non-thermal emission was detected, but limits for the mass loss rates of these objects are still derived. The emission of χ1 Ori does not come from the main target
14. Numerical Simulation of the Propagation of Type III Radio Emission
Rutkevych, B. P.; Melnik, V. N.
Recently solar Type III bursts with fine time structure have been observed by radio telescope UTR-2 at frequencies 10 - 30 MHz. For the first time Type III-like bursts with high frequency drift rates were observed at these frequencies too. All this became possible due to both high sensitivity and high time resolution of UTR-2. The properties of decameter Type III bursts can be understood if we take into account the spatial dependence of the electromagnetic wave group velocity as well as the fine spatial structure of the cloud of fast electrons responsible for Type III bursts. These effects are considered numerically in this paper. The fine time structure of Type III bursts is shown to be observed in the days when the associated active region is situated near the central meridian. In other days such structures disappeared. The Type III-like bursts with frequency drift rates of 10 - 20 MHz/s should also be observed, when the associated active region is near the central meridian. These peculiarities are confirmed by observations.
15. The spectrum and variability of radio emission from AE Aquarii
NASA Technical Reports Server (NTRS)
Abada-Simon, Meil; Lecacheux, Alain; Bastian, Tim S.; Bookbinder, Jay A.; Dulk, George A.
1993-01-01
The first detections of the magnetic cataclysmic variable AE Aquarii at millimeter wavelengths are reported. AE Aqr was detected at wavelengths of 3.4 and 1.25 mm. These data are used to show that the time-averaged spectrum is generally well fitted by a power law S(nu) varies as nu exp alpha, where alpha is approximately equal to 0.35-0.60, and that the power law extends to millimeter wavelengths, i.e., the spectral turnover is at a frequency higher than 240 GHz. It is suggested that the spectrum is consistent with that expected from a superposition of flarelike events where the frequency distribution of the initial flux density is a power law f (S0) varies as S0 exp -epsilon, with index epsilon approximately equal to 1.8. Within the context of this model, the high turnover frequency of the radio spectrum implies magnetic field strengths in excess of 250 G in the source.
16. Properties of solar energetic particle events inferred from their associated radio emission
Kouloumvakos, A.; Nindos, A.; Valtonen, E.; Alissandrakis, C. E.; Malandraki, O.; Tsitsipis, P.; Kontogeorgos, A.; Moussas, X.; Hillaris, A.
2015-08-01
Aims: We study selected properties of solar energetic particle (SEP) events as inferred from their associated radio emissions. Methods: We used a catalogue of 115 SEP events, which consists of entries of proton intensity enhancements at one AU, with complete coverage over solar cycle 23 based on high-energy (~68 MeV) protons from SOHO/ERNE. We also calculated the proton release time at the Sun using velocity dispersion analysis (VDA). After an initial rejection of cases with unrealistic VDA path lengths, we assembled composite radio spectra for the remaining events using data from ground-based and space-borne radio spectrographs. We registered the associated radio emissions for every event, and we divided the events in groups according to their associated radio emissions. In cases of type III-associated events, we extended our study to the timings between the type III radio emission, the proton release, and the electron release as inferred from VDA based on Wind/3DP 20-646 keV data. Results: The proton release was found to be most often accompanied by both type III and II radio bursts, but a good association percentage was also registered in cases accompanied by type IIIs only. The worst association was found for the cases only associated with type II. In the type III-associated cases, we usually found systematic delays of both the proton and electron release times as inferred by the particles' VDAs, with respect to the start of the associated type III burst. The comparison of the proton and electron release times revealed that, in more than half of the cases, the protons and electrons were simultaneously released within the statistical uncertainty of our analysis. For the cases with type II radio association, we found that the distribution of the proton release heights had a maximum at ~2.5 R⊙. Most (69%) of the flares associated with our SEP events were located in the western hemisphere, with a peak within the well-connected region of 50°-60° western
17. Galactic Synchrotron Emission and the Far-infrared-Radio Correlation at High Redshift
Schober, J.; Schleicher, D. R. G.; Klessen, R. S.
2016-08-01
18. An Overview of Saturn Narrowband Radio Emissions Observed by Cassini RPWS
Ye, S.-Y.; Fischer, G.; Menietti, J. D.; Wang, Z.; Gurnett, D. A.; Kurth, W. S.
Saturn narrowband (NB) radio emissions are detected between 3 and 70 kHz, with occurrence probability and wave intensity peaking around 5 kHz and 20 kHz. The emissions usually occur periodically for several days after intensification of Saturn kilometric radiation (SKR). Originally detected by the Voyagers, the extended duration of the Cassini mission and the improved capabilities of the Radio and Plasma Wave Science (RPWS) instrument have significantly advanced our knowledge about them. For example, RPWS measurements of the magnetic component have validated the electromagnetic nature of Saturn NB emissions. Evidences show that the 20 kHz NB emissions are generated by mode conversion of electrostatic upper hybrid waves on the boundary of the plasma torus, whereas direction-finding results point to a source in the auroral zone for the 5 kHz component. Similar to SKR, the 5 kHz NB emissions have a clock-like modulation and display two distinct modulation periods identical to the northern and southern hemisphere periods of SKR. Polarization measurements confirm that most NB emissions are propagating in the L-O mode, with the exception of second harmonic NB emissions. At high latitudes closer to the planet, RPWS detected right hand polarized Z-mode NB emissions below the local electron cyclotron frequency (f_ce), which are believed to be the source of the L-O mode NB emissions detected above the local f_ce. Although the energy source for the generation of the Z-mode waves is still unclear, linear growth rate calculations indicate that the observed plasma distributions are unstable to the growth of electrostatic cyclotron harmonic emission. Alternatively, electromagnetic Z-mode might be directly generated by the cyclotron maser instability. The source Z-mode waves, upon reflection, propagate to the opposite hemisphere before escaping through mode conversion, which could explain the fact that both rotational modulation periods of NB emissions are observable in each
19. Understanding the periodicities in radio and GeV emission from LS I +61°303
Jaron, F.; Torricelli-Ciamponi, G.; Massi, M.
2016-11-01
20. Rotational modulation of Saturn's radio emissions after equinox
Ye, Shengyi; Fischer, Georg; Kurth, William; Gurnett, Donald
2016-04-01
The modulation rate of Saturn kilometric radiation (SKR), originally thought to be constant, was found to vary with time by comparing the Voyager and Ulysses observations. More recently, Cassini RPWS observations of SKR revealed two different modulation rates, one associated with each hemisphere of Saturn, and it was proposed that the rotation rates are subject to seasonal change. The almost continuous observations of SKR, Saturn narrowband emission, and auroral hiss by RPWS provide a good method of tracking the rotation rates of the planet's magnetosphere. We will show that the rotation rate of the northern SKR is slower than that of the southern SKR in 2015. Auroral hiss provides another unambiguous method of tracking the rotation signals from each hemisphere because the whistler mode wave cannot cross the equator. Rotation rates of auroral hiss are shown to agree with those of SKR when both are observed at high latitudes. The dual rotation rates of 5 kHz narrowband emissions reappeared after a long break since equinox and they agree with those of auroral hiss in 2013.
1. THE VLA SURVEY OF CHANDRA DEEP FIELD SOUTH. V. EVOLUTION AND LUMINOSITY FUNCTIONS OF SUB-MILLIJANSKY RADIO SOURCES AND THE ISSUE OF RADIO EMISSION IN RADIO-QUIET ACTIVE GALACTIC NUCLEI
SciTech Connect
Padovani, P.; Mainieri, V.; Rosati, P.; Miller, N.; Kellermann, K. I.; Tozzi, P.
2011-10-10
2. Narrowband Radio Emission As A Possible Feature of Before CMEs Onset Processes
Fridman, V.; Sheiner, O.; Grechin, S.
The narrow band events in microwave radio emission were discovered during the ob- servations by RT-22 CrAO on August 12, 1989 before CMEs registration has been done. The observations were carried out using the sweeping spectrograph in 13-17 GHz range with frequency resolution of 100 MHz and sweeping time of less then 1 sec. It is well known that the period preceding the CMEs formation is characterized by sporadic radio emission of different types. We have found the existence of fast changes in temporal behavior of radio emission during the burst. They are character- ized by consistent origin of narrow-band (<1 GHz) components of emission with flux amplitude of about 1 sfu, moving from high to low frequencies in 1-3 seconds. We detected the shift of spectral maximum to short waves and appearance of narrow-band (<800 MHz) features during the CMEs formation. The results are being discussed within the framework of known models of radioemission of active region and bursts. Their application to possible conditions in formation of CMEs is also addressed in this research. This work is being supported by the Federal Science and Technology Programme "Astronomy" and the Russian Foundation for Fundamental Research.
3. Compact non-thermal radio emission from B-peculiar stars
NASA Technical Reports Server (NTRS)
1988-01-01
Some stars hotter than 10,000 K show propensity for unusual surface abundances and excessive magnetic fields. These peculiar stars, Ap and Bp in the spectral nomenclature, show unusually prominent absorption lines of heavier elements. Rapid rotation and strong magnetic fields are revealed by line shapes and Zeeman splitting. VLBI is here used to directly probe the source size and brightness temperature of weak radio emission recently discovered from two isolated Bp stars, sigma Orionis E and HD37017. The emitting zone for each star is no more than 6 stellar diameters in extent, reflecting brightness temperatures of more than one billion K. Such high surface brightness resembles gyrosynchrotron radiation from mildly relativistic electrons trapped in the strong magnetic fields surrounding these stars. Compact radio radiation from these two stars presents new opportunities for probing the physical environments of early-type stars and for precise radio astrometry.
4. A search of the SAS-2 data for pulsed gamma-ray emission from radio pulsars
NASA Technical Reports Server (NTRS)
Ogelman, H. B.; Fichtel, C. E.
1976-01-01
Data from the SAS-2 high energy gamma ray experiment were examined for pulsed emission from each of 75 radio pulsars which were viewed by the instrument and which have sufficiently well defined period and period derivative information from radio observations to allow for gamma ray periodicity searches. When gamma ray arrival times were converted to pulsar phase using the radio reference timing information, two pulsars, PSR 1747-46 and PSR 1818-04, showed positive effects, each with a probability less than 0.0001 of being a random fluctuation in the data for that pulsar. These are in addition to PSR 0531+21 and PSR 0833-45, previously reported. The results of this study suggest that gamma-ray astronomy has reached the detection threshold for gamma ray pulsars and that work in the near future should give important information on the nature of pulsars.
5. Radio Emission from Pulsar Wind Nebulae without Surrounding Supernova Ejecta: Application to FRB 121102
Dai, Z. G.; Wang, J. S.; Yu, Y. W.
2017-03-01
In this paper, we propose a new scenario in which a rapidly rotating strongly magnetized pulsar without any surrounding supernova ejecta repeatedly produces fast radio bursts (FRBs) via a range of possible mechanisms; simultaneously, an ultra-relativistic electron/positron pair wind from the pulsar sweeps up its ambient dense interstellar medium, giving rise to a non-relativistic pulsar wind nebula (PWN). We show that the synchrotron radio emission from such a PWN is bright enough to account for the recently discovered persistent radio source associated with the repeating FRB 121102 within reasonable ranges of the model parameters. Our PWN scenario is consistent with the non-evolution of the dispersion measure inferred from all of the repeating bursts observed in four years.
6. Very Large Array Detects Radio Emission from Gamma-Ray Burst
1997-05-01
NASA Technical Reports Server (NTRS)
Desch, Michael D.
1988-01-01
Using Voyager I data, a preliminary search has been made for evidence of both triggering and enhancement of Saturn Kilometric Radiation (SKR) by solar type III bursts. The interval from September 1, 1980 to September 30,1980 was examined at a frequency near the spectral peak of the SKR (385 kHz). The investigation compared emission levels before and after the arrival of Type III bursts at Saturn by subjecting the data to both superposed epoch analysis and intensity distribution analysis. Strong SKR associated with the arrival of a high-density solar wind stream at Saturn was removed to avoid possible masking of a weak triggering effect. No evidence of triggering or of enhancement of SKR due to the arrival of Type III bursts at Saturn could be found.
8. SPECTRAL INDEX STUDIES OF THE DIFFUSE RADIO EMISSION IN ABELL 2256: IMPLICATIONS FOR MERGER ACTIVITY
SciTech Connect
Kale, Ruta; Dwarakanath, K. S. E-mail: [email protected]
2010-08-01
We present a multi-wavelength analysis of the merging rich cluster of galaxies, Abell 2256 (A2256). We have observed A2256 at 150 MHz using the Giant Metrewave Radio Telescope and successfully detected the diffuse radio halo and the relic emission over a {approx}1.2 Mpc{sup 2} extent. Using this 150 MHz image and the images made using archival observations from the Very Large Array (VLA; 1369 MHz) and the Westerbrok Synthesis Radio Telescope (WSRT; 330 MHz), we have produced spectral index images of the diffuse radio emission in A2256. These spectral index images show a distribution of flat spectral index (S {proportional_to} {nu}{sup {alpha}}, {alpha} in the range -0.7 to -0.9) plasma in the region NW of the cluster center. Regions showing steep spectral indices ({alpha} in the range -1.0 to -2.3) are toward the SE of the cluster center. These spectral indices indicate synchrotron lifetimes for the relativistic plasmas in the range 0.08-0.4 Gyr. We interpret this spectral behavior as resulting from a merger event along the direction SE to NW within the last 0.5 Gyr or so. A shock may be responsible for the NW relic in A2256 and the megaparsec scale radio halo toward the SE is likely to be generated by the turbulence injected by mergers. Furthermore, the diffuse radio emission shows spectral steepening toward lower frequencies. This low-frequency spectral steepening is consistent with a combination of spectra from two populations of relativistic electrons created at two epochs (two mergers) within the last {approx}0.5 Gyr. Earlier interpretations of the X-ray and the optical data also suggested that there were two mergers in Abell 2256 in the last 0.5 Gyr, consistent with the current findings. Also highlighted in this study is the futility of correlating the average temperatures of thermal gas and the average spectral indices of diffuse radio emission in the respective clusters.
9. Detection of elusive radio and optical emission from cosmic-ray showers in the 1960s
Fegan, David J.
2012-01-01
10. X-RAY AND RADIO EMISSION FROM TYPE IIn SUPERNOVA SN 2010jl
SciTech Connect
Chandra, Poonam; Chevalier, Roger A.; Chugai, Nikolai; Fransson, Claes; Soderberg, Alicia M.
2015-09-01
We present all X-ray and radio observations of the Type IIn supernova SN 2010jl. The X-ray observations cover a period up to day 1500 with Chandra, XMM-Newton, NuSTAR, and Swift-X-ray Telescope (XRT). The Chandra observations after 2012 June, the XMM-Newton observation in 2013 November, and most of the Swift-XRT observations until 2014 December are presented for the first time. All the spectra can be fitted by an absorbed hot thermal model except for Chandra spectra on 2011 October and 2012 June when an additional component is needed. Although the origin of this component is uncertain, it is spatially coincident with the supernova and occurs when there are changes to the supernova spectrum in the energy range close to that of the extra component, indicating that the emission is related to the supernova. The X-ray light curve shows an initial plateau followed by a steep drop starting at day ∼300. We attribute the drop to a decrease in the circumstellar density. The column density to the X-ray emission drops rapidly with time, showing that the absorption is in the vicinity of the supernova. We also present Very Large Array radio observations of SN 2010jl. Radio emission was detected from SN 2010jl from day 570 onwards. The radio light curves and spectra suggest that the radio luminosity was close to its maximum at the first detection. The velocity of the shocked ejecta derived assuming synchrotron self-absorption is much less than that estimated from the optical and X-ray observations, suggesting that free–free absorption dominates.
11. A Highly Circularly Polarized Solar Radio Emission Component Observed at Hectometric Wavelengths
Reiner, M. J.; Kaiser, M. L.; Fainberg, J.; Bougeret, J.-L.
2006-04-01
12. Testing the DRM digital radio broadcast emissions as a tool for ionospheric investigation
Koperski, Piotr; Młynarczyk, Janusz; Kułak, Andrzej
2010-05-01
13. SCO X-1: Origin of the radio and hard X-ray emissions
NASA Technical Reports Server (NTRS)
Ramaty, R.; Cheng, C. C.; Tsuruta, S.
1973-01-01
The consequences of models for the central radio source and the hard X-ray ( 30 keV) emitting region in Sco X-1 are examined. It was found that the radio emission could result from noncoherent synchrotron radiation and that the X-rays may be produced by bremsstrahlung. It is shown that both mechanisms require a mass outflow from Sco X-1. The radio source is located at r approximately 3x10 to the 12th power cm from the center of the star, and its linear dimensions do not exceed 3x10 to the 13th power cm. The magnetic field in the radio source is on the order of 1 gauss. If the hard X-rays are produced by thermal bremsstrahlung, their source is located at 10 to the 9th power approximately r approximately 5x10 to the 9th power cm, the temperature is 2x10 to the 9th power K, and the emission measure is 2x10 to the 56th power/cu cm. This hot plasma loses energy inward by conduction and outward by supersonic expansion. The rates of energy loss for both processes are about 10 to the 36th power erg/s, comparable to the total luminosity of Sco X-1.
14. Variable and Polarized Radio Emission from a T6 Brown Dwarf
Williams, Peter K. G.; Gizis, John; Berger, Edo
2017-01-01
Route & Wolszczan (2016) recently detected five radio bursts from the T6 brown dwarf WISEP J112254.7+255021.5 and used the timing of these events to propose that this object rotates with an ultra-short period of ~17.3 minutes. We conducted follow-up observations with the Very Large Array and Gemini-North but found no evidence for this periodicity. We do, however, observe variable, highly circularly polarized radio emission possibly with a period of 116 minutes, although our observation lasted only 162 minutes and so more data are needed to confirm it. Our proposed periodicity is typical of other radio-active ultracool dwarfs. The handedness of the circular polarization alternates with time and there is no evidence for any unpolarized emission component, the first time such a phenomenology has been observed in radio studies of very low-mass stars and brown dwarfs. We suggest that the object’s magnetic dipole axis may be highly misaligned relative to its rotation axis.
15. Role of Microwave Radio Emission in Estimation of CMEs Geo-Effectiveness in their Formation Stage
Durasova, M.; Fridman, V.; Sheyner, O.
16. Adaptive-array Electron Cyclotron Emission diagnostics using data streaming in a Software Defined Radio system
Idei, H.; Mishra, K.; Yamamoto, M. K.; Hamasaki, M.; Fujisawa, A.; Nagashima, Y.; Hayashi, Y.; Onchi, T.; Hanada, K.; Zushi, H.; the QUEST Team
2016-04-01
Measurement of the Electron Cyclotron Emission (ECE) spectrum is one of the most popular electron temperature diagnostics in nuclear fusion plasma research. A 2-dimensional ECE imaging system was developed with an adaptive-array approach. A radio-frequency (RF) heterodyne detection system with Software Defined Radio (SDR) devices and a phased-array receiver antenna was used to measure the phase and amplitude of the ECE wave. The SDR heterodyne system could continuously measure the phase and amplitude with sufficient accuracy and time resolution while the previous digitizer system could only acquire data at specific times. Robust streaming phase measurements for adaptive-arrayed continuous ECE diagnostics were demonstrated using Fast Fourier Transform (FFT) analysis with the SDR system. The emission field pattern was reconstructed using adaptive-array analysis. The reconstructed profiles were discussed using profiles calculated from coherent single-frequency radiation from the phase array antenna.
17. The Moon as a calibrator of linearly polarized radio emission for the SPOrt project
Poppi, S.; Carretti, E.; Cortiglioni, S.; Krotikov, V. D.; Vinyajkin, E. N.
2002-03-01
The Moon could be the best external calibrator for the Sky Polarization Observatory (SPOrt) experiment, providing the highest polarized signal at large angular scales (>=7 °) in the 22-90 GHz range. Maps of linearly polarized lunar radio emission have been realized at 8.3 GHz with the 32-m radiotelescope of IRA-CNR (Medicina-Italy) at full Moon, new Moon, first and last quarter. We derived estimates of spectral and time properties of both the intensity and the linear polarization of the Moon radio emission, taking into account the radiative transfer of heat in lunar soil and the surface roughness. A comparison between predictions of the theory and observations is presented. .
PubMed
Liu, Liu; Chang, Huiting; Xu, Tao; Song, Yanan; Zhang, Chi; Hang, Zhi Hong; Hu, Xinhua
2017-07-07
The use of low-emissivity (low-e) materials in modern buildings is an extremely efficient way to save energy. However, such materials are coated by metallic films, which can strongly block radio-frequency signals and prevent indoor-outdoor wireless communication. Here, we demonstrate that, when specially-designed metallic metasurfaces are covered on them, the low-e materials can remain low emissivity for thermal radiation and allow very high transmission for a broad band of radio-frequency signals. It is found that the application of air-connected metasurfaces with subwavelength periods is critical to the observed high transmission. Such effects disappear if periods are comparable to wavelengths or metal-connected structures are utilized. The conclusion is supported by both simulations and experiments. Advantages such as easy to process, low cost, large-area fabrication and design versatility of the metasurface make it a promising candidate to solve the indoor outdoor communication problem.
19. Polarization features of solar radio emission and possible existence of current sheets in active regions
NASA Technical Reports Server (NTRS)
Gopalswamy, N.; Zheleznyakov, V. V.; White, S. M.; Kundu, M. R.
1994-01-01
We show that it is possible to account for the polarization features of solar radio emission provided the linear mode coupling theory is properly applied and the presence of current sheets in the corona is taken into account. We present a schematic model, including a current sheet that can explain the polarization features of both the low frequency slowly varying component and the bipolar noise storm radiation; the two radiations face similar propagation conditions through a current sheet and hence display similar polarization behavior. We discuss the applications of the linear mode coupling theory to the following types of solar emission: the slowly varying component, the microwave radio bursts, metric type U bursts, and bipolar noise storms.
20. Self-consistent particle-in-cell simulations of fundamental and harmonic radio plasma emission mechanisms
Tsiklauri, D.; Thurgood, J. O.
2015-12-01
first co-author Jonathan O. Thurgood (QMUL) The simulation of three-wave interaction based plasma emission, an underlying mechanism for type III solar radio bursts, is a challenging task requiring fully-kinetic, multi-dimensional models. This paper aims to resolve a contradiction in past attempts, whereby some authors report that no such processes occur and others draw conflicting conclusions, by using 2D, fully kinetic, particle-in-cell simulations of relaxing electron beams. Here we present the results of particle-in-cell simulations which for different physical parameters permit or prohibit the plasma emission. We show that the possibility of plasma emission is contingent upon the frequency of the initial electrostatic waves generated by the bump-in-tail instability, and that these waves may be prohibited from participating in the necessary three-wave interactions due to the frequency beat requirements. We caution against simulating astrophysical radio bursts using unrealistically dense beams (a common approach which reduces run time), as the resulting non-Langmuir characteristics of the initial wave modes significantly suppresses the emission. Comparison of our results indicates that, contrary to the suggestions of previous authors, a plasma emission mechanism based on two counter-propagating beams is unnecessary in astrophysical context. Finally, we also consider the action of the Weibel instability, which generates an electromagnetic beam mode. As this provides a stronger contribution to electromagnetic energy than the emission, we stress that evidence of plasma emission in simulations must disentangle the two contributions and not simply interpret changes in total electromagnetic energy as the evidence of plasma emission. In summary, we present the first self-consistent demonstration of fundamental and harmonic plasma emission from a single-beam system via fully kinetic numerical simulation. Pre-print can be found at http://astro.qmul.ac.uk/~tsiklauri/jtdt1
1. Observations of Jupiter's Low-Frequency Radio Emissions from the Juno Waves Instrument in Collaboration with the Earth-Based Radio Telescopes
Imai, M.; Kurth, W. S.; Hospodarsky, G. B.; Bolton, S. J.; Connerney, J. E. P.; Levin, S.; Zarka, P. M.; Cecconi, B.; Lecacheux, A.; Lamy, L.
2016-12-01
The radio and plasma wave instrument (Waves) onboard the Juno spacecraft, which is now successfully orbiting Jupiter, utilizes one electric dipole antenna and one magnetic search coil sensor. The Juno Waves instrument is capable of recording the entire Jovian radio spectrum (from kilometer (KOM) to decameter (DAM) through hectometer wavelength (HOM) radio components) in a wide frequency coverage of 50 Hz to 40 MHz, and of estimating a one-dimensional determination of the direction of incoming waves below 5 MHz in the framework of the short dipole approximation. During Juno's interplanetary cruise prior to the Jupiter orbit insertion on July 5, 2016, the first observations were made for KOM in March, and for HOM and DAM in May, 2016. By analyzing the Waves data from Juno's approach and initial orbit of Jupiter, we show the characteristics of each radio component as viewed from Juno at higher and lower Jovigraphic latitudes. In addition, some preliminary results of the coordinated DAM observations with Juno and Earth-based radio telescopes (e.g., Nançay Decameter Array in France) are presented. Because of the unique polar trajectory, the Juno Waves instrument may perform the first in-situ measurements of Jovian auroral radio emission sources, and stereoscopic observations of Jovian DAM emissions with Juno and the ground-based radio telescopes may lead to a better understanding of the latitudinal beaming structures from Jupiter's polar regions.
2. Probing Atmospheric Electric Fields in Thunderstorms through Radio Emission from Cosmic-Ray-Induced Air Showers.
PubMed
Schellart, P; Trinh, T N G; Buitink, S; Corstanje, A; Enriquez, J E; Falcke, H; Hörandel, J R; Nelles, A; Rachen, J P; Rossetto, L; Scholten, O; Ter Veen, S; Thoudam, S; Ebert, U; Koehn, C; Rutjes, C; Alexov, A; Anderson, J M; Avruch, I M; Bentum, M J; Bernardi, G; Best, P; Bonafede, A; Breitling, F; Broderick, J W; Brüggen, M; Butcher, H R; Ciardi, B; de Geus, E; de Vos, M; Duscha, S; Eislöffel, J; Fallows, R A; Frieswijk, W; Garrett, M A; Grießmeier, J; Gunst, A W; Heald, G; Hessels, J W T; Hoeft, M; Holties, H A; Juette, E; Kondratiev, V I; Kuniyoshi, M; Kuper, G; Mann, G; McFadden, R; McKay-Bukowski, D; McKean, J P; Mevius, M; Moldon, J; Norden, M J; Orru, E; Paas, H; Pandey-Pommier, M; Pizzo, R; Polatidis, A G; Reich, W; Röttgering, H; Scaife, A M M; Schwarz, D J; Serylak, M; Smirnov, O; Steinmetz, M; Swinbank, J; Tagger, M; Tasse, C; Toribio, M C; van Weeren, R J; Vermeulen, R; Vocks, C; Wise, M W; Wucknitz, O; Zarka, P
2015-04-24
We present measurements of radio emission from cosmic ray air showers that took place during thunderstorms. The intensity and polarization patterns of these air showers are radically different from those measured during fair-weather conditions. With the use of a simple two-layer model for the atmospheric electric field, these patterns can be well reproduced by state-of-the-art simulation codes. This in turn provides a novel way to study atmospheric electric fields.
3. CONSTRAINTS ON DARK MATTER ANNIHILATION IN CLUSTERS OF GALAXIES FROM DIFFUSE RADIO EMISSION
SciTech Connect
Storm, Emma; Jeltema, Tesla E.; Profumo, Stefano; Rudnick, Lawrence
2013-05-10
Annihilation of dark matter can result in the production of stable Standard Model particles including electrons and positrons that, in the presence of magnetic fields, lose energy via synchrotron radiation, observable as radio emission. Galaxy clusters are excellent targets to search for or to constrain the rate of dark matter annihilation, as they are both massive and dark matter dominated. In this study, we place limits on dark matter annihilation in a sample of nearby clusters using upper limits on the diffuse radio emission, low levels of observed diffuse emission, or detections of radio mini-halos. We find that the strongest limits on the annihilation cross section are better than limits derived from the non-detection of clusters in the gamma-ray band by a factor of {approx}3 or more when the same annihilation channel and substructure model, but different best-case clusters, are compared. The limits on the cross section depend on the assumed amount of substructure, varying by as much as two orders of magnitude for increasingly optimistic substructure models as compared to a smooth Navarro-Frenk-White profile. In our most optimistic case, using the results of the Phoenix Project, we find that the derived limits reach below the thermal relic cross section of 3 Multiplication-Sign 10{sup -26} cm{sup 3} s{sup -1} for dark matter masses as large as 400 GeV, for the b b-bar annihilation channel. We discuss uncertainties due to the limited available data on the magnetic field structure of individual clusters. We also report the discovery of diffuse radio emission from the central 30-40 kpc regions of the groups M49 and NGC 4636.
4. Peak-Flux-Density Spectra of Large Solar Radio Bursts and Proton Emission from Flares.
DTIC Science & Technology
1985-08-19
3(d).- 37. Juday, R. D., and Adams, G. W. (1969) Riometer measurements, solar proton intensities and radiation dose rates, Planet. Space Sci. 17:1313...emissions radioelectriques solaires de Type IV et leur relation avec d’autres phenomenes solaires et geophys- iques, Ann.- Astrophys. 24:183. 39. Harvey, G. A...1965) 2800 megacycle per second radiation associated with Type II and Type IV solar radio bursts and the relation with other phen- omena, J
5. Relationship of Solar Radio Emission at λ=1.43m and Optical Processes in the Sun
Makandarashvili, Sh.; Oghrapishvili, N.; Japaridze, D.; Maghradze, D.
2016-09-01
6. Thunderstorm electric fields probed by extensive air showers through their polarized radio emission
Trinh, T. N. G.; Scholten, O.; Bonardi, A.; Buitink, S.; Corstanje, A.; Ebert, U.; Enriquez, J. E.; Falcke, H.; Hörandel, J. R.; Hare, B. M.; Mitra, P.; Mulrey, K.; Nelles, A.; Rachen, J. P.; Rossetto, L.; Rutjes, C.; Schellart, P.; Thoudam, S.; ter Veen, S.; Winchen, T.
2017-04-01
We observe a large fraction of circular polarization in radio emission from extensive air showers recorded during thunderstorms, much higher than in the emission from air showers measured during fair-weather circumstances. We show that the circular polarization of the air showers measured during thunderstorms can be explained by the change in the direction of the transverse current as a function of altitude induced by atmospheric electric fields. Thus by using the full set of Stokes parameters for these events, we obtain a good characterization of the electric fields in thunderclouds. We also measure a large horizontal component of the electric fields in the two events that we have analyzed.
7. HST/ACS Emission Line Snapshots of nearby 3CR Radio Galaxies
Tremblay, Grant; Sparks, W. B.; Chiaberge, M.; Baum, S. A.; Allen, M. G.; Axon, D. J.; Capetti, A.; Floyd, D. J. E.; Macchetto, F. D.; Miley, G. K.; O'Dea, C. P.; Perlman, E. S.; Quillen, A. C.
2008-03-01
We present the results of a new HST/ACS snapshot program in which we have obtained emission line images of nearby (z < 0.3) 3CR radio source counterparts at low- and high- excitation. Prior to ACS failure data were acquired successfully for 20 such objects, a sample consisting of both low-power FR I and classical high-power FR II radio galaxies. While only a subset of our initially proposed sample was observed, the newly reduced data we do have are excellent and will serve as an enhancement to an already superb dataset. In future papers, we will use these data to probe fundamental relationships between warm optical line-emitting gas, radio source structure (jets and lobes) and X-ray coronal halos. We will combine our existing UV images with new emission line images to establish quantitative star formation characteristics and their relation to dust and merger scenarios. Through the use of emission-line excitation maps, we will test theories on ionization beam patterns and luminosities from active nuclei, as well as seek areas of jet induced star formation. The resulting database will be an invaluable resource to the astronomical community for years to come.
8. On the Methods of Determining the Radio Emission Geometry in Pulsar Magnetospheres
NASA Technical Reports Server (NTRS)
Dyks, J.; Rudak, B.; Harding, Alice K.
2004-01-01
We present a modification of the relativistic phase shift method of determining the radio emission geometry from pulsar magnetospheres proposed by Gangadhara & Gupta (2001). Our modification provides a method of determining radio emission altitudes which does not depend on the viewing geometry and does not require polarization measurements. We suggest application of the method to the outer edges of averaged radio pulse profiles to identify magnetic field lines associated with'the edges of the pulse and, thereby, to test the geometric method based on the measurement of the pulse width at the lowest intensity level. We show that another relativistic method proposed by Blaskiewicz et al. (1991) provides upper limits for emission altitudes associated with the outer edges of pulse profiles. A comparison of these limits with the altitudes determined with the geometric method may be used to probe the importance of rotational distortions of magnetic field and refraction effects in the pulsar magnetosphere. We provide a comprehensive discussion of the assumptions used in the relativistic methods.
9. A Stochastic Acceleration Model of Radio Emission from Pulsar Wind Nebulae
Tanaka, S.; Asano, K.
2016-06-01
The broadband emission of Pulsar Wind Nebulae (PWNe) is well described by non-thermal emissions from accelerated electrons and positrons. However, the difference of spectral indices at radio and X-rays are not reproduced by the standard shock particle acceleration and cooling processes, and then, for example, the broken power-law spectrum for the particle energy distribution at the injection has been groundlessly adopted. Here, we propose a possible resolution for the particle distribution; the radio emitting particles are not accelerated at the pulsar wind termination shock but are stochastically accelerated by turbulence inside the PWNe. The turbulence may be induced by the interaction of the pulsar wind with the supernova ejecta. We upgrade our one-zone spectral evolution model including the stochastic acceleration and apply it to the Crab Nebula. We consider both continuous and impulsive injections of particles to the stochastic acceleration process. The radio emission in the Crab Nebula is reproduced by our stochastic acceleration model. The required forms of the momentum diffusion coefficient will be discussed.
10. Radio-Continuum Emission from the Young Galactic Supernova Remnant G1.9+0.3
De Horta, A. Y.; Filipovic, M. D.; Crawford, E. J.; Stootman, F. H.; Pannuti, T. G.; Bozzetto, L. M.; Collier, J. D.; Sommer, E. R.; Kosakowski, A. R.
2014-12-01
We present an analysis of a new Australia Telescope Compact Array (ATCA) radio-continuum observation of supernova remnant (SNR) G1.9+0.3, which at an age of ˜181±25 years is the youngest known in the Galaxy. We analysed all available radio-continuum observations at 6-cm from the ATCA and Very Large Array. Using this data we estimate an expansion rate for G1.9+0.3 of 0.563±0.078 percent per year between 1984 and 2009. We note that in the 1980's G1.9+0.3 expanded somewhat slower (0.484 percent per year) than more recently (0.641 percent per year). We estimate that the average spectral index between 20-cm and 6-cm, across the entire SNR is α=-0.72±0.26 which is typical for younger SNRs. At 6-cm, we detect an average of 6 percent fractionally polarised radio emission with a peak of 17±3 percent. The polarised emission follows the contours of the strongest of X-ray emission. Using the new equipartition formula we estimate a magnetic field strength of B≈273~μ G, which to date, is one of the highest magnetic field strength found for any SNR and consistent with G1.9+0.3 being a very young remnant.
11. Searching for coronal radio emission from protostars using very-long-baseline interferometry
Forbrich, J.; Massi, M.; Ros, E.; Brunthaler, A.; Menten, K. M.
2007-07-01
Aims:In order to directly study the role of magnetic fields in the immediate vicinity of protostars, we use Very-Long-Baseline Interferometry (VLBI), aiming at the detection of non-thermal centimetric radio emission. This is technically the only possibility to study coronal emission at sub-AU resolution. Methods: We performed VLBI observations of the four nearby protostars HL Tau, LDN 1551 IRS5, EC 95, and YLW 15 in order to look for compact non-thermal centimetric radio emission. For maximum sensitivity, we used the High Sensitivity Array (HSA) where possible, involving the Very Long Baseline Array (VLBA), the phased Very Large Array (VLA), as well as the Arecibo, Green Bank, and Effelsberg radio telescopes. Results: While all four protostars were detected in VLA-only data, only one source (YLW 15 VLA 2) was detected in the VLBI data. The possibility of non-detections due to free-free absorption, possibly depending on source geometry, is considered.
12. The relationship between the carbon monoxide intensity and the radio continuum emission in spiral galaxies
NASA Technical Reports Server (NTRS)
Adler, David S.; Lo, K. Y.; Allen, Ronald J.
1991-01-01
The relationship between the velocity-integrated CO emission and the nonthermal radio continuum brightness in the disks of normal spiral galaxies is examined on a variety of length scales. On a global scale, the total CO intensity correlates strongly with the total radio continuum flux density for a sample of 31 galaxies. On scales of about 2 kpc or more in the disk of individual galaxies, it is found that the ratio I(CO)/T(20) remains fairly constant over the entire disk as well as from galaxy to galaxy. For the eight spirals in the sample, the disk-averaged values of I(CO)/T(20) range from 0.6-2.4, with the average over all eight galaxies being 1.3 +/- 0.6. It is concluded that what these various length scales actually trace are differences in the primary heating mechanism of the gas in the beam. The observed relationship between CO and nonthermal radio continuum emission can be explained by assuming that molecular gas in galactic disks is heated primarily by cosmic rays. The observed relationship is used to show that the brightness of synchrotron emission is proportional to n(cr) exp 0.4 - 0.9 in galactic disks.
13. MODELING BRIGHT γ-RAY AND RADIO EMISSION AT FAST CLOUD SHOCKS
SciTech Connect
Lee, Shiu-Hang; Patnaude, Daniel J.; Raymond, John C.; Slane, Patrick O.; Nagataki, Shigehiro; Ellison, Donald C. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
2015-06-10
Recent observations by the Large Area Telescope on board the Fermi satellite have revealed bright γ-ray emission from middle-aged supernova remnants (SNRs) inside our Galaxy. These remnants, which also possess bright non-thermal radio shells, are often found to be interacting directly with surrounding gas clouds. We explore the non-thermal emission mechanism at these dynamically evolved SNRs by constructing a hydrodynamical model. Two scenarios of particle acceleration, either a re-acceleration of Galactic cosmic rays or an efficient nonlinear diffusive shock acceleration (NLDSA) of particles injected from downstream, are considered. Using parameters inferred from observations, our models are contrasted with the observed spectra of SNR W44. For the re-acceleration case, we predict a significant enhancement of radio and GeV emission as the SNR undergoes a transition into the radiative phase. If sufficiently strong magnetic turbulence is present in the molecular cloud, the re-acceleration scenario can explain the observed broadband spectral properties. The NLDSA scenario also succeeds in explaining the γ-ray spectrum but fails to reproduce the radio spectral index. Efficient NLDSA also results in a significant post-shock non-thermal pressure that limits the compression during cooling and prevents the formation of a prominent dense shell. Some other interesting differences between the two models in hydrodynamical behavior and resulting spectral features are illustrated.
14. Radio-wave emission due to hypervelocity impacts and its correlation with optical observations
Takano, T.; Maki, K.; Yamori, A.
This paper describes the most interesting phenomena of radio-wave emission due to hypervelocity impacts. A projectile of polycarbonate with 1.1 g weight was accelerated by a rail gun to 3.8 km/sec, and hit two targets which are a 2 mm thick aluminum plate upstream and a 45 mm diameter aluminum column downstream, respectively. The projectile first breaks wires to give a triggering signal to a data recorder, then penetrates the aluminum plate, and finally hit the column, The emitted radio-waves propagate through the chamber window, and are received by antennas at each frequency band. The receivers in 22 GHz- and 2 GHz-bands consist of a low noise amplifier, a mixer, a local oscillator and an IF amplifier , respectively. The receiver in 1 MHz-band is a simple RF amplifier. The outputs of all receivers are fed to a data recorder which is actually a high-speed digital oscilloscope with a large amount of memory. The radio-waves were successfully recorded in 22 GHz-band with 500 MHz bandwidth, in 2 GHz-band with 300 MHz bandwidth, and in 1MHz-band. The waveforms in 22 GHz- and 2 GHz-bands coincide well each other, and are composed of two groups of sharp impulses with a separation of about 20 micro seconds. The width of an impulse is less than 2 n sec. which is the resolution limit of the data recorder. We carried out optical observations using an ultra-high speed camera simultaneously through another window of the chamber. The time interval between scenes is 2 micro sec. We can see a faint light of the projectile before the first impact to the plate, and then a brilliant gas exploding backward from the plate and forward to the column. After hitting the column target, the brilliant gas flows to the chamber wall and is reflected back to make a mixture with dark gas in the chamber. Excellent correlation between radio-wave emission and the observed optical phenomena was obtained in the experiment. It is easily conceived that the radio-waves consist of quite a wide frequency
15. THE ABSENCE OF RADIO EMISSION FROM THE GLOBULAR CLUSTER G1
SciTech Connect
Miller-Jones, J. C. A.; Wrobel, J. M.; Sivakoff, G. R.; Heinke, C. O.; Miller, R. E.; Plotkin, R. M.; Di Stefano, R.; Greene, J. E.; Ho, L. C.; Joseph, T. D.; Maccarone, T. J.; Kong, A. K. H.
2012-08-10
The detections of both X-ray and radio emission from the cluster G1 in M31 have provided strong support for existing dynamical evidence for an intermediate-mass black hole (IMBH) of mass (1.8 {+-} 0.5) Multiplication-Sign 10{sup 4} M{sub Sun} at the cluster center. However, given the relatively low significance and astrometric accuracy of the radio detection, and the non-simultaneity of the X-ray and radio measurements, this identification required further confirmation. Here we present deep, high angular resolution, strictly simultaneous X-ray and radio observations of G1. While the X-ray emission (L{sub X} = 1.74{sup +0.53}{sub -0.44} Multiplication-Sign 10{sup 36} (d/750 kpc){sup 2} erg s{sup -1} in the 0.5-10 keV band) remained fully consistent with previous observations, we detected no radio emission from the cluster center down to a 3{sigma} upper limit of 4.7 {mu}Jy beam{sup -1}. Our favored explanation for the previous radio detection is flaring activity from a black hole low-mass X-ray binary (LMXB). We performed a new regression of the 'Fundamental Plane' of black hole activity, valid for determining black hole mass from radio and X-ray observations of sub-Eddington black holes, finding log M{sub BH} = (1.638 {+-} 0.070)log L{sub R} - (1.136 {+-} 0.077)log L{sub X} - (6.863 {+-} 0.790), with an empirically determined uncertainty of 0.44 dex. This constrains the mass of the X-ray source in G1, if a black hole, to be <9.7 Multiplication-Sign 10{sup 3} M{sub Sun} at 95% confidence, suggesting that it is a persistent LMXB. This annuls what was previously the most convincing evidence from radiation for an IMBH in the Local Group, though the evidence for an IMBH in G1 from velocity dispersion measurements remains unaffected by these results.
16. Effect of laser intensity on radio frequency emissions from laser induced breakdown of atmospheric air
SciTech Connect
Vinoth Kumar, L.; Manikanta, E.; Leela, Ch.; Prem Kiran, P. E-mail: [email protected]
2016-06-07
The studies on the effect of input laser intensity, through the variation of laser focusing geometry, on radio frequency (RF) emissions, over 30–1000 MHz from nanosecond (ns) and picosecond (ps) laser induced breakdown (LIB) of atmospheric air are presented. The RF emissions from the ns and ps LIB were observed to be decreasing and increasing, respectively, when traversed from tight to loose focusing conditions. The angular and radial intensities of the RF emissions from the ns and ps LIB are found to be consistent with sin{sup 2}θ/r{sup 2} dependence of the electric dipole radiation. The normalized RF emissions were observed to vary with incident laser intensity (Iλ{sup 2}), indicating the increase in the induced dipole moment at moderate input laser intensities and the damping of radiation due to higher recombination rate of plasma at higher input laser intensities.
17. Remote sensing of the Io torus plasma ribbon using natural radio occultation of the Jovian radio emissions
Boudjada, M. Y.; Galopeau, P. H. M.; Sawas, S.; Lammer, H.
2014-09-01
We study the Jovian hectometric (HOM) emissions recorded by the RPWS (Radio and Plasma Wave Science) experiment onboard the Cassini spacecraft during its Jupiter flyby. We analyze the attenuation band associated with the intensity extinction of HOM radiation. This phenomenon is interpreted as a refraction effect of the Jovian hectometric emission inside the Io plasma torus. This attenuation band was regularly observed during periods of more than 5 months, from the beginning of October 2000 to the end of March 2001. We estimate for this period the variation of the electron density versus the central meridian longitude (CML). We find a clear local time dependence. Hence the electron density was not higher than 5.0 × 104 cm-3 during 2 months, when the spacecraft approached the planet on the dayside. In the late afternoon and evening sectors, the electron density increases to 1.5 × 105 cm-3 and reach a higher value at some specific occasions. Additionally, we show that ultraviolet and hectometric wavelength observations have common features related to the morphology of the Io plasma torus. The maxima of enhancements/attenuations of UV/HOM observations occur close to the longitudes of the tip of the magnetic dipole in the southern hemisphere (20° CML) and in the northern hemisphere (200° CML), respectively. This is a significant indication about the importance of the Jovian magnetic field as a physical parameter in the coupling process between Jupiter and the Io satellite.
18. Cosmic Rays, Magnetic Fields and Diffuse Emissions: Combining Observations from Radio to Gamma Rays
Michelson, Peter
With the advent of WMAP, Planck, and Fermi-LAT telescopes the diffuse emission from the Milky Way has received renewed attention. Observations of the different components of the diffuse emission reveal information on Cosmic Rays (CRs), magnetic fields (B-fields) and the interstellar medium. CRs interact with the interstellar medium and the B-fields in the Milky Way, producing diffuse emission from radio to gamma rays. The fundamental problem is that CRs, B-fields, and the interstellar medium are not precisely known. In fact, despite intensive studies, the B-field intensity and topology, and CR spectra and distribution throughout the Galaxy are still uncertain. As a consequence unequivocally disentangling and describing the diffuse components simultaneously using a single wavelength domain is impossible. Our approach to disentangling and describing the diffuse emission components is to simultaneously consider the diffuse emission in multiple frequency domains. We propose to exploit the entire database of the present radio surveys, microwave observations (WMAP and Planck), X-ray observations (INTEGRAL) and gamma-ray observations (COMPTEL and Fermi-LAT) in order to analyze their diffuse emission in a combined multi-wavelength approach. We will jointly infer information on the spectra and distribution of CRs in the Galaxy, and on Galactic B-fields, with unprecedented accuracy. Finally we will be able to describe the baseline Galactic diffuse emissions and characterize Milky Way structures and their emission mechanisms, which have attracted the attention of the scientific community recently. This project is innovative and essential for maximizing the scientific return from the presently available data in a multidisciplinary view and uses novel approaches. The results will benefit NASA-related science generally and the return from the named missions specifically.
19. Radio emission from supernovae and gamma-ray bursters and the need for the SKA
Weiler, Kurt W.; Van Dyk, Schuyler D.; Sramek, Richard A.; Panagia, Nino
2004-12-01
Study of radio supernovae (SNe) over the past 25 years includes two dozen detected objects and more than 100 upper limits. From this work it is possible to identify classes of radio properties, demonstrate conformance to and deviations from existing models, estimate the density and structure of the circumstellar material and, by inference, the evolution of the presupernova stellar wind, and reveal the last stages of stellar evolution before explosion. It is also possible to detect ionized hydrogen along the line of sight, to demonstrate binary properties of the stellar system, and to show clumpiness of the circumstellar material. Since 1997 the afterglow of γ-ray bursting sources (GRBs) has occasionally been detected in the radio, as well in other wavelength bands. In particular, the interesting and unusual γ-ray burst GRB 980425, almost certainly related to the radio supernova SN 1998bw, and the more recent SN 2003dh/GRB 030329 are links between the two classes of objects. Analyzing the extensive radio emission data available for SN 1998bw, one can describe its time evolution within the well established framework available for the analysis of radio emission from supernovae. This then allows relatively detailed description of a number of physical properties of the object. The radio emission can best be explained as the interaction of a mildly relativistic ( Γ ˜ 1.6) shock with a dense pre-explosion stellar wind-established circumstellar medium that is highly structured both azimuthally, in clumps or filaments, and radially, with observed density enhancements. From this we can support the conclusion that at least some members of the slow-soft class of GRBs are related to type Ib/c SNe and can be attributed to the explosion of a massive star in a dense, highly structured CSM that was presumably established by the pre-explosion stellar system. However, due to the lack of sensitivity of current radio telescopes, most supernovae cannot be studied if they are more
20. Phasing the Very Large Array on Galileo in the presence of Jupiter's strong radio emission
NASA Technical Reports Server (NTRS)
1991-01-01
1. Milliarcsecond Imaging of the Radio Emission from the Quasar with the Most Massive Black Hole at Reionization
Wang, Ran; Momjian, Emmanuel; Carilli, Chris L.; Wu, Xue-Bing; Fan, Xiaohui; Walter, Fabian; Strauss, Michael A.; Wang, Feige; Jiang, Linhua
2017-02-01
2. A LINK BETWEEN X-RAY EMISSION LINES AND RADIO JETS IN 4U 1630-47?
SciTech Connect
Neilsen, Joseph; Coriat, Mickaël; Fender, Rob; Broderick, Jess W.; Lee, Julia C.; Ponti, Gabriele; Tzioumis, Anastasios K.; Edwards, Philip G.
2014-03-20
Recently, Díaz Trigo et al. reported an XMM-Newton detection of relativistically Doppler-shifted emission lines associated with steep-spectrum radio emission in the stellar-mass black hole candidate 4U 1630-47 during its 2012 outburst. They interpreted these lines as indicative of a baryonic jet launched by the accretion disk. Here we present a search for the same lines earlier in the same outburst using high-resolution X-ray spectra from the Chandra HETGS. While our observations (eight months prior to the XMM-Newton campaign) also coincide with detections of steep spectrum radio emission by the Australia Telescope Compact Array, we find no evidence for any relativistic X-ray emission lines. Indeed, despite ∼5 × brighter radio emission, our Chandra spectra allow us to place an upper limit on the flux in the blueshifted Fe XXVI line that is ≳ 20 × weaker than the line observed by Díaz Trigo et al. We explore several scenarios that could explain our differing results, including variations in the geometry of the jet or a mass-loading process or jet baryon content that evolves with the accretion state of the black hole. We also consider the possibility that the radio emission arises in an interaction between a jet and the nearby interstellar medium, in which case the X-ray emission lines might be unrelated to the radio emission.
3. A Link between X-Ray Emission Lines and Radio Jets in 4U 1630-47?
Neilsen, Joseph; Coriat, Mickaël; Fender, Rob; Lee, Julia C.; Ponti, Gabriele; Tzioumis, Anastasios K.; Edwards, Philip G.; Broderick, Jess W.
2014-03-01
Recently, Díaz Trigo et al. reported an XMM-Newton detection of relativistically Doppler-shifted emission lines associated with steep-spectrum radio emission in the stellar-mass black hole candidate 4U 1630-47 during its 2012 outburst. They interpreted these lines as indicative of a baryonic jet launched by the accretion disk. Here we present a search for the same lines earlier in the same outburst using high-resolution X-ray spectra from the Chandra HETGS. While our observations (eight months prior to the XMM-Newton campaign) also coincide with detections of steep spectrum radio emission by the Australia Telescope Compact Array, we find no evidence for any relativistic X-ray emission lines. Indeed, despite ~5 × brighter radio emission, our Chandra spectra allow us to place an upper limit on the flux in the blueshifted Fe XXVI line that is >~ 20 × weaker than the line observed by Díaz Trigo et al. We explore several scenarios that could explain our differing results, including variations in the geometry of the jet or a mass-loading process or jet baryon content that evolves with the accretion state of the black hole. We also consider the possibility that the radio emission arises in an interaction between a jet and the nearby interstellar medium, in which case the X-ray emission lines might be unrelated to the radio emission.
4. A Deep Search for Prompt Radio Emission from Thermonuclear Supernovae with the Very Large Array
Chomiuk, Laura; Soderberg, Alicia M.; Chevalier, Roger A.; Bruzewski, Seth; Foley, Ryan J.; Parrent, Jerod; Strader, Jay; Badenes, Carles; Fransson, Claes; Kamble, Atish; Margutti, Raffaella; Rupen, Michael P.; Simon, Joshua D.
2016-04-01
Searches for circumstellar material around Type Ia supernovae (SNe Ia) are some of the most powerful tests of the nature of SN Ia progenitors, and radio observations provide a particularly sensitive probe of this material. Here, we report radio observations for SNe Ia and their lower-luminosity thermonuclear cousins. We present the largest, most sensitive, and spectroscopically diverse study of prompt ({{Δ }}t≲ 1 years) radio observations of 85 thermonuclear SNe, including 25 obtained by our team with the unprecedented depth of the Karl G. Jansky Very Large Array. With these observations, SN 2012cg joins SN 2011fe and SN 2014J as an SN Ia with remarkably deep radio limits and excellent temporal coverage (six epochs, spanning 5-216 days after explosion, implying \\dot{M}/{v}w≲ 5× 10-9 M⊙) yr-1/(100 km s-1), assuming ɛB = 0.1 and ɛe = 0.1). All observations yield non-detections, placing strong constraints on the presence of circumstellar material. We present analytical models for the temporal and spectral evolution of prompt radio emission from thermonuclear SNe as expected from interaction with either wind-stratified or uniform density media. These models allow us to constrain the progenitor mass loss rates, with limits in the range of \\dot{M}≲ 10-9-10-4 M⊙ yr-1, assuming a wind velocity of vw = 100 km s-1. We compare our radio constraints with measurements of Galactic symbiotic binaries to conclude that ≲10% of thermonuclear SNe have red giant companions.
5. X-ray emission associated with radio galaxies in the Perseus cluster
NASA Technical Reports Server (NTRS)
Rhee, George; Burns, Jack O.; Kowalski, Michael P.
1994-01-01
In this paper, we report on new x-ray observations of the Perseus cluster made using four separate pointings of the Roentgen Satellite (ROSAT) Positron Sensitive Proportional Counter (PSPC). We searched for x-ray emission associated with 16 radio galaxies and detected six above 3 sigma. We made use of the PSPC spectra to determine if the x-ray emission associated with radio galaxies in Perseus is thermal or nonthermal in origin (i.e., hot gas or an active galactic nuclei (AGN)). For the head-tail radio galaxy IC 310, we find that the data are best fit by a power law model with an unusually large spectral index alpha = 2.7. This is consistent with its unresolved spatial structure. On the other hand, a second resolved x-ray source associated with another radio galaxy 2.3 Mpc from the Perseus center (V Zw 331) is best fit by a thermal model. For three sources with insufficient flux for a full spectral analysis, we calculated hardness ratios. On this basis, the x-ray emission associated with the well known head-tail source NGC 1265 is consistent with thermal radiation. The x-ray spectra of UGC 2608 and UGC 2654 probably arise from hot gas, although very steep power-law spectra (alpha greater than 3.2) are also possible. The spectrum of NGC 1275 is quite complex due to the presence of an AGN and the galaxy's location at the center of a cluster cooling flow.
6. Radio emission models of colliding-wind binary systems. Inclusion of IC cooling
Pittard, J. M.; Dougherty, S. M.; Coker, R. F.; O'Connor, E.; Bolingbroke, N. J.
2006-02-01
Radio emission models of colliding wind binaries (CWBs) have been discussed by Dougherty et al. (2003). We extend these models by considering the temporal and spatial evolution of the energy distribution of relativistic electrons as they advect downstream from their shock acceleration site. The energy spectrum evolves significantly due to the strength of inverse-Compton (IC) cooling in these systems, and a full numerical evaluation of the synchrotron emission and absorption coefficients is made. We have demonstrated that the geometry of the WCR and the streamlines of the flow within it lead to a spatially dependent break frequency in the synchrotron emission. We therefore do not observe a single, sharp break in the synchrotron spectrum integrated over the WCR, but rather a steepening of the synchrotron spectrum towards higher frequencies. We also observe that emission from the wind-collision region (WCR) may appear brightest near the shocks, since the impact of IC cooling on the non-thermal electron distribution is greatest near the contact discontinuity (CD), and demonstrate that the impact of IC cooling on the observed radio emission increases significantly with decreasing binary separation. We study how the synchrotron emission changes in response to departures from equipartition, and investigate how the thermal flux from the WCR varies with binary separation. Since the emission from the WCR is optically thin, we see a substantial fraction of this emission at certain viewing angles, and we show that the thermal emission from a CWB can mimic a thermal plus non-thermal composite spectrum if the thermal emission from the WCR becomes comparable to that from the unshocked winds. We demonstrate that the observed synchrotron emission depends upon the viewing angle and the wind-momentum ratio, and find that the observed synchrotron emission decreases as the viewing angle moves through the WCR from the WR shock to the O shock. We obtain a number of insights relevant to
7. Near-field effects in radio-frequency emission from particle showers in a dense medium
Hyneman, Rachel; Wissel, Stephanie; Belov, Konstantin; Vahle, Patricia; Salzberg, David; Romero-Wolf, Andres; SLAC T-510 Collaboration
2015-04-01
Two mechanisms are expected to produce radio-frequency emission in ultra-high energy cosmic ray air showers. Askaryan emission, generated by an overall charge excess, has been studied in beam experiments previously. The emission due to Earth's magnetic field has been inferred from observations by cosmic-ray observatories, but not yet studied in a controlled laboratory environment. The SLAC T-510 experiment recently studied the effects of a magnetic field upon the radio-frequency emission from particle showers in high-density polyethylene as a way to model cosmic ray air showers. Ultra-High Frequency (UHF) and Very High Frequency (VHF) antennas were used to measure the signal from particle showers in the target at different positions. For an overview, see the talk by K. Mulrey in this conference. Several near-field runs were performed with the UHF antenna array closer to the target than in the majority of the data taking. Signal from the two mechanisms, Askaryan and Magnetic, were separated into orthogonal polarizations by the geometry of the system. We report on studies of the electric field for several positions in the near field. Initial results indicate that the electric field as a function of angle behaves consistently as the antennas are moved further from the target.
8. A Model of Jupiter's Decametric Radio Emissions as a Searchlight Beam
Imai, K.; Garcia, L.; Reyes, F.; Imai, M.; Thieman, J. R.
It has long been recognized that there is a marked long-term periodic variation in Jupiter's integrated radio occurrence probability. The period of the variation is on the order of a decade. Carr et al. [1970] showed that such variations are closely correlated with Jovicentric declination of the Earth (DE). The range of the smoothed variation of DE is from approximately +3.3 to -3.3 degrees. This DE effect was extensively studied and confirmed by Garcia [1996]. It shows that the occurrence probability of the non-Io-A source is clearly controlled by DE at 18, 20, and 22 MHz during the 1957-1994 apparitions. We propose a new model to explain the DE effect. This new model shows that the beam structure of Jupiter radio emissions, which has been thought of like a hollow-cone, has a narrow beam like a searchlight, which can be explained by assuming that the three dimensional shape of the radio source expands along the line of the magnetic field. If we consider the sizes of the radio coherent region are 1000 m along Jupiter's magnetic field line and 200 m along the latitudinal direction, the equivalent beam pattern is 1 degree wide along Jupiter's magnetic field line and 5 degrees in latitude. As the searchlight beam is fixed with Jupiter's magnetic field, the pure geometrical effect of DE can be explained by this searchlight beam model.
9. On the links between magnetodisc perturbations and radio emissions at Jupiter.
Louarn, P.
2014-04-01
We first review measurements made by the Galileo energetic particle detector (EPD), the magnetometer (MAG) and the plasma wave/radio instrument (PWS) to establish relationships between various dynamic processes occurring in the jovian magnetosdisk and in Io torus: (1) the 'energetic-events' or 'radio events' seenwith PWS [Louarn et al., 1998]), (2) in-situ signatures of reconnection seen by the magnetometer and EPD (the 'reconfiguration-events' [Kronberg et al., 2005, Vogt et al., 2010]), at 80-100 RJ and, (3) particle injections seen at 10-20 RJ [Mauk et al., 1999, Louarn et al, 2014]. We then present new analysis attempting to characterize the density/magnetic perturbations of the magnetodisk that may be related to these major disturbances. They are based on PWS and MAG observations made in the magnetodisk itself, at distances ranging from 20 to ~70 RJ. It is shown that the radio events generally correspond to increases of the plasma content of the disk (which is deduced from measurements of the upper hybrid frequency). In a few cases, it is observed that the magnetic field deviates off the meridian plane, with an azimuthal component that becomes significant. This suggests that an enhanced magnetosphere/ionosphere current system enforces the co-rotation of the more massive disk. The link between this possible enhanced current system and more powerful radio emissions is discussed.
10. EFFECTS OF ALFVEN WAVES ON ELECTRON CYCLOTRON MASER EMISSION IN CORONAL LOOPS AND SOLAR TYPE I RADIO STORMS
SciTech Connect
Zhao, G. Q.; Chen, L.; Wu, D. J.; Yan, Y. H.
2013-06-10
Solar type I radio storms are long-lived radio emissions from the solar atmosphere. It is believed that these type I storms are produced by energetic electrons trapped within a closed magnetic structure and are characterized by a high ordinary (O) mode polarization. However, the microphysical nature of these emissions is still an open problem. Recently, Wu et al. found that Alfven waves (AWs) can significantly influence the basic physics of wave-particle interactions by modifying the resonant condition. Taking the effects of AWs into account, this work investigates electron cyclotron maser emission driven by power-law energetic electrons with a low-energy cutoff distribution, which are trapped in coronal loops by closed solar magnetic fields. The results show that the emission is dominated by the O mode. It is proposed that this O mode emission may possibly be responsible for solar type I radio storms.
11. On the Jovian Machinery: from Magnetodisk Perturbations to the Generation of Radio Emissions.
Louarn, P.; Kivelson, M.; Kurth, W. S.
2015-12-01
The Galileo observations are analyzed to establish possible relationships between dynamic processes occurring in the jovian magnetosdisk and variations in the flux of the radio emissions. More specifically, it is shown that there is a general good correlation between increases of the azimuth component of the magnetic field (B_phi) seen in the middle/distant magnetodisk (distances ranging between 20 to 80 Rj) and intensification of the auroral radio emissions. A simple explanation is that the variations of B_phi are related to modifications in the current system linking the ionosphere to the disk and, thus, to variations in the intensity of the parallel currents with implications on the associated auroral processes. An interpretation is proposed using Hill's model of the enforcement of the magnetodisk rotation with, however, adaptations to the observations that require the use of a current sheet model (adapted from Nichols, 2003) . The link with possible variations in the radial mass transport is discussed, with estimates of the overall power associated to the magnetic torque that enforces the corotation and accelerates the bulk plasma. From an astrophysical perspective, this offers an interesting opportunity to quantify a transfer of rotational energy from to central body to a magnetosdisk and compared it to the resulting radiations (here in the radio domain).
12. A Numerical Model of Parsec-scale SSC Morphologies and Their Radio Emission
Richter, S.; Spanier, F.
2016-09-01
In current models for jets of active galactic nuclei and their emission a shortcoming in the description and understanding of the connection between the largest and smallest scales exists. In this work we present a spatially resolved synchrotron self-Compton model extended to parsec scales, which opens the possibility of probing the connections between the radio and high-energy properties. We simulate an environment that leads to Fermi-I acceleration of leptonic particles and includes the full time dependence of this process. Omitting the restriction of a finite downstream region, we find that the spectral energy distribution produced by the accelerated particles strongly depends on their radial confinement behind the shock. The requirement, for both the restriction of high-energy emission to a small region around the shock and the production of a flat radio spectrum, is an initial linear increase of the radius immediately behind the shock, which then slows down with increasing distance from the shock. A good representation of the data for the blazar Mrk 501 is achieved by a parameterized log function. The prediction for the shape of the radio blob is given by the flux distribution with respect to shock distance.
13. Generation of the jovian radio emission by the maser cyclotron instability: first lessons from JUNO
Louarn, Philippe; Allegrini, Frederic; Kurth, WilliamS.; Valek, Philips. W.; McComas, Dave; Bagenal, Fran; Bolton, Scott; Connerney, John; Ebert, Robert W.; Levin, Steven; Szalay, Jamey; Wilson, Robert; Zink, Jenna; André, Nicolas; Imai, Masafumi
2017-04-01
Using JUNO plasma and wave observations (JADE and Waves instruments), the scenario for the generation of jovian auroral radio emissions are analyzed. The sources of radiation are identified by localized intensifications of the radio flux at frequencies close to the electron gyrofrequency. Not surprisingly, it is shown that the cyclotron maser instability is perfectly adapted to the plasma conditions prevailing in the radio sources. However, it appears that different forms of activation of the cyclotron maser are observed. For radiation at hectometric wavelengths (one of the main emissions), pronounced loss-cones in the electron distribution functions are likely the source of free energy. The sources would be extended over several thousand km in directions traverse to the magnetic field. The applications of the theory reveals that sufficient growth rates are obtained from the distributions functions that are actually measured by JADE. This differs from the Earth scenario for which 'trapped' distribution functions drive the maser. More localized sources are also observed, possibly linked to local acceleration process. These examples may present analogies with the 'Earth' scenario, with other forms of free energy than the loss-cone. A first lesson of these direct in-situ JADE and RPWS observations is thus to confirm the maser cyclotron scenario with, however, conditions for the wave amplification and detailed maser processes that appear to be different than at Earth.
14. Neutral hydrogen in elliptical galaxies with nuclear radio sources and optical emission lines
NASA Technical Reports Server (NTRS)
Dressel, L. L.; Bania, T. M.; Oconnell, R. W.
1982-01-01
An H I detection survey of eleven elliptical galaxies with powerful nuclear radio sources was conducted, using the 305 m antenna of Arecibo Observatory, to test the hypothesis that large H I mass is conductive to the formation of nuclear radio sources in elliptical galaxies. The H I was detected in emission in UGC 09114 and was possibly detected in absorption in UGC 06671. Observations of the remaining galaxies were not sensitive enough to support or refute the hypothesis. Data was combined from other H I surveys and spectroscopic surveys to search for correlations of H I mass with other galactic properties and environmental conditions. Strong correlations of (O II) lambda 3727 emission with H I content and with nuclear radio power were found. The latter two properties may simply indicate, respectively, whether a significant amount of gas is available to be ionized and whether energy is provided by nuclear activity for ionization. No dependence of H I content on optical luminosity or on degree of isolation from other galaxies was found.
15. Creation of visible artificial optical emissions in the aurora by high-power radio waves.
PubMed
Pedersen, Todd R; Gerken, Elizabeth A
2005-02-03
Generation of artificial light in the sky by means of high-power radio waves interacting with the ionospheric plasma has been envisaged since the early days of radio exploration of the upper atmosphere, with proposed applications ranging from regional night-time street lighting to atmospheric measurements. Weak optical emissions have been produced for decades in such ionospheric 'heating' experiments, where they serve as key indicators of electron acceleration, thermal heating, and other effects of incompletely understood wave-particle interactions in the plasma under conditions difficult to replicate in the laboratory. The extremely low intensities produced previously have, however, required sensitive instrumentation for detection, preventing applications beyond scientific research. Here we report observations of radio-induced optical emissions bright enough to be seen by the naked eye, and produced not in the quiet mid-latitude ionosphere, but in the midst of a pulsating natural aurora. This may open the door to visual applications of ionospheric heating technology or provide a way to probe the dynamics of the natural aurora and magnetosphere.
16. Disk-Jet Connection in the Microquasar GRS 1915+105 and Infrared and Radio Emission
2001-02-01
We present evidence of a direct accretion disk-jet connection in the Galactic microquasar GRS 1915+105 based on our analysis of RXTE/PCA data with a spike'' in X-ray light curves. We find that the radio emission increases as the hardness ratio increases during the low hard state. We suggest that the spike,'' which separates the dips with hard and soft spectra, marks the beginning of the burst phase when the luminosity of the soft X-rays (5-15 keV) increases by a large factor (~10). This produces a major ejection episode of the synchrotron-emitting plasma termed as baby jets,'' which are associated with infrared (IR) and radio flares of about half an hour period widely reported in the literature. Subsequent short but frequent soft dips produce overlapping faint flares which result in an enhanced level of quasi-steady emission. We discuss the differences between baby jets'' and relativistic radio jets and especially investigate their signatures in X-rays.
17. The Star Formation in Radio Survey: Mapping Star Formation in Nearby Galaxies with 33GHz Emission
Dong, Dillon; Murphy, Eric J.; Momjian, Emmanuel; Nyland, Kristina; Condon, James J.; Helou, George; Meier, David S.; Ott, Juergen; Schinnerer, Eva; Turner, Jean
2015-01-01
We present initial results from the 33GHz phase of the Star Formation in Radio Survey (SFRS), including a gallery of 2" resolution Jansky Very Large Array (VLA) images and spatially resolved thermal / synchrotron emission models in a subset of sources. The SFRS is targeting 118 galaxy nuclei and extranuclear star-forming regions in 56 nearby (d < 30Mpc) galaxies included in the Spitzer/SINGS and Herschel/KINGFISH legacy programs. VLA observations of the entire sample have recently been completed at 3GHz (S band), 15GHz (Ku band) and 33GHz (Ka band). For an initial subset of 9 targets, we have also obtained 90GHz ALMA continuum and line imaging during cycle 1 observations.The frequency spacing of our complete radio data set will allow us to accurately measure the radio spectral index of these targets, in order to model the physical processes that produce the radio emission. In particular, 33GHz observations of HII regions probe free-free emission, providing a sensitive, dust-unbiased measure of the current star formation activity in each complex. We can use the differences between 33GHz derived star formation rates and those derived with other tracers such as synchrotron radiation, extinction corrected UV and Hα emission, and infrared luminosity to examine the dependence of each tracer on separately measured variables such as extinction, metallicity and ionizing radiation field strength. Consequently, these data will help calibrate other empirically-derived star formation rate diagnostics that are more easily measured for high redshift studies, and help interpret rest-frame 33GHz observations from a new generation of deep high frequency (>10GHz) radio surveys.As an example of the science that can be done with SFRS data, we have used our images along with an archival 1.4GHz and a new 5GHz VLA image to map the spectral index, spectral curvature, and the separated thermal and synchrotron components of NGC1266, a low level AGN with a mass outflow rate of > 50 M⊙ / yr
18. A model for the thermal radio-continuum emission from radiative shocks in colliding stellar winds
Montes, G.; González, R. F.; Cantó, J.; Pérez-Torres, M. A.; Alberdi, A.
2011-07-01
Context. In massive-star binary systems, the interaction of the strong stellar winds results in a wind collision region (WCR) between the stars, which is limited by two shock fronts. Besides the nonthermal emission resulting from the shock acceleration, these shocks emit thermal (free-free) radiation detectable at radio frequencies that increase the expected emission from the stellar winds. Observations and theoretical studies of these sources show that the shocked gas is an important, but not dominant, contributor to the total emission in wide binary systems, while it plays a very substantial role in close binaries. Aims: The interaction of two isotropic stellar winds is studied in order to calculate the free-free emission from the WCR. The effects of the binary separation and the wind momentum ratio on the emission from the wind-wind interaction region are investigated. Methods: We developed a semi-analytical model for calculating the thermal emission from colliding stellar winds. Assuming radiative shocks for the compressed layer, which are expected in close binaries, we obtained the emission measure of the thin shell. Then, we computed the total optical depth along each line of sight to obtain the emission from the whole configuration. Results: Here, we present predictions of the free-free emission at radio frequencies from analytic, radiative shock models in colliding wind binaries. It is shown that the emission from the WCR mainly arises from the optically thick region of the compressed layer and scales as ~D4/5, where D is the binary separation. The predicted flux density Sν from the WCR becomes more important as the frequency ν increases, showing higher spectral indices than the expected 0.6 value (Sν ∝ να, where α = 0.6) from the unshocked winds. We also investigate the emission from short-period WR+O systems calculated with our analytic formulation. In particular, we apply the model to the binary systems WR 98 and WR 113 and compare our results
19. Spatially resolved optical-emission spectroscopy of a radio-frequency driven iodine plasma source
Dedrick, James; Doyle, Scott; Grondein, Pascaline; Aanesland, Ane
2016-09-01
Iodine is of interest for potential use as a propellant for spacecraft propulsion, and has become attractive as a replacement to xenon due to its similar mass and ionisation potential. Optical emission spectroscopy has been undertaken to characterise the emission from a low-pressure, radio-frequency driven inductively coupled plasma source operating in iodine with respect to axial distance across its transverse magnetic filter. The results are compared with axial profiles of the electron temperature and density for identical source conditions, and the spatial distribution of the emission intensity is observed to be closely correlated with the electron temperature. This work has been done within the LABEX Plas@Par project, and received financial state aid managed by the Agence Nationale de la Recherche'', as part of the `Programme d'Investissements d'Avenir'' under the reference ANR-11-IDEX-0004-02.
20. TWO RADIO-EMISSION MECHANISMS IN PSR J0901–4624
SciTech Connect
Raithel, C. A.; Shannon, R. M.; Johnston, S.; Kerr, M.
2015-05-01
We have detected sporadic, bright, short-duration radio pulses from PSR J0901–4624. These pulses are emitted simultaneously with persistent, periodic emission that dominates the flux density when averaging over many periods of the pulsar. The bright pulses have energies that are consistent with a power-law distribution. The integrated profile of PSR J0901–4624 is highly polarized and shows four distinct components. The bright pulses appear to originate near the magnetic pole of the pulsar and have polarization properties unlike those of the underlying emission at the same pulse phase. We conclude that the bright pulses represent a secondary giant-micropulse emission process, possibly from a different region in the pulsar magnetosphere.
1. Progress and problems in the theory of type III solar radio emission
NASA Technical Reports Server (NTRS)
Goldman, M. V.
1983-01-01
The experimental and theoretical status of type III solar radio emission is considered in detail. Very recent developments which are relevant to the underlying plasma physics are emphasized. In particular, the identity of the submegahertz emissions as fundamental, or second harmonic, the degree of correlation between emissivities, electron streams, and plasma (Langmuir) waves, paradoxes concerned with the time-ordering of these phenomena, and the role of background density irregularities and ion-acoustic turbulence in the solar wind, are discussed. From the theoretical point of view, the current picture of the underlying Langmuir turbulence, including such effects as the interaction between Langmuir waves and stream electrons, induced scatter off ions, and strong turbulence effects such as modulational instability and soliton collapse, is discussed.
2. Research Spotlight: North and south components of Saturn's radio emissions reversed
Tretkoff, Ernie
2011-02-01
Saturn is known to emit intense radio emissions at kilometer wavelengths from its auroral regions. Observations in recent years found that the Saturn kilometric radiation (SKR) emission from the northern auroral region has a clocklike modulation with a period of about 10.6 hours, while the SKR emission from the southern auroral region has a period of about 10.8 hours. Analyzing more recent observations from the Cassini spacecraft, Gurnett et al. have now found that the rotational modulation rates of the southern and northern components reversed shortly after Saturn’s equinox on 11 August 2009, so that the southern hemisphere SKR now has the shorter rotation period. They also analyzed data from the Ulysses spacecraft to show that a similar reversal occurred during the previous equinox, in November 1995. (Geophysical Research Letters, doi:10.1029/2010GL045796, 2010)
3. Directivity of the radio emission from the K1 dwarf star AB Doradus
NASA Technical Reports Server (NTRS)
Lim, Jeremy; White, Stephen M.; Nelson, Graam J.; Benz, Arnold O.
1994-01-01
We present measurements of the spectrum and polarization of the flaring radio emission from the K1 dwarf star AB Doradus, together with previously reported single frequency measurements (with no polarization information) on 3 other days. On all 4 days spanning a 6 month period, the emission was strong and, when folded with the stellar rotation period, showed similar time variations with two prominant peaks at phase 0.35 and 0.75. These peaks coincide in longitude with two large starspots identified from the stellar optical light curve and have half-powe widths as small as 0.1 rotations and no larger than 0.2 rotations. The modulated emission shows no measurable circular polarization, and its two peaks have different turnover frequencies.
4. SLAC T-510: Radio emission from particle cascades in the presence of a magnetic field
Mulrey, Katharine
2017-03-01
Cosmic ray induced particle cascades radiate in radio frequencies in the Earth's atmosphere. Geomagnetic and Askaryan emission provide an effective way to detect ultra-high energy cosmic rays. The SLAC T-510 experiment was the first to measure magnetically induced radiation from particle cascades in a controlled laboratory setting. An electron beam incident upon a dense dielectric target produced a particle cascade in the presence of a variable magnetic field. Antennas covering a band of 30-3000 MHz sampled RF emission in vertical and horizontal polarizations. Results from T-510 are compared to particle-level RF-emission simulations which are critical for reconstructing the energy and composition of detected ultra-high energy cosmic ray air showers. We discuss the experimental set up, the data processing, the systematic errors and the main results of the experiment, which we found in a good agreement with the simulations.
5. First dynamic computations of synchrotron emission from the cygnus a radio cavity: Evidence for electron pair plasma in cavity
SciTech Connect
Mathews, William G.
2014-03-01
6. A Link Between X-ray Emission Lines and Radio Jets in 4U 1630-47?
Neilsen, Joseph; Coriat, Mickaël; Fender, Rob; Lee, Julia C.; Ponti, Gabriele; Tzioumis, A.; Edwards, Phillip; Broderick, Jess
2014-06-01
Recently, Díaz Trigo et al. reported an XMM-Newton detection of relativistically Doppler-shifted emission lines associated with steep-spectrum radio emission in the stellar-mass black hole candidate 4U 1630-47 during its 2012 outburst. They interpreted these lines as indicative of a baryonic jet launched by the accretion disk. We present a search for the same lines earlier in the same outburst using high-resolution X-ray spectra from the Chandra HETGS. While our observations (eight months prior to the XMM-Newton campaign) also coincide with detections of steep spectrum radio emission by the Australia Telescope Compact Array, we find a strong disk wind but no evidence for any relativistic X-ray emission lines. Indeed, despite ˜5× brighter radio emission, our Chandra spectra allow us to place an upper limit on the flux in the blueshifted Fe XXVI line that is ˜20× weaker than the line observed by Díaz Trigo et al. Thus we can conclusively say that radio emission is not universally associated with relativistically Doppler-shifted emission lines in 4U 1630-47. We explore several scenarios that could explain our differing results, including variations in the geometry of the jet or a mass-loading process or jet baryon content that evolves with the accretion state of the black hole. We also consider the possibility that the radio emission arises in an interaction between a jet and the nearby ISM, in which case the X-ray emission lines might be unrelated to the radio emission.
7. Radio imaging of the very-high-energy gamma-ray emission region in the central engine of a radio galaxy.
PubMed
Acciari, V A; Aliu, E; Arlen, T; Bautista, M; Beilicke, M; Benbow, W; Bradbury, S M; Buckley, J H; Bugaev, V; Butt, Y; Byrum, K; Cannon, A; Celik, O; Cesarini, A; Chow, Y C; Ciupik, L; Cogan, P; Cui, W; Dickherber, R; Fegan, S J; Finley, J P; Fortin, P; Fortson, L; Furniss, A; Gall, D; Gillanders, G H; Grube, J; Guenette, R; Gyuk, G; Hanna, D; Holder, J; Horan, D; Hui, C M; Humensky, T B; Imran, A; Kaaret, P; Karlsson, N; Kieda, D; Kildea, J; Konopelko, A; Krawczynski, H; Krennrich, F; Lang, M J; LeBohec, S; Maier, G; McCann, A; McCutcheon, M; Millis, J; Moriarty, P; Ong, R A; Otte, A N; Pandel, D; Perkins, J S; Petry, D; Pohl, M; Quinn, J; Ragan, K; Reyes, L C; Reynolds, P T; Roache, E; Roache, E; Rose, H J; Schroedter, M; Sembroski, G H; Smith, A W; Swordy, S P; Theiling, M; Toner, J A; Varlotta, A; Vincent, S; Wakely, S P; Ward, J E; Weekes, T C; Weinstein, A; Williams, D A; Wissel, S; Wood, M; Walker, R C; Davies, F; Hardee, P E; Junor, W; Ly, C; Aharonian, F; Akhperjanian, A G; Anton, G; Barres de Almeida, U; Bazer-Bachi, A R; Becherini, Y; Behera, B; Bernlöhr, K; Bochow, A; Boisson, C; Bolmont, J; Borrel, V; Brucker, J; Brun, F; Brun, P; Bühler, R; Bulik, T; Büsching, I; Boutelier, T; Chadwick, P M; Charbonnier, A; Chaves, R C G; Cheesebrough, A; Chounet, L-M; Clapson, A C; Coignet, G; Dalton, M; Daniel, M K; Davids, I D; Degrange, B; Deil, C; Dickinson, H J; Djannati-Ataï, A; Domainko, W; Drury, L O'C; Dubois, F; Dubus, G; Dyks, J; Dyrda, M; Egberts, K; Emmanoulopoulos, D; Espigat, P; Farnier, C; Feinstein, F; Fiasson, A; Förster, A; Fontaine, G; Füssling, M; Gabici, S; Gallant, Y A; Gérard, L; Gerbig, D; Giebels, B; Glicenstein, J F; Glück, B; Goret, P; Göhring, D; Hauser, D; Hauser, M; Heinz, S; Heinzelmann, G; Henri, G; Hermann, G; Hinton, J A; Hoffmann, A; Hofmann, W; Holleran, M; Hoppe, S; Horns, D; Jacholkowska, A; de Jager, O C; Jahn, C; Jung, I; Katarzyński, K; Katz, U; Kaufmann, S; Kendziorra, E; Kerschhaggl, M; Khangulyan, D; Khélifi, B; Keogh, D; Kluźniak, W; Kneiske, T; Komin, Nu; Kosack, K; Lamanna, G; Lenain, J-P; Lohse, T; Marandon, V; Martin, J M; Martineau-Huynh, O; Marcowith, A; Maurin, D; McComb, T J L; Medina, M C; Moderski, R; Moulin, E; Naumann-Godo, M; de Naurois, M; Nedbal, D; Nekrassov, D; Nicholas, B; Niemiec, J; Nolan, S J; Ohm, S; Olive, J-F; de Oña Wilhelmi, E; Orford, K J; Ostrowski, M; Panter, M; Paz Arribas, M; Pedaletti, G; Pelletier, G; Petrucci, P-O; Pita, S; Pühlhofer, G; Punch, M; Quirrenbach, A; Raubenheimer, B C; Raue, M; Rayner, S M; Renaud, M; Rieger, F; Ripken, J; Rob, L; Rosier-Lees, S; Rowell, G; Rudak, B; Rulten, C B; Ruppel, J; Sahakian, V; Santangelo, A; Schlickeiser, R; Schöck, F M; Schröder, R; Schwanke, U; Schwarzburg, S; Schwemmer, S; Shalchi, A; Sikora, M; Skilton, J L; Sol, H; Spangler, D; Stawarz, Ł; Steenkamp, R; Stegmann, C; Stinzing, F; Superina, G; Szostek, A; Tam, P H; Tavernet, J-P; Terrier, R; Tibolla, O; Tluczykont, M; van Eldik, C; Vasileiadis, G; Venter, C; Venter, L; Vialle, J P; Vincent, P; Vivier, M; Völk, H J; Volpe, F; Wagner, S J; Ward, M; Zdziarski, A A; Zech, A; Anderhub, H; Antonelli, L A; Antoranz, P; Backes, M; Baixeras, C; Balestra, S; Barrio, J A; Bastieri, D; Becerra González, J; Becker, J K; Bednarek, W; Berger, K; Bernardini, E; Biland, A; Bock, R K; Bonnoli, G; Bordas, P; Borla Tridon, D; Bosch-Ramon, V; Bose, D; Braun, I; Bretz, T; Britvitch, I; Camara, M; Carmona, E; Commichau, S; Contreras, J L; Cortina, J; Costado, M T; Covino, S; Curtef, V; Dazzi, F; De Angelis, A; De Cea del Pozo, E; Delgado Mendez, C; De los Reyes, R; De Lotto, B; De Maria, M; De Sabata, F; Dominguez, A; Dorner, D; Doro, M; Elsaesser, D; Errando, M; Ferenc, D; Fernández, E; Firpo, R; Fonseca, M V; Font, L; Galante, N; García López, R J; Garczarczyk, M; Gaug, M; Goebel, F; Hadasch, D; Hayashida, M; Herrero, A; Hildebrand, D; Höhne-Mönch, D; Hose, J; Hsu, C C; Jogler, T; Kranich, D; La Barbera, A; Laille, A; Leonardo, E; Lindfors, E; Lombardi, S; Longo, F; López, M; Lorenz, E; Majumdar, P; Maneva, G; Mankuzhiyil, N; Mannheim, K; Maraschi, L; Mariotti, M; Martínez, M; Mazin, D; Meucci, M; Miranda, J M; Mirzoyan, R; Miyamoto, H; Moldón, J; Moles, M; Moralejo, A; Nieto, D; Nilsson, K; Ninkovic, J; Oya, I; Paoletti, R; Paredes, J M; Pasanen, M; Pascoli, D; Pauss, F; Pegna, R G; Perez-Torres, M A; Persic, M; Peruzzo, L; Prada, F; Prandini, E; Puchades, N; Reichardt, I; Rhode, W; Ribó, M; Rico, J; Rissi, M; Robert, A; Rügamer, S; Saggion, A; Saito, T Y; Salvati, M; Sanchez-Conde, M; Satalecka, K; Scalzotto, V; Scapin, V; Schweizer, T; Shayduk, M; Shore, S N; Sidro, N; Sierpowska-Bartosik, A; Sillanpää, A; Sitarek, J; Sobczynska, D; Spanier, F; Stamerra, A; Stark, L S; Takalo, L; Tavecchio, F; Temnikov, P; Tescaro, D; Teshima, M; Torres, D F; Turini, N; Vankov, H; Wagner, R M; Zabalza, V; Zandanel, F; Zanin, R; Zapatero, J
2009-07-24
The accretion of matter onto a massive black hole is believed to feed the relativistic plasma jets found in many active galactic nuclei (AGN). Although some AGN accelerate particles to energies exceeding 10(12) electron volts and are bright sources of very-high-energy (VHE) gamma-ray emission, it is not yet known where the VHE emission originates. Here we report on radio and VHE observations of the radio galaxy Messier 87, revealing a period of extremely strong VHE gamma-ray flares accompanied by a strong increase of the radio flux from its nucleus. These results imply that charged particles are accelerated to very high energies in the immediate vicinity of the black hole.
8. Observations of linear polarization of background galactic radio emission in selected directions at 8.3 GHz
Vinyajkin, E. N.; Carretti, E.; Cortiglioni, S.; Poppi, S.
2002-03-01
Polarization observations of the Galactic radio emission at 8.3 GHz were made by the 32-m Medicina (Italy) radio telescope in four pixels (HPBW=4.'8). A method of tracking around the upper culmination was used in order to use the rotation of the parallactic angle for detecting the weak linearly polarized Galactic radio emission against the background of relatively strong and variable spurious and instrumental polarization. The well known source 3C 286 was used as calibrator. As a result the brightness temperatures of linearly polarized component of the Galactic radio emission and positions angles were measured for all pixels. Comparison was made for the pixels in the first Galactic quadrant with Duncan et al. 2695 MHz polarization measurements and as a result spectral indexes and rotation measures were determined. .
9. Modeling the Radio Emission from Cyg OB2 No. 5: A Quadruple System?
Kennedy, M.; Dougherty, S. M.; Fink, A.; Williams, P. M.
2010-02-01
Fifty observations at frequencies between 1.4 GHz and 43 GHz of the 6.6 day O6.5-7+O5.5-6 binary Cyg OB2 No. 5 using the Very Large Array over 20 years are re-examined. The aim is to determine the location and character of the previously detected variable radio emission. The radio emission from the system consists of a primary component that is associated with the binary, and a non-thermal source (NE), 0farcs8 to the NE of the binary that has been ascribed to a wind-collision region (WCR) between the stellar winds of the binary and that of a B-type star (Star D) to the NE. Previous studies have not accounted for the potential contribution of NE to the total radio emission, most especially in observations where the primary and NE sources are not resolved as separate sources. NE shows no evidence of variation in 23 epochs where it is resolved separately from the primary radio component, demonstrating that the variable emission arises in the primary component. Since NE is non-variable, the radio flux from the primary can now be well determined for the first time, most especially in observations that do not resolve both the primary and NE components. The variable radio emission from the primary component has a period of 6.7 ± 0.3 years which is described by a simple model of a non-thermal source orbiting within the stellar wind envelope of the binary. Such a model implies the presence of a third, unresolved stellar companion (Star C) orbiting the 6.6 day binary with a period of 6.7 years and independent of Star D to the NE. The variable non-thermal emission arises from either a WCR between Star C and the binary system, or possibly from Star C directly. The model gives a mass-loss rate of 3.4 × 10-5 M sun yr-1 for Cyg OB2 No. 5, unusually high for an Of supergiant and comparable to that of WR stars, and consistent with an unusually strong He I 1.083 µm emission line, also redolent of WR stars. An examination of radial velocity observations available from the
10. MODELING THE RADIO EMISSION FROM Cyg OB2 NO. 5: A QUADRUPLE SYSTEM?
SciTech Connect
Kennedy, M.; Dougherty, S. M.; Fink, A.; Williams, P. M. E-mail: [email protected] E-mail: [email protected]
2010-02-01
Fifty observations at frequencies between 1.4 GHz and 43 GHz of the 6.6 day O6.5-7+O5.5-6 binary Cyg OB2 No. 5 using the Very Large Array over 20 years are re-examined. The aim is to determine the location and character of the previously detected variable radio emission. The radio emission from the system consists of a primary component that is associated with the binary, and a non-thermal source (NE), 0.''8 to the NE of the binary that has been ascribed to a wind-collision region (WCR) between the stellar winds of the binary and that of a B-type star (Star D) to the NE. Previous studies have not accounted for the potential contribution of NE to the total radio emission, most especially in observations where the primary and NE sources are not resolved as separate sources. NE shows no evidence of variation in 23 epochs where it is resolved separately from the primary radio component, demonstrating that the variable emission arises in the primary component. Since NE is non-variable, the radio flux from the primary can now be well determined for the first time, most especially in observations that do not resolve both the primary and NE components. The variable radio emission from the primary component has a period of 6.7 +- 0.3 years which is described by a simple model of a non-thermal source orbiting within the stellar wind envelope of the binary. Such a model implies the presence of a third, unresolved stellar companion (Star C) orbiting the 6.6 day binary with a period of 6.7 years and independent of Star D to the NE. The variable non-thermal emission arises from either a WCR between Star C and the binary system, or possibly from Star C directly. The model gives a mass-loss rate of 3.4 x 10{sup -5} M{sub sun} yr{sup -1} for Cyg OB2 No. 5, unusually high for an Of supergiant and comparable to that of WR stars, and consistent with an unusually strong He I 1.083 mum emission line, also redolent of WR stars. An examination of radial velocity observations available
11. RESOLVE: A new algorithm for aperture synthesis imaging of extended emission in radio astronomy
Junklewitz, H.; Bell, M. R.; Selig, M.; Enßlin, T. A.
2016-02-01
We present resolve, a new algorithm for radio aperture synthesis imaging of extended and diffuse emission in total intensity. The algorithm is derived using Bayesian statistical inference techniques, estimating the surface brightness in the sky assuming a priori log-normal statistics. resolve estimates the measured sky brightness in total intensity, and the spatial correlation structure in the sky, which is used to guide the algorithm to an optimal reconstruction of extended and diffuse sources. During this process, the algorithm succeeds in deconvolving the effects of the radio interferometric point spread function. Additionally, resolve provides a map with an uncertainty estimate of the reconstructed surface brightness. Furthermore, with resolve we introduce a new, optimal visibility weighting scheme that can be viewed as an extension to robust weighting. In tests using simulated observations, the algorithm shows improved performance against two standard imaging approaches for extended sources, Multiscale-CLEAN and the Maximum Entropy Method.
12. The Lightning and Radio Emission Detector (LRD) instrument. [carried by Galileo Probe into Jupiter's atmosphere
NASA Technical Reports Server (NTRS)
Lanzerotti, L. J.; Rinnert, K.; Dehmel, G.; Gliem, F. O.; Krider, E. P.; Uman, M. A.; Umlauft, G.; Bach, J.
1992-01-01
The Lightning and Radio Emission Detector (LRD) instrument will be carried by the Galileo Probe into Jupiter's atmosphere. The LRD will verify the existence of lightning in the atmosphere and will determine the details of many of its basic characteristics. The instrument, operated in its magnetospheric mode at distances of about 5, 4, 3, and 2 planetary radii from Jupiter's center, will also measure the RF noise spectrum in Jupiter's magnetosphere. The LRD instrument is composed of a ferrite-core radio frequency antenna and two photodiodes mounted behind individual fisheye lenses. The output of the RF antenna is analyzed both separately and in coincidence with the optical signals from the photodiodes. The RF antenna provides data both in the frequency domain (with three narrow-band channels, primarily for deducing the physical properties of distant lightning) and in the time domain with a priority scheme (primarily for determining from individual RF waveforms the physical properties of closeby-lightning).
13. Collisional quenching of OH radio emission from comet Hale-Bopp.
PubMed
Schloerb, F P; Devries, C H; Lovell, A J; Irvine, W M; Senay, M; Wootten, H A
1997-01-01
Observations of comets in the 18-cm OH transitions offer a means to probe gas production, kinematics, and OH excitation in comets. We present initial results of OH observations of comet Hale-Bopp obtained with the NRAO 43 m antenna located in Greenbank, WV. Maps of the emission provide strong constraints on the amount of quenching of the inversion of the OH ground state A-doublet in the coma. Analysis of the total radio OH flux and maps of its radial brightness distribution indicate a quenched region on the order of approximately 500,000 km during March and April 1997. This large value is generally consistent with previous observations of radio OH quenching in lower production rate comets when the high production rate of comet Hale-Bopp is considered.
14. The Lightning and Radio Emission Detector (LRD) instrument. [carried by Galileo Probe into Jupiter's atmosphere
NASA Technical Reports Server (NTRS)
Lanzerotti, L. J.; Rinnert, K.; Dehmel, G.; Gliem, F. O.; Krider, E. P.; Uman, M. A.; Umlauft, G.; Bach, J.
1992-01-01
The Lightning and Radio Emission Detector (LRD) instrument will be carried by the Galileo Probe into Jupiter's atmosphere. The LRD will verify the existence of lightning in the atmosphere and will determine the details of many of its basic characteristics. The instrument, operated in its magnetospheric mode at distances of about 5, 4, 3, and 2 planetary radii from Jupiter's center, will also measure the RF noise spectrum in Jupiter's magnetosphere. The LRD instrument is composed of a ferrite-core radio frequency antenna and two photodiodes mounted behind individual fisheye lenses. The output of the RF antenna is analyzed both separately and in coincidence with the optical signals from the photodiodes. The RF antenna provides data both in the frequency domain (with three narrow-band channels, primarily for deducing the physical properties of distant lightning) and in the time domain with a priority scheme (primarily for determining from individual RF waveforms the physical properties of closeby-lightning).
15. Constraints on the dark matter neutralinos from the radio emissions of galaxy clusters
Kiew, Ching-Yee; Hwang, Chorng-Yuan; Zainal Abibin, Zamri
2017-05-01
By assuming the dark matter to be composed of neutralinos, we used the detection of upper limit on diffuse radio emission in a sample of galaxy clusters to put constraint on the properties of neutralinos. We showed the upper limit constraint on <σv>-mχ space with neutralino annihilation through b\\bar{b} and μ+μ- channels. The best constraint is from the galaxy clusters A2199 and A1367. We showed the uncertainty due to the density profile and cluster magnetic field. The largest uncertainty comes from the uncertainty in dark matter spatial distribution. We also investigated the constraints on minimal Supergravity (mSUGRA) and minimal supersymmetric standard model (MSSM) parameter space by scanning the parameters using the darksusy package. By using the current radio observation, we managed to exclude 40 combinations of mSUGRA parameters. On the other hand, 573 combinations of MSSM parameters can be excluded by current observation.
16. Constraining the neutrino emission of gravitationally lensed Flat-Spectrum Radio Quasars with ANTARES data
SciTech Connect
Adrián-Martínez, S.; Ardid, M.; Bou-Cabo, M.; André, M.; Anton, G.; Aubert, J.-J.; Bertin, V.; Brunner, J.; Busto, J.; Basa, S.; Biagi, S.; Capone, A.; Caramete, L.; and others
2014-11-01
This paper proposes to exploit gravitational lensing effects to improve the sensitivity of neutrino telescopes to the intrinsic neutrino emission of distant blazar populations. This strategy is illustrated with a search for cosmic neutrinos in the direction of four distant and gravitationally lensed Flat-Spectrum Radio Quasars. The magnification factor is estimated for each system assuming a singular isothermal profile for the lens. Based on data collected from 2007 to 2012 by the ANTARES neutrino telescope, the strongest constraint is obtained from the lensed quasar B0218+357, providing a limit on the total neutrino luminosity of this source of 1.08× 10{sup 46} erg s{sup -1}. This limit is about one order of magnitude lower than those previously obtained in the ANTARES standard point source searches with non-lensed Flat-Spectrum Radio Quasars.
17. VERITAS Upper Limit on the Very High Energy Emission from the Radio Galaxy NGC 1275
DOE PAGES
Acciari, V. A.; Aliu, E.; Arlen, T.; ...
2009-11-16
We report the recent detection by the Fermi γ-ray space telescope of high-energy γ-rays from the radio galaxy NGC 1275 that makes the observation of the very high energy (VHE: E>100 GeV) part of its broadband spectrum particularly interesting, especially for the understanding of active galactic nuclei with misaligned multi-structured jets. The radio galaxy NGC 1275 was recently observed by VERITAS at energies above 100 GeV for about 8 hr. No VHE γ-ray emission was detected by VERITAS from NGC 1275. Finally, a 99% confidence level upper limit of 2.1% of the Crab Nebula flux level is obtained at themore » decorrelation energy of approximately 340 GeV, corresponding to 19% of the power-law extrapolation of the Fermi Large Area Telescope result.« less
18. VERITAS UPPER LIMIT ON THE VERY HIGH ENERGY EMISSION FROM THE RADIO GALAXY NGC 1275
SciTech Connect
Acciari, V. A.; Benbow, W.; Aliu, E.; Boltuch, D.; Arlen, T.; Celik, O.; Aune, T.; Bautista, M.; Cogan, P.; Beilicke, M.; Buckley, J. H.; Bugaev, V.; Dickherber, R.; Bradbury, S. M.; Byrum, K.; Cannon, A.; Cesarini, A.; Ciupik, L.; Cui, W.; Duke, C.
2009-12-01
The recent detection by the Fermi gamma-ray space telescope of high-energy gamma-rays from the radio galaxy NGC 1275 makes the observation of the very high energy (VHE: E>100 GeV) part of its broadband spectrum particularly interesting, especially for the understanding of active galactic nuclei with misaligned multi-structured jets. The radio galaxy NGC 1275 was recently observed by VERITAS at energies above 100 GeV for about 8 hr. No VHE gamma-ray emission was detected by VERITAS from NGC 1275. A 99% confidence level upper limit of 2.1% of the Crab Nebula flux level is obtained at the decorrelation energy of approximately 340 GeV, corresponding to 19% of the power-law extrapolation of the Fermi Large Area Telescope result.
19. Strange doings on Io. [Jupiter radio emission modification, sodium cloud, ionized sulfur and extreme brightness
NASA Technical Reports Server (NTRS)
Goody, R.
1978-01-01
Some unusual properties of Io are discussed, and possible explanations for these are considered. The properties discussed include Io's ability to modify radio waves emitted by Jupiter in the decametric band, the satellite's ionosphere and sodium cloud, its extraordinary brightness, and the presence of ionized sulfur just inside the satellite's orbit. Io's ability to modulate Jovian decametric radio emission is explained on the basis of the hypothesis that the satellite conducts electricity and interacts with Jupiter's magnetic field. Characteristics of the sodium cloud are reviewed, and the probable mechanism responsible for this cloud is outlined. It is concluded that the only plausible explanation for the brightness of Io is the presence of cat's-eye-type reflectors, possibly composed of crystalline deposits, on the satellite's surface.
20. VERITAS Upper Limit on the Very High Energy Emission from the Radio Galaxy NGC 1275
SciTech Connect
Acciari, V. A.; Aliu, E.; Arlen, T.; Aune, T.; Bautista, M.; Beilicke, M.; Benbow, W.; Boltuch, D.; Bradbury, S. M.; Buckley, J. H.; Bugaev, V.; Byrum, K.; Cannon, A.; Celik, O.; Cesarini, A.; Ciupik, L.; Cogan, P.; Cui, W.; Dickherber, R.; Duke, C.; Fegan, S. J.; Finley, J. P.; Fortin, P.; Fortson, L.; Furniss, A.; Galante, N.; Gall, D.; Gibbs, K.; Gillanders, G. H.; Godambe, S.; Grube, J.; Guenette, R.; Gyuk, G.; Hanna, D.; Holder, J.; Horan, D.; Hui, C. M.; Humensky, T. B.; Imran, A.; Kaaret, P.; Karlsson, N.; Kertzman, M.; Kieda, D.; Konopelko, A.; Krawczynski, H.; Krennrich, F.; Lang, M. J.; LeBohec, S.; Maier, G.; McCann, A.; McCutcheon, M.; Millis, J.; Moriarty, P.; Mukherjee, R.; Ong, R. A.; Otte, A. N.; Pandel, D.; Perkins, J. S.; Pohl, M.; Quinn, J.; Ragan, K.; Reynolds, P. T.; Roache, E.; Rose, H. J.; Schroedter, M.; Sembroski, G. H.; Smith, A. W.; Steele, D.; Swordy, S. P.; Theiling, M.; Toner, J. A.; Varlotta, A.; Vassiliev, V. V.; Vincent, S.; Wagner, R. G.; Wakely, S. P.; Ward, J. E.; Weekes, T. C.; Weinstein, A.; Weisgarber, T.; Williams, D. A.; Wissel, S.; Wood, M.; Zitzer, B.; Kataoka, J.; Cavazzuti, E.; Cheung, C. C.; Lott, B.; Thompson, D. J.; Tosti, G.
2009-11-16
We report the recent detection by the Fermi γ-ray space telescope of high-energy γ-rays from the radio galaxy NGC 1275 that makes the observation of the very high energy (VHE: E>100 GeV) part of its broadband spectrum particularly interesting, especially for the understanding of active galactic nuclei with misaligned multi-structured jets. The radio galaxy NGC 1275 was recently observed by VERITAS at energies above 100 GeV for about 8 hr. No VHE γ-ray emission was detected by VERITAS from NGC 1275. Finally, a 99% confidence level upper limit of 2.1% of the Crab Nebula flux level is obtained at the decorrelation energy of approximately 340 GeV, corresponding to 19% of the power-law extrapolation of the Fermi Large Area Telescope result.
1. Self-consistent particle-in-cell simulations of fundamental and harmonic plasma radio emission mechanisms
Thurgood, J. O.; Tsiklauri, D.
2015-12-01
Aims: The simulation of three-wave interaction based plasma emission, thought to be the underlying mechanism for Type III solar radio bursts, is a challenging task requiring fully-kinetic, multi-dimensional models. This paper aims to resolve a contradiction in past attempts, whereby some studies indicate that no such processes occur. Methods: We self-consistently simulate three-wave based plasma emission through all stages by using 2D, fully kinetic, electromagnetic particle-in-cell simulations of relaxing electron beams using the EPOCH2D code. Results: Here we present the results of two simulations; Run 1 (nb/n0 = 0.0057, vb/ Δvb = vb/Ve = 16) and Run 2 (nb/n0 = 0.05, vb/ Δvb = vb/Ve = 8), which we find to permit and prohibit plasma emission respectively. We show that the possibility of plasma emission is contingent upon the frequency of the initial electrostatic waves generated by the bump-in-tail instability, and that these waves may be prohibited from participating in the necessary three-wave interactions due to frequency conservation requirements. In resolving this apparent contradiction through a comprehensive analysis, in this paper we present the first self-consistent demonstration of fundamental and harmonic plasma emission from a single-beam system via fully kinetic numerical simulation. We caution against simulating astrophysical radio bursts using unrealistically dense beams (a common approach which reduces run time), as the resulting non-Langmuir characteristics of the initial wave modes significantly suppresses emission. Comparison of our results also indicates that, contrary to the suggestions of previous authors, an alternative plasma emission mechanism based on two counter-propagating beams is unnecessary in an astrophysical context. Finally, we also consider the action of the Weibel instability which generates an electromagnetic beam mode. As this provides a stronger contribution to electromagnetic energy than the emission, we stress that
2. Detection of decametre-wavelength pulsed radio emission of 40 known pulsars
Zakharenko, V. V.; Vasylieva, I. Y.; Konovalenko, A. A.; Ulyanov, O. M.; Serylak, M.; Zarka, P.; Grießmeier, J.-M.; Cognard, I.; Nikolaenko, V. S.
2013-06-01
The study of pulsars at the lowest radio frequencies observable from the ground (10-30 MHz) is complicated by strong interstellar (dispersion, scattering) and ionospheric (scintillation, refraction) propagation effects, as well as intense Galactic background noise and interference. However, it permits us to measure interstellar plasma parameters (the effects of which increase by a power of two to >4 times the wavelength), the spectrum and the pulse profile at low frequencies more accurately. Up to now, only ˜10 pulsars have been successfully detected at these frequencies. The recent upgrade of the receivers at the Ukrainian T-shaped Radio telescope, second modification (UTR-2) has increased its sensitivity and motivated a new search for pulsed radio emissions. In this work we carried out a survey of known pulsars with declination above -10°, period >0.1 s and dispersion measure (DM) < 30 pc cm-3, i.e. a sample of 74 sources. Our goal was either to detect pulsars not recorded before in the decametre range or to identify factors that prevent their detection. As a result, we have detected the radio emission of 40 pulsars, i.e. 55 per cent of the observed sample. For 30 of them, this was a first detection at these frequencies. Parameters of their average profiles have been calculated, including the intrinsic widening of the pulse (not due to interstellar scattering) with decreasing frequency. Furthermore, two pulsars beyond the selected DM (B0138+59 with DM ≈ 35 pc cm-3 and B0525+21 with DM ≈51 pc cm-3) were also detected. Our results indicate that there is still room to detect new transient and pulsed sources with low-frequency observations.
3. PSR J0737-3039B: A PROBE OF RADIO PULSAR EMISSION HEIGHTS
SciTech Connect
Perera, B. B. P.; McLaughlin, M. A.; Lomiashvili, D.; Gourgouliatos, K. N.; Lyutikov, M.
2012-05-10
In the double pulsar system PSR J0737-3039A/B, the strong wind produced by pulsar A distorts the magnetosphere of pulsar B. The influence of these distortions on the orbital-dependent emission properties of pulsar B can be used to determine the location of the coherent radio emission generation region in the pulsar magnetosphere. Using a model of the wind-distorted magnetosphere of pulsar B and the well-defined geometrical parameters of the system, we determine the minimum emission height to be {approx}20R{sub NS} in the two bright orbital longitude regions. We can determine the maximum emission height by accounting for the amount of deflection of the polar field line with respect to the magnetic axis using the analytical magnetic reconnection model of Dungey and the semi-empirical numerical model of Tsyganenko. Both of these models estimate the maximum emission height to be {approx}2500R{sub NS}. The minimum and maximum emission heights we calculate are consistent with those estimated for normal isolated pulsars.
4. Probing Shock Breakout and Progenitors of Stripped-envelope Supernovae through their Early Radio Emissions
Maeda, Keiichi
2013-01-01
We study properties of early radio emission from stripped-envelope supernovae (SNe; those of Type IIb/Ib/Ic). We suggest there is a sub-class of stripped-envelope SNe based on their radio properties, including the optically well-studied Type Ic SNe (SNe Ic) 2002ap and 2007gr, showing a rapid rise to a radio peak within ~10 days and reaching a low luminosity (at least an order of magnitude fainter than a majority of SNe IIb/Ib/Ic). They show a decline after the peak that is shallower than that of other stripped-envelope SNe while their spectral index is similar. We show that all these properties are naturally explained if the circumstellar material (CSM) density is low and therefore the forward shock is expanding into the CSM without deceleration. Since the forward shock velocity in this situation, as estimated from the radio properties, still records the maximum velocity of the SN ejecta following the shock breakout, observing these SNe in radio wavelengths provides new diagnostics on the nature of both the breakout and the progenitor which otherwise require a quite rapid follow-up in other wavelengths. The inferred post-shock breakout velocities of SNe Ic 2002ap and 2007gr are sub-relativistic, ~0.3c. These are higher than that inferred for SN II 1987A, in line with suggested compact progenitors. However, these are lower than expected for a Wolf-Rayet (W-R) progenitor. It may reflect an as yet unresolved nature of the progenitors just before the explosion, and we suggest that the W-R progenitor envelopes might have been inflated which could quickly reduce the maximum ejecta velocity from the initial shock breakout velocity.
5. PROBING SHOCK BREAKOUT AND PROGENITORS OF STRIPPED-ENVELOPE SUPERNOVAE THROUGH THEIR EARLY RADIO EMISSIONS
SciTech Connect
Maeda, Keiichi
2013-01-01
We study properties of early radio emission from stripped-envelope supernovae (SNe; those of Type IIb/Ib/Ic). We suggest there is a sub-class of stripped-envelope SNe based on their radio properties, including the optically well-studied Type Ic SNe (SNe Ic) 2002ap and 2007gr, showing a rapid rise to a radio peak within {approx}10 days and reaching a low luminosity (at least an order of magnitude fainter than a majority of SNe IIb/Ib/Ic). They show a decline after the peak that is shallower than that of other stripped-envelope SNe while their spectral index is similar. We show that all these properties are naturally explained if the circumstellar material (CSM) density is low and therefore the forward shock is expanding into the CSM without deceleration. Since the forward shock velocity in this situation, as estimated from the radio properties, still records the maximum velocity of the SN ejecta following the shock breakout, observing these SNe in radio wavelengths provides new diagnostics on the nature of both the breakout and the progenitor which otherwise require a quite rapid follow-up in other wavelengths. The inferred post-shock breakout velocities of SNe Ic 2002ap and 2007gr are sub-relativistic, {approx}0.3c. These are higher than that inferred for SN II 1987A, in line with suggested compact progenitors. However, these are lower than expected for a Wolf-Rayet (W-R) progenitor. It may reflect an as yet unresolved nature of the progenitors just before the explosion, and we suggest that the W-R progenitor envelopes might have been inflated which could quickly reduce the maximum ejecta velocity from the initial shock breakout velocity.
6. Long-term changes in Jovian synchrotron radio emission - Intrinsic variations or effects of viewing geometry?
NASA Technical Reports Server (NTRS)
Hood, Lon L.
1993-01-01
Possible causes of the observed long-term variation of Jovian synchrotron radio emission, including both intrinsic changes in the Jovian radiation belts and apparent changes due to variations in the Jovigraphic declination of the earth, D sub E, are investigated. An increase in diffusion rate with other parameters held constant results in an inward displacement of the peak emission radial distance that is not observed. Effects of viewing geometry changes are examined. The possible importance of such effects is suggested by a correlation between the total decimetric radio flux and D sub E, which varies between -3.3 and +3.3 deg during one Jovian orbital period. Because the Jovian central meridian longitudes where the magnetic latitude passes through zero during a given Jovian rotation change substantially with D sub E and since significant longitudinal asymmetries exist in both the volume emissivity and the latitudinal profile of the beam, the total intensity should be at least a partial function of D sub E.
7. FREE-FREE EMISSION AND RADIO RECOMBINATION LINES FROM PHOTOEVAPORATING DISKS
SciTech Connect
Pascucci, I.; Gorti, U.; Hollenbach, D.
2012-06-01
Recent infrared observations have demonstrated that photoevaporation driven by high-energy photons from the central star contributes to the dispersal of protoplanetary disks. Here, we show that photoevaporative winds should produce a detectable free-free continuum emission given the range of stellar ionizing photons and X-ray luminosities inferred for young Sun-like stars. We point out that Very Large Array observations of the nearby disk around TW Hya might have already detected this emission at centimeter wavelengths and calculate the wind electron density and mass flow rate. We also estimate the intensities of H radio recombination lines tracing the wind and discuss which ones could be detected with current instrumentation. The detection and profiles of these recombination lines would unambiguously prove our inference of free-free emission from photoevaporating disks like TW Hya. In addition, radio/millimeter data can help constraining wind parameters such as temperature and electron density that are fundamental in measuring mass flow rates.
8. Modelling the multi-wavelength emission of flat-spectrum radio quasar 3C 279
Zheng, Y. G.; Yang, C. Y.
2016-04-01
We employ a length-dependent conical jet model for the jet structure and emission properties of flat-spectrum radio quasar 3C 279 in the steady state. In the model, ultra-relativistic leptons are injected at the base of the jet and propagate along the jet structure. Non-thermal photons are produced by both synchrotron emission and inverse Compton scattering off synchrotron photons and external soft photons at each segment of the jet. We derive the total energy spectra contribution through integrating every segment. We apply the model to the quasi-simultaneous multi-wavelength observed data of two quiescent epochs. Using the observed radio data of the source, we determine the length of the jet L ˜ 100 pc and the magnetic field B0 ˜ 0.1-1 G at the base of the jet. Assuming a steady geometry of the jet structure and suitable physical parameters, we reproduce the multi-wavelength spectra during two quiescent observed epochs. Our results show that the initial γ-ray emission site is ˜0.5 pc from the black hole.
9. Constraining Fully Convective Magnetic Dynamos using Brown Dwarf Auroral Radio Emission
Kao, Melodie; Hallinan, Gregg; Pineda, J. Sebastian; Escala, Ivanna; Burgasser, Adam; Bourke, Stephen; Stevenson, David
2017-05-01
An important outstanding problem in dynamo theory is understanding how magnetic fields are generated and sustained in fully convective objects, spanning stars through planets. For fully convective dynamo models to accurately predict exoplanet magnetic fields, pushing measurements to include the coolest T and Y dwarfs at the substellar-planetary boundary is critical. A number of models for possible dynamo mechanisms in this regime have been proposed but constraining data on magnetic field strengths and topologies across a wide range of mass, age, rotation rate, and temperature are sorely lacking, particularly in the brown dwarf regime.Detections of highly circularly polarized pulsed radio emission provide our only window into magnetic field measurements for objects in the ultracool brown dwarf regime. However, these detections are very rare; previous radio surveys encompassing ∼60 L6 or later targets have yielded only one detection. We have developed a selection strategy for biasing survey targets by leveraging the emergence of magnetic activity that is driven by planet-like auroral processes in the coolest brown dwarfs. Using our selection strategy, we previously observed six late L and T dwarfs with the Jansky Very Large Array (VLA) at 4-8 GHz and detected the presence of highly circularly polarized radio emission for five targets. Our initial detections provided the most robust constraints on dynamo theory in this regime, confirming magnetic fields >2.5 kG. To further probe the mechanisms driving fully convective dynamos at the substellar-planetary boundary, we present magnetic field constraints for two Y-dwarfs and 8-12 GHz radio observations of late L and T dwarfs corresponding to >3.6 kG surface fields. We additionally present initial results for a comprehensive L and T dwarf survey spanning a wide range of rotation periods to test rotation-dominated dynamo models. Finally, we present a method for comparing magnetic field measurements derived from
10. LOOKING FOR A PULSE: A SEARCH FOR ROTATIONALLY MODULATED RADIO EMISSION FROM THE HOT JUPITER, {tau} BOOeTIS b
SciTech Connect
Hallinan, G.; Bourke, S.; Sirothia, S. K.; Ishwara-Chandra, C. H.; Antonova, A.; Doyle, J. G.; Hartman, J.; Golden, A.
2013-01-01
Hot Jupiters have been proposed as a likely population of low-frequency radio sources due to electron cyclotron maser emission of similar nature to that detected from the auroral regions of magnetized solar system planets. Such emission will likely be confined to specific ranges of orbital/rotational phase due to a narrowly beamed radiation pattern. We report on GMRT 150 MHz radio observations of the hot Jupiter {tau} Booetis b, consisting of 40 hr carefully scheduled to maximize coverage of the planet's 79.5 hr orbital/rotational period in an effort to detect such rotationally modulated emission. The resulting image is the deepest yet published at these frequencies and leads to a 3{sigma} upper limit on the flux density from the planet of 1.2 mJy, two orders of magnitude lower than predictions derived from scaling laws based on solar system planetary radio emission. This represents the most stringent upper limits for both quiescent and rotationally modulated radio emission from a hot Jupiter yet achieved and suggests that either (1) the magnetic dipole moment of {tau} Booetis b is insufficient to generate the surface field strengths of >50 G required for detection at 150 MHz or (2) Earth lies outside the beaming pattern of the radio emission from the planet.
11. Jet Emission in Young Radio Sources: A Fermi Large Area Telescope Gamma-Ray View
Migliori, G.; Siemiginowska, A.; Kelly, B. C.; Stawarz, Ł.; Celotti, A.; Begelman, M. C.
2014-01-01
We investigate the contribution of the beamed jet component to the high-energy emission in young and compact extragalactic radio sources, focusing for the first time on the γ-ray band. We derive predictions on the γ-ray luminosities associated with the relativistic jet assuming a leptonic radiative model. The high-energy emission is produced via Compton scattering by the relativistic electrons in a spherical region at the considered scales (lsim10 kpc). Simulations show a wide range of γ-ray luminosities, with intensities up to ~1046-1048 erg s-1 depending on the assumed jet parameters. We find a highly linear relation between the simulated X-ray and γ-ray luminosities that can be used to select candidates for γ-ray detection. We compare the simulated luminosity distributions in the radio, X-ray, and γ-ray regimes with observations for the largest sample of X-ray-detected young radio quasars. Our analysis of ~4-yr Fermi Large Area Telescope (LAT) data does not yield any statistically significant detections. However, the majority of the model-predicted γ-ray fluxes for the sample are near or below the current Fermi-LAT flux threshold and compatible with the derived upper limits. Our study gives constraints on the minimum jet power (L jet, kin/L disk > 0.01) of a potential jet contribution to the X-ray emission in the most compact sources (lsim 1 kpc) and on the particle-to-magnetic field energy density ratio that are in broad agreement with equipartition assumptions.
12. Double-peaked Emission Lines Due to a Radio Outflow in KISSR 1219
Kharb, P.; Subramanian, S.; Vaddi, S.; Das, M.; Paragi, Z.
2017-09-01
We present the results from 1.5 and 5 GHz phase-referenced VLBA and 1.5 GHz Karl G. Jansky Very Large Array (VLA) observations of the Seyfert 2 galaxy KISSR 1219, which exhibits double-peaked emission lines in its optical spectrum. The VLA and VLBA data reveal a one-sided core-jet structure at roughly the same position angles, providing evidence of an active galactic nucleus outflow. The absence of dual parsec-scale radio cores puts the binary black-hole picture in doubt for the case of KISSR 1219. The high brightness temperatures of the parsec-scale core and jet components (>106 K) are consistent with this interpretation. Doppler boosting with jet speeds of ≳0.55c to ≳0.25c, going from parsec to kiloparsec scales, at a jet inclination ≳50° can explain the jet one-sidedness in this Seyfert 2 galaxy. A blueshifted broad emission line component in [O iii] is also indicative of an outflow in the emission line gas at a velocity of ∼350 km s‑1, while the [O i] doublet lines suggest the presence of shock-heated gas. A detailed line ratio study using the MAPPINGS III code further suggests that a shock+precursor model can explain the line ionization data well. Overall, our data suggest that the radio outflow in KISSR 1219 is pushing the emission line clouds, both ahead of the jet and in a lateral direction, giving rise to the double peak emission line spectra.
13. Radio jet emission from GeV-emitting narrow-line Seyfert 1 galaxies
Angelakis, E.; Fuhrmann, L.; Marchili, N.; Foschini, L.; Myserlis, I.; Karamanavis, V.; Komossa, S.; Blinov, D.; Krichbaum, T. P.; Sievers, A.; Ungerechts, H.; Zensus, J. A.
2015-03-01
Context. With the current study we aim at understanding the properties of radio emission and the assumed jet from four radio-loud and γ-ray-loud narrow-line Seyfert 1 galaxies that have been detected by Fermi. These are Seyfert 1 galaxies with emission lines at the low end of the FWHM distribution. Aims: The ultimate goal is twofold: first we investigate whether a relativistic jet is operating at the source producing the radio output, and second, we quantify the jet characteristics to understand possible similarities with and differences from the jets found in typical blazars. Methods: We relied on the most systematic monitoring of radio-loud and γ-ray-detected narrow-line Seyfert 1 galaxies in the cm and mm radio bands conducted with the Effelsberg 100 m and IRAM 30 m telescopes. It covers the longest time-baselines and the most radio frequencies to date. This dataset of multi-wavelength, long-term radio light-curves was analysed from several perspectives. We developed a novel algorithm to extract sensible variability parameters (mainly amplitudes and time scales) that were then used to compute variability brightness temperatures and the corresponding Doppler factors. The jet powers were computed from the light curves to estimate the energy output and compare it with that of typical blazars. The dynamics of radio spectral energy distributions were examined to understand the mechanism causing the variability. Results: The length of the available light curves for three of the four sources in the sample allowed a firm understanding of the general behaviour of the sources. They all display intensive variability that appears to be occurring at a pace rather faster than what is commonly seen in blazars. The flaring events become progressively more prominent as the frequency increases and show intensive spectral evolution that is indicative of shock evolution. The variability brightness temperatures and the associated Doppler factors are moderate, implying a mildly
14. Completing a Flux-limited Survey for X-ray Emission from Radio Jets | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9106757044792175, "perplexity": 4310.741761221854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806979.99/warc/CC-MAIN-20171123214752-20171123234752-00116.warc.gz"} |
http://mathhelpforum.com/differential-equations/189011-mixed-partials-question.html | 1. ## "Mixed partials" question
The question and my work are both attached as PDF files.
Basically, in my work I only found the partial derivatives to be different and therefore did not proceed because of this but apparently this is wrong. Could someone help me figure out what I am doing wrong?
Any help would be greatly appreciated! | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8120362758636475, "perplexity": 176.34979034303177}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945637.51/warc/CC-MAIN-20180422174026-20180422194026-00212.warc.gz"} |
http://formulas.mathcaptain.com/chemistry/atomic-mass-formula.html | Atomic mass is the mass of an atom as measured in atomic mass units. Although standards for calculating the mass of atoms were used in the past, currently scientists use the atomic mass unit. It is the average relative mass of an atom of the element as compared to the mass of C-12 isotope taken as 12 atomic mass units. In fact, atomic mass tells how may times an atom is heavier than 12th part of C-12 isotope.
Atomic mass = $\frac{Average\ mass\ of\ an\ atom\ of\ element}{\frac{1}{12} \times mass\ of\ C-12\ atom}$
Atomic mass = Atomicity $\times$ Atomic mass
Atomic mass is used in virtually all chemical reactions. Chemist often writes atomic masses as ordinary figures when used in simple calculations and equations.
Atomic Mass Formula Problems
Some of the solved problems based on Atomic Mass Formula is given below.
Question 1: A certain divalent metal salt solution is Electrolyzed in series with a silver coulometer. The weight of silver and the metal deposited are respectively 0.52 gram and 0.27 gram. Given that the equivalent mass of silver is 108, what is the atomic mass of the metal?
Solution:
Some amount of current deposits = some number of g-equivalent of meals.
0.52g of Ag = 0.27g of metal
108g of Ag = $\frac{0.27}{0.52}$ $\times$ 108
= 56g of metal
Thus, the equivalent weight of metal = 56
Since,
Equivalent mass $\times$ Valency = atomic mass
56 $\times$ 2 = 112
Hence, the atomic mass of the metal is 112.
Question 2: An element (X) having equivalent mass E forms a general oxide XmOn. What is the atomic mass of that element?
Solution:
The compound XmOn has n $\times$ 16 parts of oxygen combining with m $\times$ Atomic mass of X
Therefore, 8 parts of oxygen combines with X = $\frac{m \times Atomic\ mass}{n \times 16}$ $\times$ 8
E = $\frac{m \times Atomic\ mass}{n \times 2}$
(or) Atomic mass = $\frac{2E \times n}{m}$
Hence, the atomic mass of the given element is $\frac{2En}{m}$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9427987337112427, "perplexity": 1616.39997454111}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987795253.70/warc/CC-MAIN-20191021221245-20191022004745-00421.warc.gz"} |
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Dec8 awarded Self-Learner Apr19 answered Open source implementation elastic net in C or C++ Sep8 revised How is the intercept computed in GLMnet? added 216 characters in body Aug3 awarded Supporter Aug3 comment How is the intercept computed in GLMnet? However, even when standardization is applied (and therefore mean centering) on the predictors in the algorithm, they take the unstandardized data (therefore $\bar{x} \ne 0$, in general) to fit the different intercepts displayed by glmnet. They do use the same $\beta_0=constant=\bar{y}$ for updating the coefficients but fit an intercept with the raw data, and they do it a posteriori. Aug3 comment How is the intercept computed in GLMnet? Indeed, nervertheless the authors explicitly said in their article : $\beta_0=\bar{y}$ for all values of $\alpha$ and $\lambda$, and moreover they don't say at which point of the algorithm it is computed Aug3 awarded Teacher Aug3 awarded Scholar Aug3 accepted How is the intercept computed in GLMnet? Aug3 answered How is the intercept computed in GLMnet? Aug2 comment How is the intercept computed in GLMnet? It's ok I found the answer looking at scikit-learn python code (because the glmnet source code is in Fortran and it is not my cup of tea). I will share it later if anyone is interested. Thanks anyway ! Aug1 comment How is the intercept computed in GLMnet? Ok, no problem. The point is I already did that : standardizing the predictors ($x_i$'s) and beginning with an intercept equal to the mean of the explained variable ($\frac{1}{N}\sum_{i=1}^{N}y_i$) when all coefficient are zeros, but my intercept doesn't change with $\lambda$. Indeed since I compute the updated coefficients with the previous value of the intercept $\beta_0$, if I want to deduce the "new" $\beta_0$ from the formula above, it gives me exactly the same value as before, and therefore always the mean of the predictors $y_i$'s. Do you have an idea for getting different $\beta_0$'s? Aug1 comment How is the intercept computed in GLMnet? What do you think ? Aug1 comment How is the intercept computed in GLMnet? Thanks for your interest in my issues but equation 17 refers to another algorithm, the one for logistic regression. I'm implementing firstly the "Naive Update" mode of the elastic net (for penalized linear regression), and there are no weights assigned to the observations (else than $\frac{1}{N}$), and even if so, the intercept is not updated this way so I don't think it's the solution. I think I need to find a way to deduct an intercept considering the new updated coefficient for each $\lambda$. Something like : $\beta_0=\frac{1}{N}\sum_{i=1}^{N}(y_i-\sum_{j=1}^{p}x_{ij}\beta_j)$ Jul29 comment How is the intercept computed in GLMnet? Could you precise your idea please ? Which expression of weights should I consider ? Jul29 comment How is the intercept computed in GLMnet? I took the mean of the explained variable because in the article i quoted, the authors of this method write that they do use the mean of the Y_i (the explained variable observations) for all values of alpha and lambda. Now, looking at the output of glmnet function, i guess it's not the case for all lambdas. So that does not tell me how to compute the intercepts for each regularization parameter lambda. Jul29 awarded Student Jul29 awarded Editor Jul29 revised How is the intercept computed in GLMnet? deleted 33 characters in body Jul29 revised How is the intercept computed in GLMnet? edited tags | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8869625329971313, "perplexity": 1301.6122970564682}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697843948/warc/CC-MAIN-20130516095043-00027-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/142375/pseudoinverse-of-neumann-laplacian | # Pseudoinverse of Neumann-Laplacian
Suppose you have the following PDE: find $u \in H^1(\Omega)$ such that
$$-\Delta u = f, \\ \frac{\partial u}{\partial n} = 0.$$
Further assume a solvability condition
$$\int_\Omega f ~\mathrm{d}\mathbf{x} = 0.$$
It is known, that this problem is solvable up to a constant. So speaking in terms of operators this means that the operator $A\colon H^1(\Omega) \to \widetilde{H}^{-1}(\Omega)$ defined by $$(A u, v) := \int_\Omega \nabla u \nabla v ~ \mathrm{d}\mathbf{x}$$ is not invertible. However one can always build up the moore-penrose pseudoinverse $A^\dagger$. So the minimum-norm-solution is given by $$u = A^\dagger f$$.
My question is, whether $A^\dagger$ is also bounded and maybe coercive (or semi-elliptic) ?
Thanks!
-
Doesn't the pseudo-inverse of the Neumann-Laplacian just gives the "zero-mean solution"? – Dirk Sep 17 '13 at 11:21
Yes I think so. I'm just curious about the properties of the pseudo-inverse. Since for an bounded linear elliptic(coercive) operator there holds that the inverse operator is elliptic(coercive) as well. So my question is if one can make statements about the pseudoinverse as well. – Elias Ka Sep 17 '13 at 11:23
The operator $A$ is a continuous operator from $H^1(\Omega)$ to the mean value free subspace of its dual. This subspace is closed, such that the closed range theorem applies: there is a continuous operator $B$ from this subspace to $H^1(\Omega)$, such that $AB f = f$ for all $f$ in this subspace.
Note that $B$ is not uniquely defined. In order to select $A^\dagger$ from the possible choices for $B$, you can for instance require that for any $f$ holds \begin{gather} \int_\Omega Af\,dx = 0. \end{gather}
Definition of Pseudo-Inverse: Let $$A\colon X\to Y$$ be a bounded linear operator between two hilbert-spaces. Further define $$\widetilde{A}\colon \mathrm{ker}(A)^\perp \to \mathrm{ran}(A)$$. Then we define $$A^\dagger\colon \mathrm{ran}(A)\otimes \mathrm{ran}(A)^\perp \subset Y \to X \\ y \mapsto \widetilde{A}^{-1} P_{\mathrm{ran}(A)} y$$ Here $P_{\mathrm{ran}(A)}$ is the projector onto (the closure of) the range of $A$. – Elias Ka Sep 17 '13 at 12:36
Then $A^\dagger$ is continuous iff the range of $A$ is closed – Guido Kanschat Sep 17 '13 at 12:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9771610498428345, "perplexity": 206.4411449412126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783398075.47/warc/CC-MAIN-20160624154958-00101-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.math3ma.com/blog/on-constructing-functions-part-2 | On Constructing Functions, Part 2
This post is the second example in an ongoing list of various sequences of functions which converge to different things in different ways.
Also in this series:
Example 1: converges almost everywhere but not in $L^1$
Example 3: converges in $L^1$ but not uniformly
Example 4: $f_n$ are integrable and converge uniformly to $f$, yet $f$ is not integrable
Example 5: converges pointwise but not in $L^1$
Example 6: converges in $L^1$ but does not converge anywhere
Example 2
A sequence of functions $\{f_n:\mathbb{R}\to\mathbb{R}\}$ which converges to 0 uniformly but does not converge to 0 in $L^1$.
This works because: The sequence tends to 0 as $n\to \infty$ since the height of each function tends to 0 and the the region where $f_n$ is taking on this decreasing height is tending towards all of $\mathbb{R}^+$ ($(0,n)$ as $n\to \infty$) (and it's already 0 on $\mathbb{R}^-\cup\{0\}$). The convergence is uniform because the number of times we have to keep "squishing" the rectangles until their height is less than $\epsilon$ does not depend on $x$.
The details: Let $\epsilon>0$ and choose $N\in \mathbb{N}$ so that $N>\frac{1}{\epsilon}$ and let $n>N$. Fix $x\in \mathbb{R}$.
• Case 1 ($x\leq 0$ or $x\geq n$) Then $f_n(x)=0$ and so $|f_n(x)-0|=0< \epsilon$.
• Case 2 ($0< x < n$ ) Then $f_n(x)=\frac{1}{n}$ and so $|f_n(x)-0|=\frac{1}{n}< \frac{1}{N}<\epsilon$
Finally, $f_n\not\to 0$ in $L^1$ since $$\int_{\mathbb{R}}|f_n|=\int_{(0,n)}\frac{1}{n}=\frac{1}{n}\lambda((0,n))=1.$$
Remark: Here's a question you could ask: wouldn't $f_n=n\chi_{(0,\frac{1}{n})}$ work here too? Both are tending to 0 everywhere and both involve rectangles of area 1. The answer is "kinda." The problem is that the convergence of $n\chi_{(0,\frac{1}{n})}$ is pointwise. BUT Egoroff's Theorem gives us a way to actually "make" it uniform! We've seen this before in a previous example.
On the notation above: For a measurable set $X\subset \mathbb{R}$, denote the set of all Lebesgue integrable functions $f:X\to\mathbb{R}$ by $L^1(X)$. Then a sequence of functions $\{f_n\}$ is said to converge in $L^1$ to a function $f$ if $\displaystyle{\lim_{n\to\infty}}\int|f_n-f|=0$.
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Related Posts | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9939935803413391, "perplexity": 256.2918176811301}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376828448.76/warc/CC-MAIN-20181217065106-20181217091106-00615.warc.gz"} |
http://www.emathzone.com/tutorials/geometry/introduction-to-cone.html | # Introduction to Cone
A cone is a solid figure generated by a line, one end of which is fixed and the other end describe a closed curve in a plane.
A circular cone is a solid figure whose base is a circle and whose lateral surface area (i.e. curved surface area) tapers uniformly to a point: which is called the vertex or apex. The axis of the cone is a straight line drawn from the vertex to the center of the base.
A right circular cone is a cone whose base is a circle and whose axis is perpendicular to the base. Such a cone can also be described as solid formed by a right triangle rotated about one of its sides as an axis; it may, therefore, be called a cone of revolution. Altitude of a cone is the perpendicular line from the vertex to the base. ($OF$ as shown in the figure).
The slant height is the length of a straight line drawn from the vertex to the circumference of the base ($CF$ as shown in the figure). If $C$ is any point on the circle (base of the cone), we obtain by Pythagorean Theorem,
Where
$CF = l$, being slant height of the cone
$OF =$ altitude of the cone
$OC = r$, radius of the base of the cone
A pyramid with a circular base is given the special name of cone i.e., a cone may be considered the limiting case of a pyramid when the number of sides of the base polygon increases indefinitely. | {"extraction_info": {"found_math": true, "script_math_tex": 6, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8503645658493042, "perplexity": 179.12868769893768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720737.84/warc/CC-MAIN-20161020183840-00349-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/114372-limits-riemann-sums-print.html | # Limits of Riemann Sums
• November 13th 2009, 02:09 PM
ipreferhistory
Limits of Riemann Sums
I have to answer three questions about limits of Riemann sums, and I can't remember how to figure it out. I know it involves sequences with sigma but I don't know where to start now.
the first one I have is written with the integral from 2 to 5 (x^2 - 1)dx
can someone please get me started or show the steps so I can do the rest of my homework?
• November 13th 2009, 02:52 PM
tonio
Quote:
Originally Posted by ipreferhistory
I have to answer three questions about limits of Riemann sums, and I can't remember how to figure it out. I know it involves sequences with sigma but I don't know where to start now.
the first one I have is written with the integral from 2 to 5 (x^2 - 1)dx
can someone please get me started or show the steps so I can do the rest of my homework?
As the function is continuous everywhere it is so in the given interval and thus it is Riemann integrable there. Now subdivide $[2,5]\,\, in \,\,n$ subintervals of equal length $\frac{5-2}{n}=\frac{3}{n}$, and choose to evaluate the function $f(x)=x^2-1$ at the left endpoints of each subinterval (we can do that since we know the functions is Riemann int. and thus we can freely choose the partition ,as long as it length parameter tends to zero when $n\rightarrow\infty\$, and the points at each subinterval at which the function's evaluated:
$\int\limits_2^5(x^2-1)dx=\lim_{n\to\infty}\frac{3}{n}\sum\limits_{k=0} ^{n-1}\left[\left(2+\frac{3k}{n}\right)^2-1\right]=\lim_{n\to\infty}\frac{3}{n}\sum\limits_{k=0}^{n-1}\left[4+\frac{12}{n}k+\frac{9}{n^2}k^2-1\right]$ $=\lim_{n\to\infty}\frac{3}{n}\left[4n+\frac{12}{n}\frac{(n-1)n}{2}+\frac{9}{n^2}\frac{n(n+1)(2n+1)}{6}-n\right]=$
$\lim_{n\to\infty}3\left[3+\frac{6(n-1)n}{n^2}+\frac{3(2n+1)(n+1)n}{2n^3}\right]=3(3+6+3)=36$
Tonio
• November 13th 2009, 02:55 PM
Quote:
Originally Posted by ipreferhistory
I have to answer three questions about limits of Riemann sums, and I can't remember how to figure it out. I know it involves sequences with sigma but I don't know where to start now.
the first one I have is written with the integral from 2 to 5 (x^2 - 1)dx
can someone please get me started or show the steps so I can do the rest of my homework?
If you need to right the integral as a sum, then this is what you're looking for.
$\int_a^bf(x)dx=\lim_{n->\infty}\Sigma_{i=1}^nf(x_i)\Delta x$
$x_i=a+i\Delta x$
$\Delta x =\frac{b-a}{n}$
Do you understand how to apply this? It's pretty straight forward.
• November 22nd 2009, 07:27 AM
Blakjax
I have a similar question
Find a formula for right hand endpoint sum by dividing the interval into n equal subintervals. Then take the limit of these sums as n approaches infinity to calculate area under the curve [a,b]. f(x)=5x^2 over [1,2]
• November 23rd 2009, 03:38 AM
mr fantastic
Quote:
Originally Posted by Blakjax
Find a formula for right hand endpoint sum by dividing the interval into n equal subintervals. Then take the limit of these sums as n approaches infinity to calculate area under the curve [a,b]. f(x)=5x^2 over [1,2]
You have been given a fair bit of help. Where are you stuck?
• November 23rd 2009, 04:07 AM
Blakjax
unsure
This is what I got, but I'm not sure if it's right.
R=∑(5k^2/n^2 + 5)1/n
5/n^3(n(n+1)(2n+1)/6) + 5
lim ((5n(n+1)(2n+1))/6n^3) + 5
= 20/3....my problem is I don't think it's the right answer
• November 23rd 2009, 05:07 PM
mr fantastic
Quote:
Originally Posted by Blakjax
This is what I got, but I'm not sure if it's right.
R=∑(5k^2/n^2 + 5)1/n
5/n^3(n(n+1)(2n+1)/6) + 5
lim ((5n(n+1)(2n+1))/6n^3) + 5
= 20/3....my problem is I don't think it's the right answer
Find $\lim_{n \to +\infty} \frac{5}{n} \sum_{i=1}^{n} \left( 1 + \frac{i}{n}\right)^2$.
Note that by direct integration you expect the above limit to equal 35/3 (so you should be very sure about whether or not you have the correct answer). | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9864215850830078, "perplexity": 368.4279088382653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463453.54/warc/CC-MAIN-20150226074103-00192-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://cms.math.ca/10.4153/CJM-1997-015-x | location: Publications → journals → CJM
Abstract view
# On some alternative characterizations of Riordan arrays
Published:1997-04-01
Printed: Apr 1997
• Donatella Merlini
• Douglas G. Rogers
• Renzo Sprugnoli
• M. Cecilia Verri
Format: HTML LaTeX MathJax PDF PostScript
## Abstract
We give several new characterizations of Riordan Arrays, the most important of which is: if $\{d_{n,k}\}_{n,k \in {\bf N}}$ is a lower triangular array whose generic element $d_{n,k}$ linearly depends on the elements in a well-defined though large area of the array, then $\{d_{n,k}\}_{n,k \in {\bf N}}$ is Riordan. We also provide some applications of these characterizations to the lattice path theory. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.905638575553894, "perplexity": 4230.40513647931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172156.69/warc/CC-MAIN-20170219104612-00209-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://plainmath.net/70149/given-a-set-x-for | # Given a set {-3, x,3,4,6,5, -3, 2}, for what x
Given a set {-3, x,3,4,6,5, -3, 2}, for what x would the mean of the set be -1?
You can still ask an expert for help
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Cristian Rosales
Explanation:
Given the set
{-3, x,3,4,6,5, -3, 2}
There are 8 values in this set
and the set has a total value of 14+x
If the mean is (-1) then the total value of the set must be $8×\left(-1\right)=-8$
Therefore
14+x=-8
$\to x=-22$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8178656697273254, "perplexity": 2637.150234872604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572408.31/warc/CC-MAIN-20220816151008-20220816181008-00445.warc.gz"} |
https://www.arxiv-vanity.com/papers/1902.01677/ | arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.
# Stability results of properties related to the Bishop-Phelps-Bollobás property for operators
María D. Acosta Universidad de Granada, Facultad de Ciencias, Departamento de Análisis Matemático, 18071 Granada, Spain and Maryam Soleimani-Mourchehkhorti School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
###### Abstract.
We prove that the class of Banach spaces such that the pair has the Bishop-Phelps-Bollobás property for operators is stable under finite products when the norm of the product is given by an absolute norm. We also provide examples showing that previous stability results obtained for that property are optimal.
The first author was supported by Junta de Andalucía grant FQM–185 and also by Spanish MINECO/FEDER grant MTM2015-65020-P. The second author was supported by a grant from IPM
## 1. Introduction
This paper is motivated by recent research on extensions of the so-called Bishop-Phelps-Bollobás theorem for operators. Bishop-Phelps theorem [8] states that every continuous linear functional on a Banach space can be approximated (in norm) by norm attaining functionals. Before to state precisely a “quantitative version” of that result proved by Bollobás [9] we recall some notation. We denote by , and the closed unit ball, the unit sphere and the topological dual of a Banach space , respectively. If and are both real or both complex Banach spaces, denotes the space of (bounded linear) operators from to , endowed with its usual operator norm.
Bishop-Phelps-Bollobás Theorem (see [10, Theorem 16.1], or [12, Corollary 2.4]). Let be a Banach space and . Given and with , there are elements and such that , and .
A lot of attention has been devoted to extending Bishop-Phelps theorem to operators and interesting results have been obtained about that topic (see for instance [19] and [11]). In [2] the reader may find most of the results on the topic known until 2006 and some open questions on the subject. The survey paper [20] contains updated results for Bishop-Phelps property for the space of compact operators. It deserves to point out that in general the subset of norm attaining compact operators between two Banach spaces is not dense in the corresponding space of compact operators [21, Theorem 8].
In 2008 the study of extensions of Bishop-Phelps-Bollobás theorem to operators was initiated by Acosta, Aron, García and Maestre [3]. In order to state some of these extensions it will be convenient to recall the following notion.
###### Definition 1.1 ([3, Definition 1.1]).
Let and be either real or complex Banach spaces. The pair is said to have the Bishop-Phelps-Bollobás property for operators (BPBp) if for every there exists such that for every , if satisfies , then there exist an element and an operator satisfying the following conditions
∥S(u0)∥=1, ∥u0−x0∥<ε and ∥S−T∥<ε.
In the paper already mentioned it is shown that the pair has the BPBp whenever and are finite-dimensional spaces [3, Proposition 2.4]. The same result also holds true in case that has a certain isometric property (called property of Lindenstrauss), for every Banach space [3, Theorem 2.2]. For instance, the spaces and have such geometric property. It is known that every Banach space admits an equivalent norm with the property . In case that the domain is there is a characterization of the Banach spaces such that has the BPBp [3, Theorem 4.1]. The geometric property appearing in the previous characterization was called the almost hyperplane series property (in short AHSp) (see Definition 2.5).
In general there are a few results about stability of the BPBp under direct sums both on the domain or on the range. For instance, it was shown in [6, Proposition 2.4] that the pairs and satisfy the Bishop-Phelps-Bollobás property for operators whenever all pairs have the Bishop-Phelps-Bollobás property for operators “uniformly”. On the other hand, on the range the BPBp is not stable under -sums for (see [15, Theorem, p. 149] and [1, Theorem 2.3]). Indeed it is a long-standing open question if for every Banach space , the subset of norm attaining operators from into the euclidean space is dense in the corresponding space of operators.
In case that the domain is , there are some more known results for the stability of the class of Banach spaces such that has the BPBp. In view of the characterization already mentioned, we will list some known results of stability of the AHSp.
As a consequence of [3, Theorem 4.1] and [6, Proposition 2.4], if the family of Banach spaces has AHSp “uniformly”, then the spaces and have AHSp. Also it was proved the stability of AHSp under finite -sums for every [4, Theorems 2.3 and 2.6]. Recently this result was extended to any absolute sum of two summands (see Definition 2.3) [5, Theorem 2.6]. The paper [5] also contains some stability result for , where is a Banach sequence space satisfying certain additional assumptions [5, Theorem 2.10].
The goal of this paper is to obtain some more stability results. Now we briefly describe the content of the paper. In section we recall the definition of absolute norm on , the class of norms induced on a finite product of normed spaces by absolute norms and some properties that will be used later. We also provide an example showing that, in general, an absolute norm on cannot be written in terms of two absolute norms on (see Example 2.7 for details).
Later in section , we prove that AHSp is stable under products of any finite number of Banach spaces with the same property, when the product is endowed with an absolute norm. Notice that the proof of this general result is far from the one for the case of the product of two spaces. We will provide more detailed arguments in section 3 for that assertion. Let us just mention now that a simple induction argument does not work in view of Example 2.7. It is worth to notice that in general the product of two spaces with AHSp does not necessarily has such property.
In section 4 we show the parallel stability result for AHp (see Definition 4.1). Let us mention that AHp is a property stronger than AHSp. Finally we provide a simple example showing that AHSp is not preserved in general by an infinite product in case that the norm is given by a Banach lattice sequence, even in the case that all the factors have AHp uniformly. This example shows that the stability result proved in [5, Theorem 2.10] is optimal.
## 2. Definitions and notation
In this section we recall the notions of absolute norm on , the norm endowed by an absolute norm on a finite product of normed spaces and some main properties that we will use later. We also recall the notion of approximate hyperplane series property that will be essential in this paper.
The notion of an absolute norm for was introduced in [10, §21], where the reader can find some properties of these norms. In different contexts this class of norms has been used in order to study geometric properties of the direct sum of Banach spaces (see for instance [25], [23] and [26]). Although we will use properties of absolute norms that are well known we recall the notion that we use and state properties useful to our purpose.
The following notion is a particular case of the one used in [18, Section 2]. It suffices for our purpose.
###### Definition 2.1.
A norm on is called absolute if it satisfies that
f((xi))=f((|xi|)), ∀(xi)∈RN.
An absolute norm is said to be normalized if for every , where is the canonical basis of .
Clearly the usual norms on are absolute norms. The following statement gathers some properties of absolute norms. Proofs can be found for instance in [18, Remark 2.1]. Since we consider finite dimensional spaces next assertions can be also checked by using a similar argument to the one used in [10, Lemmas 21.1 and 21.2]
###### Proposition 2.2.
Let be an absolute normalized norm on . The following assertions hold
• If and for each then .
• It is satisfied that
∥x∥∞≤f(x)≤∥x∥1, ∀x∈RN.
• If and for each then .
Of course, the topological dual of can be identified with and the identification is given by the mapping defined by
Φ(y)(x)=N∑i=1yixi, ∀y,x∈RN.
Under this identification, by defining the mapping
f∗(y)=max{Φ(y)(x):x∈RN,f(x)≤1},
it is immediate that is also an absolute normalized norm in case that is an absolute normalized norm on and is a surjective linear isometry from to the dual of the space .
Next concept is standard and has been used in the literature very frequently for the product of two spaces (see for instance [7], [22], [23], [24] and [17])).
###### Definition 2.3.
Let be a nonnegative integer, a Banach space for each and be an absolute norm. Then the mapping given by
∥x∥f=f((∥xi∥)), ∀x=(xi)∈N∏i=1Xi
is a norm on . In what follows, we denote , endowed with the norm .
The following result describes the dual and the duality mapping of the space , that is essentially well known. In any case there is a proof in [16, Proposition 3.3].
###### Proposition 2.4.
Under the previous setting the dual space can be identified with the space , endowed with the absolute norm . More precisely, the mapping given by
Ψ((x∗i))(xi)=N∑i=1x∗i(xi), ∀(xi)∈N∏i=1Xi, (x∗i)∈N∏i=1X∗i
is a surjective linear isometry from to the topological dual of , where we consider in the norm associated to , that is,
∥(x∗i)∥f∗=f∗((∥x∗i∥)), ∀(x∗i)∈N∏i=1X∗i.
Moreover, if and , then if and only if
x∗i(xi)=∥x∗i∥∥xi∥, ∀i≤N.
In what follows by a convex series we mean a series of nonnegative real numbers such that . Now we recall other notion essential in our paper which is related to the Bishop-Phelps-Bollobás property for operators.
###### Definition 2.5 ([3, Remark 3.2]).
A Banach space has the approximate hyperplane series property (AHSp) if for every there exist and with such that for every sequence in and every convex series with
∥∥∥∞∑k=1αkxk∥∥∥>1−ηX(ε),
there exist a subset and a subset satisfying the following conditions
1. and
2. there is such that for all
Finite-dimensional spaces, uniformly convex spaces, the classical spaces ( is a compact and Hausdorff space) and ( is a positive measure) have AHSp (see [3, Section 3]).
It is convenient to recall the following characterization of AHSp.
###### Proposition 2.6 ([4, Proposition 1.2]).
Let be a Banach space. The following conditions are equivalent.
• has the AHSp.
• For every there exist and with such that for every sequence in and every convex series with there are a subset with , an element , and such that for all
• For every there exists such that for any sequence in and every convex series with there are a subset with , an element , and such that for all
• The same statement holds as in but for every sequence in .
Acosta, Mastyło and Soleimani-Mourchehkhorti proved that the AHSp is stable under product of two spaces, endowed with an absolute norm [5, Theorem 2.6]. The argument for extending that result for more summands is not obvious. Next we provide an example of an absolute norm on that cannot be expreseed in terms of two absolute norms on . As a consequence, induction cannot be applied directly to prove the stability result of AHSp under absolute norms.
###### Example 2.7.
Consider the function on given by
|(x,y,z)|=max{√x2+y2,|x|+|z|} ((x,y,z)∈R3).
Then is an absolute normalized norm on and there are no absolute norms and on satisfying any of the following three assertions
###### Proof.
It is immediate to check that is an absolute normalized norm on .
i) Assume that it is satisfied the equality
|(x,y,z)|=f(g(y,z),x), ∀(x,y,z)∈R3.
Since we have that
1=f(g(1,0),0)=g(1,0)f(1,0), 1=f(g(0,1),0)=g(0,1)f(1,0)
and so
g(1,0)=g(0,1).
As a consequence we obtain that
√2=|(1,1,0)|=f(g(1,0),1)=f(g(0,1),1)=|(1,0,1)|=2,
which is a contradiction. So condition i) cannot be satisfied.
ii) Assume now that it is satisfied
|(x,y,z)|=f(g(x,z),y), ∀(x,y,z)∈R3.
So
(2.1) |x|+|z|=|(x,0,z)|=f(g(x,z),0)=g(x,z)f(1,0), ∀(x,z)∈R2.
Hence we obtain that
√x2+y2=|(x,y,0)|=f(g(x,0),y)=f(xf(1,0),y), ∀(x,y)∈R2.
That is,
f(x,y)=√(f(1,0)x)2+y2, ∀(x,y)∈R2.
As a consequence, in view of the previous equality and (2.1) we deduce that
f(g(x,z),y))=√(f(1,0)g(x,z))2+y2=√(|x|+|z|)2+y2, ∀(x,y,z)∈R3.
But the last equality contradicts the assumption of ii).
iii) Assume now that
|(x,y,z)|=f(g(x,y),z), ∀(x,y,z)∈R3.
Hence we get that
(2.2) √x2+y2=f(g(x,y),0)=g(x,y)f(1,0), ∀(x,y)∈R2.
As a consequence we have that
|x|+|z|=|(x,0,z)|=f(g(x,0),z)=f(xf(1,0),z), ∀(x,z)∈R2,
that is,
(2.3) f(x,z)=f(1,0)|x|+|z|, ∀(x,z)∈R2.
For each in view of (2.3) and (2.2) we obtain that
max{√x2+y2,|x|+|z|} =f(g(x,y),z) =f(1,0)g(x,y)+|z| ∀(x,y,z)∈R3 =√x2+y2+|z|,
which is a contradiction. So cannot satisfy condition iii). ∎
## 3. Stability result of the approximate hyperplane series property
As we already mentioned in the introduction, the goal of this section is to prove that the AHSp is stable under finite products in case that the norm of the product is given by an absolute norm. For product of two spaces that result was proved in [5, Theorem 2.6].
In the proof of the stability of AHSp for the product of two spaces Lemma 2.5 in [5] plays an essential role. But the statement of that result does not hold in case that we replace by . For instance, this is the case of the absolute norm on whose closed unit ball is the convex hull of the set given by
{(x,y,0):x2+y2≤1}∪{(x,0,z):x2+z2≤1}
∪{(0,y,z):y2+z2≤1}∪{1√2(r,s,t):r,s,t∈{1,−1}}.
The following result is a consequence of [3, Lemma 3.3].
###### Lemma 3.1.
Let be a sequence of complex numbers with for any nonnegative integer and let and be a convex series such that . If we define then
∑k∈Aαk>1−η.
The next statement is a refinement of [3, Lemma 3.4] that will be very useful.
###### Lemma 3.2.
Assume that is a norm on . Then for every , there is such that whenever , there exists satisfying for all , where and also for every such that .
###### Proof.
For a subset we define
ZG:={z∗∈S(RN)∗:z∗(ei)=0,∀i∈G}.
It is clear that is a compact set of .
We argue by contradiction. So assume that there is a set , some positive real number such that for each there is such that for each there is some element such that .
So there are sequences , such that for all By compactness of , we may assume that for some . By the previous condition there is a sequence in satyisfying for each and such that
(3.1) \rm dist(an,F(a∗))≥ε0, ∀n∈N .
By passing to a subsequence, if needed, we also may assume that converges to some . Since and both sequences are convergent, it follows that ; that is, . As a consequence we obtain that for every . Since converges to , the previous inequality contradicts (3.1). ∎
###### Theorem 3.3.
Assume that is an absolute normalized norm on and are Banach spaces having the AHSp, then has the AHSp, where is endowed with the norm given by
∥(x1,…,xN)∥=|(∥x1∥,…,∥xN∥)|, (xi∈Xi,∀i≤N).
###### Proof.
For a set we define by
PG(z)(i)=zi if i∈G and PG(z)(i)=0 if i∈{1,2,…,N}∖G.
For each we denote by for every .
We can clearly assume that for each . We will prove the result by induction on . For the result is trivially satisfied. So we assume that and the result is true for the space for any subset such that . We will prove the result for . To this end we use that in view of [3, Proposition 3.5] finite-dimensional spaces have AHSp.
Assume that and let be a function such that
a) the pair satisfies condition c) in Proposition 2.6 for the space and for the Banach spaces for each such that ,
b) the pair satisfies Lemma 3.2 for and
c) for every .
We will show that satisfies condition d) in Proposition 2.6 for . Assume that is a sequence in and is a convex series such that
∥∥∥∞∑k=1αkuk∥∥∥>1−η′.
By Hahn-Banach theorem there is a functional such that
(3.2) 1−η′<\rm Reu∗(∞∑k=1αkuk)=\rm Re(∞∑k=1αk(N∑i=1u∗i(uk(i)))).
Now we define the set by
F={i≤N:∥u∗i∥>8√η′} and Fc={i∈N:i≤N}∖F.
Since , in view of Proposition 2.4 and assertion b) in Proposition 2.2 we obtain that . We consider two cases.
Case 1. Assume that .
Notice that
1−η′ <\rm Re∞∑k=1αku∗(uk) =\rm Re∞∑k=1αk(∑i∈Fu∗i(uk(i)))+\rm Re∞∑k=1αk(∑i∈Fcu∗i(uk(i))) ≤\rm Re∞∑k=1αk(∑i∈Fu∗i(uk(i)))+∞∑k=1αk(∑i∈Fc8√η′) ≤\rm Re∞∑k=1αk(∑i∈Fu∗i(uk(i))))+N8√η′ ≤\rm Re∞∑k=1αk(∑i∈Fu∗i(uk(i)))+η(η(ε4N))2.
So
(3.3) \rm Re∞∑k=1αk(∑i∈Fu∗i(uk(i)))>1−η′−η(η(ε4N))2>1−η(η(ε4N)).
By assumption the space has AHSp, and in view of a) there is a set and such that
(3.4) ∑k∈Aαk>1−η(ε4N)>1−ε4N>1−ε
and for every there is such that
(3.5) v∗(vk)=∑i∈Fv∗i(vk(i))=1, ∀k∈A
and
(3.6)
Now we define as follows
G={i∈F:∃k∈A,v∗i(vk(i))≠0}.
By (3.5) we have that
(3.7) ∑i∈Gv∗i(vk(i)))=∑i∈Fv∗i(vk(i))=v∗(vk)=1, ∀k∈A.
As a consequence . In view of Proposition 2.4 we have that
(3.8) v∗i(vk(i))=∥v∗i∥∥vk(i)∥, ∀i∈F,k∈A.
Now we define the element as follows
w∗i={v∗iif i∈G0if i∈{j∈N:j≤N}∖G.
It is trivially satisfied that and by (3.7) we have
(3.9) w∗(vk)=∑i∈Gw∗i(vk(i))=∑i∈Gv∗i(vk(i)))=1, ∀k∈A.
So by (3.6) for each we have that
\rm Rew∗(uk)=\rm Rew∗(PF(uk))≥\rm Rew∗(vk)−∥∥vk−PF(uk)∥∥>1−η(ε4N).
That is, for each it is satisfied that
1−η(ε4N)<\rm ReN∑i=1w∗i(uk(i)))≤N∑i=1∥w∗i∥∥uk(i)∥=∑i∈G∥v∗i∥∥uk(i)∥.
By using condition b) there exists such that for every , and for every there exists such that
(3.10) N∑k=1sirk(i)=1, ∣∣(rk(i))i≤N−(∥∥uk(i))∥∥)i≤N∣∣<ε4N<ε4.
Finally we define as follows
z∗i=⎧⎨⎩siv∗i∥v∗i∥if i∈G0if i∈{j∈N:j≤N}∖G.
By Proposition 2.4 we have that , so .
Notice that for every there exists such that . For every we choose and for every we define as follows
zk(i)=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩rk(i)vk(i)∥vk(i)∥if i∈F and vk(i)≠0rk(i)vki0(i)∥vki0(i)∥if i∈G and vk(i)=0rk(i)xiif i∈F∖G and vk(i)=0rk(i)uk(i)∥uk(i)∥if i∈{j∈N:j≤N}∖F and uk(i)≠0rk(i)xiif i∈{j∈N:j≤N}∖F and uk(i)=0.
Since | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9922006726264954, "perplexity": 336.54712457943697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141188800.15/warc/CC-MAIN-20201126142720-20201126172720-00231.warc.gz"} |
http://meetings.aps.org/Meeting/DPP08/Event/88977 | ### Session TI2: Boundaries, Fluctuations and Transport
9:30 AM–12:30 PM, Thursday, November 20, 2008
Room: Landmark B
Chair: Robert La Haye, General Atomics
Abstract ID: BAPS.2008.DPP.TI2.6
### Abstract: TI2.00006 : Drift-Kinetic Simulations of Neoclassical Transport
12:00 PM–12:30 PM
Preview Abstract MathJax On | Off Abstract
#### Author:
E.A. Belli
(General Atomics)
A new $\delta f$ Eulerian kinetic code NEO has been developed for numerical studies of neoclassical transport. NEO serves a dual role: in addition to its practical value as a tool for high-accuracy neoclassical calculations, NEO also functions as a stepping-stone (together with the nonlinear GK code GYRO) toward a full-F gyrokinetic code which integrates neoclassical transport and microturbulence. NEO solves a hierarchy of equations derived by expanding the drift-kinetic equation in powers of $\rho_{*i}$, the ratio of the ion gyroradius to system size, and thus provides a first-principles calculation of the neoclassical transport coefficients for general plasma shape directly from solution of the distribution function. NEO extends previous numerical studies by including the self-consistent coupling of electrons and multiple ion species, the calculation of the first-order electrostatic potential via coupling with the Poisson equation, and rapid toroidal rotation effects. Systematic calculations of the second-order particle and energy fluxes and first-order plasma flows, poloidal rotation, and bootstrap current and comparisons with analytical theories are presented for multispecies plasmas. The ambipolar relation, which requires complete cross-species collisional coupling, is confirmed, and finite mass-ratio corrections due to this collisional coupling are identified. Parameterized studies of the effects of shaping are performed, and the application of analytic formulae obtained for circular plasmas to shaped cases is discussed. Results using DIII-D experimental profiles and the effects of strong rotation are also presented. Finally, finite orbit width effects are studied via solution of the higher-order drift-kinetic equations, and the implications of non-local transport on the validity of the $\delta f$ formulation for steep gradients in the H-mode edge are discussed.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2008.DPP.TI2.6 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.835858941078186, "perplexity": 3808.393873055034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368708664942/warc/CC-MAIN-20130516125104-00051-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.ck12.org/book/CK-12-Algebra-I/r2/section/8.6/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 8.6: Exponential Decay Functions
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Graph an exponential decay function.
• Compare graphs of exponential decay functions.
• Solve real-world problems involving exponential decay.
## Introduction
In the last section, we looked at graphs of exponential functions. We saw that exponentials functions describe a quantity that doubles, triples, quadruples, or simply gets multiplied by the same factor. All the functions we looked at in the last section were exponentially increasing functions. They started small and then became large very fast. In this section, we are going to look at exponentially decreasing functions. An example of such a function is a quantity that gets decreased by one half each time. Let’s look at a specific example.
For her fifth birthday, Nadia’s grandmother gave her a full bag of candy. Nadia counted her candy and found out that there were 160 pieces in the bag. As you might suspect Nadia loves candy so she ate half the candy on the first day. Her mother told her that if she eats it at that rate it will be all gone the next day and she will not have anymore until her next birthday. Nadia devised a clever plan. She will always eat half of the candy that is left in the bag each day. She thinks that she will get candy every day and her candy will never run out. How much candy does Nadia have at the end of the week? Would the candy really last forever?
Let’s make a table of values for this problem.
\begin{align*}& \text{Day} && 0 && 1 && 2 && 3 && 4 && 5 && 6 && 7 \\ & \text{No. of Candies} && 160 && 80 && 40 && 20 && 10 && 5 && 2.5 && 1.25\end{align*}
You can see that if Nadia eats half the candies each day, then by the end of the week she only has 1.25 candies left in her bag.
Let’s write an equation for this exponential function.
\begin{align*}& \text{Nadia started with}\ 160\ \text{pieces}. && y = 160 \\ & \text{After the first she has}\ \frac{1}{2}\ \text{of that amount.} && y = 160 \cdot \frac{1} {2} \\ & \text{After the second day she has}\ \frac{1}{2}\ \text{of the last amount. } && y = 160 \cdot \frac{1} {2}\cdot \frac{1} {2}\end{align*}
You see that in order to get the amount of candy left at the end of each day we keep multiplying by \begin{align*}\frac{1}{2}\end{align*}.
We can write the exponential function as
\begin{align*} y = 160 \cdot \frac{1} {2}^x\end{align*}
Notice that this is the same general form as the exponential functions in the last section.
\begin{align*}y=A \cdot b^x\end{align*}
Here \begin{align*}A = 160\end{align*} is the initial amount and \begin{align*} b =\frac{1}{2}\end{align*} is the factor that the quantity gets multiplied by each time. The difference is that now \begin{align*}b\end{align*} is a fraction that is less than one, instead of a number that is greater than one.
This is a good rule to remember for exponential functions.
If \begin{align*}b\end{align*} is greater than one, then the exponential function increased, but
If \begin{align*}b\end{align*} is less than one (but still positive), then the exponential function decreased
Let’s now graph the candy problem function. The resulting graph is shown below.
So, will Nadia’s candy last forever? We saw that by the end of the week she has 1.25 candies left so there doesn’t seem to be much hope for that. But if you look at the graph you will see that the graph never really gets to zero.
Theoretically there will always be some candy left, but she will be eating very tiny fractions of a candy every day after the first week!
This is a fundamental feature of an exponential decay function. Its value get smaller and smaller and approaches zero but it never quite gets there. In mathematics we say that the function asymptotes to the value zero. This means that it approaches that value closer and closer without ever actually getting there.
## Graph an Exponential Decay Function
The graph of an exponential decay function will always take the same basic shape as the one in the previous figure. Let’s graph another example by making a table of values.
Example 1
Graph the exponential function \begin{align*} y = 5 \cdot \left (\frac{1} {2} \right)^x\end{align*}
Solution
Let’s start by making a table of values.
\begin{align*}x\end{align*} \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^x\end{align*}
\begin{align*}-3\end{align*} \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^{-3} = 5.2^3 = 40\end{align*}
-2 \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^{-2} = 5.2^2 = 20\end{align*}
-1 \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^{-1} = 5.2^1 = 10\end{align*}
0 \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^0 = 5.1 = 5\end{align*}
1 \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^1 = \frac{5} {2}\end{align*}
2 \begin{align*}y = 5 \cdot \left (\frac{1} {2} \right)^2 = \frac{5} {4}\end{align*}
Now let's graph the function.
Remember that a fraction to a negative power is equivalent to its reciprocal to the same positive power.
We said that an exponential decay function has the same general form as an exponentially increasing function, but that the base \begin{align*}b\end{align*} is a positive number less than one. When \begin{align*}b\end{align*} can be written as a fraction, we can use the Property of Negative Exponents that we discussed in Section 8.3 to write the function in a different form.
For instance, \begin{align*} y = 5 \cdot \left (\frac{1} {2} \right) ^x\end{align*} is equivalent to \begin{align*} 5 \cdot 2 ^{-x}\end{align*}.
These two forms are both commonly used so it is important to know that they are equivalent.
Example 2
Graph the exponential function \begin{align*}y=8\cdot 3^{-x}\end{align*}.
Solution
Here is our table of values and the graph of the function.
\begin{align*}x\end{align*} \begin{align*}y =8\cdot 3^{-x}\end{align*}
\begin{align*}-3\end{align*} \begin{align*}y=8.3^{-(-3)}=8\cdot 3^{3}= 216\end{align*}
-2 \begin{align*}y =8.3^{-(-2)}=8\cdot 3^{2}=72\end{align*}
-1 \begin{align*}y=8.3^{-(-1)}=8\cdot 3^1=24\end{align*}
0 \begin{align*}y=8\cdot 3^0=8\end{align*}
1 \begin{align*}y=8 \cdot 3^{-1}=\frac{8}{3}\end{align*}
2 \begin{align*}y=8\cdot 3^{-2}=\frac{8}{9}\end{align*}
## Compare Graphs of Exponential Decay Functions
You might have noticed that an exponentially decaying function is very similar to an exponentially increasing function. The two types of functions behave similarly, but they are backwards from each other.
The increasing function starts very small and increases very quickly and ends up very, very big. While the decreasing function starts very big and decreases very quickly to soon become very, very small. Let’s graph two such functions together on the same graph and compare them.
Example 3
Graph the functions \begin{align*}y=4^x\end{align*} and \begin{align*}y=4^{-x}\end{align*} on the same coordinate axes.
Solution
Here is the table of values and the graph of the two functions.
Looking at the values in the table we see that the two functions are “backwards” of each other in the sense that the values for the two functions are reciprocals.
\begin{align*}x\end{align*} \begin{align*}y =4^x\end{align*} \begin{align*}y=4^{-x}\end{align*}
\begin{align*}-3\end{align*} \begin{align*}y =4^{-3} = \frac{1}{64}\end{align*} \begin{align*}y=4^{-(-3)} = 64\end{align*}
-2 \begin{align*}y =4^{-2} = \frac{1}{16}\end{align*} \begin{align*}y=4^{-(-2)} = 16\end{align*}
-1 \begin{align*}y =4^{-1}=\frac{1}{4}\end{align*} \begin{align*}y=4^{-(-1)}=4\end{align*}
0 \begin{align*}y =4^{0} = 1\end{align*} \begin{align*}y=4^{0}= 1\end{align*}
1 \begin{align*}y =4^{1} = 4\end{align*} \begin{align*}y=4^{-1} = \frac{1}{4}\end{align*}
2 \begin{align*}y =4^{2}=16\end{align*} \begin{align*}y=4^{-2}=\frac{1}{16}\end{align*}
3 \begin{align*}y =4^{3} =64\end{align*} \begin{align*}y=4^{-3}= \frac{1}{64}\end{align*}
Here is the graph of the two functions. Notice that the two functions are mirror images of each others if the mirror is placed vertically on the \begin{align*}y-\end{align*}axis.
## Solve Real-World Problems Involving Exponential Decay
Exponential decay problems appear in several application problems. Some examples of these are half-life problems, and depreciation problems. Let’s solve an example of each of these problems.
Example 4 Half-Life
A radioactive substance has a half-life of one week. In other words, at the end of every week the level of radioactivity is half of its value at the beginning of the week. The initial level of radioactivity is 20 counts per second.
a) Draw the graph of the amount of radioactivity against time in weeks.
b) Find the formula that gives the radioactivity in terms of time.
c) Find the radioactivity left after three weeks
Solution
Let’s start by making a table of values and then draw the graph.
0 20
1 10
2 5
3 2.5
4 1.25
5 0.625
Exponential decay fits the general formula
\begin{align*} y=A \cdot b^x\end{align*}
In this case
\begin{align*}y\end{align*} is the amount of radioactivity
\begin{align*}x\end{align*} is the time in weeks
\begin{align*}A=20\end{align*} is the starting amount
\begin{align*}b=\frac{1}{2}\end{align*} since the substance losses half its value each week
The formula for this problem is: \begin{align*} y = 20 \cdot \left (\frac{1} {2} \right)^x\end{align*} or \begin{align*} y = 20 \cdot 2^{-x}\end{align*}.
Finally, to find out how much radioactivity is left after three weeks, we use \begin{align*}x=3\end{align*} in the formula we just found.
\begin{align*} y = 20 \cdot \left (\frac{1} {2} \right)^3 = \frac{20} {8} = 2.5\end{align*}
Example 5 Depreciation
The cost of a new car is 32,000. It depreciates at a rate of 15% per year. This means that it looses 15% of each value each year. Draw the graph of the car’s value against time in year. Find the formula that gives the value of the car in terms of time. Find the value of the car when it is four years old. Solution Let’s start by making a table of values. To fill in the values we start with 32,000 at time \begin{align*}t = 0\end{align*}. Then we multiply the value of the car by 85% for each passing year. (Since the car looses 15% of its value, that means that it keeps 85% of its value). Remember that 85% means that we multiply by the decimal 0.85. Time Value(Thousands) 0 32 1 27.2 2 23.1 3 19.7 4 16.7 5 14.2 Now draw the graph Let’s start with the general formula \begin{align*}y=A \cdot b^x\end{align*} In this case: \begin{align*}y\end{align*} is the value of the car \begin{align*}x\end{align*} is the time in years \begin{align*}A=32\end{align*} is the starting amount in thousands \begin{align*}b=0.85\end{align*} since we multiply the amount by this factor to get the value of the car next year The formula for this problem is \begin{align*}y=32 \cdot (0.85)^x\end{align*}. Finally, to find the value of the car when it is four years old, we use \begin{align*}x=4\end{align*} in the formula we just found. \begin{align*}y=32 \cdot (0.85)^4=16.7\end{align*} thousand dollars or16,704 if we don’t round.
## Review Questions
Graph the following exponential decay functions.
1. \begin{align*} y = \frac{1} {5}^x\end{align*}
2. \begin{align*} y = 4 \cdot \left (\frac{2} {3} \right)^x\end{align*}
3. \begin{align*} y = 3^{-x}\end{align*}
4. \begin{align*} y = \frac{3} {4} \cdot 6^{-x}\end{align*}
Solve the following application problems.
1. The cost of a new ATV (all-terrain vehicle) is \$7200. It depreciates at 18% per year. Draw the graph of the vehicle’s value against time in years. Find the formula that gives the value of the ATV in terms of time. Find the value of the ATV when it is ten year old.
2. A person is infected by a certain bacterial infection. When he goes to the doctor the population of bacteria is 2 million. The doctor prescribes an antibiotic that reduces the bacteria population to \begin{align*}\frac{1}{4}\end{align*} of its size each day.
1. Draw the graph of the size of the bacteria population against time in days.
2. Find the formula that gives the size of the bacteria population in term of time.
3. Find the size of the bacteria population ten days after the drug was first taken.
4. Find the size of the bacteria population after 2 weeks (14 days)
1. Formula \begin{align*}y=7200 \cdot (0.82)^x\end{align*} At \begin{align*}x=10, y= \989.62\end{align*}
1. Formula \begin{align*}y = 2,000,000 \cdot 4-x\end{align*} or \begin{align*}y = 2,000,000 \cdot (0.25)^x\end{align*}
2. At \begin{align*}x=5, y=1953\end{align*} bacteria
3. At \begin{align*}x=10, y = 1.9\end{align*} (\begin{align*}\approx 2\end{align*} bacteria)
4. At \begin{align*}x = 14, y = 0.007\end{align*} (bacteria effectively gone)
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https://arxiv.org/abs/1001.1176 | hep-th
(what is this?)
# Title: A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model
Abstract: In this paper we consider the Spontaneous Symmetry Breaking Mechanism (SSBM) in the Standard Model of particles in the unitary gauge. We show that the computation usually presented of this mechanism can be conveniently performed in a slightly different manner. As an outcome, the computation we present can change the interpretation of the SSBM in the Standard Model, in that it decouples the SU(2)-gauge symmetry in the final Lagrangian instead of breaking it.
Comments: 16 pages Subjects: High Energy Physics - Theory (hep-th) Report number: CPT-P002-2010, LPT-Orsay 10-03 Cite as: arXiv:1001.1176 [hep-th] (or arXiv:1001.1176v1 [hep-th] for this version)
## Submission history
From: Thierry Masson [view email]
[v1] Fri, 8 Jan 2010 16:12:39 GMT (14kb) | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.853401780128479, "perplexity": 2128.934235133595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512421.5/warc/CC-MAIN-20181019170918-20181019192418-00331.warc.gz"} |
http://link.springer.com/article/10.1007%2Fs10699-012-9307-6 | Article
Foundations of Science
, Volume 18, Issue 4, pp 809-821
First online:
# How Computational Models Predict the Behavior of Complex Systems
• John SymonsAffiliated withDepartment of Philosophy, University of Kansas Email author
• , Fabio BoschettiAffiliated withCSIRO Marine and Atmospheric ResearchSchool of Earth and Geographical Sciences, The University of Western Australia
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## Abstract
In this paper, we argue for the centrality of prediction in the use of computational models in science. We focus on the consequences of the irreversibility of computational models and on the conditional or ceteris paribus, nature of the kinds of their predictions. By irreversibility, we mean the fact that computational models can generally arrive at the same state via many possible sequences of previous states. Thus, while in the natural world, it is generally assumed that physical states have a unique history, representations of those states in a computational model will usually be compatible with more than one possible history in the model. We describe some of the challenges involved in prediction and retrodiction in computational models while arguing that prediction is an essential feature of non-arbitrary decision making. Furthermore, we contend that the non-predictive virtues of computational models are dependent to a significant degree on the predictive success of the models in question.
### Keywords
Computational models Prediction Complexity | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8298656344413757, "perplexity": 1063.1816239462746}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257827077.13/warc/CC-MAIN-20160723071027-00273-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://wangcc.me/LSHTMlearningnote/competing-risk.html | # 第 76 章 競爭風險模型 competing risk
## 76.1 Cause-specific hazard
$h_k(t) = \lim_{\delta t \rightarrow 0} \frac{1}{\delta t}\text{Pr}\{ t\leqslant T < t + \delta t, D = k | T\geqslant t \}$
(Cumulative cause-specific hazard)累積因素別風險方程則可以被定義為：
$H_k(t) = \int_0^t h_k(s)ds$
$S_k(t) = \exp(-H_k(t))$
Overall hazard is the sum of all cause-specific hazards:
\begin{aligned} h(t) & = \sum_{e=1}^K \lim_{\delta t\rightarrow 0} \frac{1}{\delta t}\text{Pr}\{ t\leqslant T < t + \delta t, D = e | T\geqslant t \} \\ & = \lim_{\delta t \rightarrow 0} \frac{1}{\delta t}\text{Pr}\{ t\leqslant T < t + \delta t | T \geqslant t \} \end{aligned}
It follows that the overall survival can be written as useful application of this cause-specific survivor function:
$S(t) = \exp[-\sum_{e=1}^KH_e(t)] = \prod_{e = 1}^K \exp(-H_e(t))$
### 76.1.1 Cause-specific hazards models
$h_k(t|x) = h_{k, 0} (t)e^{\beta_k x}$
• People are censored at the time of any event that is not the event of interest
• We fit a separate Cox model for each event type
• $$\beta_k$$ represents the impact of $$x$$ on the hazard for event type k,** among those at risk of event type k**
## 76.2 Cumulative incidence function
Other names: absolute cause-specific risk/Crude Probabilty of event
$I_k(t) = \int_0^t h_k(s)S(s)ds$
## 76.3 Subdistribution hazard - Fine and Gray model
The approach uses an alternative definition of the hazard, called the subdistribution hazard, which represents the instantaneous risk of dying from cause k given that an individual has not already died from cause k, that is:
$h^s_k(t) = \lim_{\delta t \rightarrow 0} \frac{1}{\delta t} \{ \text{Pr}(t \leqslant T < t + \delta t, K = k | T > t \text{ or } (T \leqslant t, K \neq k)) \}$
This differs from the cause-specific hazard in its risk set; here individuals are not removed from the risk set if they die from another competing cause of death than cause k.
### 76.3.1 Subdistribution hazard model
$h_k^s(t) = -\frac{d}{dt} \log(1 - I_k(t))$
$h_k^s(t|x) = h_{0,k}(t)e^{\beta^T_k x}$
The relationsship between the CIFs in the two treatment groups is given by:
$1 - I_k(t|1) = [1 - I_k(t|0)]^{\exp(\beta_kx)}$
## 76.4 Multi-state models
### 76.4.1 The Markov model
A common assumption for multi-state mode is that upon entering a particular state i, individuals are subject to common trasition rate for movement to state j, irrespective of their history. In other words, we assume that the transition rate does not differ according to the previous states an individual has been in. This is called the Markov assumption, and is often quite a strong assumption to make.
### 76.4.2 Cox proportional hazards model for transition intensities
The transition intensities for transition i to j is given by:
$h_{ij} (t | x) = h_{ij,0} (t)\exp(\beta_{ij}^Tx)$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9572867155075073, "perplexity": 2625.151100635416}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574501.78/warc/CC-MAIN-20190921125334-20190921151334-00416.warc.gz"} |
http://pchojecki.impan.pl/weil.html | Workshop on Weil conjectures
organizers: Piotr Achinger and Przemyslaw Chojecki
Date: 31st May - 2nd June 2012
Place: room number 403 (lecture 6 on 1st June will take place in room 321) in IMPAN, ul. Śniadeckich 8, Warsaw, Poland.
Attention: there will be "Wine and cheese" meeting for the participants on 1st June at 17.30 in room 409. Each participant willing to take part in it, should contribute 10 zl.
Description of the workshop:
The Weil conjectures express some natural properties of zeta functions of varieties over finite fields. If X is a non-singular n-dimensional projective variety over the finite field F_q with q elements, then the zeta function of X is a rational function \prod P_i(T) (-1) ^{i+1} (product being taken from 0 to 2n) and writing each polynomial P_i as a product of (1-a_ij T), where T is a variable, the Riemann hypothesis (part of Weil conjectures) says that the absolute value of each a_ij is equal to q^{i/2}. This was proved by Pierre Deligne in [De1] (and the proof is discussed at length in [FK]). Later on, Deligne generalized Weil conjectures largely.
A constructible sheaf on a scheme X of finite type over F_q is called pure of weight b if for all x in X, all the eigenvalues of the Frobenius morphism at x have absolute value N(x) ^{b/2}. It is called mixed of weight <b, if we can write it as repeated extensions of pure sheaves of weight smaller than b. The main theorem of [De2] says that if F is a mixed sheaf of weight <b, then the sheaves R^if_! F are mixed of weight <b+1. We retrieve original Weil conjectures by taking F to be equal to Q_l (l-adic numbers).
The goal of the seminar is to motivate Weil conjectures, show some applications of them and understand [De1] and some parts of [De2]. We will follow in that mostly [Ka] and [KW] who give a simplified proof of [De2] based on [Lau].
References:
[De1] P. Deligne "La conjecture de Weil I" (Weil I)
[De2] P. Deligne "La conjecture de Weil II" (Weil II)
[FK] E. Freitag, R. Kiehl "Etale cohomology and the Weil conjectures", book
[Ka] N. Katz "L-functions and monodromy: four lectures on Weil II"
[KW] R. Kiehl, R. Weissauer "Weil conjectures, perverse sheaves and l-adic Fourier transform", book
[Lau] G. Laumon "Prerequesities: It is advisable to be acquainted with foundations of etale cohomology: definitions, basic properties on the level of Arcata from SGA 4 1/2.
Timetable:
31st May:
Lecture 1 (Piotr Achinger) 10.15-11.45
Description: Zeta function of a scheme. Proof of the Weil conjectures for elliptic curves. Sketch of a proof for curves. Statement of the Weil conjectures.
Lecture 2 (Jakub Byszewski) 12.00-13.30
Description: Lefschetz trace formula in etale cohomology. How the existence of good cohomology theory implies Weil conjectures (besides Riemann hypothesis).
Description: Applications of Weil conjectures. K3 surfaces.
1st June:
Lecture 4 (Przemysław Chojecki) 10.15-11.45
Description: General description of the content of Weil I and Weil II, proof of how Weil II implies Weil I. Brief sketch of the strategy of proof of Weil II.
Description: l-adic sheaves, l-adic cohomology, weights and the target theorem. After the first lecture of Katz in [Ka].
Lecture 6 (Jakub Byszewski) 14.45-16.15 (room 321)
Description: The Artin-Schreier sheaf and the purity theorem. Reduction of the target theorem to the purity theorem. After the second lecture of Katz in [Ka].
Wine and cheese at 17.30 in room 409
2nd June:
Lecture 7 (Piotr Achinger) 10.15-11.45
Description: Reduction of the purity theorem to the monodromy theorem. After the third lecture of Katz in [Ka].
Lecture 8 (Piotr Achinger) 12.00-13.30
Description: Proof of the monodromy theorem. Some applications of Weil II. After the fourth lecture of Katz in [Ka].
Lecture 9 (Przemyslaw Chojecki) 14.45-16.15
Description: Analogues of Weil II in characteristic 0, Deligne's weight-monodromy conjecture and perfectoid spaces (after [Sch]). | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8979126811027527, "perplexity": 2915.6954464283554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256381.7/warc/CC-MAIN-20190521122503-20190521144503-00493.warc.gz"} |
https://www.mathcounterexamples.net/the-skew-field-of-hamilton-quaternions/ | # The skew field of Hamilton’s quaternions
We give here an example of a division ring which is not commutative. According to Wedderburn theorem every finite division ring is commutative. So we must turn to infinite division rings to find a non-commutative one, i.e. a skew field.
Let’s introduce the skew field of the Hamilton’s quaternions $\mathbb H = \left\{\begin{pmatrix} u & -\overline{v} \\ v & \overline{u} \end{pmatrix} \ | \ u,v \in \mathbb C\right\}$
### $$\mathbb H$$ is a subring of $$\mathcal M_2(\mathbb C)$$ (the set of matrices of dimension $$2$$ over $$\mathbb C$$)
One can easily verify that the identity matrix is an element of $$\mathbb H$$ taking $$(u,v)=(1,0)$$. Also the sum and the product of two elements of $$\mathbb H$$ belong to $$\mathbb H$$.
### The non-zero elements of $$\mathbb H$$ are invertible
Take $$(0,0) \neq (u,v) \in \mathbb C^2$$. The determinant of $$A=\begin{pmatrix} u & -\overline{v} \\ v & \overline{u} \end{pmatrix}$$ is $$\delta=\det A = \vert u \vert^2 + \vert v \vert^2 >0$$. Hence $$A$$ is invertible and $A^{-1}=\frac{1}{\delta}\begin{pmatrix} \overline{u} & \overline{v} \\ -v & u \end{pmatrix}$
Hence $$\mathbb H$$ is a division ring.
### $$\mathbb H$$ is not commutative
We denote $$\textbf{id}=\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$,
$$i=\begin{pmatrix} i & 0 \\ 0 & -i \end{pmatrix}$$, $$j=\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$$ and $$k=\begin{pmatrix} 0 & i \\ i & 0 \end{pmatrix}$$. All are elements of $$\mathbb H$$. The identities hold $i^2=j^2=k^2=ijk=-1$ as well as following ones
$ij=-ji=k$ $jk=-kj=i$ $ki=-ik=j$
proving that $$\mathbb H$$ is not commutative. $$\mathbb H$$ is a skew field.
### $$\mathbb H$$ is a vector space of dimension $$4$$ over $$\mathbb R$$
One can verify that any matrix $$P=\begin{pmatrix} a+bi & c+di \\ -c+di & a-bi \end{pmatrix}$$ of $$\mathbb H$$ (with $$a,b,c,d \in \mathbb R^4$$) can be written $P=a \textbf{id} + bi +cj +dk$ As $$(\textbf{id}, i, j, k)$$ is an independent family, it is a basis of $$\mathbb H$$. Hence the result. One can also verify that $$\mathbb R \textbf{id}$$ is included in $$\mathbb H$$ center. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9780518412590027, "perplexity": 122.8497835181182}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088471.40/warc/CC-MAIN-20210416012946-20210416042946-00037.warc.gz"} |
https://mathoverflow.net/questions/157701/seeking-criteria-for-threadable-pairs-of-centrosymmetric-polyhedra/157702 | # Seeking criteria for “threadable” pairs of centrosymmetric polyhedra
Let $A$ and $B$ be origin-centered centrosymmetric polyhedra in $\mathbb{R}^3$: "for every point $(x, y, z)$ [...] there is an indistinguishable point $(-x, -y, -z)$." Say that $A$ and $B$ are threadable (my terminology) iff there is a scaling and rotation of $B$ to $B'$ such that (a) Every vertex of $A$ is exterior to $B'$, and (b) Every vertex of $B'$ is exterior to $A$. (I am exploring this notion of "threadability" as a measure of shape similarity.)
Two examples. (1) For $A$ a cube (blue) and $B$ a cuboctahedron (red), $(A,B)$ is threadable, e.g.:
Note that $A$ and $B$ are not duals; for duals, threadability is obvious.
(2) For $A$ a truncated icosahedron (red) and $B$ a vertically stretched pentagonal bipyramid (blue), I believe (but have not proved) it is not possible to scale & rotate $B$ to thread with $A$:
Computing whether or not $A$ and $B$ are threadable seems quite difficult, only achievable exactly via an $O(n^k)$ algoithm for $n$-vertex polyhedra, for $k$ an exponent that captures all the combinatorial possibilities. Perhaps $k=6$ would be necessary; I haven't thought that through carefully, but certainly it would a high computational complexity.
So, here, finally, is my question.
Q. Are there succinct sufficiency criteria for when a pair $(A,B)$ are guaranteed to be threadable?
What I have in mind here is something like this: "If the diameter/width ratio of $A$ and $B$ is approximately (or even: exactly) the same, then $A$ and $B$ are threadable." I don't believe this, but it gives the flavor of sufficiency conditions I seek. I have a sense that no such "simple" sufficiency conditions exist, because of the seeming dependence upon the micro- combinatorial structure of $A$ and $B$. But perhaps others can see more clearly through this thicket than I ... ?
It seems to me that two convex polyhedras are threadable if and only if (after scaling and rotation) they can be inscribed in the same strictly convex domain: If $A$ and $B$ are both inscribed in a strictly convex $D$ and two vertices do not meet, then $A$ and $B$ are threaded. If two vertices do coincide, then I guess that by moving $A$ or $B$ a little bit, one should obtain a threading. Conversely, given a threading of $A$ and $B$, one can take the convex hull of the vertices and it should be possible to make it strictly convex by blowing some air in it keeping the vertices fixed. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8830347657203674, "perplexity": 279.7932153725458}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141194982.45/warc/CC-MAIN-20201128011115-20201128041115-00508.warc.gz"} |
http://math.stackexchange.com/questions/300464/power-series-ratio-test | # Power Series Ratio Test
Last time ive checked the ratio test was limit to infinity of a+1 / a
However, Ive approached a good amount of question that uses the inverse of that formula such as the following given below. Anyone want to explain why they inverted it?
-
It immediately gives you the radius of convergence. If you applied the Ratio Test proper, you'd be lead to solving the equation $|x-1|\lim\limits_{n\rightarrow\infty}{|c_{n+1}|\over |c_n|}<1$. – David Mitra Feb 11 '13 at 19:33
It's just an arbitrary choice.
$\frac{|a_{n+1}|}{|a_n|}$ converges to something smaller than $1$ exactly when $\frac{|a_n|}{|a_{n+1}|}$ converges to something larger than $1$ (or to +infinity).
So they are really the same test. Sometimes one of the limits is slightly easier to calculate than the other one, but which one it is varies.
-
It is not ratio test. Here you are using ratio test however, that's not all. R is the radius of convergence. So let's say the series is $c_k(x-a)^k$ After you perform ratio test, you get $\lim {c_{n+1}\over c_n}(x-a)$. In order for the series to converge, this must be less than 1, so you get the invert. So basically it comes from the definition of radius of convergence. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.996734082698822, "perplexity": 166.20788246348073}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999677213/warc/CC-MAIN-20140305060757-00070-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.mathallstar.org/Problem/Details/59 | ComputeArea AIME Intermediate
2015
Problem - 59
In the diagram below, $ABCD$ is a square. Point $E$ is the midpoint of $\overline{AD}$. Points $F$ and $G$ lie on $\overline{CE}$, and $H$ and $J$ lie on $\overline{AB}$ and $\overline{BC}$, respectively, so that $FGHJ$ is a square. Points $K$ and $L$ lie on $\overline{GH}$, and $M$ and $N$ lie on $\overline{AD}$ and $\overline{AB}$, respectively, so that $KLMN$ is a square. The area of $KLMN$ is $99$. Find the area of $FGHJ$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8570625185966492, "perplexity": 36.07612280885918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514423.60/warc/CC-MAIN-20210118061434-20210118091434-00246.warc.gz"} |
https://zbmath.org/?q=an:1110.39002 | ×
# zbMATH — the first resource for mathematics
On the oscillation of solutions of third order linear difference equations of neutral type. (English) Zbl 1110.39002
Summary: We consider the third order linear difference equations of neutral type $$\Delta ^{3}[x(n)-p(n)x(\sigma (n))]+\delta q(n)x(\tau (n))=0$$, $$n \in N(n_0),$$ where $$\delta =\pm 1$$, $$p,q\: N(n_0)\rightarrow \mathbb R_+;$$ $$\sigma ,\tau \: N(n_0)\rightarrow \mathbb N$$, $$\lim _{n \rightarrow \infty }\sigma (n)= \lim \limits _{n \rightarrow \infty }\tau (n)= \infty .$$ We examine the following two cases: \begin{aligned} \{0<p(n)&\leq 1, \;\sigma (n)=n+k,\;\tau (n)=n+l\},\\ \{p(n)&>1, \;\sigma (n)=n-k,\;\tau (n)=n-l\}, \end{aligned} where $$k$$, $$l$$ are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.
##### MSC:
39A11 Stability of difference equations (MSC2000)
Full Text: | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9750179052352905, "perplexity": 1521.6512700853843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088264.43/warc/CC-MAIN-20210415222106-20210416012106-00632.warc.gz"} |
https://riemannianhunger.wordpress.com/solutions-to-algebraic-topology-by-allen-hatcher/hatcher-0-4/ | # Hatcher 0.4
Hatcher, Algebraic Topology, Chapter 0
4. A deformation retraction in the weak sense of a space $X$ to a subspace $A$ is a homotopy $f_t:X\to X$ such that $f_0=1_X$, $f_1(X)\subset A$, and $f_t(A)\subset A$ for all $t$. Show that if $X$ deformation retracts to $A$ in this weak sense, then the inclusion $A\hookrightarrow X$ is a homotopy equivalence.
Proof. For preliminary information regarding the definitions of homotopy equivalences, homotopy inverses, etc., see previous results.
Let $X$ be a topological space, let $A\subset X$ be a subset, and suppose that $X$ deformation retracts weakly onto $A$ by way of the homotopy $f_t:X\to X$. Let $\iota:A\to X$ denote inclusion. It suffices to show that $\iota$ is a homotopy equivalence, i.e. that there exists a map $g:X\to A$ for which $\iota g\simeq 1_X$ and $g\iota\simeq 1_A$. Note that $f_1(X)\subset A$, and so while $f_1:X\to X$, it’s natural to consider $f_1$ as a map $X\to A$. For that reason, the obvious candidate for the map $g$ mentioned above is
$g(x)\overset{\text{def}}{=}f_1(x)$ for all $x\in X$.
It suffices to show that the this choice of $g$ has the desired properties.
By hypothesis, there is a homotopy $f_t:X\to X$. Let $F:X\times I\to X$ denote this homotopy (that is, let $f_t(x)=F(x,t)$ for all $x\in X,t\in I$). It follows, then, that $F(x,0)=id_X$ and that $F(x,1)=g(x)$. In particular, because $f_1(X)=g(X)\subset A$, $\iota\circ g=g$ for all $x\in X$. Thus,
$F(x,0)=id_X$ and $F(x,1)=f_1(x)=g(x)=\iota\circ g(x)$ for all $x\in X$,
and so $F$ is a homotopy connecting $f_0=id_X$ to $g=\iota\circ g$. Hence, it follows that $\iota\circ g\simeq id_X$.
Next, define a map $G:A\times I\to A$ by $G(a,t)=F(a,t)=f_t(a)$ for all $a\in A$, where $F$ is the homotopy above. Then $G(a,0)=F(a,0)=f_0(a)$, i.e. $G(\cdot,0)=f_0|_A=id_X|_A=id_A$. Similarly, $latex$G(a,1)=F(a,1)=f_1(a)=g(a)=(g\circ\iota)(a)\$ for all $a\in A$. Hence, $G$ is a homotopy connecting $g\circ\iota$ to $id_A$, whereby it follows that $g\circ\iota\simeq id_A$. This, combined with the result above, verifies that $\iota$ is a homotopy equivalence with homotopy inverse $g=f_1$. $\square$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 58, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9983435273170471, "perplexity": 51.674146366078745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105341.69/warc/CC-MAIN-20170819105009-20170819125009-00117.warc.gz"} |
https://www.flyingcoloursmaths.co.uk/ask-uncle-colin-integrating-sec-and-cosec/ | # Ask Uncle Colin: Integrating $\sec$ and $\cosec$
Dear Uncle Colin,
I keep forgetting how to integrate $\sec(x)$ and $\cosec(x)$. Do you have any tips?
- Literally Nothing Memorable Or Distinctive
Hi, LNMOD, and thanks for your message!
Integrating $\sec(x)$ and $\cosec(x)$ relies on a trick, and one the average mathematician probably wouldn't come up with without a hint.
### Multiply by 1
Two of the mathematician's greatest tricks are "adding zero" and "multiplying by 1" (in a sense, that's only one trick). Here, we'll be multiplying by 1; the tricky bit of the trick is to pick exactly how to multiply by 1.
For $\int \sec(x) \dx$, the way to do it is to multiply by $\frac{1 + \sin(x)}{1+\sin(x)}$ -- one more than the 'other' trig function.
Now you have $\int \frac{1}{\cos(x)} \cdot \frac{1 + \sin(x)}{1+\sin(x)} \dx$ or $\frac{1+\sin(x)}{\cos(x)\br{1+\sin(x)}}$.
Split the 1 on top up into $\cos^2(x) + \sin^2(x)$ and do a little factorising magic to make it $\frac{\cos^2(x) + \sin(x)\br{1+\sin(x)}}{\cos(x)\br{1+\sin(x)}}$.
Now you can split the fraction into two as $\frac{\cos^2(x)}{\cos(x)\br{1+\sin(x)} }+ \frac{\sin(x)\br{1+\sin(x)}}{\cos(x)\br{1+\sin(x)}}$, or $\frac{\cos(x)}{1+\sin(x)} + \frac{\sin(x)}{\cos(x)}$.
We know how to integrate both of those things! Either you spot that $\int \frac{\cos(x)}{1+\sin(x)} \dx$ is function-derivative, or you use the substitution $u = 1+\sin(x)$ and find that it's $\ln \left| 1 + \sin(x) \right|+C$. Meanwhile, $\int \tan(x) \dx = \ln | \sec(x) | + c$.
Adding those together gives $\ln |1 + \sin(x) | + \ln |\sec(x)| + K$, or $\ln | \sec(x) + \tan(x) | + K$ - the way the answer is typically given.
### And for $\cosec(x)$?
It goes almost exactly the same way - the only real differences being that the multiplier is $\frac{1+\cos(x)}{1+\cos(x)}$ and there are minus signs knocking about in the integral.
Hope that helps!
- Uncle Colin
## Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.
### 2 comments on “Ask Uncle Colin: Integrating $\sec$ and $\cosec$”
• ##### Barney Maunder-Taylor
Clever – now I can throw away my redundant A-level formula sheet! Thanks Colin.
• ##### Colin
I still keep mine in case I need the angle product formulas!
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##### Where do you teach?
I teach in my home in Abbotsbury Road, Weymouth.
It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9253067374229431, "perplexity": 2212.557150552781}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107879537.28/warc/CC-MAIN-20201022111909-20201022141909-00220.warc.gz"} |
https://thespectrumofriemannium.wordpress.com/tag/planck-scale/ | # LOG#121. Basic Neutrinology(VI).
Models where the space-time is not 3+1 dimensional but higher dimensional (generally D=d+1=4+n dimensional, where n is the number of spacelike extra dimensions) are popular since the beginnings of the 20th century.
The fundamental scale of gravity need not to be the 4D “effective” Planck scale $M_P$ but a new scale $M_f$ (sometimes called $M_D$), and it could be as low as $M_f\sim 1-10TeV$. The observed Planck scale $M_P$ (related to the Newton constant $G_N$) is then related to $M_f$ in $D=4+n$ dimensions by a relationship like the next equation:
$\eta^2=\left(\dfrac{M_f}{M_D}\right)^2\sim\dfrac{1}{M_f^2R^n}$
Here, $R$ is the radius of the typical length of the extra dimensions. We can consider an hypertorus $T^n=(S^1)^n=S^1\times \underbrace{\cdots}_{n-times} \times S^1$ for simplicity (but other topologies are also studied in the literature). In fact, the coupling is $M_f/M_P\sim 10^{-16}$ if we choose $M_f\sim 1TeV$. When we take more than one extra dimension, e.g., taking $n=2$, the radius R of the extra dimension(s) can be as “large” as 1 millimeter! This fact can be understood as the “proof” that there could be hidden from us “large” extra dimensions. They could be only detected by many, extremely precise, measurements that exist at present or future experiments. However, it also provides a new test of new physics (perhaps fiction science for many physicists) and specially, we could explore the idea of hidden space dimensions and how or why is so feeble with respect to any other fundamental interaction.
According to the SM and the standard gravity framework (General Relativity), every group charged particle is localized on a 3-dimensional hypersurface that we could call “brane” (or SM brane). This brane is embedded in “the bulk” of the higher dimensional Universe (with $n$ extra space-like dimensions). All the particles can be separated into two categories: 1) those who live on the (SM) 3-brane, and 2) those who live “everywhere”, i.e., in “all the bulk” (including both the extra dimensions and our 3-brane where the SM fields only can propagate). The “bulk modes” are (generally speaking) quite “model dependent”, but any coupling between the brane where the SM lives and the bulk modes should be “suppressed” somehow. One alternative is provided by the geometrical factors of “extra dimensions” (like the one written above). Another option is to modify the metric where the fields propagate. This last recipe is the essence of non-factorizable models built by Randall, Sundrum, Shaposhnikov, Rubakov, Pavŝiĉ and many others as early as in the 80’s of the past century. Graviton and its “propagating degrees of freedom” or possible additional neutral states belongs to the second category. Indeed, the observed weakness of gravity in the 3-brane can be understood as a result of the “new space dimensions” in which gravity can live. However, there is no clear signal of extra dimensions until now (circa 2013, July).
The small coupling constant derived from the Planck mass above can also be used in order to explain the smallness of the neutrino masses! The left-handed neutrino $\nu_L$ having weak isospin and hypercharge is thought to reside in the SM brane in this picture. It can get a “naturally samll” Dirac mass through the mixing with some “bulk fermion” (e.g., the right-handed neutrino or any other neutral fermion under the SM gauge group) which can be interpreted as a right-handed neutrino $\nu_R$:
$\mathcal{L}(m,Dirac)\sim h\eta H\bar{\nu}_L\nu_R$
Here, $H,h$ are the two Higgs doublet fields and the Yukawa coupling, respectively. After spontaneous symmetry breaking, this interaction will generate the Dirac mass term
$m_D=hv\eta\sim 10^{-5}eV$
The right-handed neutrino $\nu_R$ has a hole tower of Kaluza-Klein relatives $\nu_{i,R}$. The masses of these states are given by
$M_{i,R}=\dfrac{i}{R}$ $i=0,\pm 1,\pm 2,\ldots, \pm \infty$
and the $\nu_L$ couples with all KK state having the same “mixing” mass. Thus, we can write the mass lagrangian as
$\mathcal{L}=\bar{\nu}_LM\nu_R$
with
$\nu_L=(\nu_L,\tilde{\nu}_{1L},\tilde{\nu}_{2L},\ldots)$
$\nu_R=(\nu_{0R},\tilde{\nu}_{1R},\tilde{\nu}_{2R},\ldots)$
Are you afraid of “infinite” neutrino flavors? The resulting neutrino mass matrix M is “an infinite array” with structure:
$\mathbb{M}=\begin{pmatrix}m_D &\sqrt{2}m_D &\sqrt{2}m_D &\ldots &\sqrt{2}m_D &\ldots \\ 0 &1/R &0 &\ldots &0 & \ldots\\ 0 & 0 &2/R & \ldots & 0 &\ldots \\ \ldots & \ldots & \ldots & \ldots & k/R & \ldots\\ \ldots & \ldots & \ldots & \ldots & \ldots & \ldots\end{pmatrix}$
The eigenvalues of the matrix $MM^+$ are given by a trascendental equation. In the limit where $m_DR\sim 0$, or $m_D\sim 0$, the eigenvalues are $\lambda\sim k/R$, where $k\in \mathbb{Z}$ and $\lambda=0$ is a double eigenvalue (i.e., it is doubly degenerated). There are other examples with LR symmetry. For instance, $SU(2)_R$ right-handed neutrinos that, living on the SM brane, were additional neutrino species. In these models, it has been showed that the left-handed neutrino is exactly massless whereas the assumed bulk and “sterile” neutrino have a mass related to the size of the extra dimensions. These models produce masses that can be fitted to the expected values $\sim 10^{-3}eV$ coming from estimations at hand with the neutrino oscillation data, but generally, this implies that there should be at least one extra dimension with size in the micrometer range or less!
The main issues that extra dimension models of neutrino masses do have is related to the question of the renormalizability of their interactions. With an infinite number of KK states and/or large extra dimensions, extreme care have to be taken in order to not spoil the SM renormalizability and, at some point, it implies that the KK tower must be truncated at some level. There is no general principle or symmetry that explain this cut-off to my knowledge.
May the neutrinos and the extra dimensions be with you!
See you in my next neutrinological post!
# LOG#057. Naturalness problems.
In this short blog post, I am going to list some of the greatest “naturalness” problems in Physics. It has nothing to do with some delicious natural dishes I like, but there is a natural beauty and sweetness related to naturalness problems in Physics. In fact, they include some hierarchy problems and additional problems related to stunning free values of parameters in our theories.
Naturalness problems arise when the “naturally expected” property of some free parameters or fundamental “constants” to appear as quantities of order one is violated, and thus, those paramenters or constants appear to be very large or very small quantities. That is, naturalness problems are problems of untuning “scales” of length, energy, field strength, … A value of 0.99 or 1.1, or even 0.7 and 2.3 are “more natural” than, e.g., $100000, 10^{-4},10^{122}, 10^{23},\ldots$ Equivalently, imagine that the values of every fundamental and measurable physical quantity $X$ lies in the real interval $\left[ 0,\infty\right)$. Then, 1 (or very close to this value) are “natural” values of the parameters while the two extrema $0$ or $\infty$ are “unnatural”. As we do know, in Physics, zero values are usually explained by some “fundamental symmetry” while extremely large parameters or even $\infty$ can be shown to be “unphysical” or “unnatural”. In fact, renormalization in QFT was invented to avoid quantities that are “infinite” at first sight and regularization provides some prescriptions to assign “natural numbers” to quantities that are formally ill-defined or infinite. However, naturalness goes beyond those last comments, and it arise in very different scenarios and physical theories. It is quite remarkable that naturalness can be explained as numbers/contants/parameters around 3 of the most important “numbers” in Mathematics:
$(0, 1, \infty)$
REMEMBER: Naturalness of X is, thus, being 1 or close to it, while values approaching 0 or $\infty$ are unnatural. Therefore, if some day you heard a physicist talking/speaking/lecturing about “naturalness” remember the triple $(0,1,\infty)$ and then assign “some magnitude/constant/parameter” some quantity close to one of those numbers. If they approach 1, the parameter itself is natural and unnatural if it approaches any of the other two numbers, zero or infinity!
I have never seen a systematic classification of naturalness problems into types. I am going to do it here today. We could classify naturalness problems into:
1st. Hierarchy problems. They are naturalness problems related to the energy mass or energy spectrum/energy scale of interactions and fundamental particles.
2nd. Nullity/Smallness problems. These are naturalness problems related to free parameters which are, surprisingly, close to zero/null value, even when we have no knowledge of a deep reason to understand why it happens.
3rd. Large number problems (or hypotheses). This class of problems can be equivalently thought as nullity reciprocal problems but they arise naturally theirselves in cosmological contexts or when we consider a large amount of particles, e.g., in “statistical physics”, or when we face two theories in very different “parameter spaces”. Dirac pioneered these class of hypothesis when realized of some large number coincidences relating quantities appearing in particle physics and cosmology. This Dirac large number hypothesis is also an old example of this kind of naturalness problems.
4th. Coincidence problems. This 4th type of problems is related to why some different parameters of the same magnitude are similar in order of magnitude.
The following list of concrete naturalness problems is not going to be complete, but it can serve as a guide of what theoretical physicists are trying to understand better:
1. The little hierarchy problem. From the phenomenon called neutrino oscillations (NO) and neutrino oscillation experiments (NOSEX), we can know the difference between the squared masses of neutrinos. Furthermore, cosmological measurements allow us to put tight bounds to the total mass (energy) of light neutrinos in the Universe. The most conservative estimations give $m_\nu \leq 10 eV$ or even $m_\nu \sim 1eV$ as an upper bound is quite likely to be true. By the other hand, NOSEX seems to say that there are two mass differences, $\Delta m^2_1\sim 10^{-3}$ and $\Delta m^2_2\sim 10^{-5}$. However, we don’t know what kind of spectrum neutrinos have yet ( normal, inverted or quasidegenerated). Taking a neutrino mass about 1 meV as a reference, the little hierarchy problem is the question of why neutrino masses are so light when compared with the remaining leptons, quarks and gauge bosons ( excepting, of course, the gluon and photon, massless due to the gauge invariance).
Why is $m_\nu << m_e,m_\mu, m_\tau, m_Z,M_W, m_{proton}?$
We don’t know! Let me quote a wonderful sentence of a very famous short story by Asimov to describe this result and problem:
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
2. The gauge hierarchy problem. The electroweak (EW) scale can be generally represented by the Z or W boson mass scale. Interestingly, from this summer results, Higgs boson mass seems to be of the same order of magnitue, more or less, than gauge bosons. Then, the electroweak scale is about $M_Z\sim M_W \sim \mathcal{O} (100GeV)$. Likely, it is also of the Higgs mass order. By the other hand, the Planck scale where we expect (naively or not, it is another question!) quantum effects of gravity to naturally arise is provided by the Planck mass scale:
$M_P=\sqrt{\dfrac{\hbar c}{8\pi G}}=2.4\cdot 10^{18}GeV=2.4\cdot 10^{15}TeV$
or more generally, dropping the $8\pi$ factor
$M_P =\sqrt{\dfrac{\hbar c}{G}}=1.22\cdot 10^{19}GeV=1.22\cdot 10^{16}TeV$
Why is the EW mass (energy) scale so small compared to Planck mass, i.e., why are the masses $M_{EW}< so different? The problem is hard, since we do know that EW masses, e.g., for scalar particles like Higgs particles ( not protected by any SM gauge symmetry), should receive quantum contributions of order $\mathcal{O}(M_P^2)$
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
3. The cosmological constant (hierarchy) problem. The cosmological constant $\Lambda$, from the so-called Einstein’s field equations of classical relativistic gravity
$\mathcal{R}_{\mu\nu}-\dfrac{1}{2}g_{\mu\nu}\mathcal{R}=8\pi G\mathcal{T}_{\mu\nu}+\Lambda g_{\mu\nu}$
is estimated to be about $\mathcal{O} (10^{-47})GeV^4$ from the cosmological fitting procedures. The Standard Cosmological Model, with the CMB and other parallel measurements like large scale structures or supernovae data, agree with such a cosmological constant value. However, in the framework of Quantum Field Theories, it should receive quantum corrections coming from vacuum energies of the fields. Those contributions are unnaturally big, about $\mathcal{O}(M_P^4)$ or in the framework of supersymmetric field theories, $\mathcal{O}(M^4_{SUSY})$ after SUSY symmetry breaking. Then, the problem is:
Why is $\rho_\Lambda^{obs}<<\rho_\Lambda^{th}$? Even with TeV or PeV fundamental SUSY (or higher) we have a serious mismatch here! The mismatch is about 60 orders of magnitude even in the best known theory! And it is about 122-123 orders of magnitude if we compare directly the cosmological constant vacuum energy we observe with the cosmological constant we calculate (naively or not) with out current best theories using QFT or supersymmetric QFT! Then, this problem is a hierarchy problem and a large number problem as well. Again, and sadly, we don’t know why there is such a big gap between mass scales of the same thing! This problem is the biggest problem in theoretical physics and it is one of the worst predictions/failures in the story of Physics. However,
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
4. The strong CP problem/puzzle. From neutron electric dipople measurements, theoretical physicists can calculate the so-called $\theta$-angle of QCD (Quantum Chromodynamics). The theta angle gives an extra contribution to the QCD lagrangian:
$\mathcal{L}_{\mathcal{QCD}}\supset \dfrac{1}{4g_s^2}G_{\mu\nu}G^{\mu\nu}+\dfrac{\theta}{16\pi^2}G^{\mu\nu}\tilde{G}_{\mu\nu}$
The theta angle is not provided by the SM framework and it is a free parameter. Experimentally,
$\theta <10^{-12}$
while, from the theoretical aside, it could be any number in the interval $\left[-\pi,\pi\right]$. Why is $\theta$ close to the zero/null value? That is the strong CP problem! Once again, we don’t know. Perhaps a new symmetry?
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
5. The flatness problem/puzzle. In the Stantard Cosmological Model, also known as the $\Lambda CDM$ model, the curvature of the Universe is related to the critical density and the Hubble “constant”:
$\dfrac{1}{R^2}=H^2\left(\dfrac{\rho}{\rho_c}-1\right)$
There, $\rho$ is the total energy density contained in the whole Universe and $\rho_c=\dfrac{3H^2}{8\pi G}$ is the so called critical density. The flatness problem arise when we deduce from cosmological data that:
$\left(\dfrac{1}{R^2}\right)_{data}\sim 0.01$
At the Planck scale era, we can even calculate that
$\left(\dfrac{1}{R^2}\right)_{Planck\;\; era}\sim\mathcal{O}(10^{-61})$
This result means that the Universe is “flat”. However, why did the Universe own such a small curvature? Why is the current curvature “small” yet? We don’t know. However, cosmologists working on this problem say that “inflation” and “inflationary” cosmological models can (at least in principle) solve this problem. There are even more radical ( and stranger) theories such as varying speed of light theories trying to explain this, but they are less popular than inflationary cosmologies/theories. Indeed, inflationary theories are popular because they include scalar fields, similar in Nature to the scalar particles that arise in the Higgs mechanism and other beyond the Standard Model theories (BSM). We don’t know if inflation theory is right yet, so
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
6. The flavour problem/puzzle. The ratios of successive SM fermion mass eigenvalues ( the electron, muon, and tau), as well as the angles appearing in one gadget called the CKM (Cabibbo-Kobayashi-Maskawa) matrix, are roughly of the same order of magnitude. The issue is harder to know ( but it is likely to be as well) for constituent quark masses. However, why do they follow this particular pattern/spectrum and structure? Even more, there is a mysterious lepton-quark complementarity. The analague matrix in the leptonic sector of such a CKM matrix is called the PMNS matrix (Pontecorvo-Maki-Nakagawa-Sakata matrix) and it describes the neutrino oscillation phenomenology. It shows that the angles of PMNS matrix are roughly complementary to those in the CKM matrix ( remember that two angles are said to be complementary when they add up to 90 sexagesimal degrees). What is the origin of this lepton(neutrino)-quark(constituent) complementarity? In fact, the two questions are related since, being rough, the mixing angles are related to the ratios of masses (quarks and neutrinos). Therefore, this problem, if solved, could shed light to the issue of the particle spectrum or at least it could help to understand the relationship between quark masses and neutrino masses. Of course, we don’t know how to solve this puzzle at current time. And once again:
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
7. Cosmic matter-dark energy coincidence. At current time, the densities of matter and vacuum energy are roughly of the same order of magnitude, i.e, $\rho_M\sim\rho_\Lambda=\rho_{DE}$. Why now? We do not know!
“THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER.”
And my weblog is only just beginning! See you soon in my next post! 🙂 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 75, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9354382753372192, "perplexity": 751.73377981994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425254.88/warc/CC-MAIN-20170725142515-20170725162515-00435.warc.gz"} |
http://mathhelpforum.com/trigonometry/51875-trigonometric-equation.html | # Math Help - trigonometric equation
1. ## trigonometric equation
Hi, I have problem that asks, "Prove that the equations are identities."
I tried for hours to solve it, but I'm lost... I would really appreciate it if someone could help me on this.
cot A + tan A + 1 = (cot A)/(1-tan A) + (tan A)/(1-cot A)
The stipulation is that I can only use the trigonometric identities that I've learned so far..
Such as:
csc a = 1/sin a
sec a = 1/csc a
tan a = sin a/cos a
etc...
The pythgorean identities and Opposite angle formulas
So far I've tried switching it sines and cosines, tangent, and a few others but it never seems to come out right...
Thanks to anyone who can help.
2. Originally Posted by mi986
Hi, I have problem that asks, "Prove that the equations are identities."
I tried for hours to solve it, but I'm lost... I would really appreciate it if someone could help me on this.
cot A + tan A + 1 = (cot A)/(1-tan A) + (tan A)/(1-cot A)
The stipulation is that I can only use the trigonometric identities that I've learned so far..
Such as:
csc a = 1/sin a
sec a = 1/csc a
tan a = sin a/cos a
etc...
The pythgorean identities and Opposite angle formulas
So far I've tried switching it sines and cosines, tangent, and a few others but it never seems to come out right...
Thanks to anyone who can help.
start by adding the fractions on the right hand side and simplify. now do you see how to get it?
3. That's one of the first things I did. :-s
4. Hello, mi986!
Here's one way . .
$\cot A + \tan A + 1 \:= \:\frac{\cot A}{1-\tan A} + \frac{\tan A}{1-\cot A}$
The right side is: . $\frac{\frac{1}{\tan A}}{1 - \tan A} + \frac{\tan A}{1 - \frac{1}{\tan }}$
Multiply each fraction by $\frac{\tan A}{\tan A}\!:\quad {\color{blue}\frac{\tan A}{\tan A}}\cdot\frac{\frac{1}{\tan A}}{1 - \tan A} + {\color{blue}\frac{\tan A}{\tan A}} \cdot\frac{\tan A}{1 - \frac{1}{\tan A}}$
. . $=\; \frac{1}{\tan A(1 - \tan A)} + \frac{\tan^2A}{\tan A - 1} \;=\;\frac{1}{\tan A(1 - \tan A)} - \frac{\tan^2\!A}{1-\tan A}$
Multiply the second fraction by $\frac{\tan A}{\tan A}\!:\quad\frac{1}{\tan A(1 - \tan A)} - \frac{\tan^3\!A}{\tan A(1 - \tan A)}$
. . and we have: . $\frac{1-\tan^3\!A}{\tan (1 - \tan A)}\;\;^{\leftarrow\;\text{difference of cubes}}$
Factor: . $\frac{(1-\tan A)(1 + \tan A + \tan^2\!A)}{\tan A(1 - \tan A)} \;=\;\frac{1 + \tan A + \tan^2\!A}{\tan A}$
. . $= \;\frac{1}{\tan A} + \frac{\tan A}{\tan A} + \frac{\tan^2\!A}{\tan A} \;=\; \cot A + 1 + \tan A$
5. Ooh! Thank you so much! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.982426643371582, "perplexity": 1430.1256213942365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701174607.44/warc/CC-MAIN-20160205193934-00250-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/199871-cosine-transform-question.html | 1. ## Cosine Transform Question
Hi,
I'm trying to solve:
$\displaystyle f(t) = cos(\omega t) : 0 < t < T$
And I've got as far as this:
$\displaystyle \frac{1}{\omega}(\frac{\omega T}{2}+\frac{sin2 \omega T}{4})$
$\displaystyle \frac{\omega T}{2 \omega}+\frac{1}{4 \omega}sin2 \omega T$
$\displaystyle \frac{T}{2}+\frac{1}{4 \omega}sin2 \omega T$
However I don't understand how to algebraically solve this for the given answer:
$\displaystyle \frac{T}{2}(1+\frac{sin2 \omega T}{2 \omega T})$
I don't see how the right term has obtained the denominator $\displaystyle T$ underneath $\displaystyle sin2 \omega T$
I'm wondering if my tutor has made a mistake?
Any help would be appreciated. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.930798351764679, "perplexity": 377.52696689949227}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794871918.99/warc/CC-MAIN-20180528044215-20180528064215-00269.warc.gz"} |
http://zung.zetamu.net/2013/07/integrable-p-vector-fields-and-singular-foliations/ | # Integrable p-vector fields and singular foliations
There seems to be a lot of confusion (among my colleagues, and also of myself) concerning the relationships between singular foliations and integrable p-vector fields (a.k.a. Nambu structures). The aim of this note is to make some clarifications.
1) How to construct a singular foliation from an integrable p-vector field ?
The obvious (but stupid) way is to make only 2 kinds of leaves: regular leaves (where the p-vector field does not vanish) and 0-dimensional leaves (where it vanishes). This is stupid, because general singular foliations will have singular leaves of positive dimension, and not just zero-rank points.
A smarter way is to define the rank of a point with respect to an integrable p-vector field Lambda as follows
rank_Lambda (x) = max d such that there is a local coordinate system (y_i) and a (p-d)-vector field Pi which is invariant w.r.t. \partial y_1, …, \partial y_d, such that:
$\Lambda = \partial y_1 \wedge \hdots \wedge \partial y_d \wedge \Pi$
Proposition. Given Lambda, there is a unique singular foliation F such that Lambda is tangent to F, and the rank of every point wrt F is the same as its rank wrt to Lambda.
We will say that F is generated by Lambda. Of course, F can have leaves of any dimension from 0 to the rank of Lambda.
2) How to create an integrable p-vector field from a singular foliation ?
The following process works well locally, at least for analytic foliations (generated by analytic vector fields):
Take an arbitrary family of p vector fields X_1, …, X_p which are tangent to the foliation, and which are linearly independent almost everywhere, then put
$\Pi = X_1 \wedge \hdots \wedge X_p$
The problem of Pi is that it may be non-reduced, in the sense that it vanishes at too many points (or has multiplicity at the points where it vanishes). But it’s not a big problem, because we can divide Pi by a function to make it reduced. For example, if the zero set of Pi is of codimension 1, while the singular set of F has codimension at least 2, then there is a function f which vanishes on the zero set of Pi (without multiplicities), and we can write Pi = f Lambda, where Lambda is still tangent to F.
Some precise definitions:
Pi is called tangent to F is Pi vanishes at every singular point of F, and P gives the tangent space to F at the points where it does not vanish (Pi is allowed to vanish at some regular points of F too)
Pi is called associated to F if Pi is tangent to F, and for any other Lambda tangent to F we have Lambda = g Pi where g is a regular function
Proposition. Locally, up to multiplication by a function which is non-zero everywhere, there exists a unique associated integrable p-vector field
Corollary. the sheaf of local tangent integrable p-vector field to a foliation F is a locally free of rank 1, i.e. is a line bundle.
Of course, the existence of a global associated integrable p-vector field is equivalent to the global triviality of the above line bundle.
3) Saturation of foliations
Two foliations are called almost the same if their tangent spaces coincide almost everywhere.
The composed map
folitation F_1 -> associated integrable p-vector field -> generated foliation F_2
is not an identity map, but is almost identity: F_2 is almost the same as F_1.
The process F_1 -> F_2 is a kind of saturation
Proposition ? Each leaf of F_1 lies in a leaf of F_2
Proposition ? If repeats the process F_1 -> F_2-> F_3 then in fact F_3 = F_2
Division lemma ? If Lambda is integrable and \partial x_1 \wedge \Lambda = 0 then locally \Lambda = \partial x_1 \wedge \Pi where \Pi is invariant wrt \partial x_1. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9317421317100525, "perplexity": 840.5148951813962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743282.69/warc/CC-MAIN-20181117040838-20181117062838-00548.warc.gz"} |
http://math.stackexchange.com/questions/275490/solution-of-first-order-differential-equation-frac-mathrm-di-mathrm-dt-ani?answertab=votes | # Solution of first-order differential equation $\frac{\mathrm dI}{\mathrm dt}=aNI(t)-aI^2(t)$ [duplicate]
Possible Duplicate:
How do you solve the Initial value probelm $dp/dt = 10p(1-p), p(0)=0.1$?
I am reading a proceeding paper where I encountered this differential equation. Can any one kindly write steps of solution (given below) of this equation. $$\frac{\mathrm dI}{\mathrm dt}=aNI(t)-aI^2(t)$$ This first order ordinary differential equation has the following general solution: $$I(t)=\frac N{1+CNe^{-aNt}}$$
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## marked as duplicate by Hans Lundmark, Stefan Hansen, QiL, Davide Giraudo, Ittay WeissJan 11 '13 at 9:42
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
## 1 Answer
The equation is separable: $$\frac{dI}{NI-I^2} = a\,dt.$$ To solve it, integrate both sides.
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thank you. Shall I use partial fractions here.. I am sorry, I am kind of stuck. – Osman Khalid Jan 11 '13 at 0:39
I solved the above equation using partial fractions. I got the same answer I(t) except that there is no 'N' in the denominator... can any one please confirm. Thanks. – Osman Khalid Jan 11 '13 at 3:04
@OsmanKhalid There should be an $N$ in the denominator, i.e. the form given in the question is correct. – mrf Jan 11 '13 at 7:12
@OsmanKhalid (But if you like, you can include it in the constant, of course: rename $C$ to $CN$.) – mrf Jan 11 '13 at 7:24
Thank you again for reply. So do you mean we can multiply N with constant C. Is it possible in maths? Actually, I am not getting N in denominator... kind of frustrated. Is it possible to provide some hints. Thanks in advance. – Osman Khalid Jan 11 '13 at 22:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9462029933929443, "perplexity": 543.9553003634277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860123840.94/warc/CC-MAIN-20160428161523-00153-ip-10-239-7-51.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/159719/can-we-construct-a-hilbert-space-where-the-operator-a-u-v-frac12-v | # Can we construct a Hilbert space where the operator $A_u v := -\frac{1}{2} v'' + (vF + v\int_\mathbb{R} Su + u\int_\mathbb{R} Sv )'$ is symmetric?
It seems not to be a easy problem.
I'd like to know if one can define a pertinent Hilbert space where the operator $$A_p v := -\frac{1}{2} v^{\prime\prime} + (vF + v\int_\mathbb{R} Sp + p\int_\mathbb{R} Sv )^\prime$$ is symmetric. Here, $p$ satisfies the following differential equation with $p \in L^2_1(\mathbb{S})\cap C^\infty(\mathbb{S})$ $$\frac{p^\prime}{2p} = F + \int Sp$$ and $u,v$ and $F,S$ can be taken to satisfy at least the following weak regularity conditions:
• $u,v \in L^2_0(\mathbb{R})\cap C^2(\mathbb{R})$
• $F,S \in C^\infty(\mathbb{R})$ and odd
but the regularity will probably be restricted much more by choosing the nice Hilbert space that we wish. We note that $\int_\mathbb{R} Sp= \int_\mathbb{R} S(x) p(x) dx$.
My motivation for a possible positive answer for this question comes from the following similar problem. Given a fixed $p \in L^2_1(\mathbb{S})\cap C^\infty(\mathbb{S})$ ($\mathbb{S} = \mathbb{R}/(2\pi\mathbb{Z})$ and $p \neq 0$), solution of $\frac{p^\prime}{2p}= S*p$ ($S(\theta) = \sin(\theta)$) for, the operator
$$B_p v := -\frac{1}{2} v^{\prime\prime} + ( v\int_\mathbb{S} S*p + p\int_\mathbb{S} S*v )^\prime$$
a such Hilbert space is $H_ {-1,1/p}$ provided with $\left\langle f,g\right\rangle_{H_ {-1,1/p}} := \int \frac{\mathcal{F}\mathcal{G}}{p}$ where $\mathcal{F}$ and $\mathcal{G}$ are respectively the primitives in $L^2(\mathbb{R})$ of $f$ and $g$ such that $\int \frac{\mathcal{F}} {p} = \int \frac{\mathcal{G}} {p} =0$ . Here $H_ {-1,1/p}:= H_{1,p}^\prime$ (notation:$V^\prime$ is the dual space of $V$), $H_{1,p}:=${$\overline{ f \in C^1(\mathbb{S}): \int f =0 } ^H$} (which is also a Hilbert space with scalar product $\left\langle f,g\right\rangle_{H_ {1,p}} := \int (f^\prime g^\prime p)$ ) and $H =L^2 _0 (\mathbb{S})$.
We can prove for this case that $$\left\langle f,B_pg\right\rangle_{H_ {-1,1/p}} = \left\langle B_pf,g\right\rangle_{H_ {-1,1/p}}=-\frac{1}{2}\int\frac{fg}{p}+\int fS^\prime *g$$ then $B_p$ is clearly symetric in $H_ {-1,1/p}$
I expected had well motivated my question. I've tried several integral and derivative restrictions under spaces similar to $H_ {-1,1/p}$ but I've not been successful yet. I'd be glad for some advice. If you visit the topic please leave a message with your opinion.
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Please clarify the ambiguity in the last integrals: Do you mean $\int(Su)$ or $(\int S)u$? – Dirk Jun 18 '12 at 6:31
There's no more ambiguity in the text. I mean $\int (Su)$. – Paul Jun 18 '12 at 21:35
Crossposted to MO: mathoverflow.net/questions/99907/… – user16299 Jun 19 '12 at 2:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9863808751106262, "perplexity": 212.72752919850552}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375097861.54/warc/CC-MAIN-20150627031817-00257-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.fiberoptics4sale.com/blogs/wave-optics/two-mode-coupling | # Two-Mode Coupling
This is a continuation from the previous tutorial - coupled-mode theory.
In most applications, we are interested in the coupling between two modes. This includes coupling between two modes in the same waveguide, such as that in a periodic waveguide, or coupling between two parallel waveguides, such as that in a directional coupler. For coupling between two modes, the coupled-mode equations can be written in a simple form that can be solved analytically. In this tutorial, we consider the general formulation and general solutions for this important case of two-mode coupling. The characteristics of specific couplers are discussed in later tutorials.
We have shown that both coupling among modes in the same waveguide and coupling among multiple waveguides can be described by coupled-mode equations of the same form as given in (33) and (39) [refer to the coupled-mode theory tutorial]. The only difference is that the coupling coefficients in (39) for multiple-waveguide coupling are defined differently from those in (33) for single-waveguide mode coupling. This is convenient because general solutions of the coupled-mode equations can be applied to both cases. For a particular problem, we only have to calculate the coupling coefficients specific to the problem under consideration.
For two-mode coupling either in a single waveguide or between two separate waveguides, the field expansion in (25) and (26) [refer to the coupled-mode theory tutorial] consists of only two modes with amplitudes A and B. Thus, coupled-mode equations of the form given in (33) or (39) simply reduces to the following two coupled equations:
$\tag{45}\pm\frac{\text{d}A}{\text{d}z}=\text{i}\kappa_{aa}A+\text{i}\kappa_{ab}B\text{e}^{\text{i}(\beta_b-\beta_a)z}$$\tag{46}\pm\frac{\text{d}B}{\text{d}z}=\text{i}\kappa_{bb}B+\text{i}\kappa_{ba}A\text{e}^{\text{i}(\beta_a-\beta_b)z}$
For coupling in a single waveguide, the coupling coefficients in these equations are simply given by (34) [refer to the coupled-mode theory tutorial] in the case of an isotropic waveguide or by (36) in the case of an anisotropic waveguide. According to (37), we also have $$\kappa_{ab}=\kappa_{ba}^*$$ if the waveguide is lossless.
For coupling between two waveguides, the coupling coefficients are given by (40) [refer to the coupled-mode theory tutorial], which can be expressed explicitly as
\tag{47}\begin{align}\kappa_{aa}=\frac{\tilde{\kappa}_{aa}-c_{ab}\tilde{\kappa}_{ba}/c_{bb}}{1-c_{ab}c_{ba}/c_{aa}c_{bb}},\qquad\kappa_{ab}=\frac{\tilde{\kappa}_{ab}-c_{ab}\tilde{\kappa}_{bb}/c_{bb}}{1-c_{ab}c_{ba}/c_{aa}c_{bb}},\\\kappa_{ba}=\frac{\tilde{\kappa}_{ba}-c_{ba}\tilde{\kappa}_{aa}/c_{aa}}{1-c_{ab}c_{ba}/c_{aa}c_{bb}},\qquad\kappa_{bb}=\frac{\tilde{\kappa}_{bb}-c_{ba}\tilde{\kappa}_{ab}/c_{aa}}{1-c_{ab}c_{ba}/c_{aa}c_{bb}}.\end{align}
As discussed earlier and expressed in (43) and (44) [refer to the coupled-mode theory tutorial], in general, $$\kappa_{ab}\ne\kappa_{ba}^*$$ for coupling between two waveguides.
There is a self-coupling term in each of the coupled equations (45) and (46). These terms are caused by the fact that normal modes see an index profile in the perturbed waveguide different from that of the original waveguide where the modes are defined. They can be removed from these equations by expressing the normal-mode expansion coefficient as follows:
$\tag{48}A(z)=\tilde{A}(z)\exp\left[\pm\text{i}\displaystyle\int\limits_0^z\kappa_{aa}(z)\text{d}z\right]$$\tag{49}B(z)=\tilde{B}(z)\exp\left[\pm\text{i}\displaystyle\int\limits_0^z\kappa_{bb}(z)\text{d}z\right]$
where a plus or minus sign is chosen for a forward-propagating or backward-propagating mode, respectively.
Before transforming (45) and (46) into two coupled equations in terms of $$\tilde{A}$$ and $$\tilde{B}$$ to remove the self-coupling terms, we have to consider the fact that all of the coupling coefficients can be a function of z because $$\Delta\boldsymbol{\epsilon}$$ can be a function of z but the integration in (36) and (42) is carried out only over x and y [refer to the coupled-mode theory tutorial]. In case $$\kappa_{ab}(z)$$ and $$\kappa_{ba}(z)$$ are arbitrary functions of z, the coupled-mode equations in (45) and (46) cannot be solved analytically. In this situation, there is no need to simplify the coupled-mode equations further because they can only be solved numerically. However, for waveguide structures of practical interest that are designed for two-mode coupling, $$\Delta\boldsymbol{\epsilon}$$ is either independent of z or is a periodic function of z. Then, the coupling coefficients are either constant or periodic in z. In either case, (45) and (46) can be reduce to the following general form:
$\tag{50}\pm\frac{\text{d}\tilde{A}}{\text{d}z}=\text{i}\kappa_{ab}\tilde{B}\text{e}^{\text{i}2\delta z}$$\tag{51}\pm\frac{\text{d}\tilde{B}}{\text{d}z}=\text{i}\kappa_{ba}\tilde{A}\text{e}^{-\text{i}2\delta z}$
in terms of $$\tilde{A}$$ and $$\tilde{B}$$ with $$\kappa_{ab}$$ and $$\kappa_{ba}$$ in these two equations being constants independent of z. The parameter $$2\delta$$ is the phase mismatch between the two modes being coupled. Phase-matched coupling with $$\delta=0$$ between two modes is always symmetric with $$\kappa_{ab}=\kappa_{ba}^*$$ irrespective of whether these two modes belong to the same waveguide or two different waveguides.
The general form of (50) and (51) applies to both cases of constant and periodic perturbations, but the details of the parameters in these two equations vary.
1. Constant perturbation. In this case, $$\Delta\boldsymbol{\epsilon}$$ is not a function of z. Then all of the coupling coefficients $$\kappa_{aa}$$, $$\kappa_{bb}$$, $$\kappa_{ab}$$, and $$\kappa_{ba}$$ are constant that are independent of z. We then find that
$\tag{52}A(z)=\tilde{A}(z)\text{e}^{\pm\text{i}\kappa_{aa}z}\qquad\text{and}\qquad B(z)=\tilde{B}(z)\text{e}^{\pm\text{i}\kappa_{bb}z}$
and
$\tag{53}2\delta=(\beta_b\pm\kappa_{bb})-(\beta_a\pm\kappa_{aa})$
The choice of sign in each ± here is consistent with that in (48) and (49) discussed above. The physical meaning of the self-coupling coefficients is a change in the propagating constant of each normal mode. While the propagation constants of the normal modes in the original waveguide are $$\beta_a$$ and $$\beta_b$$, their values are changed because of the perturbation on the waveguide. These modes now propagate with the modified propagation constants $$\beta_a\pm\kappa_{aa}$$ and $$\beta_b\pm\kappa_{bb}$$, respectively, which take into account the effect of the perturbation. In addition, they couple to each other through $$\kappa_{ab}$$ and $$\kappa_{ba}$$.
2. Periodic perturbation. In this case, $$\Delta\boldsymbol{\epsilon}$$ is a periodic function of z and so are the coupling coefficients $$\kappa_{aa}(z)$$, $$\kappa_{bb}(z)$$, $$\kappa_{ab}(z)$$, and $$\kappa_{ba}(z)$$. The periodic perturbation has a period $$\Lambda$$ and a wavenumber
$\tag{54}K=\frac{2\pi}{\Lambda}$
The coupling coefficients $$\kappa_{ab}(z)$$ and $$\kappa_{ba}(z)$$, being periodic in z with a periodicity $$\Lambda$$, can be expanded in a Fourier series with constant coefficients $$\kappa_{ab}(q)$$ and $$\kappa_{ba}(q)$$ and a phase factor $$qK$$, where $$q$$ is an integer. Because $$\kappa_{aa}(z)$$ and $$\kappa_{bb}(z)$$ are periodic in z, we find that
$\tag{55}\left|\displaystyle\int\limits_0^z\kappa_{aa}(z)\text{d}z\right|\ll Kz\qquad\text{and}\qquad\left|\displaystyle\int\limits_0^z\kappa_{bb}(z)\text{d}z\right|\ll Kz$
Therefore, the contribution to the phase-mismatch parameter $$2\delta$$ by $$\kappa_{aa}$$ and $$\kappa_{bb}$$ is negligible compared to the contribution by $$qK$$. As a result, we find that the coupled-mode equations in the case of periodic perturbation can also be expressed in the form of (50) and (51) but with $$\kappa_{ab}=\kappa_{ab}(q)$$ and $$\kappa_{ba}=\kappa_{ba}(q)$$ being constants that are independent of z and
$\tag{56}2\delta=\Delta\beta+qK=\beta_b-\beta_a+qK$
where $$\Delta\beta=\beta_b-\beta_a$$ and $$q$$ is an integer that minimizes the value of $$\delta$$.
With these general considerations, (50) and (51) represent the most general coupled equations for two-mode coupling in waveguide structures of practical interest. They can be solved analytically and their solutions apply to many different two-mode coupling problems.
Codirectional coupling
First, we consider the coupling of two modes propagating in the same direction, say the forward direction in $$z$$, over a length $$l$$, as is shown in figure 3 below. In this case, $$\beta_a>0$$ and $$\beta_b>0$$. The coupled equations are
$\tag{57}\frac{\text{d}\tilde{A}}{\text{d}z}=\text{i}\kappa_{ab}\tilde{B}\text{e}^{\text{i}2\delta z}$$\tag{58}\frac{\text{d}\tilde{B}}{\text{d}z}=\text{i}\kappa_{ba}\tilde{A}\text{e}^{-\text{i}2\delta z}$
These equations for codirectional coupling are generally solved as an initial-value problem with the initial values of $$\tilde{A}(z_0)$$ and $$\tilde{B}(z_0)$$ given at $$z=z_0$$ to find the values of $$\tilde{A}(z)$$ and $$\tilde{B}(z)$$ at any other location $$z$$. The general solution can be expressed in the following matrix form:
$\tag{59}\begin{bmatrix}\tilde{A}(z)\\\tilde{B}(z)\end{bmatrix}=\mathbf{F}(z;z_0)\begin{bmatrix}\tilde{A}(z_0)\\\tilde{B}(z_0)\end{bmatrix}$
where the forward-coupling matrix $$\mathbf{F}(z;z_0)$$ relates the field amplitudes at the location $$z_0$$ to those at the location $$z$$. It has the form
\tag{60}\begin{align}\mathbf{F}(z;z_0)&=\\&\begin{bmatrix}\frac{\beta_c\cos\beta_c(z-z_0)-\text{i}\delta\sin\beta_c(z-z_0)}{\beta_c}\text{e}^{\text{i}\delta(z-z_0)}&\frac{\text{i}\kappa_{ab}}{\beta_c}\sin\beta_c(z-z_0)\text{e}^{\text{i}\delta(z+z_0)}\\\frac{\text{i}\kappa_{ba}}{\beta_c}\sin\beta_c(z-z_0)\text{e}^{-\text{i}\delta(z+z_0)}&\frac{\beta_c\cos\beta_c(z-z_0)+\text{i}\delta\sin\beta_c(z-z_0)}{\beta_c}\text{e}^{-\text{i}\delta(z-z_0)}\end{bmatrix}\end{align}
where
$\tag{61}\beta_c=(\kappa_{ab}\kappa_{ba}+\delta^2)^{1/2}$
We consider a simple case when power is launched only into mode $$a$$ at $$z = 0$$. Then the initial values are $$\tilde{A}(0)\ne0$$ and $$\tilde{B}(0)=0$$. By applying these conditions to (59) and taking $$z_0=0$$ in (60), we find that
$\tag{62}\tilde{A}(z)=\tilde{A}(0)\left(\cos\beta_c z-\frac{\text{i}\delta}{\beta_c}\sin\beta_c z\right)\text{e}^{\text{i}\delta z}$$\tag{63}\tilde{B}(z)=\tilde{A}(0)\left(\frac{\text{i}\kappa_{ba}}{\beta_c}\sin\beta_c z\right)\text{e}^{-\text{i}\delta z}$
The power in the two modes varies with $$z$$ as follows:
$\tag{64}\frac{P_a(z)}{P_a(0)}=\left|\frac{A(z)}{A(0)}\right|^2=\left|\frac{\tilde{A}(z)}{\tilde{A}(0)}\right|^2=\frac{\kappa_{ab}\kappa_{ba}}{\beta_c^2}\cos^2\beta_c{z}+\frac{\delta^2}{\beta_c^2}$$\tag{65}\frac{P_b(z)}{P_a(0)}=\left|\frac{B(z)}{A(0)}\right|^2=\left|\frac{\tilde{B}(z)}{\tilde{A}(0)}\right|^2=\frac{|\kappa_{ba}|^2}{\beta_c^2}\sin^2\beta_c{z}$
The coupling efficiency for a length $$l$$ is
$\tag{66}\eta=\frac{P_b(l)}{P_a(0)}=\frac{|\kappa_{ba}|^2}{\beta_c^2}\sin^2\beta_c{l}$
Thus, power is exchanged periodically between two modes with a coupling length
$\tag{67}l_c=\frac{\pi}{2\beta_c}$
where maximum power transfer occurs. Figure 4 below shows the periodic power exchange between the two coupled modes as a function of $$z$$. As can be seen from figure 4, complete power transfer can occur only in the phase-matched condition when $$\delta=0$$.
We now consider the coupling of two modes propagating in opposite directions over a length $$l$$, as is shown in figure 5 below where mode $$a$$ is forward propagating and mode $$b$$ is backward propagating.
In this case, $$\beta_a\gt0$$ and $$\beta_b\lt0$$. Thus, the coupled equations are
$\tag{68}\frac{\text{d}\tilde{A}}{\text{d}z}=\text{i}\kappa_{ab}\tilde{B}\text{e}^{\text{i}2\delta{z}}$$\tag{69}-\frac{\text{d}\tilde{B}}{\text{d}z}=\text{i}\kappa_{ba}\tilde{A}\text{e}^{-\text{i}2\delta{z}}$
These equations for contradirectional coupling are generally solved as a boundary-value problem with the boundary values of $$\tilde{A}(0)$$ at one end and $$\tilde{B}(l)$$ at the other end to find the values of $$\tilde{A}(z)$$ and $$\tilde{B}(z)$$ at any location $$z$$ between the two ends. The general solution can be expressed in the following matrix form:
$\tag{70}\begin{bmatrix}\tilde{A}(z)\\\tilde{B}(z)\end{bmatrix}=\mathbf{R}(z;0,l)\begin{bmatrix}\tilde{A}(0)\\\tilde{B}(l)\end{bmatrix}$
where the reverse-coupling matrix $$\mathbf{R}(z;0,l)$$ relates the filed amplitudes $$\tilde{A}(0)$$ at $$z=0$$ and $$\tilde{B}(l)$$ at $$z=l$$ to those at location $$z$$. It has the following form:
$\tag{71}\mathbf{R}(z;0,l)=\begin{bmatrix}\frac{\alpha_c\cosh\alpha_c(l-z)+\text{i}\delta\sinh\alpha_c(l-z)}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{\text{i}\delta{z}}&\frac{\text{i}\kappa_{ab}\sinh\alpha_cz}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{\text{i}\delta(z+l)}\\\frac{\text{i}\kappa_{ba}\sinh\alpha_c(l-z)}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{-\text{i}\delta{z}}&\frac{\alpha_c\cosh\alpha_cz+\text{i}\delta\sinh\alpha_cz}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{-\text{i}\delta(z-l)}\end{bmatrix}$
where
$\tag{72}\alpha_c=(\kappa_{ab}\kappa_{ba}-\delta^2)^{1/2}$
we consider a simple case when power is launched only into mode $$a$$ at $$z=0$$. Then the boundary values are $$\tilde{A}(0)\ne0$$ and $$\tilde{B}(l)=0$$. By applying these conditions to (70), we find that
$\tag{73}\tilde{A}(z)=\tilde{A}(0)\frac{\alpha_c\cosh\alpha_c(l-z)+\text{i}\delta\sinh\alpha_c(l-z)}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{\text{i}\delta{z}}$$\tag{74}\tilde{B}(z)=\tilde{A}(0)\frac{\text{i}\kappa_{ba}\sinh\alpha_c(l-z)}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}\text{e}^{-\text{i}\delta{z}}$
The power in the two contradirectionally coupled modes varies with $$z$$ as follows:
$\tag{75}\frac{P_a(z)}{P_a(0)}=\left|\frac{A(z)}{A(0)}\right|^2=\left|\frac{\tilde{A}(z)}{\tilde{A}(0)}\right|^2=\frac{\cosh^2\alpha_c(l-z)-\delta^2/\kappa_{ab}\kappa_{ba}}{\cosh^2\alpha_cl-\delta^2/\kappa_{ab}\kappa_{ba}}$$\tag{76}\frac{P_b(z)}{P_a(0)}=\left|\frac{B(z)}{A(0)}\right|^2=\left|\frac{\tilde{B}(z)}{\tilde{A}(0)}\right|^2=\frac{\kappa_{ba}^*}{\kappa_{ab}}\frac{\sinh^2\alpha_c(l-z)}{\cosh^2\alpha_cl-\delta^2/\kappa_{ab}\kappa_{ba}}$
Because mode $$b$$ is propagating backward with no input at $$z=l$$ but an output at $$z=0$$, the coupling efficiency for a length $$l$$ is
$\tag{77}\eta=\frac{P_b(0)}{P_a(0)}=\frac{\kappa_{ba}^*}{\kappa_{ab}}\frac{\sinh^2\alpha_cl}{\cosh^2\alpha_cl-\delta^2/\kappa_{ab}\kappa_{ba}}$
Figure 6 below shows the power exchange between the two contradirectionally coupled modes as a function of $$z$$. As can be seen from figure 6, complete power transfer occurs as $$l\rightarrow\infty$$ if $$\delta^2\lt\kappa_{ab}\kappa_{ba}$$.
In the case when $$\tilde{A}(0)\ne0$$ and $$\tilde{B}(l)=0$$, as considered above, contradirectional coupling can be viewed as reflection of the field amplitude $$\tilde{A}(0)$$ at $$z=0$$ with a reflection coefficient
$\tag{78}r=|\text{r}|\text{e}^{\text{i}\varphi_\text{DBR}}=\frac{\tilde{B}(0)}{\tilde{A}(0)}=\frac{\text{i}\kappa_{ba}\sinh\alpha_cl}{\alpha_c\cosh\alpha_cl+\text{i}\delta\sinh\alpha_cl}$
The reflectivity is $$R=|\text{r}|^2=\eta$$ as is given in (77). The phase shift is
$\tag{79}\varphi_{\text{DBR}}=\varphi_\text{B}-\tan^{-1}\left(\frac{\delta}{\alpha_c}\tanh\alpha_cl\right)$
Conservation of Power
Conservation of power requires that in a lossless waveguide structure the net power flowing across any cross section of the waveguide be a constant independent of the longitudinal location of the cross section. For codirectional coupling with the power initially launched into only one mode so that $$P_a(0)\ne0$$ but $$P_b(0)=0$$, this requirement suggests that the sum of power in the two waveguides, $$P_a(z)+P_b(z)$$, is a constant because the power in the two modes flows in the same direction. For contradirectional coupling with the power launched into only one mode so that $$P_a(0)\ne0$$ and $$P_b(l)=0$$, this requirement suggests that $$P_a(z)-P_b(z)$$ is a constant because the power in mode $$b$$ flows in the backward direction while that in mode $$a$$ flows in the forward direction. These conclusions are correct for mode coupling in a single waveguide, but they do not generally hold for coupling between different waveguides.
It can be seen from (64) and (65) that $$P_a(z)+P_b(z)$$ is not a constant for codirectional coupling unless $$\kappa_{ab}=\kappa_{ba}^*$$. Similarly, from (75) and (76), it is also found that $$P_a(z)-P_b(z)$$ is not a constant for contradirectional coupling when $$\kappa_{ab}\ne\kappa_{ba}^*$$. It seems that the total power is not conserved in a lossless waveguide structure in the case of asymmetric coupling with $$\kappa_{ab}\ne\kappa_{ba}^*$$. A close examination reveals that because $$c_{ab}\ne0$$ [refer to the coupled-mode theory tutorial] in this case of asymmetric coupling, the two modes being coupled are not orthogonal to each other. Therefore, the total power flow cannot be fully accounted for by gathering the power in each individual mode as if the modes were orthogonal to each other. Indeed, by taking the total electric field and the total magnetic field expanded as (25) and (26), respectively, [refer to the coupled-mode theory tutorial], for two modes to calculate the power of the entire structure, we find that the total power flow as a function of space is
\tag{80}\begin{align}P(z)&=c_{aa}|A(z)|^2+c_{bb}|B(z)|^2+2\text{Re}[c_{ab}A^*(z)B(z)\text{e}^{\text{i}\Delta\beta{z}}]\\&=c_{aa}P_a(z)+c_{bb}P_b(z)+P_{ab}(z)\end{align}
where $$P_{ab}(z)=2\text{Re}[c_{ab}A^*(z)B(z)\text{e}^{\text{i}\Delta\beta{z}}]$$ can be considered as the power residing between the two nonorthogonal modes of the two different waveguides. As defined in the coupled-mode theory tutorial, $$c_{\nu\nu}=1$$ if mode $$\nu$$ is forward propagating and $$c_{\nu\nu}=-1$$ if mode $$\nu$$ is backward propagating. It can be shown, using (62) and (63) for the case of codirectional coupling and using (73) and (74) for the case of contradirectional coupling, that $$P(z)$$ is a constant independent of $$z$$ no matter whether $$\kappa_{ab}=\kappa_{ba}^*$$ or $$\kappa_{ab}\ne\kappa_{ba}^*$$. Therefore, conservation of power holds as expected.
When $$P_{ab}(z)=0$$, it can be shown simply by applying conservation of power that $$\kappa_{ab}=\kappa_{ba}^*$$; hence the coupling is symmetric. Conversely, if the coupling is symmetric, $$P_{ab}(z)$$ always vanishes even when mode $$a$$ and mode $$b$$ are not orthogonal to each other. Two conclusions can thus be made:
1. When $$c_{ab}=0$$, mode $$a$$ and mode $$b$$ are orthogonal to each other. Then $$P_{ab}(z)=0$$ and $$\kappa_{ab}=\kappa_{ba}^*$$ even when $$\delta\ne0$$ so that the two waveguide modes are not phase matched.
2. When the two modes are phase matched, $$\delta=0$$. In this case, $$P_{ab}(z)=0$$ and $$\kappa_{ab}=\kappa_{ba}^*$$ even when mode $$a$$ and mode $$b$$ are not orthogonal to each other with $$c_{ab}\ne0$$.
Consequently, coupling between two modes $$a$$ and $$b$$ is symmetric with $$\kappa_{ab}=\kappa_{ba}^*$$ if these two modes are orthogonal to each other or if they are phase matched.
Phase Matching
As can be seen from figure 4 and 6 above, power transfer is most efficient when $$\delta=0$$. The parameter $$\delta$$ is a measure of phase mismatch between the two modes being coupled. For the simple case when $$2\delta=\Delta\beta=\beta_b-\beta_a$$, the phase-matching condition $$\delta=0$$ is achieved when $$\beta_a=\beta_b$$. Then, the two modes have the same phase velocity and are synchronized. In case $$\delta$$ includes a contribution from additional structure, such as a periodic grating, phase matching of the two modes being coupled can be accomplished by matching the difference $$\Delta\beta=\beta_b-\beta_a$$ with a grating phase factor to make $$\delta=0$$. When considering phase matching between two modes, it is important always to include all sources of contribution to the phase-mismatch parameter $$\delta$$.
Phase-matched coupling is always symmetric, meaning that $$\kappa_{ab}=\kappa_{ba}^*$$ whenever $$\delta=0$$. This statement is true even when $$c_{ab}\ne0$$ and $$\beta_a\ne\beta_b$$. However, symmetric coupling does not necessarily imply a phase-matched condition. Therefore, it is also possible to have $$\kappa_{ab}=\kappa_{ba}^*$$ while $$\delta\ne0$$. The most obvious example of this situation is the coupling between two phase-mismatched modes in the same waveguide.
When perfect phase matching is accomplished, we can take
$\tag{81}\kappa=\kappa_{ab}=\kappa_{ba}^*\qquad\text{with}\qquad\kappa=|\kappa|\text{e}^{\text{i}\varphi}$
Because $$\delta=0$$, we find that
$\tag{82}\beta_c=\alpha_c=|\kappa|$
With these relations under the condition of perfect phase matching, the matrix $$\mathbf{F}(z;z_0)$$ for codirectional coupling is reduced to the simple form
$\tag{83}\mathbf{F}_{\text{PM}}(z;z_0)=\begin{bmatrix}\cos|\kappa|(z-z_0)&\text{ie}^{\text{i}\varphi}\sin|\kappa|(z-z_0)\\\text{ie}^{-\text{i}\varphi}\sin|\kappa|(z-z_0)&\cos|\kappa|(z-z_0)\end{bmatrix}$
and the matrix $$\mathbf{R}(z;0,l)$$ for contradirectional coupling is reduce to
$\tag{84}\mathbf{R}_{\text{PM}}(z;0,l)=\begin{bmatrix}\frac{\cosh|\kappa|(l-z)}{\cosh|\kappa|l}&\text{ie}^{\text{i}\varphi}\frac{\sinh|\kappa|z}{\cosh|\kappa|l}\\\text{ie}^{-\text{i}\varphi}\frac{\sinh|\kappa|(l-z)}{\cosh|\kappa|l}&\frac{\cosh|\kappa|z}{\cos|\kappa|l}\end{bmatrix}$
For codirectional coupling with perfect phase matching, the coupling efficiency is
$\tag{85}\eta_{\text{PM}}=\sin^2|\kappa|l$
and the coupling length is
$\tag{86}l_c^{\text{PM}}=\frac{\pi}{2|\kappa|}$
By choosing the interaction length to be $$l=l_c^{\text{PM}}$$, or any odd multiple of $$l_c^{\text{PM}}$$, 100% power transfer from one mode to the other with $$\eta_{\text{PM}}=1$$ can be accomplished.
Example 1
A phase-matched codirectional coupler has a coupling length of $$l_c^{\text{PM}}=1 \text{mm}$$ for a 100% coupling efficiency. What is the coupling coefficient of the coupler? For the same coupling coefficient, what is the length of a 3-dB codirectional coupler that has a 50% coupling efficiency?
From (86), we find that the coupling coefficient has a value
$|\kappa|=\frac{\pi}{2l_c^{\text{PM}}}=1.57\text{ mm}^{-1}$
From (85), we find that $$\eta_\text{PM}=1/2$$ when $$|\kappa|l=\pi/4$$. Therefore, the length of the 3-dB codirectional coupler is simply
$l_\text{3dB}=\frac{\pi}{4|\kappa|}=\frac{l_c^{\text{PM}}}{2}=0.5\text{ mm}$
A 3-dB codirectional coupler can be made by cutting the length of a 100% codirectional coupler in half. This statement is true even if the 100% coupler has a length longer than $$l_c^{\text{PM}}$$ at any odd integral multiple of $$l_c^{\text{PM}}$$.
For contradirectional coupling with perfect phase matching, the coupling efficiency is
$\tag{87}\eta_{\text{PM}}=\tanh^2|\kappa|l$
For an interaction length of $$l=l_c^{\text{PM}}$$ defined in (86), this gives a coupling efficiency of $$\eta_\text{PM}\approx84\%$$. Although complete power transfer with 100% efficiency cannot be accomplished in the case of contradirectional coupling, most power is transferred in a length comparable to the coupling length of codirectional coupling if phase matching is accomplished.
Example 2
A phase-matched contradirectional coupler has the same coupling coefficient as that of the codirectional coupler in example 1. What is the length of the contradirectional coupler for a 99% coupling efficiency? What is the length of a 3-dB contradirectional coupler with a 50% coupling efficiency?
A contradirectional coupler only approaches 100% efficiency asymptotically. From (87), we find that $$\eta_{\text{PM}}=99\%$$ when $$|\kappa|l=3\approx0.96\pi$$. Therefore, the length of the 99% contradirectional coupler with $$|\kappa|=1.57\text{ mm}^{-1}$$ as found in example 1 is
$l=\frac{3}{|\kappa|}=1.91\text{ mm}$
which is almost twice the length of the 100% codirectional coupler of the same coupling coefficient. We also find from (87) that $$\eta_\text{PM}=0.5$$ when $$|\kappa|l=0.88\approx0.28\pi$$. The length of the 3-dB contradirectional coupler is thus
$l_\text{3dB}=\frac{0.88}{|\kappa|}=0.56\text{ mm}$
which again is longer than the 3-dB codirectional coupler of the same coupling coefficient found in example 1. We also see that, unlike codirectional couplers, a 3-dB contradirectional coupler cannot be made by cutting in half a contradirectional coupler of nearly completely coupling at 99% efficiency.
In the presence of phase mismatch, symmetric coupling with $$\kappa_{ab}=\kappa_{ba}^*$$ is also true for coupling between two modes in the same waveguide but is not necessarily true for coupling between two different waveguides. Nevertheless, to illustrate the effect of phase mismatch on the coupling efficiency between two modes, we consider the simple case that $$\kappa=\kappa_{ab}=\kappa_{ba}^*$$, as expressed in (81). Then the coupling efficiency obtained in (66) for codirectional coupled modes can be written as
$\tag{88}\eta=\frac{1}{1+|\delta/\kappa|^2}\sin^2(|\kappa|l\sqrt{1+|\delta/\kappa|^2})$
The maximum efficiency is
$\tag{89}\eta_\text{max}=\frac{1}{1+|\delta/\kappa|^2}$
at a coupling length of
$\tag{90}l_c=\frac{l_c^{\text{PM}}}{\sqrt{1+|\delta/\kappa|^2}}$
The maximum coupling efficiency is clearly less than unity when $$\delta\ne0$$. As shown in figure 7(a) below, both $$l_c$$ and $$\eta_\text{max}$$ decreases as $$|\delta/\kappa|$$ increases. If the interaction length is fixed at $$l=l_c^{\text{PM}}$$, the efficiency also drops quickly as $$|\delta/\kappa|$$ increases, as shown in figure 7(b) below.
For contradirectional coupled modes, the coupling efficiency can also be expressed in terms of $$|\kappa|l$$ and $$|\delta/\kappa|$$:
$\tag{91}\eta=\frac{\sinh^2(|\kappa|l\sqrt{1-|\delta/\kappa|^2})}{\cosh^2(|\kappa|l\sqrt{1-|\delta/\kappa|^2})-|\delta/\kappa|^2}$
The coupling efficiency also decreases as phase mismatch increases, as shown in figure 8 below.
Example 3
Find the coupling efficiencies of codirectional and contradirectional couplers when the phase mismatch has the same magnitude as the coupling coefficient.
For a codirectional coupler with $$|\delta/\kappa|=1$$, we find from (88) that
$\tag{92}\eta=\frac{1}{2}\sin^2(\sqrt{2}|\kappa|l)$
For a contradirectional coupler with $$|\delta/\kappa|=1$$, we find from (91) that
$\tag{93}\eta=\frac{|\kappa|^2l^2}{1+|\kappa|^2l^2}$
It is interesting to see that when the phase mismatch has the same magnitude as the coupling coefficient, a codirectional coupler can only have a maximum coupling efficiency of 50% but a contradirectional coupler can still have an efficiency higher than 50% if $$|\kappa|l\gt1$$. However, the coupling efficiency of a contradirectional coupler varies with $$|\kappa|l$$ sinusoidally when $$|\delta/\kappa|\gt1$$ rather than monotonically as it does when $$|\delta/\kappa|\lt1$$.
In summary, to accomplish efficient coupling between two waveguide modes, the following three parameters have to be considered:
1. Coupling coefficient. The coupling coefficient $$\kappa$$ has to exist and be large enough.
2. Phase matching. The phase mismatch has to be minimized so that $$|\delta/\kappa|$$ is made as small as possible. Ideally, perfect phase matching with $$\delta=0$$ is desired.
3. Interaction length. For codirectional coupling, the length has to be properly chosen as the efficiency oscillates with interaction length. An overly long length is neither required nor beneficial. For contradirectional coupling, the length has to be sufficiently long but does not have to critically chosen as the efficiency increases monotonically with interaction length. A very long length is not necessary, either.
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# Selina solutions for Concise Physics Class 7 ICSE chapter 1 - Physical Quantities and Measurement [Latest edition]
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## Chapter 1: Physical Quantities and Measurement
Objective QuestionsShort/Long Answer QuestionsNumericals
#### Selina solutions for Concise Physics Class 7 ICSE Chapter 1 Physical Quantities and Measurement Exercise Objective Questions
Objective Questions | Q 1.1
Write true or false for a given statement
The S.I. unit of volume is the liter.
• True
• False
Objective Questions | Q 1.2
Write true or false for a given statement
A measuring beaker of capacity 200 ml can measure only the volume. 200 ml of a liquid.
• True
• False
Objective Questions | Q 1.3
Write true or false for a given statement
cm2 is a smaller unit of area than m2
• True
• False
Objective Questions | Q 1.4
Write true or false for a given statement
Equal volumes of two different substances have equal masses.
• True
• False
Objective Questions | Q 1.5
Write true or false for a given statement
The S.I. unit of density is g cm-3.
• True
• False
Objective Questions | Q 1.6
Write true or false for a given statement
1 g cm-3 = 1000 kg m-3.
• True
• False
Objective Questions | Q 1.7
Write true or false for a given statement.
The density of water is maximum at 4°C.
• True
• False
Objective Questions | Q 1.8
Write true or false for a given statement.
The speed 5 ms-1 is less than 25 km h-1.
• True
• False
Objective Questions | Q 1.9
Write true or false for a given statement.
The S.I. unit of speed is ms-1.
• True
• False
Objective Questions | Q 2.1
Fill in the blank
l m3 =..........cm3
Objective Questions | Q 2.2
Fill in the blank
The volume of an irregular solid is determined by the method of _____
Objective Questions | Q 2.3
Fill in the blank
Volume of a cube = _________
Objective Questions | Q 2.4
Fill in the blank
The area of an irregular lamina is measured by using a _______
Objective Questions | Q 2.5
Fill in the blank
Mass = density × _______
Objective Questions | Q 2.6
Fill in the blank
The S.I. unit of density is _______
Objective Questions | Q 2.7
Fill in the blank
1 g cm-3 = _______ kg m-3.
Objective Questions | Q 2.8
Fill in the blank
36 km h-1 = _______ ms-1.
Objective Questions | Q 2.9
Fill in the blank
Distance travelled d = ________ × time t
Objective Questions | Q 3
Match the following:
Column A Column B 1.Volume of a liquid 1. kg m^-3 2. Area of a leaf 2. m^3 3. S.I. unit of volume 3. graph paper 4. S.I. unit of density 4. m s^-1 5. S.I.unit of speed 5. measuring cylinder
Objective Questions | Q 4.1
Select the correct alternative
One litre is equal to :
• 1 cm-3
• 1 m3
• 10-3 cm3
• 10-3 m3
Objective Questions | Q 4.2
Select the correct alternative
A metallic piece displaces water of volume 15 ml. The volume of piece is :
• 15 cm
• 15 m 3
• 15 × 103 cm3
• 15 × 103 cm
Objective Questions | Q 4.3
Select the correct alternative
A piece of paper of dimensions 1.5 m x 20 cm has area :
• 30 m2
• 300 cm2
• 0.3 m2
• 3000 m3
Objective Questions | Q 4.4
Select the correct alternative
The correct relation is :
• d = M × V
• M = d × V
• V = d × M
• d = M + V
Objective Questions | Q 4.5
Select the correct alternative
The density of alcohol is 0.8 g cm-3. In S.I. unit, it will be :
• 0.8 kg m-3
• 0.0008 kg m-3
• 800 kg m-3
• 8 x 103 kg m-3
Objective Questions | Q 4.6
Select the correct alternative
The density of aluminium is 2.7 g cm-3 and of brass is 8.4 g cm-3. For the same mass, the volume of:
• both will be same
• aluminium will be less than that of brass
• aluminium will be more than that of brass
• nothing can be said.
Objective Questions | Q 4.7
Select the correct alternative
A block of wood of density 0.8 g cm-3 has a volume of 60 cm3. The mass of block will be :
• 60.8 g
• 75 g
• 48 g
• 0.013
Objective Questions | Q 4.8
Select the correct alternative
The correct relation for speed is
• Speed = distance x time
• speed = distance / time
• speed = time / distance
• speed = 1 / distance x time
Objective Questions | Q 4.9
Select the correct alternative
A boy travels a distance 150 m in 1 minute. His speed is
• 150 m s-1
• 2.5 m s-1
• 25 m s-1
• 9 m s-1
#### Selina solutions for Concise Physics Class 7 ICSE Chapter 1 Physical Quantities and Measurement Exercise Short/Long Answer Questions
Short/Long Answer Questions | Q 1
Define the term volume of an object.
Short/Long Answer Questions | Q 2
State and define the S.I. unit of volume.
Short/Long Answer Questions | Q 3
State two smaller units of volume. How are they related to the S.I. unit?
Short/Long Answer Questions | Q 4
How will you determine the volume of a cuboid ? Write the formula you will use.
Short/Long Answer Questions | Q 5
Name two devices which are used to measure the volume of an object. Draw their neat diagrams.
Short/Long Answer Questions | Q 6
How can you determine the volume of an irregular solid (say a piece of brass) ? Describe in steps with neat diagrams.
Short/Long Answer Questions | Q 7
You are required to take out 200 ml of milk from a bucket full of milk. How will you do it ?
Short/Long Answer Questions | Q 8
Describe the method in steps to find the area of an irregular lamina using a graph paper.
Short/Long Answer Questions | Q 9
Define the term density of a substance.
Short/Long Answer Questions | Q 10
State the S.I. and C.G.S. units of density. How are they inte related ?
Short/Long Answer Questions | Q 11
‘The density of brass is 8.4 g cm’3’. What do you mean by the statement ?
Short/Long Answer Questions | Q 12
Arrange the following substances in order of their increasing density:
(a) iron
(b) cork
(c) brass
(d) water
(e) mercury
Short/Long Answer Questions | Q 13.1
How does the density of water changes when it is heated from 0°C to 4°C,
Short/Long Answer Questions | Q 13.2
How does the density of water changes when it is heated from 4°C to 10°C ?
Short/Long Answer Questions | Q 14
Write the density of water at 4°C.
Short/Long Answer Questions | Q 15
Explain the meaning of the term speed.
Short/Long Answer Questions | Q 16
Write the S.I. unit of speed.
Short/Long Answer Questions | Q 17
A car travels with a speed 12 m s”1, while a scooter travels with a speed 36 km h-1. Which of the two travels faster ?
#### Selina solutions for Concise Physics Class 7 ICSE Chapter 1 Physical Quantities and Measurement Exercise Numericals
Numericals | Q 1
The length, breadth and height of a water tank are 5 m, 2.5 m and 1.25 m respectively. Calculate the capacity of the water tank in (a) m3 (b) litre.
Numericals | Q 2
A solid silver piece is immersed in water contained in a measuring cylinder. The level of water rises from 50 ml to 62 ml. Find the volume of silver piece.
Numericals | Q 3
Find the volume of a liquid present in a dish of dimensions 10 cm x 10 cm x 5 cm.
Numericals | Q 4
A rectangular field is of length 60 m and breadth 35 m. Find the area of the field.
Numericals | Q 5
Find the approximate area of an irregular lamina of which boundary line is drawn on the graph paper shown in fig. 1.16. below.
Numericals | Q 6
A piece of brass of volume 30 cm3 has a mass of 252 g. Find the density of brass in (i) g cm-3, (ii) kg m-3.
Numericals | Q 7
The mass of an iron ball is 312 g. The density of iron is 7.8 g cm-3. Find the volume of the ball.
Numericals | Q 8
A cork has a volume 25 cm3. The density of cork is 0.25 g cm-3. Find the mass of cork.
Numericals | Q 9
The mass of 5 litre of water is 5 kg. Find the density of water in g cm-3.
Numericals | Q 10
A cubical tank of side 1 m is filled with 800 kg of a liquid. Find:
(i) the volume of tank,
(ii) the density of liquid in kg m-3.
Numericals | Q 11
A block of iron has dimensions 2 m × 0.5 m × 0.25 m. The density of iron is 7.8 g cm-3. Find the mass of block.
Numericals | Q 12.1
The mass of a lead piece is 115 g. When it is immersed into a measuring cylinder, the water level rises from 20 ml mark to 30 ml mark.
Find the volume of the lead piece.
Numericals | Q 12.2
The mass of a lead piece is 115 g. When it is immersed into a measuring cylinder, the water level rises from 20 ml mark to 30 ml mark ,
Find the density of the lead in kg m-3.
Numericals | Q 13
The density of copper is 8.9 g cm-3. What will be its density in kg m-3 ?
Numericals | Q 14.1
A car travels a distance of 15 km in 20 minute. Find the speed of the car in km h-1.
Numericals | Q 14.2
A car travels a distance of 15 km in 20 minute. Find the speed of the car in m s-1.
Numericals | Q 15
How long a train will take to travel a distance of 200 km with a speed of 60 km h-1 ?
Numericals | Q 16
A boy travels with a speed of 10 m s-1 for 30 minute. How much distance does he travel ?
Numericals | Q 17
Express 36 km h-1 in m s-1
Numericals | Q 18
Express 15 m s-1 in km h-1.
## Chapter 1: Physical Quantities and Measurement
Objective QuestionsShort/Long Answer QuestionsNumericals
## Selina solutions for Concise Physics Class 7 ICSE chapter 1 - Physical Quantities and Measurement
Selina solutions for Concise Physics Class 7 ICSE chapter 1 (Physical Quantities and Measurement) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Physics Class 7 ICSE solutions in a manner that help students grasp basic concepts better and faster.
Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.
Concepts covered in Concise Physics Class 7 ICSE chapter 1 Physical Quantities and Measurement are Measurement of Volume (3d Concept), Concept of Unit Volume, Measurement of Area, Estimate the Area of Irregular Shape Using a Graph Paper, Measurement of Densiy of Regular Solids - Basic Concept, Measurement of Density of Regular Solids - Formula, Concept of Physical Quantities and Measurement.
Using Selina Class 7 solutions Physical Quantities and Measurement exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 7 prefer Selina Textbook Solutions to score more in exam.
Get the free view of chapter 1 Physical Quantities and Measurement Class 7 extra questions for Concise Physics Class 7 ICSE and can use Shaalaa.com to keep it handy for your exam preparation
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https://www.arxiv-vanity.com/papers/0805.1476/ | arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Read this paper on arXiv.org.
# Role of backflow correlations for the non-magnetic phase of the t−t′ Hubbard model
Luca F. Tocchio, Federico Becca, Alberto Parola, and Sandro Sorella, International School for Advanced Studies (SISSA), Via Beirut 2, I-34014 Trieste, Italy
CNR-INFM-Democritos National Simulation Centre, Trieste, Italy.
Dipartimento di Fisica e Matematica, Università dell’Insubria, Via Valleggio 11, I-22100 Como, Italy
August 7, 2020
###### Abstract
We introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting systems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio .
###### pacs:
71.10.Fd, 71.27.+a, 71.30.+h, 75.10.-b
Introduction. Recently, the interest in the role of frustrating interactions in electronic systems has considerably increased since in this regime new exotic phases may appear. Many experiments suggest the possibility to have disordered phases down to very low-temperatures (much smaller than what one would expect from a mean-field approach) or even to zero temperature. Such phases are generically called spin liquids. In this respect, the organic molecular materials -(ET)X, X being a monovalent anion, kanoda1 ; kanoda2 represent an interesting example, since they show a particularly rich phase diagram. In the conducting layers, ET molecules are strongly dimerized and form a two-dimensional (2D) triangular lattice. Since the valence of each ET dimer is , the conduction band is half filled. By acting with an external pressure, it is possible to vary the ratio between the on-site Coulomb repulsion and the bandwidth, driving the system through a metal-insulator transition (MIT).
The minimal model to describe the physics of correlated electrons is the Hubbard model
H=−∑i,j,σtijc†i,σcj,σ+H.c.+U∑ini,↑ni,↓, (1)
where creates (destroys) an electron with spin on site , , is the hopping amplitude, that determines the bandwidth, and is the on-site Coulomb repulsion. In this work, we focus our attention on the half-filled case with electrons on sites and consider the square lattice with both nearest- and next-nearest-neighbor hoppings, denoted by and , respectively. This model represents the prototype for frustrated electronic materials, hirsch and, recently, it has been widely studied by different numerical techniques, with contradictory outcomes. imada1 ; imada2 ; imada3 ; ogata ; tremblay Here we present the results for the zero-temperature phase diagram, obtained by using projected wave functions, which only after considering backflow correlations are accurate enough to describe the highly-correlated regime.
The variational approach. Variational wave functions for the unfrustrated Hubbard model, describing the antiferromagnetic phase, can be constructed by considering the ground state of a mean-field Hamiltonian containing a band contribution and a magnetic term , where is the component of the spin operator . In order to have the correct spin-spin correlations at large distance, we have to apply a suitable long-range spin Jastrow factor, namely , with , which governs spin fluctuations orthogonal to the magnetic field becca
On the other hand, spin-liquid (i.e., disordered) states can be constructed by considering the ground state of a BCS Hamiltonian and then applying to it the so-called Gutzwiller projector, , where and anderson ; gros In pure spin models, where the is infinite and charge fluctuations are completely frozen, these kind of states can be remarkably accurate and provide important predictions on the stabilization of disordered spin-liquid ground states. capriotti ; yunoki However, whenever is finite, the variational state must also contain charge fluctuations. In this regard, the simplest generalization of the Gutzwiller projector with , that allows doubly occupied sites, is known to lead to a metallic phase. shiba In order to obtain a Mott insulator with no magnetic order, it is necessary to consider a sufficiently long-range Jastrow factor , being the local density. capello Nevertheless, the accuracy of the resulting wave function can be rather poor in 2D for large on-site interactions, capellophd especially in the presence of frustration (see below). Therefore, other contributions beyond the Jastrow factor must be included.
An alternative way, suitable to describe the strong-coupling regime, is to start from the fully-projected state and then apply the unitary transformation, that was introduced long time ago to connect the Heisenberg and the Hubbard models, girvin namely . This kind of approach is rather difficult to implement for large clusters, since, in contrast to the Jastrow term, is non-diagonal in the natural basis where the electrons with spins quantized along occupy the lattice sites. The expression valid for strong coupling, i.e., , is clearly not accurate for large system sizes, since it can allow a single doubly-occupied site at most. In this respect, accurate results for small clusters can be also obtained by performing one Lanczos step, becca or by considering (where and are variational parameters and is the hopping Hamiltonian). baeriswyl
The backflow wave function. In order to improve in a size-consistent way the previous wave functions and , we want to modify the single-particle orbitals, noteph in the same spirit of the backflow correlations, which have been proposed long time ago by Feynman and Cohen, to obtain a quantitative description of the roton excitation in liquid Helium. feynman The backflow has been implemented within quantum Monte Carlo calculations to study bulk liquid He, schmidt1 ; schmidt2 and used to improve the description of the electron jellium both in two and three dimensions. ceperley1 ; ceperley2 More recently, it has been applied to metallic Hydrogen. ceperley3 Originally, the backflow term corresponds to consider fictitious coordinates of the electrons , which depend upon the positions of the other particles, so to create a return flow of current:
rbα=rα+∑βηα,β[x](rβ−rα), (2)
where are the actual electonic positions and are variational parameters depending in principle on all the electronic coordinates, namely on the many-body configuration . The variational wave function is then constructed by means of the orbitals calculated in the new positions, i.e., . Alternatively, the backflow can be introduced by considering a linear expansion of each single-particle orbital:
ϕk(rbα)≃ϕbk(rα)≡ϕk(rα)+∑βcα,β[x]ϕk(rβ), (3)
where are suitable coefficients. The definition (3) is particularly useful in lattice models, where the coordinates of the particles may assume only discrete values. In particular, in the Hubbard model, the form of the new “orbitals” can be fixed by considering the limit, so to favor a recombination of neighboring charge fluctuations (i.e., empty and doubly-occupied sites):
ϕbk(ri,σ)≡ϵϕk(ri,σ)+η∑jtij(DiHj)ϕk(rj,σ), (4)
where we used the notation that , being the eigenstates of the mean-field Hamiltonian, , , with , so that and are non zero only if the site is doubly occupied or empty, respectively; finally and are variational parameters (we can assume that if ). As a consequence, already the determinant part of the wave function includes correlation effects, due to the presence of the many body operator . The previous definition of the backflow term preserves the spin SU(2) symmetry. A further generalization of the new “orbitals” can be made, by taking all the possible virtual hoppings of the electrons:
ϕbk(ri,σ)≡ϵϕk(ri,σ)+η1∑jtij(DiHj)ϕk(rj,σ)+ η2∑jtij(ni,σhi−σnj,−σhjσ)ϕk(rj,σ)+ η3∑jtij(Dinj,−σhjσ+ni,σhi−σHj)ϕk(rj,σ), (5)
where , , , and are variational parameters. The latter two variational parameters are particularly important for the metallic phase at small , whereas they give only a slight improvement of the variational wave function in the insulator at strong coupling. The definition Eq. (Role of backflow correlations for the non-magnetic phase of the Hubbard model) may break the SU(2) symmetry, however, the optimized wave function always has a very small value of the total spin square, i.e., for 50 sites. All the parameters of the wave function (contained in the mean-field Hamiltonian, in the Jastrow term, and in the backflow term) can be optimized by using the method of Ref. yunoki, . Finally, the variational results can be compared with more accurate (and still variational) ones obtained by Green’s function Monte Carlo, nandini implemented with the so-called fixed-node (FN) approximation. ceperleyfn
Results. Let us start by considering the comparison of the variational results with the exact ones on the 18-site cluster at half filling. In Fig. 1, we show the accuracy of the variational BCS state (with and without backflow correlations) and the overlap with the exact ground state for two values of the frustrating ratio, i.e., and . The backflow term is able to highly improve the accuracy both for weak and strong couplings. We also notice that backflow correlations are more efficient than applying one Lanczos step, i.e., , that was used in previous calculations. becca The overlap between the exact ground state and the backflow state remains very high, even for large , and the improvement with respect to the BCS state is crucial, especially in the frustrated regime.
Backflow correlations remain efficient also for larger sizes and provide much lower energy than the Lanczos step wave function, e.g., for sites with and , the energy per site with the backflow wave function is , while the one with one Lanczos step is (for sites they are and ). The FN energy obtained with the backflow state is , rather close to our estimation of the exact value (based upon an extrapolation obtained with zero and one Lanczos step) that is .
By increasing , the variational energy extrapolates to the one obtained by taking the fully-projected state in the spin model. On the contrary, without using backflow terms, the energy of the BCS state, even in presence of a fully optimized Jastrow factor, is few hundredths of higher than the expected value, see Fig. 2. Moreover, whenever frustration is large enough, backflow correlations are useful also in the antiferromagnetic state , while for they are not necessary to extrapolate correctly to the value of the spin model, see Fig. 2.
In order to draw the ground-state phase diagram of the Hubbard model, we consider three different wave functions with backflow correlations: Two antiferromagnetic states with and , relevant for small and large , and the non-magnetic state . The variational phase diagram is reported in Fig. 3. The first important outcome is that, without backflow terms, the energies of the spin-liquid wave function are always higher than those of the magnetically ordered states, for any value of frustration . Instead, by inserting backflow correlations, a spin-liquid phase can be stabilized at large enough and frustration (see also Fig. 2). The small energy difference between the pure variational and the FN energies demonstrates the accuracy of the backflow states, see Fig. 3. Notice that and have different nodal surfaces, implying different FN energies.
For small Coulomb repulsion and finite the static density-density correlations (where is the Fourier transform of the local density ) have a linear behavior for , typical of a conducting phase. A very small superconducting parameter with symmetry can be stabilized, suggesting that long-range pairing correlations, if any, are tiny. By increasing , a MIT is found and acquires a quadratic behavior in the insulating phase, indicating a vanishing compressibility. This behavior does not change when considering the FN approach, though the metal-insulator transition may be slightly shifted. In Fig. 4, we show the variational results for as a function of for . The insulator just above the transition is magnetically ordered and the variational wave function has a large ; the transition is likely to be first order. By further increasing , there is a second transition to a disordered insulator. Indeed, for , the energy of the BCS wave function becomes lower than the one of the antiferromagnetic state. In this respect, the key ingredient to have such an insulating behavior is the presence of a singular Jastrow term , that turns a BCS superconductor into a Mott insulator. capello In contrast to previous investigations, imada1 ; imada2 ; imada3 ; ogata ; tremblay for intermediate on-site couplings, our calculations indicate the possibility to have a direct (first-order) transition between two magnetic states, see Fig. 3.
In order to verify the magnetic properties obtained within the variational approach, we can consider the static spin-spin correlations over the FN ground state. Although the FN approach may break the SU(2) spin symmetry, favoring a spin alignment along the axis (this is what we find for small lattices, by a direct comparison with exact results), is particularly simple to evaluate within this approach, nandini and it gives important insights into the magnetic properties of the ground state. In Fig. 4, we report the comparison between the variational and the FN results by considering the non-magnetic state . Remarkably, in the unfrustrated case, where antiferromagnetic order is expected, the FN approach is able to increase spin-spin correlations at , even by considering the non-magnetic wave function to fix the nodes. A finite value of the magnetization is also plausible in the insulating region just above the metallic phase at strong frustration (i.e., ), confirming the pure variational calculations. On the contrary, by increasing the electron correlation, the FN results change only slightly the variational value of , indicating the stability of the disordered state.
In conclusion, we have introduced a novel wave function, that highly improves the accuracy of the projected states, used so far. Our variational ansatz is particularly useful to describe non-magnetic phases, that can be stabilized in the strong-coupling regime of the Hubbard model on the square lattice.
We acknowledge partial support from CNR-INFM.
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http://slideplayer.com/slide/4261771/ | # Morgan Ulloa March 20, 2008 Magnetic Resonance Imaging and the Fourier Transform.
## Presentation on theme: "Morgan Ulloa March 20, 2008 Magnetic Resonance Imaging and the Fourier Transform."— Presentation transcript:
Morgan Ulloa March 20, 2008 Magnetic Resonance Imaging and the Fourier Transform
Outline The Fourier transform and the inverse Fourier transform Fourier transform example 2-D Fourier transform for 2-D images Magnetic Resonance Imaging (MRI) Basic MRI physics K-Space and the inverse Fourier transform Overview of how an MRI machine works 3-D MRI
What is the Fourier transform A component of Fourier Analysis named for French mathematician Joseph Fourier (1768-1830) The Fourier transform in an operator that inputs a function and outputs a function Inputs a function in the time-domain and outputs a function in the frequency-domain the Fourier transforms is used in many different ways Continuous Fourier transform is used for MRI
What the Fourier transform looks like Written as an integral: f(t) is a function in the time-domain ω=2πf known as the angular frequency i = square root of -1 (imaginary number) t is the variable time The Fourier transform takes a function in the time-domain into the frequency-domain
Inverse transform Also an integral: F(ω) is our Fourier transform in the frequency-domain ω=2πf known as the angular frequency i is the square root of -1 t is the variable time 1/(2 π) is a conversion factor The inverse Fourier transform takes a function in the frequency-domain back into the time-domain
Different functions and their Fourier transforms
Example: 1) Define time-domain function 2) Compute our integral: = Improper integral = = Note: Has a real part and an imaginary part
from the definition of the integral of products of trigonometric functions = simplifying the fractions = 3) Understanding what this means - searching for a specific frequency (ω)
The 2-D Fourier transform Begin with a 2-D array of data: t’ by t’’ Since this data is two dimensional we say that the data is in the spatial domain
1 st Fourier Transform First Fourier transform in one direction: t’
2 nd Fourier Transform Finally in the t’’ direction The spike corresponds to the intensity and location of the frequency within the 2-D frequency domain
What is MRI? Originally called nuclear magnetic resonance (NMR) but now it is called MRI in the medical field because of negative associations with the word nuclear –Thus, on the atomic level MRI utilizes properties of the nucleus, specifically the protons It takes tomographic images of structures inside the human body similar to an x-ray machine –Unlike the x-ray this imaging technique is non-ionizing
Tomography Tomography: slice selection, with insignificant thickness, of a 3-D object
Spin and spin states Certain atoms have protons that create tiny magnetic fields in one of two directions: this is called spin –some common and important types of atoms with this property are 1 H, 13 C, 19 F, 31 P –Hydrogen protons are used for MRI in the human body Usually the spins of protons in a compound are oriented randomly but if they are exposed to a magnetic field they either align themselves with it, called parallel alignment, or against it, called antiparallel alignment. The parallel and antiparallel alignments are called spin states The energy difference between the spin states lies within the radio frequency spectrum
Resonance When a magnetic field is applied the protons oscillate between their two spin states: between antiparallel and parallel alignment A radio frequency is applied by the MRI machine and varied until it matches the frequency of the oscillation: this is called resonance Whilst in this state of resonance the protons will absorb and release energy –This is then measured by a radio frequency receiver on the MRI machine The energy difference of the two spin states depends on the response of protons to the magnetic field in which it lies and, since the magnetic field is affected by the electrons of nearby atoms, each MRI scan produces a spectrum that is unique to the compounds present in the tomographic slice
Radio Frequency Spectrum Spectrum: the distribution of energy emitted by a radiant source
Axes of a 2-D slice x-axis called the phase-encoding axis y-axis called the frequency encoding axis
Regions of spin A region of spin is simply a location within the 2-D slice plane where protons are expressing their unique characteristic: spin For the purposes of explaining the 2-D Fourier transform we will use 2 regions of spin with similar material compositions but different locations: labeled 1 and 2
Imagining these regions of spin These regions of spin can be depicted visually by vectors (magnetization vectors) rotating around the origin at a frequency corresponding to their rates of oscillation
x-axis: Phase Encoding Magnetic field gradient is applied to the slice along the x-axis to both regions of spin The radio frequency bursts are applied and both regions of spin resonate at different frequencies because they have different positions –when the gradient is turned off they will have a different phase angle, φ Phase angle: the angle between the reference axis (y) and the magnetization vectors
Phase encoding: Cuts the slice into rows
y-axis: Frequency encoding The magnetic field gradient is then applied along the y-axis This results in the two spin vectors rotating at unique frequencies about the origin Thus each region of spin now has a unique rotational frequency and a unique phase angle
Frequency encoding: cuts the slice into columns
Using the Fourier transform with this data Mapping these rotations about the origin as functions of time we get two unique time-domain signals each with a unique phase and rotational frequency and we can create a 2-D array of data with our rows and columns To these we can apply the Fourier transform as we did before in the t’ and t’’ directions but this time in the frequency encoding direction and the phase encoding direction – therefore our data is in the spatial domain, not the time domain as with 1-D Fourier transform This process identifies the the position and the intensity of the spin within the 2-D slice plane
A visual of how this works… We have our two unique signals plotted as a 2-D array of data
… First Fourier transform in the frequency encoding direction
… Then Fourier transform in the phase encoding direction The spikes indicate frequency intensity and location of our regions of spin
What is the K-space? A matrix known as a temporary image space which holds the spatial frequency data from a 2-D Fourier transform The number of entries in each row and column correspond to the number of regions of spin within the slice plane and their location Each matrix entry is given a pixel intensity and thus each entry contains both frequency and spatial data These entries form a grayscale image –Whiter entries correspond to high intensity signals –Darker entries correspond to low intensity signals
K-space for the two regions of spin The k-space for our two regions of spin is the following matrix which clearly demonstrates the position and intensity (here the difference in color) of each region
K-space and the Image
From the K-space to a recognizable image Inverse transforming the K-space yields a new grayscale image that corresponds to the physical slice plane, thus creating an accurate image representation of the slice in vivo
MRI imaging process A slice is selected from the body Magnetic Field gradient is applied to the slice in the Phase encoding and Frequency encoding directions –only the protons within the slice to oscillate between their two energy states (spin states) At the same time radio frequency pulses are applied to the slice with a bandwidth capable of exciting all resonances simultaneously The emitted energy is measured by a radio frequency receiver and converted into a spectrum in the time- domain in the x-direction and y-direction thereby creating a 2-D array of data in the spatial domain
…MRI process continued The two time-domain functions of the spatial-domain is then Fourier transformed into a 2-D frequency- domain function with information about the position and frequency intensity of the spin regions This data is entered into the K-space and then inverse Fourier transformed creating a corresponding accurate image of the physical slice
Stacking Slices: the 3-D image
References: Campbell, Iain D., and Raymond A. Dwek. Biological Spectroscopy. Menlo Park, Ca: Benjamin/Cummings Company, 1984. Gadian, David G. Nuclear Magnetic Resonance and Its Applications to Living Systems. New York: Oxford UP, 1982. Hornak, Joseph P. "The Basics of MRI." 1996. Rochester Institute of Technology. 30 Sept. 2007. Hsu, Hwei P. Applied Fourier Analysis. Orlando: Harcourt Brace Jovanovich, 1984. Knowles, P. F., D. Marsh, and H.W.E. Rattle. Magnetic Resonance of Biomolecules. John Wiley & Sons, 1976. Mansfield, P., and P. G. Morris. NMR Imaging in Biomedicine. New York: Academic P, 1982. Swartz, Harold M., James R. Bolton, and Donald C. Borg. Biological Applications of Electron Spin Resonance. John Wiley & Sons, 1972.
Many thanks to Professor Ron Buckmire & the Occidental Mathematics Department
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http://claesjohnson.blogspot.com/2013/02/low-emissivity-of-atmospheric-co2.html | ## söndag 17 februari 2013
### Low Emissivity of Atmospheric CO2
Recent posts suggest a low emissivity of atmospheric CO2 away from its main resonance at wave number 667. To check let us compute the transmittance of a transparent atmosphere at 225 K after adding 400 ppm CO2 over a distance of 100 m at a pressure of 200 mb using the free version of the commercial software SpectralCalc to get the following spectrum with a blowup around 667:
We see that the transmittance is zero in the narrow interval 664 - 668, where 400 ppm CO2 makes the atmosphere opaque, while outside this interval the transmittance is low only in a small portion of the spectrum. In other words, the total emissivity of 400 ppm CO2 is very small which means that CO2 has a very limited capability to "block radiation" from the Earth surface, thus contradicting typical OLR spectra with full blocking in the interval 600 - 800.
Further, changing to 600 ppm gives almost the same transmittance spectrum, signaling small radiative forcing from doubling of the preindustrial concentration of CO2:
PS Further evidence is given by Ed Caryl. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8169493675231934, "perplexity": 1626.2889823188789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806620.63/warc/CC-MAIN-20171122175744-20171122195744-00415.warc.gz"} |
http://www.egri-nagy.hu/post/201709_math_of_digital_world/ | # Mathematics of the Digital World
I start every course with a sort of philosophical introduction. It is usually about asking `What is the most important idea of …?’, and by trying to answer the question, I can give an overview of the whole course. Today I started a computing-focused discrete math course, so the question was:
What is the most fundamental idea of digital computation?
This handout is an attempted answer. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9037230610847473, "perplexity": 896.8382414019495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156857.16/warc/CC-MAIN-20180921053049-20180921073449-00349.warc.gz"} |
https://www.siyavula.com/read/maths/grade-10/probability/14-probability-01 | We think you are located in South Africa. Is this correct?
# Relative Frequency
## 14.2 Relative frequency (EMA7X)
Relative frequency
The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted.
The relative frequency is not a theoretical quantity, but an experimental one. We have to repeat an experiment a number of times and count how many times the outcome of the trial is in the event set. Because it is experimental, it is possible to get a different relative frequency every time that we repeat an experiment.
The following video explains the concept of relative frequency using the throw of a dice.
Video: 2GW7
## Worked example 2: Relative frequency and theoretical probability
We toss a coin $$\text{30}$$ times and observe the outcomes. The results of the trials are shown in the table below.
trial $$\text{1}$$ $$\text{2}$$ $$\text{3}$$ $$\text{4}$$ $$\text{5}$$ $$\text{6}$$ $$\text{7}$$ $$\text{8}$$ $$\text{9}$$ $$\text{10}$$ outcome H T T T H T H H H T trial $$\text{11}$$ $$\text{12}$$ $$\text{13}$$ $$\text{14}$$ $$\text{15}$$ $$\text{16}$$ $$\text{17}$$ $$\text{18}$$ $$\text{19}$$ $$\text{20}$$ outcome H T T H T T T H T T trial $$\text{21}$$ $$\text{22}$$ $$\text{23}$$ $$\text{24}$$ $$\text{25}$$ $$\text{26}$$ $$\text{27}$$ $$\text{28}$$ $$\text{29}$$ $$\text{30}$$ outcome H H H T H T H T T T
What is the relative frequency of observing heads after each trial and how does it compare to the theoretical probability of observing heads?
### Count the number of positive outcomes
A positive outcome is when the outcome is in our event set. The table below shows a running count (after each trial $$t$$) of the number of positive outcomes $$p$$ we have observed. For example, after $$t = 20$$ trials we have observed heads $$\text{8}$$ times and tails $$\text{12}$$ times and so the positive outcome count is $$p = 8$$.
$$t$$ $$\text{1}$$ $$\text{2}$$ $$\text{3}$$ $$\text{4}$$ $$\text{5}$$ $$\text{6}$$ $$\text{7}$$ $$\text{8}$$ $$\text{9}$$ $$\text{10}$$ $$p$$ $$\text{1}$$ $$\text{1}$$ $$\text{1}$$ $$\text{1}$$ $$\text{2}$$ $$\text{2}$$ $$\text{3}$$ $$\text{4}$$ $$\text{5}$$ $$\text{5}$$ $$t$$ $$\text{11}$$ $$\text{12}$$ $$\text{13}$$ $$\text{14}$$ $$\text{15}$$ $$\text{16}$$ $$\text{17}$$ $$\text{18}$$ $$\text{19}$$ $$\text{20}$$ $$p$$ $$\text{6}$$ $$\text{6}$$ $$\text{6}$$ $$\text{7}$$ $$\text{7}$$ $$\text{7}$$ $$\text{7}$$ $$\text{8}$$ $$\text{8}$$ $$\text{8}$$ $$t$$ $$\text{21}$$ $$\text{22}$$ $$\text{23}$$ $$\text{24}$$ $$\text{25}$$ $$\text{26}$$ $$\text{27}$$ $$\text{28}$$ $$\text{29}$$ $$\text{30}$$ $$p$$ $$\text{9}$$ $$\text{10}$$ $$\text{11}$$ $$\text{11}$$ $$\text{12}$$ $$\text{12}$$ $$\text{13}$$ $$\text{13}$$ $$\text{13}$$ $$\text{13}$$
### Compute the relative frequency
Since the relative frequency is defined as the ratio between the number of positive trials and the total number of trials,
$f=\frac{p}{t}$
The relative frequency of observing heads, $$f$$, after having completed $$t$$ coin tosses is:
$$t$$ $$\text{1}$$ $$\text{2}$$ $$\text{3}$$ $$\text{4}$$ $$\text{5}$$ $$\text{6}$$ $$\text{7}$$ $$\text{8}$$ $$\text{9}$$ $$\text{10}$$ $$f$$ $$\text{1,00}$$ $$\text{0,50}$$ $$\text{0,33}$$ $$\text{0,25}$$ $$\text{0,40}$$ $$\text{0,33}$$ $$\text{0,43}$$ $$\text{0,50}$$ $$\text{0,56}$$ $$\text{0,50}$$ $$t$$ $$\text{11}$$ $$\text{12}$$ $$\text{13}$$ $$\text{14}$$ $$\text{15}$$ $$\text{16}$$ $$\text{17}$$ $$\text{18}$$ $$\text{19}$$ $$\text{20}$$ $$f$$ $$\text{0,55}$$ $$\text{0,50}$$ $$\text{0,46}$$ $$\text{0,50}$$ $$\text{0,47}$$ $$\text{0,44}$$ $$\text{0,41}$$ $$\text{0,44}$$ $$\text{0,42}$$ $$\text{0,40}$$ $$t$$ $$\text{21}$$ $$\text{22}$$ $$\text{23}$$ $$\text{24}$$ $$\text{25}$$ $$\text{26}$$ $$\text{27}$$ $$\text{28}$$ $$\text{29}$$ $$\text{30}$$ $$f$$ $$\text{0,43}$$ $$\text{0,45}$$ $$\text{0,48}$$ $$\text{0,46}$$ $$\text{0,48}$$ $$\text{0,46}$$ $$\text{0,48}$$ $$\text{0,46}$$ $$\text{0,45}$$ $$\text{0,43}$$
From the last entry in this table we can now easily read the relative frequency after $$\text{30}$$ trials, namely $$\frac{13}{30} = \text{0,4}\dot{3}$$. The relative frequency is close to the theoretical probability of $$\text{0,5}$$. In general, the relative frequency of an event tends to get closer to the theoretical probability of the event as we perform more trials.
A much better way to summarise the table of relative frequencies is in a graph:
The graph above is the plot of the relative frequency of observing heads, $$f$$, after having completed $$t$$ coin tosses. It was generated from the table of numbers above by plotting the number of trials that have been completed, $$t$$, on the $$x$$-axis and the relative frequency, $$f$$, on the $$y$$-axis. In the beginning (after a small number of trials) the relative frequency fluctuates a lot around the theoretical probability at $$\text{0,5}$$, which is shown with a dashed line. As the number of trials increases, the relative frequency fluctuates less and gets closer to the theoretical probability.
## Worked example 3: Relative frequency and theoretical probability
While watching $$\text{10}$$ soccer games where Team 1 plays against Team 2, we record the following final scores:
Trial $$\text{1}$$ $$\text{2}$$ $$\text{3}$$ $$\text{4}$$ $$\text{5}$$ $$\text{6}$$ $$\text{7}$$ $$\text{8}$$ $$\text{9}$$ $$\text{10}$$ Team 1 $$\text{2}$$ $$\text{0}$$ $$\text{1}$$ $$\text{1}$$ $$\text{1}$$ $$\text{1}$$ $$\text{1}$$ $$\text{0}$$ $$\text{5}$$ $$\text{3}$$ Team 2 $$\text{0}$$ $$\text{2}$$ $$\text{2}$$ $$\text{2}$$ $$\text{2}$$ $$\text{1}$$ $$\text{1}$$ $$\text{0}$$ $$\text{0}$$ $$\text{0}$$
What is the relative frequency of Team 1 winning?
### Count the number of positive outcomes
We are interested in the event where Team 1 wins. From the table above we see that this happens $$\text{3}$$ times.
### Compute the relative frequency
The total number of trials is $$\text{10}$$. This means that the relative frequency of the event is
$\frac{3}{10} = \text{0,3}$
It is important to understand the difference between the theoretical probability of an event and the observed relative frequency of the event in experimental trials. The theoretical probability is a number that we can compute if we have enough information about the experiment. If each possible outcome in the sample space is equally likely, we can count the number of outcomes in the event set and the number of outcomes in the sample space to compute the theoretical probability.
The relative frequency depends on the sequence of outcomes that we observe while doing a statistical experiment. The relative frequency can be different every time we redo the experiment. The more trials we run during an experiment, the closer the observed relative frequency of an event will get to the theoretical probability of the event.
So why do we need statistical experiments if we have theoretical probabilities? In some cases, like our soccer experiment, it is difficult or impossible to compute the theoretical probability of an event. Since we do not know exactly how likely it is that one soccer team will score goals against another, we can never compute the theoretical probability of events in soccer. In such cases we can still use the relative frequency to estimate the theoretical probability, by running experiments and counting the number of positive outcomes.
You can use this Phet simulation on probability to do some experiments with dropping a ball through a triangular grid.
# Success in Maths and Science unlocks opportunities
Exercise 14.2
A die is tossed 44 times and lands 5 times on the number 3.
What is the relative frequency of observing the die land on the number 3? Write your answer correct to 2 decimal places.
Recall the formula: $f = \frac{p}{t}$
Identify variables needed: \begin{align*} p & = \text{number of positive trials} = \text{5} \\ f & = \text{total number of trials} = \text{44} \end{align*}
Calculate the relative frequency: \begin{align*} f & = \frac{p}{t} \\ & = \frac{\text{5}}{\text{44}} \\ & = \text{0,11} \end{align*}
Therefore, the relative frequency of observing the die on the number 3 is $$\text{0,11}$$.
A coin is tossed 30 times and lands 17 times on heads.
What is the relative frequency of observing the coin land on heads? Write your answer correct to 2 decimal places.
Recall the formula: $f = \frac{p}{t}$
Identify variables needed: \begin{align*} p & = \text{number of positive trials} = \text{17} \\ f & = \text{total number of trials} = \text{30} \end{align*}
Calculate the relative frequency: \begin{align*} f & = \frac{p}{t} \\ & = \frac{\text{17}}{\text{30}} \\ & = \text{0,57} \end{align*}
Therefore, the relative frequency of observing the coin on heads is $$\text{0,57}$$.
A die is tossed 27 times and lands 6 times on the number 6.
What is the relative frequency of observing the die land on the number 6? Write your answer correct to 2 decimal places.
Recall the formula: $f = \frac{p}{t}$
Identify variables needed: \begin{align*} p & = \text{number of positive trials} = \text{6} \\ f & = \text{total number of trials} = \text{27} \end{align*}
Calculate the relative frequency: \begin{align*} f & = \frac{p}{t} \\ & = \frac{\text{6}}{\text{27}} \\ & = \text{0,22} \end{align*}
Therefore, the relative frequency of observing the die on the number 6 is $$\text{0,22}$$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9932074546813965, "perplexity": 180.61598595315948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370507738.45/warc/CC-MAIN-20200402173940-20200402203940-00297.warc.gz"} |
http://astronomy.stackexchange.com/questions/1478/sph-simulations | # SPH simulations
Are there any simulations that can be obtained that use smooth particle hydrodynamics and can be configured to include different initial conditions? I wish to simulate planetary collisions and their impact. I wish to exactly replicate the following link.
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It would be awesome if you could tell a bit more precisely, what do you really wish for. There are plenty of algorithms, inlcuding SPH and its variations, many codes written and many nice outputs produced, planetary collisions included. – Alexey Bobrick Jan 17 '14 at 18:01
The algorithm that I am looking for should be able to simulate collisions like the following link : youtube.com/watch?v=Fwl_JBQtH9o – Artemisia Jan 18 '14 at 2:44
I am trying to exactly duplicate the code used for that YouTube link. – Artemisia Jan 18 '14 at 2:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8593215942382812, "perplexity": 1010.0162729463418}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860111365.36/warc/CC-MAIN-20160428161511-00179-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://okayama.pure.elsevier.com/en/publications/effects-of-thermodynamic-inhibitors-on-the-dissociation-of-methan | # Effects of thermodynamic inhibitors on the dissociation of methane hydrate: A molecular dynamics study
Takuma Yagasaki, Masakazu Matsumoto, Hideki Tanaka
Research output: Contribution to journalArticlepeer-review
39 Citations (Scopus)
## Abstract
We investigate the effects of methanol and NaCl, which are known as thermodynamic hydrate inhibitors, on the dissociation kinetics of methane hydrate in aqueous solutions by using molecular dynamics simulations. It is shown that the dissociation rate is not constant but changes with time. The dissociation rate in the initial stage is increased by methanol whereas it is decreased by NaCl. This difference arises from the opposite effects of the two thermodynamic inhibitors on the hydration free energy of methane. The dissociation rate of methane hydrate is increased by the formation of methane bubbles in the aqueous phase because the bubbles absorb surrounding methane molecules. It is found that both methanol and NaCl facilitate the bubble formation. However, their mechanisms are completely different from each other. The presence of ions enhances the hydrophobic interactions between methane molecules. In addition, the ions in the solution cause a highly non-uniform distribution of dissolved methane molecules. These two effects result in the easy formation of bubbles in the NaCl solution. In contrast, methanol assists the bubble formation because of its amphiphilic character.
Original language English 32347-32357 11 Physical Chemistry Chemical Physics 17 48 https://doi.org/10.1039/c5cp03008k Published - 2015
## ASJC Scopus subject areas
• Physics and Astronomy(all)
• Physical and Theoretical Chemistry
## Fingerprint
Dive into the research topics of 'Effects of thermodynamic inhibitors on the dissociation of methane hydrate: A molecular dynamics study'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8605496883392334, "perplexity": 2879.839133282417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00381.warc.gz"} |
https://stupidsid.com/previous-question-papers/download/strength-of-materials-18375 | MORE IN Strength of Materials
VTU Civil Engineering (Semester 3)
Strength of Materials
May 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary
1(a) Draw the stress versus strain curve for mild steel specimen subjected to axial tension and indicate the salient points.
5 M
1(b) Derive an expression for the deformation of the tapering cirular bar subjected to an axial force P. Use standard notations.
8 M
1(c) The bar shown in fig. Q1(c) is tested in a universal testing machine. It is observed that at a load of 40 kN the total extension is 0.285mm. Determine the Young's modulus of the material.
7 M
2(a) Derive relation between Modulus of Rigidity, Young's modulus and Poisson's ratio.
6 M
2(b) A steel rod is of 20m long at a temperature of 20°C. Find the free expansion of the bar, when the temperature is raised to 65°C. Also calculate the tempreature stress produced for the following cases: i) When the expansion of the rod is prevented. ii) When the rod is premitted to expand by 5.8mm. Take α = 12 × 10-6/°C and E = 200GPa.
6 M
2(c) A load of 2MN is applied on a column 500mm × 500mm. The column is reinforced with four steel bars of 10mm diameter, one in each corner. Find the stresses in the concrete and steel bars, Take E for steel as 2.1 × 105N/mm2 and for concrete as 1.4 ×104N/mm2.
8 M
3(a) Define : i) Principal plane ii) Principal stresses.
4 M
3(b) Determine the magnitude and direction of resultant stresses on a plane inclined at an angle of 60° to major principal stress plane, when the bar is subjected to principal stresses at a point 200MPa tensile and 100MPa compressive. Also determine the resultant stress and its obliquity.
6 M
3(c) Two wooden pieces 100mm × 100mm in cross section are glued together along line AB as shown in fig. Q3(c). What maximum axial force 'P' can be applied if the applied if the allowable shearing stress along AB is 1.2N/mm2?
10 M
4(a) Define i) Bending moment ii) Point of contraflexture.
4 M
4(b) For the cantilever beam shown in fig. Q4(b), obtain SFD and BMD.
6 M
4(c) Draw the Shear force and bending diagrams for the beam shown in Fig. Q4(c).
10 M
5(a) Derive the equation of theory of simple bending with usual notations.
6 M
5(b) A simply supported beam of span 6m has a cross section as shown in fig. Q5(b), it carries two point loads each of 30kN at a distance of 2m from each support. Calculate the bending stress and shear stress for maximum values of bending moment and shear force respectively. Draw nea diagram of bending stress and shear stress distriution across the cross section.
14 M
6(a) Explain the terms : i) Slope ii) Deflection iii) Deflection curve.
6 M
6(b) A simply supported beam 8m long, carries two concentrated loads of 80kN and 60kN at distances of 3m and 6m from left end support respectively. Calculate slope and deflection under loads. Given E = 2.0 × 105 Mpa and I = 300 ×106mm4.
14 M
7(a) State the assumptions made in the theory of Pure Torsion.
4 M
7(b) A hollow shaft to internal diameter 400mm and external diameter 460mm is required to trensmit power at 180rpm. Determine the power it can transmit, if the shear stress is not to exceed 60N/mm2 and the maximum torque exceeds the mean by 30%.
6 M
7(c) A solid circular shaft is to transmit 250kN at 100 rpm. If the shear stress is not to exceed 75N/mm2, what should be the diameter is 0.6 times external diameter, determine the size and percentage saving in weight, maximum shear stress being the same.
10 M
8(a) Derive an expression for Euler's cripping load for a column with both ends fixed.
8 M
8(b) Compare the crippling loads given by Euler's and Rankine's formula for a column of circular section 2.3 m long and of 30mm diameter. The column is hinged at both ends. Take yield stress as 335N/mm2 and $$\text Rankine's constant \alpha =\dfrac{1}{7500}$$and E = 2 × 105N/mm2.For what ratio of L/K, the Euler's formula cease to apply for this column?
12 M
More question papers from Strength of Materials | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8864918947219849, "perplexity": 2600.818154612008}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201922.85/warc/CC-MAIN-20190319073140-20190319095140-00154.warc.gz"} |
https://scicomp.stackexchange.com/questions/21554/inverse-of-diagonally-not-dominant-matrix/21556 | # Inverse of "diagonally not dominant matrix"
I want to frame a higher order Central difference scheme of about $20^{th}$ order for first derivative. I'm using $20^{th}$ order because I need one scheme with good modified wave number. To find the co-efficient matrix (eg. for CD-2 it is [-1/2,1/2]), I have to solve $Ax=b$ equation. $x=A^{-1}*b$. I tried to solve that equation using
Build-in inverse (inv(A)) command of matlab,
"solve" command in R,
Gauss Seidel algorithm,
Gauss Jacobi
Gauss Seidel and Jacobi may fail because of the matrix is not diagonally dominant. Matlab gave answer with a warning and that answer is wrong. R- gave an error message because of poor conditional number.
Matrix $A$ is $20*20$ matrix :
Matrix $b$ is $20*1$ matrix
Is there any sophisticated algorithm or build-in command of any programming language to solve this? Please help me out.
• That matrix is $20\times21$ it seems to me. Dec 13 '15 at 9:32
• @Kirill Sorry Its my mistake CD schemes so for I have seen doesn't has $0^{th}$ (mid point) so I didn't mention it. I tried to type the full matrix but latex didn't support that so I truncated it and posted as image. Please note that there is no 0 in -10 -9 -8 ... rows .
– AGN
Dec 13 '15 at 9:37
One easy way to derive finite-difference approximations to derivatives is as follows. To find the coefficients $c_k$ corresponding to order-$s$ derivative on points $uh,(u+1)h,\ldots,vh$ ($u=-10,v=10,s=1$ in your case), write the condition defining, using Taylor theorem, as $$\sum_{j=u}^{v}c_k e^{j h \partial} = \partial^s,$$ which should hold asymptotically as $h\to0$.
Introducing a change of variable $z=e^{h\partial}$, this is equivalent to $$z^u p(z) = h^{-s}(\log z)^s,$$ where $p$ is the polynomial $p(z) = c_u + c_{u+1}z + \cdots + c_v z^{v-u}$. Thus $$p(z) = h^{-s}\frac{(\log z)^s}{z^u}.$$
So just compute the approximating Taylor polynomial around $z=1$ for $z^{-u}(\log z)^s$ to order $v-u$, this will be the polynomial with the finite-difference coefficients.
With $u=-10$, $v=10$, $s=1$, this polynomial is easily computed. The coefficients are: $$h^{-1}\left\{\frac{1}{1847560},-\frac{5}{415701},\frac{5}{38896},-\frac{15}{17017},\frac{5}{1144},-\frac{12}{715},\frac{15}{286},-\frac{20}{143},\frac{15}{44},-\frac{10}{11},0,\frac{10}{11},-\frac{15}{44},\frac{20}{143},-\frac{15}{286},\frac{12}{715},-\frac{5}{1144},\frac{15}{17017},-\frac{5}{38896},\frac{5}{415701},-\frac{1}{1847560}\right\}.$$
• Thanks for the answer. Sorry, it is little bit difficult for me to understand the notation used here. If you provide some external link where they solved using this style that will be helpful for me. I have some suggestions:1) Most of the CD schemes (so for I have seen) don't has mid point but this stencil has that. 2) I used $h^{-20}$ =sum(1,-20,190....184756) (Please correct me weather am I right). and cross checked the stencil by $A*x=b$ but i didn't get $b$ matrix. please check this when you are free.
– AGN
Dec 13 '15 at 9:18
• @ArunGovindNeelanA Sorry, I misread the question, the coefficients should be correct now, you're asking about 1st derivative, not 20th. Dec 13 '15 at 9:38
• Thanks , I guess the answer is 3 or 4 decimal accuracy. Could you provide some link or refrence to calculate the co-efficients using this procedure
– AGN
Dec 13 '15 at 10:00
• @ArunGovindNeelanA I'm not sure I know a reference, but I think it's standard. The coefficients are exact, what do you mean by accuracy? If you mean the residual $Ax-b$, then that can be expected as your (Vandermonde) matrix is very ill-conditioned. Dec 13 '15 at 10:12
• @ArunGovindNeelanA I used (x**10 * log(x)).taylor(x, 1, 20).coefficients() in sage to get the coefficients. Dec 14 '15 at 1:29
I would not generally expect a "20th order" derivative estimate to typically be very stable/reliable/useful (e.g. due to well known artifacts of high-order polynomial interpolation).
That said, a general procedure for deriving finite-difference stencils is to solve an appropriate polynomial interpolation problem. I will use Matlab-style notation, as you mention that program. In 1D, if you have a "stencil-grid" $x=-m:m$, then you can fit an interpolating polynomial $p(x)$ of degree $2m$ to any set of function values $f(x)$. The derivatives $\partial_x^kp$ evaluated at $x=0$ are then central-difference estimates of the corresponding derivatives of $f(x)$.
For a particular set of function values this would be done via $polyfit$ and $polyder$ in Matlab. To solve for the stencil coefficients themselves, this is indeed one of the few times I have found a need to actually compute a matrix inverse. The procedure is:
1) assemble the Vandermonde matrix $A$ for the stencil $x$.
2) Invert this matrix via $C=A\backslash I$, where $I$ is the identity matrix (i.e. solve a set of $2m+1$ interpolation problems, where the columns of $I$ are your "$b$" vectors).
3) The rows of $C$ now give "filters" for the $2m+1$ coefficients of interpolating the polynomial (i.e. the coefficient vector would be $c=Cf$ for given data $f$). So, the second row of $C$ gives the coefficients of your 1st derivative stencil (divide this by $\Delta x$ for a grid with non-unit spacing).
Note that to get the stencils for the first $2m$ derivatives, you would just compute $C(k+1,:)/(k!\Delta x^{k-1})$ for the $k$th derivative. Similarly, $x=-m:m$ assumes central differences on a uniform grid, but an arbitrary $x$ can be used, e.g. to compute off-center derivatives on a non-uniform grid. And you can get moving-least-squares stencils by having a rectangular $A$ matrix (note that the Matlab "$\backslash$" command automatically solves the normal equations in this case).
Hope this helps!
• Thanks for the answer. I think step 2 need inverse calculation $C=A\I$, where I got "badly scaled" warning. Could you give me any suggestions.
– AGN
Dec 13 '15 at 9:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9411745667457581, "perplexity": 571.5512405553636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056900.32/warc/CC-MAIN-20210919190128-20210919220128-00391.warc.gz"} |
http://mathhelpforum.com/advanced-algebra/143971-determinant-two-matrices.html | # Thread: Determinant of two matrices
1. ## Determinant of two matrices
Hi,
I didn't get so well what this problem is asking. Mostly how the B matrix is generated.
Let $\lambda \in R$. The matrix B is generated by the matrix A by addition of the $\lambda$ multiple of the j-th row to the i-th row ( $i \neq j$). Show that detB = detA.
2. Originally Posted by TheFangel
Hi,
I didn't get so well what this problem is asking. Mostly how the B matrix is generated.
Let $\lambda \in R$. The matrix B is generated by the matrix A by addition of the $\lambda$ multiple of the j-th row to the i-th row ( $i \neq j$). Show that detB = detA.
For example, if $A= \begin{pmatrix}1 & 3 & 3 \\ 4 & 5 & 1 \\ 3 & 2 & 3\end{pmatrix}$ and B "is generated by the matrix A by addition of the $\lambda$ multiple of the 3rd row the the first row" (taking j= 3 and i= 1), then $B= \begin{pmatrix}1+ 3\lambda & 3+ 2\lambda & 3+ 3\lambda \\ 4 & 5 & 1\\ 3 & 2 & 3 \end{pmatrix}$.
A determinant is a sum of products, each of which involves exactly one factor from each row. Here, such a product, $a_{1i}a_{2j}a_{3k}...$ will be replace by $a_{1i}a_{2j}(a_{3k}+ \lambda a_{nk})...$. Multiply that out.
3. Wow!
Thanks very much! | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.913398265838623, "perplexity": 744.6865296271811}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171171.24/warc/CC-MAIN-20170219104611-00329-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://clay6.com/qa/131606/if-a-begin-1-3-2-1-end-then-the-determinant-of-a-2-2a-is- | # If $A=\begin{bmatrix} 1&3\\2&1 \end{bmatrix}$, then the determinant of $A^2-2A$ is :
( A ) $25$
( B ) $5$
( C ) $-5$
( D ) $-25$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9831370115280151, "perplexity": 1416.4403841832145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575484.57/warc/CC-MAIN-20190922094320-20190922120320-00354.warc.gz"} |
https://www.physicsforums.com/threads/partial-limit.469192/ | # Partial limit
• Start date
• #1
241
0
## Homework Statement
I have to find all the partial limits {I hope this is how this term named in English} of a sequences
## Homework Equations
$$a_1=0$$
$$a_{2n}=\frac {a_{2n-1}} {3}$$
$$a_{2n+1} = 1/3 + a_{2n}$$
## The Attempt at a Solution
I have tried to prove first that sequences of all the even terms converges due to fact that sequence is monotonic and have a suprimum, but have failed to prove it.
Another problem is that subsequences of odd term is non monotonic, but I also can't use the Cantor's Lemma.
Could you please suggest how to approach this problem?
Thanks.
Last edited:
• #2
Mark44
Mentor
34,904
6,648
## Homework Statement
I have to find all the partial limits {I hope this is how this term named in English} of a sequences
## Homework Equations
$$a_1=0$$
$$a_{2n}=\frac {a_{2n-1}} {3}$$
$$a_{2n+1} = 1/3 + 2_{2n}$$
In the equation above do you mean a2n+1 = 1/3 + 22n?
## The Attempt at a Solution
I have tried to prove first that sequences of all the even terms converges due to fact that sequence is monotonic and have a suprimum, but have failed to prove it.
Another problem is that subsequences of odd term is non monotonic, but I also can't use the Cantor's Lemma.
Could you please suggest how to approach this problem?
Thanks.
• #3
241
0
Sorry, have fixed it in my first post.
• #4
Mark44
Mentor
34,904
6,648
You're looking at the two subsequences: one with the odd-index terms and the other with the even-index terms. Have you calculated the first dozen or so terms of your sequence?
• #5
241
0
I've calculated again some terms of the sequence and found out that I did a mistake in my previous calculation as both subsequences seem to be monotonic, but I can't find a way to prove that the sequences have suprimums.
0, 0, 81/243, 27/243, 108/243, 36/243, 36/243, 117/243, 39/243, 120/243, 40/243, 121/243
• #6
241
0
I have figured it out, thanks.
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994 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9457942843437195, "perplexity": 1286.567634856582}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991801.49/warc/CC-MAIN-20210515100825-20210515130825-00525.warc.gz"} |
https://nool.ontariotechu.ca/mathematics/functions/domain-range/domain-and-range-of-trigonometric-functions.php | # Domain and Range of Trigonometric Functions
The domain of a function is the specific set of values that the independent variable in a function can take on. The range is the resulting values that the dependant variable can have as x varies throughout the domain.
### Domain and range for sine and cosine functions
There are no restrictions on the domain of sine and cosine functions; therefore, their domain is such that x ∈ R. Notice, however, that the range for both y = sin(x) and y = cos(x) is between -1 and 1. Therefore, transformations of these functions in the form of shifts and stretches will affect the range but not the domain.
### The domain and range for tangent functions
Notice that y = tan(x) has vertical asymptotes at . Therefore, its domain is such that . However, its range is such at y ∈ R, because the function takes on all values of y. In this case, transformations will affect the domain but not the range.
Example: Find the domain and range of y = cos(x) – 3
Solution:
Domain: x ∈ R
Range: - 4 ≤ y ≤ - 2, y ∈ R
Notice that the range is simply shifted down 3 units.
Example: Find the domain and range of y = 3 tan(x)
Solution:
Domain: , x ∈ R
Notice that the domain is the same as the domain for y = tan(x) because the graph was stretched vertically—which does not change where the vertical asymptotes occur.
Range: y ∈ R
Example 1:
Example 2: | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8412875533103943, "perplexity": 339.0792593546004}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657169226.65/warc/CC-MAIN-20200716122414-20200716152414-00061.warc.gz"} |
https://ifrf.net/research/archive/characteristics-of-natural-gas-combustion-in-a-circulating-fluidized-bed/ | • ### Characteristics of Natural Gas Combustion in a Circulating Fluidized Bed
• Publication date:
October 2015
### Summary
Interest is growing in extending fluidized bed combustion (FBC) to fuels that are difficult to handle and those that present difficulties because their combustion is associated with particularly challenging air pollution problems. Such fuels include biomass (such as straw), plastic wastes, black liquors and heavy liquid fuels. As all of these have very high volatiles contents, they tend to be treated as easy to burn, and instead solid fuels and char combustion have received more attention in the literature. Nonetheless, understanding the gas-phase chemistry of such fuels is helpful in optimizing their combustion. This paper presents a study of natural gas combustion in a fluidized bed, as a model system for investigating the gas-phase reactions involving C/H/N/O chemistry taking place in the absence of char. The experimental work was conducted using a pilot-scale mini circulating FBC (CFBC) unit of 0.1 m diameter and 5 m height. Combustion characteristics and emissions were investigated by varying the operating conditions and in particular the combustion temperature, fluidizing velocity and bed material. The results fit with the general current consensus that FBC chemistry is associated with super-equilibrium free radical processes, similar to high-temperature flame systems. A CFBC model has been developed based on the general kinetic model and a NO/N2O formation model. It uses the semi-theoretical approach with some measured parameters as inputs and appears to be capable of providing a reasonable description of the nitrogen chemistry and the concentration profiles of NH3, HCN, NO, and N2O for the case of burning natural gas.
• Research: Journal
• Key Words | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8089668154716492, "perplexity": 3236.3221189991186}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141193221.49/warc/CC-MAIN-20201127131802-20201127161802-00542.warc.gz"} |
https://papers.neurips.cc/paper/2019/hash/7b66b4fd401a271a1c7224027ce111bc-Abstract.html | #### Authors
Yaqi Xie, Ziwei Xu, Mohan S. Kankanhalli, Kuldeep S Meel, Harold Soh
#### Abstract
In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph Convolutional Network (GCN). To generate semantically-faithful embeddings, we develop techniques to recognize node heterogeneity, and semantic regularization that incorporate structural constraints into the embedding. Experiments show that our approach improves the performance of models trained to perform entailment checking and visual relation prediction. Interestingly, we observe a connection between the tractability of the propositional theory representation and the ease of embedding. Future exploration of this connection may elucidate the relationship between knowledge compilation and vector representation learning. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8965420126914978, "perplexity": 2163.2429174397157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154356.39/warc/CC-MAIN-20210802172339-20210802202339-00093.warc.gz"} |
https://www.esaral.com/q/the-angles-a-b-c-of-a-abc-are-in-ap-and-the-sides-a-b-86188/ | The angles A, B, C of a ∆ABC are in AP and the sides a, b,
Question:
The angles ABC of a ∆ABC are in AP and the sides abc are in G.P. If a2 + c2 = λb2, then λ = ____________.
Solution:
Since ABC are A.P
$\Rightarrow 2 B=A+C$
Since $A+B+C=\pi$ (By angle sum property)
$\Rightarrow 3 B=\pi$
i. e $B=\frac{\pi}{3}$ ….(1)
Also,
Since abc are in g.p
$\Rightarrow b^{2}=a c$ …(2)
Using $\cos B=\frac{a^{2}+c^{2}-b^{2}}{2 a c}$
i.e $\cos \frac{\pi}{3}=\frac{a^{2}+c^{2}-a c}{2 a c} \quad$ from (1) and (2).
$\Rightarrow \frac{1}{2}=\frac{a^{2}+c^{2}-a c}{2 a c}$
$\Rightarrow a c=a^{2}+c^{2}-a c$
$\Rightarrow a^{2}+c^{2}=2 a c$
$\Rightarrow a^{2}+c^{2}=2 b^{2}$ from (2)
Hence $\lambda=2$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8682906031608582, "perplexity": 2101.0269449986004}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335504.22/warc/CC-MAIN-20220930181143-20220930211143-00585.warc.gz"} |
https://cs.stackexchange.com/questions/linked/265?sort=hot&pagesize=30 | 18k views
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I have laid out the various cases that would make this not a context free language already and proved all but one for this set: $$A = \{a^f b^g \mid f = g^2\}$$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.872768759727478, "perplexity": 1600.8732365483247}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540501887.27/warc/CC-MAIN-20191207183439-20191207211439-00101.warc.gz"} |
http://mathhelpforum.com/differential-geometry/195496-proving-function-injective.html | # Thread: Proving function is injective
1. ## Proving function is injective
Hey guys.
I've got the following problem:
Let $\displaystyle U = (0, \infty ) \times R \subset R^2$ og let $\displaystyle f : U \rightarrow R^2$ be defined by : $\displaystyle f(x,y) = (x, y^3+xy)$
(a) Show that $\displaystyle f(U) = U$ Done that already.
(b) Show that $\displaystyle f$ is injective
(Hint: When is $\displaystyle g: R \rightarrow R$ given by $\displaystyle g(y)= y^3 + ay + b$ monotonic?)
(c)... some more questions.
I've already found the solution to (a), but I cant quite figure out how to solve (b). This is pretty much what I've tried so far:
For $\displaystyle f : U \rightarrow R$ to be injective, the following has to be true : $\displaystyle q \neq p \Rightarrow f(q) \neq f(p) \forall q, p \in U$.
So, for proof by contradiction, we assume that for a pair $\displaystyle q \neq p \in U$ we have that $\displaystyle f(p) = f(q)$.
Since $\displaystyle f(q) = f(p)$ we have that $\displaystyle x_q = x_p \wedge y_q^3+x_q y_q = y_p^3+x_p y_p$ (1).
But since $\displaystyle q \neq p$ we have that $\displaystyle x_q \neq x_p \vee y_q \neq y_p$.
According to (1) we know that $\displaystyle x_q = x_p$ so $\displaystyle y_q \neq y_p$ must be the case.
From here I dont know exacly where to go. I can see that I'm not really using the hint.
I know that all monotonic functions are injective, but how can I prove that f is monotonic?
I can see by visualization that f will be monotonic, because x is defined to be positive, but how do I prove that rigorously?
Morten
2. ## Re: Proving function is injective
the function is clearly continuous, since each component function is continuous. there is a theorem that says that a continuous real-valued function is injective if and only if it is strictly monotonic. but im not sure if there is an analogous theorem for $\displaystyle \mathbb{R}^2$
3. ## Re: Proving function is injective
Yes I understand that, but how do I prove that it is monotonic? | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9861281514167786, "perplexity": 190.89539930678333}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867095.70/warc/CC-MAIN-20180624215228-20180624235228-00170.warc.gz"} |
https://appliedprobability.blog/2018/03/09/merton-portfolio-optimization/ | # Merton Portfolio Optimization
We consider a specific diffusion control problem. We focus on setting where there is one risky asset and one riskless asset, though we will see that much of the analysis passes over to multiple assets.
Def. [The Merton Problem – Plant Equation] In the Merton problem you wish to optimise your long run consumption. You may invest your wealth in a bank account receiving riskless interest $r$, or in a risky asset with value $S_t$ obeying the following SDE
where each $B=(B_t:t\geq 0)$ is an independent standard Brownian motion.
Wealth $(W_t : t\geq 0)$ obeys the SDE
You can control $c_t$ your rate of consumption at time $t$ and $n_t$ the number of stocks the risky asset at time $t$. Also, we define $\theta_t = n_t S_t$ to be the wealth in the risky asset at time $t$.
Def. [The Merton Problem – Objective] Given the above plant equation, , the objective is to maximize the long-term utility of consumption
Here $\rho$ is a positive constant and $u(c)$ is a concave increasing utility function. The set $\mathcal P(w_0)$ is the set of policies given initial wealth $w_0$. Further, let $V(w,t)$ be the optimal objective with the integral starting for time $t$ with $w_t=w$.
Let’s write the wealth respect to integrals in $dt$ and $dB_t$:
Ex 1. Show that
Ans 1.
Ex 2. Show that
Ans 2. Notice if we shift time by $\tau$, a factor $e^{-\rho t}$ comes out,
Ex 3. Show that the HJB equation for the Merton Problem can be written as
or, alternatively, as
Ans 3. Recall that informally the HJB equation is
Notice that if we apply Ito’s formula to $V(W_t)$ we get that
Applying this to the above term gives as required
Ex 4. [Continued] Optimizing the HJB over $\theta$, show that
Ans 4. Differentiating the HJB equation in [[cDP:MertonHJB]] wrt $\theta$ gives
Now rearrange for $\theta^*$.
Ex 5. [Continued] Given $\theta^*$, show that the HJB equation becomes
Ans 5. Substituting gives
## Merton for CRRA Utility
We focus on the case of CRRA utility, that is:
for $R >0$ (Recall the discussion on utility functions, Section [Util]). Thus we wish to solve for
Ex 6. Show that
Ans 6. Here we note that having a policy for initial wealth $\lambda w_0$ is the same as having a policy of wealth $w_0$ and then multiplying each amount invested by $\lambda$:
Ex 7. Show that
for some position constant $\gamma >0$.
Ans 7. In [6], let $\lambda=w^{-1}$ and $\gamma = (1-R)V(1)$.
Ex 8. Show that
Ans 8. Trival.
Ex 9. Show that if we define
then for a CARA utility
Ans 9. Differentiating gives $c^{-R} = z$ now rearrange and substitute.
Ex 10. Show that, when optimizing over $c$, the HJB equation is optimized by
Ans 10.
which since $u'(c)=c^{-R}$, gives the required formed.
Ex 11. [Merton:CARA4] Show that
Ex 12. [Continued]Show that
Ans 12. By [8] and [10]
Ex 13. Given the optimal choices of $c$ and $\theta$, Show that the HJB equation to be satisfied it must be that
where
To summarize: we notice we have show that the parameters given by
in exercises [4, 10, 13] give a solution to the HJB equation for the Merton problem. (Although we have not yet proven them to be optimal.)
We now give rigourous argument for the optimality of parameters $c^*$, $\theta^*$ and $\gamma^*$ for the Merton problem with CRRA utility. (This section can be skipped if preferred.)
Ex 14. Show that
where
(Hint: $u(y)$ is concave.)
Ans 14. Since $u(y)$ is concave we have that $u(y) \leq u(x) + (y-x) u'(x)$. Thus
Ex 15. Verify that
is a positive local martingale. [Hint: apply Ito’s formula to
]
Ex 16. [Continued] Show that
[Hint: Doob’s Martingale Convergence Theorem.]
Ans 16. Recall from stochastic integration theory that every positive local martingale is a supermartingale. Doob’s Martingale Convergence Theorem applied to [15] gives
Ex 17. [Continued] By direct calculation show that
[Hint: apply Fubini’s Theorem and note that
]
Ex 18. Now show that
Ans 18. Combining [16] and [17], we see that
Applying this to [14] we see that
as required. Thus $c^*_t$ is optimal.
The last exercise shows that the portfolio $\theta^*,c^*$ is optimal for the Merton problem with CRRA utility. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 46, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9764128923416138, "perplexity": 1294.9017131856867}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198887.3/warc/CC-MAIN-20200921014923-20200921044923-00774.warc.gz"} |
http://www.boredofstudies.org/wiki/index.php?title=Current_and_emerging_understanding_about_time_and_space_has_been_dependent_upon_earlier_models_of_the_transmission_of_light&redirect=no | # Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light
BikiCrumbs: Current and em…ission of light
## Students learn to:
#### 1. Outline the features of the aether model for the transmission of light
• The aether was thought to be the medium that light travelled trough.
• The aether filled all space.
In the 2003 HSC Notes from the Examination Centre - Physics, Question 18(a) the examiners comment on the difference between features and properties of the aether.
#### 2. Describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether
• Michelson and Morley attempted to measure the ether wind, similar to the wind caused when a car travels through still air. The experiment was set up as shown above, with an interference pattern showing up on the inferometer. The experiment was then rotated 90 degrees with the idea being that the aether wind would affect the path of at least one of the light beams causing a different interference pattern to appear. The interference pattern observed was the same. This null result meant that the aether was not acting in this experiment and as such was not necessary for light to propagate.
• Michelson and Morley attempted to measure the relative speed of the earth through the aether, a substance conjectured to be the medium in which light is propagated, that filled all space. Their method involved splitting a beam of light, from a single source into two beams that travelled perpendicular to each other. The two beams were brought together and shown on a screen, creating an interference pattern. If the earth moves relative to the aether, then the speed of one beam will be different from that of the other, just as the speed of a boat going first upstream and then downstream is different from that of a boat travelling across the stream. The difference in speed of the two beams would alter the interference pattern, when the apparatus is rotated through 90degrees. No such alteration was found. This and similar failures to detect the motion of the earth through the aether led later to the development by Einstein of the special theory of relativity, and the subsequent abolishment of the aether theory.
#### 3. Discuss the role of the Michelson-Morley experiment in making determinations about competing theories
The Michelson-Morley experiment made determinations about the aether theory because they provided evidence against it. It was not until Einstein, however, that the null result was explained and the aether model disproven.
#### 4. Outline the nature of inertial frames of reference
It is a non-accelerating frame of reference where Newton’s First Law is obeyed.
#### 5. Discuss the principle of relativity
Galilean relativity states that the same laws of physics apply in stationary frames of reference and frames of reference with a constant velocity.
Newtonian relativity states that in an inertial frame of it is impossible to disinguish between moving at a constant velocity and being stationary.
Einstein’s special relativity had two postulates: -the laws of physics are the same in all inertial frames of reference -the speed of light is constant and is independent of the velocity of the source or the observer
#### 6. Describe the significance of Einstein’s assumption of the constancy of the speed of light
This assumption explained the null result of Michelson-Morley and showed that the aether was not necessary. It also suggests that nothing can travel faster than the speed of light. This assumption also allowed Einstein to propose his theories of time dilation, length contraction and mass dilation.
#### 7. Identify that if c is constant then space and time become relative
In classical physics space is relative to the observer, but time is constant. In the theory of relativity, time becomes relative as well as space. This means that time passes differently for different observers, depending upon their velocity. If a man is sitting in a train travelling at c and looks into a mirror he will see his reflection. If an outside observer looks into the train they will see the light travel twice as far to reach the mirror. If c is constant this means that time slows down inside the train according to the outside observer as c=distance/time.
#### 8. Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard
Up until recently the metre was defined as the distance between two marks on a platinum-iridium bar in Paris. But now the definition of the speed of light as well as the definition of a second have become more accurate than our definition of the metre. So now the metre is defined as the distance travelled by a beam of light in a vacuum in 1/c seconds. As such the speed of light has been set at a given number of metres per second, so as our measurements become more accurate our definition of the metre will be revised, while c will remain constant. This also means that the metre is the same for any frame of reference, meaning that it is unaffected by length contraction and time dilation.
#### 9. Explain qualitatively and quantitatively the consequences of special relativity in relation to:
##### -Relativity of simultaneity
The Relativity of Simultaneity
If two flashes of light occur at the same distance from a person, that person will judge these two events to be simultaneous. Another person standing in another position may not judge these events to be simultaneous. Therefore simultaneity is dependent upon the frame of reference.
When a flash of light is emitted from person A, they should see the light hit the two ends at the same time. This is because the speed of light is constant irrelevant of the frame of references motion. However person B will see things differently, he will see the light reach the back of the train before it hits the start of the train, this is because the back of the train has moved closer to the source and the front of the train has moved away from the source.
Equivalence between mass and energy
The rest mass of an object is equal to a certain quantity of energy. In nuclear reactions this mass can be converted into energy, and conversely energy can be converted into mass according to E = mc2. The Laws of Conservation of Mass and Energy are now replaced by the Law of Conservation of Mass-Energy in special relativity.
Length contraction
The length of an object at rest is known as its proper length (L0), and this length is contracted (Lv) when the object’s velocity approaches the speed of light. This is expressed by the equation:
$l_v = l_0 \sqrt{1 - \frac {v^2}{c^2}}$
Time dilation
The time for an event to occur in the rest from is called to, but observers in different frames of reference will judge this time to be longer (tv). This is expressed by the equation:
$t_v = \frac {t_0}{\sqrt{1 - \frac {v^2}{c^2}}}$
Mass dilation
As the velocity of an object increases, so does its mass. This mass change is only really noticeable at speeds close to c. The mass varies according to the equation:
$m_v = \frac {m_0}{\sqrt{1 - \frac {v^2}{c^2}}}$
Where:
m0 = rest mass
mv = relativistic mass
#### 10. Discuss the implications of mass increase, time dilation and length contraction for space travel
Mass increase means that if a particle was accelerated to the speed of light it would have infinite mass, so to accelerate it to this point would require infinite energy, which is an impossibility. Therefore an object cannot be accelerated to the speed of light.
Time dilation means that if someone were to take a journey to a distant star at say 0.8c and the trip seemed to take 17 years on the Earth, the man in the spacecraft would only experience 10 years passing. This means that it is theoretically possible to travel to stars thousands of light years away within a lifetime of an astronaut if a spacecraft can be accelerated close to the speed of light, however, when they returned to earth, they would find that hundreds of years would have passed.
As the spacecraft accelerates to faster and faster speeds the length it has to travel becomes shorter.
## Students:
#### 1. Perform an investigation and gather first-hand or secondary data to model the Michelson-Morley experiment
This may have reference to a boat analogy where boats travel in different directions but the current of the water will affect their velocity. A swimmer swimming with the current would have trouble returning, whereas a swimmer swimming perpendicular to the current would have trouble on both the way to and back. An observer on a riverbank would thus see that the swimmer swimming perpendicular would have traced an open triangular path.
#### 2. Perform an investigation to help distinguish between inertial and non-inertial frames of reference
This can be determined by allowing a pendulum to hang, and then dropping an object from the pivot of the pendulum, if there is an angle between the two then your frame of reference is non-inertial.
#### 3. Analyse and interpret some of Einstein’s thought experiments involving mirrors and trains and discuss the relationship between thought and relativity
One limitation of thought experiments is that their outcomes often rely upon common sense, and sometimes new areas of science don’t make immediate sense. This was particularly true in Einstein’s case, but his only choice to experiment at near light velocities was thought experiments.
The following is one of Einstein’s most famous thought experiments:
Imagine that you are sitting in a train facing forwards. The train is moving at the speed of light. You hold up a mirror in front of you, at arm’s length. Will you be able to see your reflection in the mirror? There are two possible outcomes:
• No. This answer is in keeping with the aether model because light can only travel at a set speed, but violates the principle of relativity which states that when in inertial frame of reference you cannot conduct any experiment to tell if you are stationary or moving at a constant velocity.
• Yes. Because according to Newtonian relativity, in an inertial frame of reference it is impossible
• since light moves at a constant velocity time must pass differently inside and outside the train
• the aether is superflous
#### 4. Analyse information to discuss the relationship between theory and the evidence supporting it, using Einstein’s predictions based on relativity that were made many years before evidence was available to support it
Any theory, no matter how logical it may seem, cannot stand without experimental evidence. This also holds true in Einstein’s case, where proof for his theory of relativity only came later with particle accelerators and nuclear reactors. Examples of proof include:
• Two extremely accurate atomic clocks were sycronised. One remained on the Earth’s surface while the other was flown around the world in jet aeroplanes. When the second clock returned there was found to be a slight difference in time between the two. This indicates that time dilation has occurred.
• Many muons can be detected at sea level, but the trip from the upper atmosphere to the surface would take longer than the muon’s lifetime at the speed it is travelling. This also suggests that time dilation and length contraction have occurred.
• The fact that energy can be produced from fission reactions verifies energy-mass equivalence.
#### 5. Solve problems and analyse information using:
E = mc2
$l_v = l_0 \sqrt{1 - \frac {v^2}{c^2}}$
$t_v = \frac {t_0}{\sqrt{1 - \frac {v^2}{c^2}}}$
$m_v = \frac {m_0}{\sqrt{1 - \frac {v^2}{c^2}}}$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8181041479110718, "perplexity": 368.68068915757965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696383156/warc/CC-MAIN-20130516092623-00067-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://dizziness.academickids.com/encyclopedia/index.php/Lefschetz_fixed-point_theorem | # Lefschetz fixed-point theorem
In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some imputed multiplicity at a fixed point. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle).
For a formal statement, let
[itex]f:X \rightarrow X[itex]
be a continuous map from a compact triangulable space X to itself. A point x of X is a fixed point of f if f(x)=x. Denote the Lefschetz number of f by
[itex]\Lambda_f.\,[itex]
By definition this is
[itex]\sum(-1)^k\mathrm{Tr}(f_*|H_k(X,Q))[itex],
the alternating (finite) sum of the matrix traces of the linear maps induced by f on the homology of X, with rational number coefficients.
Then the Lefschetz fixed-point theorem states that if
[itex]\Lambda_f \neq 0[itex],
then f has a fixed point. In fact, since the Lefschetz number has been defined at the homology level, our conclusion can be extended to say that any map homotopic to f has a fixed point.
## Historical Context
Lefschetz presented his fixed point theorem in his 1926 paper Intersections and Transformations of Complexes and Manifolds in volume 28 of the Transactions of the American Mathematical Society. Lefschetz's focus was not on fixed points of mappings, but rather on what are now called coincidence points of mappings.
Given two maps f and g from a manifold X to a manifold Y, the Lefschetz coincidence number of f and g is defined as
[itex]\Lambda_{f,g} = \sum (-1)^k \mathrm{Tr}( D_X \circ g^* \circ D_Y^{-1} \circ f_*) [itex],
where f* is as above, g* is the mapping induced by g on the cohomology groups with rational number coefficients, and DX and DY are the Poincaré duality isomorphisms for X and Y, respectively.
Lefschetz proves that if the coincidence number is nonzero, then f and g have a coincidence point. He notes in his paper that letting X=Y and letting g be the identity map gives a simpler result, which we now know as the fixed point theorem.
• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9773821234703064, "perplexity": 458.48879213885226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738562.5/warc/CC-MAIN-20200809162458-20200809192458-00399.warc.gz"} |
https://www.physicsforums.com/threads/elastic-collision-in-2d.197719/ | # Elastic collision in 2d
1. Nov 12, 2007
### fliinghier
1. The problem statement, all variables and given/known data
there are two masses, the smaller sitting still, and the larger with 5 times the mass of the smaller hits it going 12 m/s. the smaller rebounds at an 80 degree angle from the direction of the original mass. the collision is elastic. find the speed of both objects and the angle of the larger one after the collision.
2. Relevant equations
1/2mv^2 (KE, which is conserved)
mv (momentum, which is conserved)
3. The attempt at a solution
so far i have tried using sin and cos of theta and 80 degrees to find equivalent equations using momentum(5V2sin(theta)=V1sin(80) and 60=5V2cos(theta)+V1cos(80)) and then i tried to plug variables into the KE equation or solve the equations simultaneously.
2. Nov 12, 2007
### Staff: Mentor
You are on the right track. Try this: Use the momentum equations to find V2 in terms of V1. Then plug that into the KE equation. (Hint: Take advantage of the trig identity $\sin^2\theta + \cos^2\theta = 1$.)
3. Nov 12, 2007
### fliinghier
after trying this way again i got stuck (again) when i reached the following:
720=(V1^2)(1+(.970/(sin(theta))^2))
4. Nov 12, 2007
### Staff: Mentor
Use the hint I gave to eliminate theta before plugging into the KE equation.
5. Nov 12, 2007
### fliinghier
thanks i think i got it now.
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https://www.physicsforums.com/threads/the-photon-vs-maxwells-equations.257767/ | The photon vs Maxwell's Equations
1. Sep 20, 2008
enotstrebor
I was reading "understanding light'' on this forum.
If one wants to know what a photon is one first must ask, does one want to know what the physics is or does one want to know what the mathematics says.
A physicist might ask a the question, "Are Maxwell's equations (the E,B fields) a representation (even if classical in nature) of the photon or are they a representation of the interaction between the photon and matter." in order to understand the physical process that is occuring.
If the equations are an interaction theory (which I would suggest is the case) then one might want to suggest that matter reacts to the photon field(s?) with an E type interaction (reaction) as well as a B-type interaction (reaction-a spin related gyroscopic reaction?).
For example, a single photon field could produce both type reactions. (Mathematically this is can be done using the A vector potential to represent a single field that can produce both E and B, but the same can be done physically using a directional rotating field.)
Going down the road to the answer to the question "Are Maxwell's equations (the E,B fields) a representation (even if classical in nature) of the photon or are they a representation of the interaction between the photon and matter." also ask the question "What is matter." For example what is an electron or a proton, why do these particles that according to the SM are of such different construction both emit and absorb photons (how does the photon get emitted - what is the physics process of absorbtion not the mathematics) and behave the same toward light (given the SM view of the proton, the proton's composite quarks somehow must together react to absorb a photon) just like SM "point" electron (This forum "Does the electron have a makeup" - actually the only thing we realy know is that the experimental data indicates that one can describe the collisions of electrons as if the electron was a point. Objects with spin can act and react gyroscopically through the centerpoint of spin, i.e behave point like)
Unfortunately, for the purely physical physicist (though not the mathematical physicist), the SM despite its elequent mathematical representation of the interaction behaviors of particles, does not give, from a physical perspective, a satisfying answer for the physic(s)al nature of massed particles nor the photon.
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https://mathprelims.wordpress.com/2008/10/27/the-lebesgue-stieltjes-measure/ | # Mathematics Prelims
## October 27, 2008
### The Lebesgue-Stieltjes Measure
Filed under: Analysis,Measure Theory — cjohnson @ 5:19 pm
Consider an increasing, right-continuous function $F : \mathbb{R} \to \mathbb{R}$. We can measure the length of an interval $I$ in $\mathbb{R}$ with end points $a$ and $b$ (e.g., ${}[a, b]$) as
$\displaystyle \ell_F(I) = F(b) - \lim_{x \to a^-} F(a)$.
(Capinski uses $\ell_F(I) = F(b) - F(a)$ with the interval $I$ restricted to being of the form $(a, b]$, but I believe this gives the same measure in the end.)
Using this definition of the length of an interval, we can then construct an outer measure on $\mathbb{R}$, call it $\mu_F^*$, as follows.
$\displaystyle \mu_F^*(A) = \inf\left\{ \sum_{n=1}^\infty \ell_F(I_n) : A \subseteq \bigcup_{n=1}^\infty I_n \right\}$
Where each $I_n$ is a bounded interval. Proceeding as we would in defining the usual Lebesgue measure on $\mathbb{R}$, we will let $\mu_F$ be a measure on $\mathcal{M}_F$ where
$\displaystyle \mathcal{M}_F = \{ E \subseteq \mathbb{R} : \forall A \subseteq \mathbb{R}, \, \mu_F^*(A) = \mu_F^*(A \cap E) + \mu_F^*(A \cap E^\complement) \}$
Now we’ve gone from an increasing, right-continuous function to a measure on $\mathbb{R}$. Note that sets that were null with the Lebesgue measure, may not be anymore, depending on our choice of $F$. For instance, if we have
$\displaystyle F(X) = \left\{ \begin{array}{ll} x & : x < 0 \\ 1 + x &: x \geq 0 \end{array}\right.$
Then $\mu_F(\{0\}) = 1$, though with the standard Lebesgue measure we have $\mu(\{0\}) = 0$.
It will be convenient to have the convention that if $F$ is an increasing, right-continuous function that
$\displaystyle \int_E g \, dF$
is actually short-hand for the Lebesgue integral of $g$ over $E$ using the measure obtained from $F$ as we’ve described above. This is normally referred to as the Lebesgue-Stieltjes integral with integrator $F$.
1. […] that is an increasing, right-continuous function with and . Using the ideas from the Lebesgue-Stieltjes measure article, we can have that gives us a measure and sigma-algebra on . Let and be the measure and […]
Pingback by Distribution of a Random Variable « Mathematics Prelims — November 1, 2008 @ 12:27 pm
2. The first line seems wrong.
The function is defined as right continuous. x tends to a+ not a- .
Comment by N. Srinivasan — April 13, 2010 @ 9:08 am
• F(a+)=F(a) by right continuity, and so, we do not need F(a+); but we need F(a-), since F(b)-F(a) is the measure of (a,b] rather than [a,b]; in fact, F(a)-F(a-) is the measure of {a}=[a,a].
Comment by Boris Tsirelson — February 29, 2012 @ 8:46 am
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http://advances.sciencemag.org/content/4/4/eaao4513 | Research ArticleCONDENSED MATTER PHYSICS
# Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal
See allHide authors and affiliations
Science Advances 06 Apr 2018:
Vol. 4, no. 4, eaao4513
DOI: 10.1126/sciadv.aao4513
## Abstract
In all known fermionic superfluids, Cooper pairs are composed of spin-1/2 quasi-particles that pair to form either spin-singlet or spin-triplet bound states. The “spin” of a Bloch electron, however, is fixed by the symmetries of the crystal and the atomic orbitals from which it is derived and, in some cases, can behave as if it were a spin-3/2 particle. The superconducting state of such a system allows pairing beyond spin-triplet, with higher spin quasi-particles combining to form quintet or septet pairs. We report evidence of unconventional superconductivity emerging from a spin-3/2 quasi-particle electronic structure in the half-Heusler semimetal YPtBi, a low-carrier density noncentrosymmetric cubic material with a high symmetry that preserves the p-like j = 3/2 manifold in the Bi-based Γ8 band in the presence of strong spin-orbit coupling. With a striking linear temperature dependence of the London penetration depth, the existence of line nodes in the superconducting order parameter Δ is directly explained by a mixed-parity Cooper pairing model with high total angular momentum, consistent with a high-spin fermionic superfluid state. We propose a kp model of the j = 3/2 fermions to explain how a dominant J = 3 septet pairing state is the simplest solution that naturally produces nodes in the mixed even-odd parity gap. Together with the underlying topologically nontrivial band structure, the unconventional pairing in this system represents a truly novel form of superfluidity that has strong potential for leading the development of a new series of topological superconductors.
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.
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https://okayama.pure.elsevier.com/en/publications/effect-of-retreating-sea-ice-on-arctic-cloud-cover-in-simulated-r-2 | # Effect of retreating sea ice on Arctic cloud cover in simulated recent global warming
M. Abe, T. Nozawa, T. Ogura, K. Takata
Research output: Contribution to journalArticlepeer-review
2 Citations (Scopus)
## Abstract
This study investigates the effect of sea ice reduction on Arctic cloud cover in historical simulations with the coupled atmosphere-ocean general circulation model MIROC5. During simulated global warming since the 1970s, the Arctic sea ice extent has reduced substantially, particularly in September. This simulated reduction is consistent with satellite observation results. However, the Arctic cloud cover increases significantly during October at grids with significant reductions in sea ice because of the enhanced heat and moisture flux from the underlying ocean. Cloud fraction increases in the lower troposphere. However, the cloud fraction in the surface thin layers just above the ocean decreases despite the increased moisture because the surface air temperature rises strikingly in the thin layers and the relative humidity decreases. As the cloud cover increases, the cloud radiative effect in surface downward longwave radiation (DLR) increases by approximately 40-60 % compared to a change in clear-sky surface DLR. These results suggest that an increase in the Arctic cloud cover as a result of a reduction in sea ice could further melt the sea ice and enhance the feedback processes of the Arctic amplification in future projections.
Original language English 17527-17552 26 Atmospheric Chemistry and Physics Discussions 15 12 https://doi.org/10.5194/acpd-15-17527-2015 Published - Jun 30 2015
## ASJC Scopus subject areas
• Atmospheric Science
• Space and Planetary Science
## Fingerprint
Dive into the research topics of 'Effect of retreating sea ice on Arctic cloud cover in simulated recent global warming'. Together they form a unique fingerprint. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8342400789260864, "perplexity": 4562.6750791144805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057973.90/warc/CC-MAIN-20210926205414-20210926235414-00639.warc.gz"} |
https://www.physicsforums.com/threads/strain-of-a-cantilever-beam.872722/ | # Strain of a Cantilever beam
• #1
8
0
Hi,
Well i have a system with a excited (in y axis) cantilever beam. I struggling to obtain a expression that gives the strain based on the dislocation y.
I know that the displacement of the beam is given by:
Ya=PL^3/(3EI)
but how i make a correlation between this and the strain of the surface of the beam?
Resuming, i am integrating a system, in this system i have the displacement of the beam in y axis (X(1) in my program) but i want the strain of the surface of the beam.
• #2
JBA
Gold Member
1,540
461
Strain = Stress/E, so take the two equations and resolve them into one equation for Stress as a function of L and D, with D known, integrate that equation for L from 0 to L and divide the result by E to obtain the resulting total strain in the outer fibers of the beam. + for the tension side and - for compression side.
• #3
8
0
Sorry, but In this case what is the D?
• #4
8
0
Stress=(ya*3E*I)/(A*L^3)
Strain=Stress/E
Strain=(ya*3*I)/(L^3*A)
Where:
A= Area
I=Inertia
E=young modulus
My question now is, as i am integrating this system (Matlab, ode45) i need to derive this equation, no?
• #5
JBA
Gold Member
1,540
461
My D = deflection, sorry, I should have used y.
• #6
PhanthomJay
Homework Helper
Gold Member
7,166
507
You are using the deflection at the free end of the cantilever, where the strain is 0. You should instead be using the general deflection along the entire beam length as a function of x. Also, stress in bending is not P/A, it is Mc/I at the outer fibers, where M at any point is Px (where x is 0 at the free end).
• #7
8
0
PhantomJay, i have tried here:
X(1)=(P*(L^3))/(3*E*I) %%%Equation of the deflection, where x(1) is the variation of the deflection in time
P=(X(1)*3*E*I)/(L^3)
Substituing in the equation
Stress=Mc/I
Strain=Stress/E
Strain=(X(1)*3*I*c*x)/(I*L^3)
Is that correct?
• #8
PhanthomJay
Homework Helper
Gold Member
7,166
507
No. What do you mean that x is variation of deflection in time? Are you trying to find the strain at the outer fibers of the beam at some distance x from the the free end? And as a function of the displacement y at that distance? I am not sure why. You are also getting hung up by looking at the displacement at the free end and not as a function of the length x along the beam. As mentioned, bending strain is bending stress/E. And bending stress at outer fibers is Mc/I. So strain is Mc/EI, and since M is Px, strain is Pxc/EI, positive at top fibers and negative at bottom fibers.
• #9
JBA
Gold Member
1,540
461
Gerrgegeorge,
You need to draw a moment diagram for your beam under load/deflection. When you do this, you will see that the magnitudes of the moment, stress and strain are continuously variable along the length of the beam. (Assuming you are working with a cantilever beam the moment will be zero at the free end of the beam and linearly increase to its maximum at the base connection of the beam.) This is the reason that, for any given beam load/deflection, it is necessary to integrate the stress along the beam to determine the total accumulated strain in the top and bottom surfaces of the beam at any given deflection.
Last edited:
• #10
8
0
Sorry for the incorrect use of some constants,
the deflection is Ya=X(1) and do not have relationship with the x who is based in the lenght of the beam.
• #11
Nidum
Gold Member
2,990
848
@Gerrgegeorge .
(1) Your first posting does not make it clear whether this is a static deflection problem or a vibration problem .
(2) I think that you may not properly understand what strain is .
Please explain again what you are trying to do . Use simple words rather than technical terms and include a diagram .
Last edited:
• #12
8
0
In a simple form, i am integrating some differential equations in matlab.
One of this equations need the strain of the beam (in this case). As the beam is vibrating i have the information of the displacement, who varies in time (vibration).
In this question i want a function who gives the strain based in the vertical displacement of the cantilever beam (the information that i have).
• #13
Nidum
Gold Member
2,990
848
Please post a diagram as requested in post #11 .
Last edited:
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6K | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9328488111495972, "perplexity": 913.1764411235229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088245.37/warc/CC-MAIN-20210416161217-20210416191217-00314.warc.gz"} |
http://mathhelpforum.com/advanced-applied-math/57309-forces-walls-print.html | # Forces in walls?
• Nov 3rd 2008, 10:30 AM
TriKri
Forces in walls?
Hi!
I have a question about forces inside of walls.
When you concider the walls of a house, they have a certain density $\delta$ and they create a force downwards, which becomes bigger closer to the ground. Assume we don't need to care about the weight of the roof or that of the atmosphere. The force in each wall, will be
$\overbrace{\underbrace{w\cdot h\cdot t}_\texttt{total volume}\cdot \delta}^\texttt{total weight}\cdot g$
where w is the width of the wall, h is the heigth up to the top of the wall, and t is the thickness of the wall. So, independent of the width and the thickness of the wall, the pressure create by the wall above will be
$h\cdot\delta\cdot g$
Now to my question: Is the pressure uniform? That is, will the pressure be the same in all directions, vertically as horizontally? The pressure vertically will be $h\cdot\delta\cdot g$, since when the material gets squeezed from the top and the bottom, it gets compressed vertically, so it creates a pressure vertically since it wants to expand in that direction. Besides, it needs to support its own weigth. But what about horizontally, does it want to expand it that direction as well? How big will the pressure be in that direction? Near to the pressure vertically, or almost zero? Does it depend on the material of the wall? (wood/concrete/metal?) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8118351101875305, "perplexity": 354.6405509979873}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187828134.97/warc/CC-MAIN-20171024033919-20171024053919-00473.warc.gz"} |
https://brilliant.org/discussions/thread/help-16/ | ×
HELP!
Does anyone have a non-trigonometry solution for this problem:
Suppose we have a triangle $$ABC$$.It is known that $$C=30$$ degrees.From $$A$$ draw a segment $$AD$$ such that $$D$$ is on $$BC$$ and $$ADC$$ is $$40$$ degrees.Also $$AB=CD$$.Find $$B$$.
Note by Lawrence Bush
2 years ago
Sort by:
My thinking is as follows: Locate the circum-centre of triangle ADC . Let's call it O. /AOD=2*/ACD=2*30 or 60°. This makes triangle AOD equilateral or AD=CO = R, the circumradius of Tr. ADC. Now in triangles BAD & DCO, we've AB=CD (Given), AD=CO & /_ BDA=/DOC both =140° . This isn't the included angle but since it is clearly the largest angle of each triangle, this is a special case of congruence. This means /ABD or /_ B = /_CDO = 20° · 1 year, 12 months ago
Thanks · 1 year, 12 months ago
Amazing! You're awesome @One Top How did you think of it? I though of drawing the circumcircle of $$\Delta ABC$$... · 1 year, 12 months ago | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8839535117149353, "perplexity": 2905.482791085834}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720356.2/warc/CC-MAIN-20161020183840-00052-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://search.datacite.org/works/10.4230/LIPICS.FSTTCS.2010.308 | ### Computing Rational Radical Sums in Uniform TC^0
Paul Hunter, Patricia Bouyer, Nicolas Markey, JoëL Ouaknine & James Worrell
A fundamental problem in numerical computation and computational geometry is to determine the sign of arithmetic expressions in radicals. Here we consider the simpler problem of deciding whether $\sum_{i=1}^m C_i A_i^{X_i}$ is zero for given rational numbers $A_i$, $C_i$, $X_i$. It has been known for almost twenty years that this can be decided in polynomial time. In this paper we improve this result by showing membership in uniform TC0. This requires several significant departures from... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9815275073051453, "perplexity": 616.7101680449176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805417.47/warc/CC-MAIN-20171119061756-20171119081756-00391.warc.gz"} |
https://gmatclub.com/forum/in-a-bag-of-balloons-the-ratio-of-red-balloons-to-other-is-2696.html | It is currently 27 Jun 2017, 17:39
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In a bag of balloons, the ratio of red balloons to other is
Author Message
CEO
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In a bag of balloons, the ratio of red balloons to other is 1:5
if 3 Balloons are selected at random, what is the probability that
1. at least one balloon is red
2. exactly one balloon is red
Intern
Joined: 29 Aug 2003
Posts: 47
Location: Detroit, MI
Re: PS : Probability ..Balloons [#permalink]
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02 Oct 2003, 07:23
praetorian123 wrote:
In a bag of balloons, the ratio of red balloons to other is 1:5
if 3 Balloons are selected at random, what is the probability that
1. at least one balloon is red
2. exactly one balloon is red
The probability of getting a red balloon = 1/6
(2)Prob. that exactly exactly one balloon is red
The first balloon can be red or the second one or the third one
= 3 * (1/6)((5/6)^2) = 25/72 or 75/216
(1) Probabilti that atleast one balloon is red = Prob. that only 1 balloon is red + Prob. that only 2 balloons are red + Prob. that all 3 balloons are red
= 75/216 + (3 * ((1/6)^2) * (5/6)) + (1/6)^3 = 91/216
Eternal Intern
Joined: 22 Sep 2003
Posts: 51
Location: Illinois State University, Normal, IL
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02 Oct 2003, 07:38
take a FINITE MATH Course it will help on probablity i learned this in class.
Eternal Intern
Joined: 22 Sep 2003
Posts: 51
Location: Illinois State University, Normal, IL
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02 Oct 2003, 07:39
take a FINITE MATH Course it will help on probablity i learned this in class.
Consultant
Joined: 03 Feb 2003
Posts: 5
Location: Moscow, Russia
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02 Oct 2003, 07:41
Dear All,
please explain - why do you think that the bag contains 6 balls. The problems states "the ratio of red to other"!!! it can be 1:5, 2:10 etc
maybe I am missing smth?
Good luck,
Hakob
Intern
Joined: 29 Aug 2003
Posts: 47
Location: Detroit, MI
Re: PS : Probability ..Balloons [#permalink]
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02 Oct 2003, 07:54
Hakob wrote:
Dear All,
please explain - why do you think that the bag contains 6 balls. The problems states "the ratio of red to other"!!! it can be 1:5, 2:10 etc
maybe I am missing smth?
Good luck,
Hakob
Hakob,
The ratio is given as 1:5. The multiples given by you, of that ratio are also right. If the ratio is 1:5, it means that there is 1 red ball for 5 balls of other kinds.
Say there are n balls in all.
Number of red balls = r
Number of other balls = o
r + o = n
and r/o = 1/5 => o=5*r
So, 6*r = n => r = n/6 which means that the number of red balls equals a sixth of the total number of balls.
Hope that makes it clear.
CEO
Joined: 15 Aug 2003
Posts: 3454
Re: PS : Probability ..Balloons [#permalink]
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02 Oct 2003, 12:24
amarsesh wrote:
praetorian123 wrote:
In a bag of balloons, the ratio of red balloons to other is 1:5
if 3 Balloons are selected at random, what is the probability that
1. at least one balloon is red
2. exactly one balloon is red
The probability of getting a red balloon = 1/6
(2)Prob. that exactly exactly one balloon is red
The first balloon can be red or the second one or the third one
= 3 * (1/6)((5/6)^2) = 25/72 or 75/216
(1) Probabilti that atleast one balloon is red = Prob. that only 1 balloon is red + Prob. that only 2 balloons are red + Prob. that all 3 balloons are red
= 75/216 + (3 * ((1/6)^2) * (5/6)) + (1/6)^3 = 91/216
Good work..Amar.
Just a simpler way
1. Probability that atleast one balloon is red = 1 - Prob none are red
prob that a balloon is red = 1/6
so prob that its not red = 5/6
Prob none of the three are red = (5/6)^ 3 =125/216
So required prob = 1- 125/216 = 91/216
2. Prob that exactly one is red
we can get exactly one in any of the three ways
R O O
O R O
O O R
so it follows
1/6 * 5/6 * 5/6 * 3 = 75/216
CEO
Joined: 15 Aug 2003
Posts: 3454
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12 Oct 2003, 05:14
Amar,
A question
Did we assume in the above that we replace the balloons?
Can we assume replacement if not given in the problem?
Thanks
Praetorian
Intern
Joined: 29 Aug 2003
Posts: 47
Location: Detroit, MI
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12 Oct 2003, 19:35
Yes,
I did assume that. I wouldn't expect the actual GMAT questions to be ambiguous like this one. If they were, I would go with both the approaches (replaced and not replaced) and try to see which one yileds a solution. If both are present, then we are at a loss.
Amar.
12 Oct 2003, 19:35
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https://www.physicsforums.com/threads/inelastic-or-elastic-collision.135570/ | # Inelastic or elastic collision?
1. Oct 9, 2006
### bearhug
A 4.0 kg firework is tossed onto a hockey rink. As it slides, it explodes into exactly two 2 kg pieces. There is an x-y coordinate system painted under the ice. One part of the exploded firework has velocity 3.0 m/s along the y direction. The other part has a velocity of 5.0 m/s at an angle of +30 degrees relative to the x-axis.
(a) What is the original speed of the firework on the ice (before the explosion)
My biggest question is that in order to solve this problem should I treat it as an inelastic collision or any collision for that matter? Since technically there is no collision, just an explosion.
2. Oct 9, 2006
### Staff: Mentor
You need to decide what's conserved and what's not. What do you think?
3. Oct 9, 2006
### bearhug
I was thinking it was elastic.
4. Oct 9, 2006
### bearhug
seriously any help on this problem is appreciated.
5. Oct 10, 2006
### Staff: Mentor
Answer my question: What's conserved and what's not conserved?
Similar Discussions: Inelastic or elastic collision? | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8530563116073608, "perplexity": 2454.958266669292}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189252.15/warc/CC-MAIN-20170322212949-00160-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://vulcanhammer.org/2013/05/08/determining-the-characteristic-polynomial-of-the-companion-matrix-by-use-of-a-large-matrix/ | # Determining the Characteristic Polynomial of the Companion Matrix by Use of a Large Matrix
Most proofs of the characteristic polynomial of the companion matrix–an important specific case–proceed by induction, and start with a $2\times2$ matrix. It strikes me that an inductive proof has more force (or at least makes more sense) if a larger matrix is used. In this case we will use a “large” (numerical analysts will laugh at this characterisation) $10\times10$ matrix.
Let us begin by making a notation change. Consider the general polynomial
For this to be monic (one of the requirements for the polynomial in question) we should divide by the last coefficient, thus
Our object is thus to prove that this (or a variation of this, as we will see) is the characteristic polynomial of
The characteristic polynomial of this is the determinant of the following:
(For another application of the characteristic polynomial and the companion matrix, click here.)
To find the determinant, we expand along the first row. But then we discover that only two minors that matter: the one in the upper left corner and the one in the upper right. Breaking this up into minors and cofactors yields the following:
The second matrix, however, is an upper triangular matrix with ones for all of its diagonal entries. Its determinant, therefore, is unity. Also rewriting the coefficient of the second term, we have
or
Repeating this process for the next set of minors and cofactors yields
Note carefully the inclusion of $-\lambda$ in the second term. We can also write this as
Repeating this process until the end, it is easy to see that
or more generally
where $n$ is the degree of the polynomial (and the size of the companion matrix.) If we drop the terms we used to make the polynomial monic, we have at last | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9031208157539368, "perplexity": 308.1839959688779}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103639050.36/warc/CC-MAIN-20220629115352-20220629145352-00337.warc.gz"} |
https://questions.examside.com/past-years/jee/question/if-a-function-fx-defined-by-brbrfleft-x-right-jee-main-mathematics-limits-continuity-and-differentiability-emnodwwkli5shwac | 1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
If a function f(x) defined by
$$f\left( x \right) = \left\{ {\matrix{ {a{e^x} + b{e^{ - x}},} & { - 1 \le x < 1} \cr {c{x^2},} & {1 \le x \le 3} \cr {a{x^2} + 2cx,} & {3 < x \le 4} \cr } } \right.$$
be continuous for some $$a$$, b, c $$\in$$ R and f'(0) + f'(2) = e, then the value of of $$a$$ is :
A
$${e \over {{e^2} - 3e - 13}}$$
B
$${1 \over {{e^2} - 3e + 13}}$$
C
$${e \over {{e^2} - 3e + 13}}$$
D
$${e \over {{e^2} + 3e + 13}}$$
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let [t] denote the greatest integer $$\le$$ t and $$\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A$$.
Then the function, f(x) = [x2]sin($$\pi$$x) is discontinuous, when x is equal to :
A
$$\sqrt {A + 1}$$
B
$$\sqrt {A + 5}$$
C
$$\sqrt {A + 21}$$
D
$$\sqrt {A}$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let a function ƒ : [0, 5] $$\to$$ R be continuous, ƒ(1) = 3 and F be defined as :
$$F(x) = \int\limits_1^x {{t^2}g(t)dt}$$ , where $$g(t) = \int\limits_1^t {f(u)du}$$
Then for the function F, the point x = 1 is :
A
a point of inflection.
B
a point of local maxima.
C
a point of local minima.
D
not a critical point.
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Let ƒ be any function continuous on [a, b] and twice differentiable on (a, b). If for all x $$\in$$ (a, b), ƒ'(x) > 0 and ƒ''(x) < 0, then for any c $$\in$$ (a, b), $${{f(c) - f(a)} \over {f(b) - f(c)}}$$ is greater than :
A
1
B
$${{b - c} \over {c - a}}$$
C
$${{b + a} \over {b - a}}$$
D
$${{c - a} \over {b - c}}$$
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http://www.physicsforums.com/showthread.php?p=4223489 | # Probability question: testing whether a population is 50/50
by Curl
Tags: 50 or 50, population, probability, testing
P: 751 Say I have a "large" population (larger than 1000) of red cards and blue cards which I want to find if it is evenly split (1:1 red:blue ratio). So I do an experiment and pull out 125 cards at random, and find that I have 50 red and 75 blue. Based on this experiment, what can I say about the red:blue ratio in the population? What is the "confidence" that the ratio is NOT 1:1? I'm unsure what "confidence" means here, I can find for example the probability of getting more than 75 blue cards out of 125 by using the normal approx. to the binomial distribution but I'm not sure what that says about the population. Can anyone give me some help on how to analyze this kind of data? How much information can we extract from this one experiment?
P: 4,568 Hey Curl. The confidence refers a way to describe the probability you wish to use for estimating the parameter. The parameter is potentially with any sample between 0 and 1 (not including the two only on special occasions) and a finite sample won't give you enough information to conclude specifically the absolute value of the parameter. More confidence allows for more taking into account more possibilities of the parameter in a statistical manner. Basically you should apply the Normal approximation and test the hypothesis that 0.5 is in your confidence interval: If it is then you retain the hypothesis and if not you fail to retain it.
HW Helper P: 2,115 This is the same kind of thing that comes up in elections polling. Often instead of assuming the split is even (which can also be done) we can find the confidence interval of the observed split. $$\text{C.I.}=p \pm z_{1-\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$ where p (probability) is 75/125 n=125 z is the desired confidence 1.96 for 95% Assuming the probability is equal we could consider the probability of 75/125 $$\left(\frac{1}{2}\right)^{125} \binom{125}{50}\sim 0.00587$$ more importantly the chance of drawing less than 75 is 98.4%
P: 1,168
## Probability question: testing whether a population is 50/50
You can also do a quick Chi-squared:
http://www2.lv.psu.edu/jxm57/irp/chisquar.html
P: 3,086
Quote by Curl Based on this experiment, what can I say about the red:blue ratio in the population?
Without some assumptions about the population, you can't say anything except for the trivial fact that the population contains at least 50 red and 75 blue cards and so that establishes some bounds for the ratio.
Other posters have given you methods to produce some numbers. The methods work by assuming information about the population. The numbers they produce are often misinterpreted by laymen. I'll focus my post on the conceptual aspects.
Two divisions of statistics are "hypothesis testing" and "estimation".
Hypothesis Testing
Typical statistical "hypothesis" testing involves making a specific enough assumption about the population to compute the probability distribution for some statistic of the sample. For example, if the statistic is the ratio of red to blue cards in the sample, the assumption that the the population has the same number of red cards as blue cards is specific enough to let you compute the probability distribution of this ratio in samples. The assumption that the ratio is *not* 1:1 in the population is not specific enough to let you compute the distribution of that statistic.
Hypothesis testing is a procedure. You make a sufficiently specific assumption (a "null hypothesis") to know the probability distribution of some statistic. You define an "acceptance region" for the statistic. If the statistic computed from the observed data falls within the "acceptance region" you "accept" the hypothesis. Otherwise you "reject it". The quantitative behavior of the procedure is specified by the probability that the statistic would fall outside of the acceptance region if the null hypothesis were true.
(i.e. that the hypothesis testing would make the wrong decision if the null hypothesis were true.)
Hypothesis testing isn't a proof of something and it does not find the probability that the null hypothesis is true or the probability that it is false. Hypothesis testing is just a procedure that has been found to be empirically useful in many real life situations.
Estimation
Estimation refers to using some function of the sample data to estimate a parameter of the distribution of the population.
The technical definition of "confidence" refers to the scenario of "estimation" , not to "hypothesis testing". The numerical calculations in computing confidence are often the same as those used in hypothesis testing, but the interpretation of the numbers is different.
An empirical version of "confidence" in estimation is illustrated by the following:
Imagine there is a lab, to which you send samples. The lab reports an estimate of some property of the sample ( e.g. its mass). The report is given as an interval (e.g. 9.75 to 10.25 milligrams). If you have a way of doing more precise measurements on the same sample that determine its "true" mass, you can note whether the true mass is within the interval reported by the lab. By accumulating data on how often the lab was correct, you can quantify your "confidence" in the lab. If the interval reported by the lab contains the true mass of the sample 95% of the time, you can say that the lab gives a "95% confidence" interval for the true mass.
It's important to note that you cannot apply this "confidence" number to one particular lab report. For example if the lab reports an interval of "100.5 to 102.0 grams" , you cannot assert that there is a 0.95 probability that the true mass of that sample is in the interval 100.5 to 102.0 grams. For example, suppose the lab uses different measuring instruments on small samples and large samples. One of their instruments might be more reliable than the other. The 0.95 probability is not based on analyzing the behavior of the lab in enough detail to account for such a situation. It is only based on data about how often the lab was correct or incorrect.
A typical statistical version of "confidence" is analogous to the above example. You assume the population comes from a specific family of distributions (e.g. a binomial, or a gaussian). You pick a particular algorithm that computes an estimate of one of the parameters of the distribution in the form of an interval. You compute the probability that the algorithm produces an interval containing the true value of the parameter. This probability is the "confidence" associated with the estimate. (It is often possible to compute this probability only knowing the family of distributions that are involved. You don't need to assume a specific numbers for the true value of the population's distribution parameters.)
Just as in the empirical example, if you are using an algorithm that produces 95% confidence intervals, then you cannot claim that there is a 95% probability the the true value of the parameter is in one particular interval. For example if you are using a algorithm that works with 95% confidence to estimate the ratio of red to black cards and the algorithm produces the interval ( 0.47, 0.49) from your sample data, you can't claim that there is a 0.95 probability that population ratio is in that interval.
Math problems involving the same formulas can be posed in various ways, by changing which values are "given" and which are solved for. The common way to pose a "confidence interval" problem is state the estimation algorithm and the desired confidence as givens (e.g. 95%) and to solve for the number of samples needed to produce intervals that will give the estimate that level of confidence. That's the approach other posters have suggested.
Bayesian Statistics
The above methods are those of "frequentist" statistics, the type of statistics taught in most introductory courses. Essentially, frequentist statistics only tells you numbers that characterize the probability of the data given some assumption about the population distribution. It doesn't tell you the probability that some fact about the population is true given the observed data. (There is a difference in meaning between Pr(A|B) and Pr(B|A) and the two need not be numerically equal.)
If you want to solve for something like "The probability that the ratio of red to black cards in the population is in the interval (0.47, 0.49) given the observed data" then you have to assume a scenario where there is something probabilistic about how the population ratio came into being. If you don't assume such a scenario, there isn't enough given information to solve for such a probability.
Bayesian Statistics involves making assumptions about how the population parameters were selected from some distribution, called the "prior distribution". If you want to compute the answer to the question in the previous paragraph, you'll have to use Bayesian statistics.
Sci Advisor P: 1,168 Nice explanation, Stephen Tashi, you've been accepted into my 'Favorites' links.
Homework Sci Advisor HW Helper Thanks P: 8,912 Yes, very good Stephen. Just some elaboration on Bayesian stats... The Bayesian approach requires you to say what you would have guessed about the ratio before you did the experiment. How likely was it to be 50:50?, 60:40?, and so on. I.e. an entire probability distribution for the ratio. The result of the experiment revises that curve to give you a new distribution. The more data you collect, the less your original assumptions matter - within reason. Soapbox alert. Classical hypothesis testing hides the need to do this by making you pick an acceptance region. In my view, hiding it this way too often leads to poor choices of that.
Sci Advisor P: 1,168 Still, Stepen Tashi, the Chi-Squared test does not seem to fall in either of your categories, since the test, as I understand it, makes no assumption about the distribution of any sample statistic.
HW Helper P: 2,115 Why all this talk about defective scales and unknown distributions? We know this is a binomial distribution. The only trouble is conditional probability, but that cannot be eliminated. No amount of trials can confirm a model, but we can become increasingly sure that if the model is wrong we have observed an unlikely event.
P: 3,086
Quote by Bacle2 Still, Stepen Tashi, the Chi-Squared test does not seem to fall in either of your categories, since the test, as I understand it, makes no assumption about the distribution of any sample statistic.
A common form of the chi-square test involves computing a statistic that depends on the difference between the observed frequency and the "theoretical" frequency. So when you assume a certain "theoretical" frequency, you make an assumption about the distribution of the population.
P: 3,086
Quote by lurflurf Why all this talk about defective scales and unknown distributions? We know this is a binomial distribution.
It is "a binomial distribution" the sense of being from that family of distributions. We don't know which particular binomial distribution it is.
The only trouble is conditional probability, but that cannot be eliminated. No amount of trials can confirm a model, but we can become increasingly sure that if the model is wrong we have observed an unlikely event.
I don't know which defective scales and conditional probably you are talking about - and which model.
It's interesting to me that answers to statistical questions, on this and other math forums, are often granted a kind of exception to the standards of mathematics that are applied to other questions. Incorrect or imprecise statements in questions (and answers) about linear algebra, topology, and real analysis are usually set straight by some interested party. With statistics, we often see the original posters imprecise question quickly interpreted as specific kind of textbook statistics problem and answered that way.
I prefer to get the original question clarified. I don't claim this approach has any bottom line superiority. I suspect that most people who ask imprecise statistical questions, would eventually settle for some textbook way of posing their problem. It takes a very mathematically sophisticated mind to tranlsate practical problems into questions involving probability. Approaching real world problems also requires a tolerance for detail and complication. Most questioners aren't likely to exert that much effort.
A person who posted in the physics section and asked "What is the best way to build a perpertual motion machine to provide electricity to lower my electric bills?" would get a predictable reception. He would be set straight (and perhaps not so gently) about the conservation of energy and the difference between perpetual motion and the motion that produces usable work. A person in the math section asking a question like "How many random samples from an urn would I need to be sure that an urn contains exactly as many black balls as white balls?" is asking a question that is just as intellectually outrageous as the question about perpetual motion. However, it's common to hear this and similar outrageous questions in the field of statistics, so I suppose the questioners should be given more slack.
Sci Advisor P: 1,168 Sorry for my previous nonsensical comment. I was thinking of Mann-Whitney's U-test, which is non-parametric, and I mistakenly wrote about the Chi-squared . It is too late to edit, so I am just writing a correction.
Sci Advisor P: 3,086 True, the Mann-Whitney U-test doesn't assume that two populations have any specific distribution. The null hypothesis is that the two populations have the same (unspecified) distribution. However, this does amount to assuming a specific distribution for the statistic (the rank sum).
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http://stats.stackexchange.com/questions/18972/drawing-from-a-conditional-density/23721 | # Drawing from a conditional density
I have a simple question. Suppose $X=(X_1,X_2,X_3)$ is multivariate normal. What's the best (quickest) way to draw from the conditional density $X_1\mid \exp(X_1)+\exp(X_2)+X_3$?
-
This is not a simple question. Have you derived the conditional density by the Jacobian formula? – Xi'an Nov 26 '11 at 7:08
Define a Markov chain like this.
1. Start with any point $x=(x_1,x_2,x_3)\in\mathbb{R}^3$ that satisfies $e^{x_1}+e^{x_2}+x_3=r$.
2. Draw independent $e_i\sim N(0,\epsilon_i)$, and define $z_i=x_i+e_i$, for $i=1,2,3$.
3. Define $$(u_1,u_2,u_3)=\left( \frac{r\,e^{z_1}}{e^{z_1}+e^{z_2}+z_3}, \frac{r\,e^{z_2}}{e^{z_1}+e^{z_2}+z_3}, \frac{r\,z_3}{e^{z_1}+e^{z_2}+z_3}\right) \, .$$
4. Define $y=(y_1,y_2,y_3)=(\log u_1,\log u_2, u_3)$. It's clear that $e^{y_1}+e^{y_2}+y_3=r$.
5. Accept this proposal point $y$ as the next value of the chain with probability $\min \left\{ \frac{f(y)}{f(x)},1 \right\}$, where $f$ is the multivariate normal density, or reject the proposal and keep the old value of $x$ as the next value of the chain.
6. Repeat from step 2 with the new value of the chain playing the role of $x$.
The first coordinate of each value of this Markov chain will have as equilibrium distribution exactly what you need. You should discard the first, say, $5000$ thousand values of the chain, which correspond to the so called burn-in period. You have to find small values for the $\epsilon_i$'s that make the Markov chain mix properly. Large values of the $\epsilon_i$'s will make you reject all the proposals. My sugestion is to target an acceptance rate of about $50\%$ and do a graphical monitoring of the chain.
I've just seen on the bookstore the book "Monte Carlo Statistical Methods" by Robert and Casella that explain all you need to know to justify this Random Walk Metropolis Algorithm.
Good luck!
P.S. As clarified latter by cardinal, Prof. Robert is our fellow user Xi'an, who posted the first answer to this question!
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I've just seen on the bookstore a couple of amazing books on MCMC by some guy named Robert: Is this a joke? Here's a fun idea: Click on the user name of Xi'an (the first commenter to the OP in this thread) and follow the link to his blog. – cardinal Feb 27 '12 at 15:04
Cool! I didn't know that Xi'an = Prof. Robert.Thanks, cardinal! – Zen Feb 27 '12 at 16:42
You're welcome. The juxtaposition is great! I'm sure the honest commentary makes Xi'an (rightfully) feel good. – cardinal Feb 27 '12 at 17:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8674448132514954, "perplexity": 825.6357928608612}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928076.40/warc/CC-MAIN-20150521113208-00023-ip-10-180-206-219.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/827072/finding-an-equation-of-circle-which-passes-through-three-points | # Finding an equation of circle which passes through three points
How to find the equation of a circle which passes through these points $(5,10), (-5,0),(9,-6)$ using the formula $(x-q)^2 + (y-p)^2 = r^2$.
I know i need to use that formula but have no idea how to start, I have tried to start but don't think my answer is right.
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Can you share what you've tried, and explain what you're having trouble with? You have three data points, and three variables to solve for. – user61527 Jun 8 '14 at 17:48
So far i have the following but it just doesn't seem to sit right with me as being correct Sqareroot[(9-5-5)^2 + (-6-0-10)^2] and that would be the radius – help Jun 8 '14 at 18:14
I know i need to use that formula but have no idea how to start
\begin{equation*} \left( x-q\right) ^{2}+\left( y-p\right) ^{2}=r^{2}\tag{0} \end{equation*}
A possible very elementary way is to use this formula thrice, one for each point. Since the circle passes through the point $(5,10)$, it satisfies $(0)$, i.e.
$$\left( 5-q\right) ^{2}+\left( 10-p\right) ^{2}=r^{2}\tag{1}$$
Similarly to the second point $(-5,0)$:
$$\left( -5-q\right) ^{2}+\left( 0-p\right) ^{2}=r^{2},\tag{2}$$
and to $(9,-6)$:
$$\left( 9-q\right) ^{2}+\left( -6-p\right) ^{2}=r^{2}.\tag{3}$$
We thus have the following system of three simultaneous equations and the three unknowns $p,q,r$:
$$\begin{cases} \left( 5-q\right) ^{2}+\left( 10-p\right) ^{2}=r^{2} \\ \left( -5-q\right) ^{2}+p^{2}=r^{2} \\ \left( 9-q\right) ^{2}+\left( 6+p\right) ^{2}=r^{2} \end{cases}\tag{4}$$
To solve it, we can start by subtracting the second equation from the first
$$\begin{cases} \left( 5-q\right) ^{2}+\left( 10-p\right) ^{2}-\left( 5+q\right) ^{2}-p^{2}=0 \\ \left( 5+q\right) ^{2}+p^{2}=r^{2} \\ \left( 9-q\right) ^{2}+\left( 6+p\right) ^{2}=r^{2} \end{cases}$$
Expanding now the left hand side of the first equation we get a linear equation
$$\begin{cases} 100-20q-20p=0 \\ \left( 5+q\right) ^{2}+p^{2}=r^{2} \\ \left( 9-q\right) ^{2}+\left( 6+p\right) ^{2}=r^{2} \end{cases}$$
Solving the first equation for $q$ and substituting in the other equations, we get
$$\begin{cases} q=5-p \\ \left( 10-p\right) ^{2}+p^{2}-\left( 4+p\right) ^{2}-\left( 6+p\right) ^{2}=0 \\ \left( 4+p\right) ^{2}+\left( 6+p\right) ^{2}=r^{2} \end{cases}$$
If we simplify the second equation, it becomes a linear equation in $p$ only
$$\begin{cases} q=5-p \\ 48-40p=0 \\ \left( 4+p\right) ^{2}+\left( 6+p\right) ^{2}=r^{2} \end{cases}$$
We have reduced our quadratic system $(4)$ to two linear equations plus the equation for $r^2$. From the second equation we find $p=6/5$, which we substitute in the first and in the third equations to find $q=19/5$ and $r^2=1972/25$, i.e
$$\begin{cases} q=5-\frac{6}{5}=\frac{19}{5} \\ p=\frac{6}{5} \\ r^{2}=\left( 4+\frac{6}{5}\right) ^{2}+\left( 6+\frac{6}{5}\right) ^{2}= \frac{1972}{25}. \end{cases}\tag{5}$$
So the equation of the circle is
\begin{equation*} \left( x-\frac{19}{5}\right) ^{2}+\left( y-\frac{6}{5}\right) ^{2}=\frac{1972}{25}. \end{equation*}
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Suppose the points are $A,B,C$. Then intersect the equations of perpendicular bisectors of $AB$ and $BC$. This is the center of the desired circle. (with your notation $(p,q)$)
Now calculate the distance between $(p,q)$ and $A$. Now $r$ is also found.
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$\begin{vmatrix} x^2+y^2&x&y&1\\ 5^2+10^2&5&10&1\\ (-5)^2+0^2&-5&0&1\\ 9^2+(-6)^2&9&-6&1\\ \end{vmatrix}= \begin{vmatrix} x^2+y^2&x&y&1\\ 125&5&10&1\\ 25&-5&0&1\\ 117&9&-6&1\\ \end{vmatrix} = 0$
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The simplest answer. – whatever Jun 8 '14 at 20:12
what does it say ? – Fardad Pouran Jun 8 '14 at 21:00
if the problem has a solution (the three points are on a circle) then you only need to calculate the equations of the two mediators and the intersection should be the center and the distance between one of the points and this center gives you r.
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Perhaps you could show how? At least show some guidelines. – user88595 Jun 8 '14 at 18:19
This method that I wrote creates a circle object which has a radius and a centre point. (written in Objective-C but can be port to many other languages)
- (Circle*)findCirclePassingThroughPoint1:(CGPoint)point1 point2:(CGPoint)point2 point3:(CGPoint)point3{
double x1 = point1.x; double x2 = point2.x; double x3 = point3.x;
double y1 = point1.y; double y2 = point2.y; double y3 = point3.y;
double mr = (y2-y1) / (x2-x1);
double mt = (y3-y2) / (x3-x2);
if (mr == mt) {
return nil;
}
double x = (mr*mt*(y3-y1) + mr*(x2+x3) - mt*(x1+x2)) / (2*(mr-mt));
double y = (y1+y2)/2 - (x - (x1+x2)/2) / mr;
double radius = pow((pow((x2-x), 2) + pow((y2-y), 2)), 0.5);
CGPoint center = CGPointMake(x, y); | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9217535257339478, "perplexity": 620.6430039752995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281363.50/warc/CC-MAIN-20160524002121-00157-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.wordaz.com/Dense.html | # Definition of Dense. Meaning of Dense. Synonyms of Dense
Here you will find one or more explanations in English for the word Dense. Also in the bottom left of the page several parts of wikipedia pages related to the word Dense and, of course, Dense synonyms and on the right images related to the word Dense.
## Definition of Dense
Dense
Dense Dense, a. [L. densus; akin to Gr. ? thick with hair or leaves: cf. F. dense.] 1. Having the constituent parts massed or crowded together; close; compact; thick; containing much matter in a small space; heavy; opaque; as, a dense crowd; a dense forest; a dense fog. All sorts of bodies, firm and fluid, dense and rare. --Ray. To replace the cloudy barrier dense. --Cowper. 2. Stupid; gross; crass; as, dense ignorance.
## Meaning of Dense from wikipedia
- in the density of the heated fluid, which causes it to rise relative to denser unheated material. The reciprocal of the density of a substance is occasionally...
- Dense granules (also known as dense bodies or delta granules) are specialized secretory organelles. Dense granules are found only in platelets and are...
- related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of...
- Dense breast tissue, also known as dense ****, is a condition of the **** where a higher proportion of the **** are made up of glandular tissue...
- In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges...
- 1137/0218003. Charikar (2000). "Greedy approximation algorithms for finding dense components in a graph". In Klaus Jansen; Samir Khuller (eds.). APPROX '00:...
- PIM-SM generally scales fairly well for wide-area usage. PIM Dense Mode (PIM-DM) uses dense multicast routing. It implicitly builds shortest-path trees...
- Dense connective tissue, also called dense fibrous tissue, is a type of connective tissue with fibers as its main matrix element. The fibers are mainly...
- Dense Pack is a strategy for basing intercontinental ballistic missiles (ICBMs) for the purpose of maximizing their survivability in case of a surprise...
- partial order or total order < on a set X {\displaystyle X} is said to be dense if, for all x {\displaystyle x} and y {\displaystyle y} in X {\displaystyle... | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9226412177085876, "perplexity": 3435.1658399959324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358323.91/warc/CC-MAIN-20211127223710-20211128013710-00300.warc.gz"} |
http://tex.stackexchange.com/questions/553/what-packages-do-people-load-by-default-in-latex?answertab=oldest | # What packages do people load by default in LaTeX?
I'm getting the impression from reading the answers written by some of the real experts here that there are quite a few little packages that just tweak LaTeX2e's default behaviour a little to make it more sensible here and there.
Rather than try to pick these up one by one as I read answers to questions (and thus risk missing them), I thought I'd ask up front what LaTeX2e packages people load by default in (almost) every document.
As this is a "big list" question, I'm making it CW. I don't know if there are standard rules across all SE/SO sites for such questions, but on MathOverflow the rule is generally: one thing (in this case, package) per answer. I guess that if a couple of packages really do go together then it would be fine to group them.
This is perhaps a little subjective and a little close to the line, so I'll not be offended if it gets closed or voted down! (But please explain why in the comments.)
Also see our community poll question: “I have used the following packages / classes”
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Personally, I'd find a single list, separated by headings (Ex. Format, Math, Bib,Images, Other for this question), with a list of everyone's packages and how they're different from other packages in the section much more readable and useful. That amsmath is the highest voted just says that the MO community is here in full force. The less-known, but equally relevant formatting packages linked by Vivi, Joseph, and András are invisible without a lot of scrolling and reading. – Kevin Vermeer Jul 29 '10 at 22:37
I think the list of one package per answer is a good idea, as we can vote on individual packages... – Amir Rachum Jul 30 '10 at 11:30
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The family of AMS math packages. At least amsmath and amssymb. Also amsthm if I need theorems and the class I'm using doesn't already define them.
Particularly for writing equations, the AMS packages define a rich set of environments to group and align formulas in many different and useful ways. I also like that it encourages the use of semantic commands (e.g. the cases environment) over syntactic commands (e.g. a \left\{ followed by an array).
Its documentation can be found running texdoc amsldoc on a command line.
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In particular, amsthm provides an easy way to set up different theorem styles, amsmath provides the \text command, and amssymb contains several often-used symbols. – András Salamon Jul 29 '10 at 12:40
+1 for the (oblique) reference to texdoc. I only discovered that recently and I wonder how I ever lived without it! – Andrew Stacey Jul 29 '10 at 18:08
I believe amssymb loads amsfonts. There's rarely any need to load it yourself. – TH. Sep 11 '10 at 9:13
Note that the ams math packages are loaded automatically if you use one of their document classes, such as amsart. – Erik P. Jan 18 '12 at 19:08
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Edited by doncherry: Removed packages mentioned in separate answers.
I use TeX for a variety of documents: research papers, lectures/tutorials, presentations, miscellaneous documents (some in Japanese). Each of these different uses, requires different packages.
Depending on my mood, I like to use different fonts. A particular nice combination for mathematics papers is
\usepackage[T1]{fontenc} % better treatment of accented words
\usepackage{eulervm} % Zapf's Euler fonts
\usepackage{tgpagella} % TeXGyre Pagella fonts
For references,...
\usepackage[notref,notcite]{showkeys} % useful when writing the paper
\usepackage[noadjust]{cite} % [1,2,3,4,5] --> [1-5] useful in hep-th!
For lecture notes (again mathematical) I often like to section the document into "lectures" instead of sections and to add some colours to the titles,.... To do this it's useful to use
\usepackage{fancyhdr} % fancy headers
\usepackage{titlesec} % to change how sections are displayed
\usepackage{color} % to be able to do this in colour
and I also like to decorate using some silly glyphs, for which these fonts are useful:
\usepackage{wasysym,marvosym,pifont}
and also box equations and other things
\usepackage{fancybox,shadow}
I like adding pictures, whence
\usepackage[rflt]{floatflt}
\usepackage{graphicx,subfigure,epic,eepic}
You may want to hide the answers to tutorial exercises, problems,... and this can be achieved with
\usepackage{version,ifthen} % ifthen allows controlling exclusions
I use XeLaTeX for documents containing Japanese, which works better with
\usepackage{fontspec} % makes it very easy to select fonts in XeLaTeX
\usepackage{xunicode} % accents
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As the question suggested, could you write an answer per package/topic and explain what these packages do or why do you need them? – Juan A. Navarro Jul 29 '10 at 10:51
can you please add comments like \ usepackage{foo} % to get following features within your code? – Dima Jul 29 '10 at 11:06
To avoid breaking them up all the way, you could try grouping them a little (say, if there's one package that you wouldn't consider using without another one then put them together). – Andrew Stacey Jul 29 '10 at 13:04
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Nothing surprising here: I use natbib, hyperref and hypernat together.
Natbib for referencing.
Hyperref adds bookmarks for sections and lists and turns references and urls into links.
Hypernat allows natbib and hyperref to work together.
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I'm pretty sure that hypernat is superfluous these days. With only loading natbib and hyperref I get references as [1-5] with both 1 and 5 being hyperlinks. – Lev Bishop Aug 8 '10 at 14:51
And? Was it superfluous in 2010? Is it now? ;) – K.-Michael Aye Nov 23 '12 at 5:18
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Another package I use is float. It allows for the placement H for floats, which is somewhat equivalent to h!, but a bit stronger, making sure the figure or table goes exactly where I want it to be.
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\usepackage[parfill]{parskip}
I much prefer no indentation and space between paragraphs, so the parskip package is a must for me!
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Have a look at the KOMA-Script-classes - they include a parskip option that is more powerful than the package of the same name. – lockstep Aug 8 '10 at 17:39
I use hyperref for setting PDF metadata and to create links, both within the document and for clickable URLs. Even Elsevier has used urlbst to update their bibliography style to support URLs and DOIs; hyperref does the actual work of rendering url = and doi = BibTeX fields into clickable PDF links.
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The 'rich' document classes such as memoir and KOMA-Script include a lot of functionality that is not available from the LaTeX kernel. So the packages you load when using the article class might be rather different from those when using memoir. A lot of packages that get used by many people with the base classes (things like float, caption, tocbibind and titlesec) are covered by the richer document classes.
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\begin{gripe} My problems with these richer document classes are that it makes it very difficult to pick and choose, and that it is a major pain when Big Shot Journal says "please rewrite your document to use our class file" (there's even a journal that won't let you send an accompanying style file). \end{gripe} – Andrew Stacey Jul 29 '10 at 13:19
I tend to stick to article + packages, myself, so I can sympathise. All the more reason for me to get on and get LaTeX3 finished, so we can have a good set of abilities out of the box! – Joseph Wright Jul 29 '10 at 14:33
\begin{joke} Then stop wasting time here and get on with it! \end{joke} – Andrew Stacey Jul 29 '10 at 18:11
If only it were that easy :-) If you want to see that things are happening, there is an RSS feed for SVN checkins: latex-project.org/latex3svn.rss – Joseph Wright Jul 29 '10 at 21:36
That gripe seems a gripe with the journals, rather than with the rich document classes. Also, if you're writing a journal article, memoir doesn't seem like an obvious way to go, if you are going to end up having to conform to some journal's style eventually. Again, that's not an issue with rich document classes, that's just a matter of picking the right tool for the job. And for journal submissions, minimal package requirements and basic document classes seems a good modus operandi – Seamus Aug 1 '10 at 10:41
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I almost always load microtype. It plays with ever-so-slightly shrinking and stretching of the fonts and with the extent to which text protrudes into the margins in a way that yields results that look better, that have fewer instances of hyphenation, and fewer overfull hboxes. It doesn't work with latex, you have to use pdflatex instead. It also works with lualatex and (protrusion only) with xelatex.
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You may want to use \usepackage[stretch=10]{microtype}, which allows font expansion up to 1% (default is 2%). – lockstep Aug 6 '10 at 12:03
Can we have an example of with versus without? – levesque Nov 15 '10 at 18:28
there's a nice example in the documentation for microtype mirror.ctan.org/macros/latex/contrib/microtype/microtype.pdf, though it requires adobe acrobat for the inline examples – Noah Aug 12 '11 at 22:37
Here is another example. – Juri Robl Oct 11 '12 at 11:13
The only texts for which I don't use microtype are those set raggedright. It seems to maximally stretch practically all lines. In any case, ragged2e then becomes the must include package. – Christian Jun 27 '13 at 16:41
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One package that’s really general purpose is nag: It doesn’t do anything, per se, it just warns when you accidentally use deprecated LaTeX constructs from l2tabu (in German) (in English).
From the documentation:
Old habits die hard. All the same, there are commands, classes and packages which are outdated and superseded. nag provides routines to warn the user about the use of those. As an example, we provide an extension that detects many of the “sins” described in l2tabu.
Therefore, I now always have the following in my header (before the \documentclass, thanks qbi):
\RequirePackage[l2tabu, orthodox]{nag}
It’s a bit like having use strict; in Perl: a useful best practice.
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Somewhat better is \RequirePackage[l2tabu,orthodox]{nag} before \documentclass. The package docu also recommends this. – qbi Jul 29 '10 at 18:40
This package sounds useful. However, when I tested it with a large project, I started to get the message "Label(s) may have changed. Rerun to get cross-references right." no matter how many times I re-run Latex. – Jukka Suomela Jul 31 '10 at 9:36
Edited by doncherry: Removed packages mentioned in separate answers.
The complete header Part of my header for most of my documents looks as follows:
\documentclass[ngerman,draft,parskip=half*,twoside]{scrreprt}
\usepackage{ifthen}
For some things I need if-then-constructs. This package provides an easy way to realise it.
\usepackage{index}
For generating an index.
\usepackage{xcolor}
xcolor is needed by several packages. For some historical reason I load it manually.
\usepackage{babel}
\usepackage{nicefrac}
nicefrac allows typesetting fractions like 1/2. It is sometimes more readable than \frac.
\usepackage[T1]{fontenc}
\usepackage[intlimits,leqno]{amsmath}
\usepackage[all,warning]{onlyamsmath}
This package warns if non-amsmath-environments are used.
\usepackage{amssymb}
\usepackage{fixmath}
Provides ISO conform greek letters.
\usepackage[euro]{isonums}
Defines comma as decimal delimiter.
\usepackage[amsmath,thmmarks,hyperref]{ntheorem}
for Theorems, definitions and stuff.
\usepackage{paralist}
Improves enumerate and itemize. Also provides some compact environments.
\usepackage{svn}
I work with VCS and svn displays some informations (keywords) from SVN.
\usepackage{ellipsis}
corrects \dots
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
These are the definitions for absolute value and norm.
\SVN $LastChangedRevision$
\SVN $LastChangedDate$
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"one thing (in this case, package) per answer" – Jukka Suomela Jul 29 '10 at 19:02
Could you break this up into multiple answers please, so they can be voted on? Having a dozen answers is ok! – ShreevatsaR Jul 30 '10 at 14:41
It is usually recommended to load hyperref last. – Alex Hirzel May 1 '12 at 20:20
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Usually I write German texts. We have new and old rules for spelling. The package hyphsubst provides some new hyphenation pattern. That's why I load it in addition to babel:
\RequirePackage[ngerman=ngerman-x-latest]{hyphsubst}
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For mathematical texts I instead use amsmath & Co. One very useful package is onlyamsmath. I load it as
\usepackage[all,warning]{onlyamsmath}
So it looks for $$..$$, eqnarray and produces a warning if some of them are used. If you left out warning, it will result in an error and compile will stop. This package is normally very useful if you edit a text with many authors.
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I save my documents in an SVN repository. The svn package helps to extract some informations out of the version control system. The document has somewhere a hint what revision number and what date it is. For this you have to set svn keywords and declare in your LaTeX document what you need:
\SVN $LastChangedRevision$
\SVN $LastChangedDate$
Wihtin the document you can refer to that information with \SVNLastChangedRevision and \SVNDate.
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I use url to typeset urls.
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In addition to many packages already listed here, I always include mathtools. It provides implementations of \mathclap (and similar commands) as well as nice extensible arrow.
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\mathclap is great. I use it to great effect for things like \sum_{\mathclap{big long thing}}. (It's also amusingly named with at least one off-color meaning.) – TH. Aug 27 '10 at 9:36
\shortintertext is also provided by the \mathtools package and provids tighter vertical spacing compared to \intertext from the amsmath package. – Peter Grill May 2 '12 at 0:47
\usepackage{lmodern} % better i18n Postscript version of Knuth's cm fonts
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This question assumes you are making a LaTeX document for personal use. If you are planning to submit the document to a journal, it's safer to avoid using too many unusual classes, because they may be incompatible with the journal's LaTeX classes or may be incompatible with the style that the journal will impose on your paper. Very common packages like amsthm are usually safe. (I would leave this as a comment, but I don't have enough reputation yet.)
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Yes and no. Given that I rarely know what paper it is intended for when I start writing a paper, and given how useful some of these packages are, I include them all and try to get away with it! Sometimes I'm successful, sometimes I need to include the package .sty file along with my submission. – Andrew Stacey Aug 4 '10 at 7:03
The package xspace lets you define commands that don't eat up whitespace after them. So you can define an abbreviation like
\newcommand{\sA}{\mathcal{A}\xspace}
and then you can type objects of \sA are called widgets instead of objects of \sA\ are called widgets.
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On comp.text.tex there's a series of messages "xspace and italic correction" about spacing inconsistencies created by xspace. There, Will Robertson suggested "delimited macros" as an alternative to xspace. Using \newcommand* only to ensure that no existing command is overriden, the above example would look like this: \newcommand*{\sA}{}\def\sA/{\mathcal{A}} To quote Will Robertson: "In the source you must always type "\foo/" [here: "\sA/"] (or TeX will throw an error), and spaces after it won't be gobbled." – lockstep Aug 6 '10 at 15:04
The main advantage of \sa/ is that an error message will occur if you happen to forget the closing slash. On the contrary, if you happen to forget the closing backslash of \sA\ , you'll end with gobbled space without noticing it. – lockstep Aug 11 '10 at 20:50
I used xspace one time in a paper with other authors. It was a huge pain since some macros didn't behave like others. It led to all sort of confusion, especially when thinks like \foo bar no long work as you expect because \foo's definition ends with \xspace. I've never tried \foo/. The main advantage I see with that is if your macro is \m/... – TH. Aug 27 '10 at 9:32
I don't especially like the look of \sA/ but I can't think of a better delimiter to use. Perhaps a semicolon would be fine (after HTML): \sA;. My personal belief is that non-delimited macros without arguments (i.e., the ones that gobble spaces) are just plain wrong for document commands because of the spacing problems. Even experienced LaTeX authors trip up with them. – Will Robertson Sep 2 '10 at 9:28
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I nearly always use the tikz package. Once you learn how to draw with it, you can do almost any vector graphic you need.
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You can produce almost any diagram with Tikz. Check the tikz examples page. texample.net/tikz/examples However, it is fairly complicated to get the hang on large diagrams since you have to type everything and nearly always you can't see what you are doing. But if you are using a Debian/KDE combination, you can use Ktikz/Qtikz which is really helpful since it compiles tikz code in real time. – fabikw Nov 16 '10 at 0:42
TikZ is awesome with a capital A. But load it by default? It takes up a lot of time and space. I would say only load it if you need it. – Matthew Leingang Nov 22 '10 at 12:53
@levesque: Tikz has a fairly steep learning curve, but it is beautifully documented and provides rich libraries. I find the vector graphics that I produce in tikz to be superior to those I produced in inkscape. It seems easier on my brain to stay in keyboard mode as well. – philosodad Dec 29 '10 at 4:56
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I have a whole slew of commands that that provide a nice short hand for standard idioms of mine. (and which if I ever share tex source would make someone grumpy if i made it a package)
So the meta habit is: whatever personal short hands you think would be nice, have them defined at the top of your template file!
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For papers on the arXiv (maths, physics and computer science mostly) there's a list of packages sorted by frequency of use.
The top twenty packages are:
1. article
2. graphicx
3. amssymb
4. amsmath
5. revtex
6. revtex4
7. epsfig
8. amsfonts
9. bm
10. latexsym
11. amsart
12. dcolumn
13. amsthm
14. graphics
15. aastex
16. amscd
17. epsf
18. color
19. aa
20. times
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Since my files nowadays has UTF-8 character encoding, I use this
\usepackage[utf8]{inputenc}
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XeLaTeX or LuaLaTeX would be my choice for this – Joseph Wright Aug 15 '10 at 13:05
Isn't it \usepackage[utf8x]{inputenc}? – Olivier Jul 19 '11 at 8:17
I've experienced several cases where utf8x had a symbol that utf8 hadn't – Mog Nov 24 '12 at 11:47
@Olivier: utf8 is LaTeX base, while utf8x comes from the ucs package. So utf8 is portable. – Martin Schröder Jun 27 '13 at 14:39
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To use the palatino font (it's just a nice looking font)
\usepackage[sc]{mathpazo}
Note that the old palatino package is deprecated.
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You should probably also load mathpazo with the [sc] option to get real small caps and better kerning. – Will Robertson Sep 2 '10 at 9:24
Depending on taste, you may want to use [osf] instead of [sc] to get old style numerals as well as the real small caps and better kerning. I for one find old style numerals prettier and classier than lining figures in text mode (using [osf] will keep lining figures in math mode). – spet May 29 '13 at 8:52
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To make sure you have ISO formated dates (YYYY-MM-DD).
\usepackage[english]{isodate}
or
\usepackage{datetime}
\renewcommand{\dateseparator}{-}
\newcommand{\todayiso}{\the\year \dateseparator \twodigit\month \dateseparator \twodigit\day}
-
I can't live without listings --- pretty-printing (colours, formatting and all) algorithms and code is indispensable --- in pretty much any programming languages and dialects under the sun. Plus, I can import a source file directly from the repository, and the latest version will be automatically rendered.
-
show 1 more comment
For citations and bibliographies, biblatex is the package of my choice. Key points:
• biblatex includes a wide variety of built-in citation/bibliography styles (numeric, alphabetic, author-year, author-title, verbose [full in-text-citations], with numerous variants for each one). A number of custom styles have been published.
• Modifications of the built-in or custom styles can be accomplished using LaTeX macros instead of having to resort to the BibTeX programming language.
• biblatex offers well-nigh every feature of other bibliography-related LaTeX packages (e.g. multiple/subdivided bibliographies, sorted/compressed citations, entry sets, ibidem functionality, back references). If a feature is not included, chances are high it is on the package authors' to-do list.
• The babel package is supported, and biblatex comes with localization files for about a dozen languages (with the list still growing).
• Although the current version of biblatex (2.7) still allows to use BibTeX as a database backend, by default it cooperates with Biber which supports bibliographies using Unicode. Biber (currently at version 1.7) is included in TeX Live and MiKTeX. Many features introduced since biblatex 1.1 (e.g., advanced name disambiguation, smart crossref data inheritance, configurable sorting schemes, dynamic datasource modification) are "Biber only".
-
Nevertheless one should append about the usage of biblatex that some papers do not accept its usage. See: Biblatex: submitting to a journal – strpeter Jan 16 at 9:25
A nice commenting environment is provided by the package:
\usepackage{verbatim}
For debugging purposes I find this package indispensable. Before I found this package I would have to enter % before each line I wished to comment. The environment works as follows:
\begin{comment}
Text in this environment will be ignored by LaTeX.
\end{comment}
The packages
\usepackage{comment}
\usepackage{xcomment}
provide even greater commenting capabilities (i.e. the ability to selectively typeset certain environments) though I personally haven't had much use for these extended features.
-
In any decent editor, you can easily comment out/in several lines at once. Due to that, I find the usefulness of the comment environment greatly reduced – i.e. I don’t use it at all. – Konrad Rudolph Sep 11 '10 at 8:14
I simply use \newcommand{\comment}[1]{}. Put \comment{ before the block and } after to comment out any part of the file. – András Salamon Sep 11 '10 at 10:45
show 1 more comment
The todonotes package is a must have in all my documents.
\usepackage{todonotes}
The package enables you to insert small notes in the text marking things to do in the document. Something like
\todo{Rewrite this answer \ldots}
At any location in the document a list of the inserted notes can be generated with the
\listoftodos
command.
-
For multiuser comment support, and configurability with regard to the kinds of notes/themes available, the fixme package is quite nice (I use it quite regularly). – Mark Mar 25 '11 at 22:29
show 5 more comments
\usepackage[scaled=0.8]{luximono}
which is a fixed-width font which supports boldface. This is useful when typesetting source code.
-
\usepackage[margin=1in]{geometry} % set page margins automatically
This is generally poor style. The design of the page is pretty involved and lots of thought has went into (La)TeX's default designs. If you're interested in just saving paper, consider the packages savetrees or fullpage. – Quadrescence Apr 16 '11 at 23:15
Both savetrees and fullpage change other things too; Anyway, the point of of the answer is that geometry is a must use package, no matter what margins you choose for it. The appropriateness of 1in margins also depends on the kind of documents you produce. – Alan Munn Apr 16 '11 at 23:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8303930759429932, "perplexity": 4006.776011738726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678678233/warc/CC-MAIN-20140313024438-00005-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://forum.mackichan.com/node/234 | ## Font style times!
Hello everyone,
I use scientific WorkPlace version 5 to write papers that contain both text and mathematics. I have added the following packages: amsmath, amsfonts, amssymb, eurosym, harvard,setspace, footmisc, color, geometry and caption. My problem:
I should use the font style Times. I actually do not know what my current font style is. However, it does not look like Times. How can I change the font style for my whole article (both text and mathematics) to Times? I have tried to add the additional packages "times" or/and "mathptmx" and if I then typeset the file to pdf it will be told that there is a fatal error and the pdf cannot be completed. What is wrong? What should I do?
Thanks a lot for your help!
Best regards!
### Hi George, 1. I have to fit
Hi George,
1. I have to fit the following journal requirements regarding Page Layout and Spacing:
- Indent all paragraphs except those following a section heading. (fulfilled)
- An indent should be at least 10 em-spaces. This is what I am asking.
2. It's OK.
3. Do you mean that if I have 12 pt in the main text then the font size in the footnotes is automatically adjusted to 10pt?
### Hi George, Thank you very
Hi George,
Thank you very much for your quick answer. Indeed, I use Windows 7. I have downloaded the updated patch. If I want to times font style for both text and mathematics in my paper, which package should I add? times or mathptmx or both or something else? Are these times packages in conflict with anyone of my existing font packages, and do I have to remove these packages before I add times package(s)? Should I also add a line like \usepackage{mathptmx} in the preamble?
### Hi, I still have some
Hi, I still have some questions:
1. What do I have to do to ensure that the indent is at least 10 em-spaces?
2. I have added the package setspace and have set single-space in the category line spacing. Does it mean that the footnotes and the citations in the reference section are thus single-spaced? If not, what should I do?
3. I have choosen font size 12 pt as the body text point size in the class options. But the footnotes must have 10 pt. What should I do?
Thanks a lot!
### None of your questions can be
None of your questions can be answered without knowing the underlying typesetting specification.
1. What indent?
2. Most typesetting specifications use single spacing as the basic line spacing, so using setspace with the single line option shouldn't be necessary.
3. Probably nothing.
Post a sample document if you still need help.
### If you are compiling for DVI,
If you are compiling for DVI, then you can use the mathtime package with the No TS1 option and both text and math will use Times New Roman. The mathtime package was developed by Kinch to work with the TrueTeX Previewer. See the online help (use Help, Search and find the mathtime package index entry and topic) which includes links to the TrueTeX documentation for the mathtime package.
If you are compiling for PDF, then you can use the mathptmx package to use Times New Roman for both text and math.
Adding a \usepackage command to the document preamble is the same as using Typeset, Options and Packages and the package options tab to add a package. The next time you open the document the package will appear in this dialog rather than in the document preamble.
In general, font packages conflict, so the actual packages being used would need to be known to determine if there is a conflict. I would expect the last package listed to select the font, but there could be LaTeX errors generated when using multiple font packages.
### You must be using Version
You must be using Version 5.0 with Windows Vista or Windows 7 and have not applied the patch that fixes problems that were introduced by updated fonts in those versions of Windows. After following the instructions in the section Ligature issues with OpenType fonts in the article at http://www.mackichan.com/techtalk/737.htm you can then use the times package when compiling for DVI or PDF or the mathptmx package when compiling for PDF. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9407497048377991, "perplexity": 2055.340836782611}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400196999.30/warc/CC-MAIN-20200920062737-20200920092737-00129.warc.gz"} |
https://hal-insu.archives-ouvertes.fr/insu-03198834 | # Intermittency of Velocity Circulation in Quantum Turbulence
Abstract : The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation is quantized, taking discrete values that are directly related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loops, the circulation provides a measure of the dependence of the flow structure on the considered scale. Here, we consider the scale dependence of circulation statistics in quantum turbulence, using high-resolution direct numerical simulations of a generalized Gross-Pitaevskii model. Results are compared to the circulation statistics obtained from simulations of the incompressible Navier-Stokes equations. When the integration path is smaller than the mean intervortex distance, the statistics of circulation in quantum turbulence displays extreme intermittent behavior due to the quantization of circulation, in stark contrast with the viscous scales of classical flows. In contrast, at larger scales, circulation moments display striking similarities with the statistics probed in the inertial range of classical turbulence. In particular, we observe the emergence of the power-law scalings predicted by Kolmogorov's 1941 theory, as well as intermittency deviations that closely follow the recently proposed bifractal model for circulation moments in classical flows. To date, these findings are the most convincing evidence of intermittency in the large scales of quantum turbulence. Moreover, our results strongly reinforce the resemblance between classical and quantum turbulence, highlighting the universality of inertial-range dynamics, including intermittency, across these two a priori very different systems. This work paves the way for an interpretation of inertialrange dynamics in terms of the polarization and spatial arrangement of vortex filaments.
Keywords :
Document type :
Journal articles
https://hal-insu.archives-ouvertes.fr/insu-03198834
Contributor : Nathalie Pothier Connect in order to contact the contributor
Submitted on : Thursday, April 15, 2021 - 10:53:23 AM
Last modification on : Tuesday, October 19, 2021 - 7:00:15 PM
Long-term archiving on: : Friday, July 16, 2021 - 6:22:49 PM
### File
PhysRevX.11.011053.pdf
Publication funded by an institution
`
### Citation
Nicolás P. Müller, Juan Ignacio Polanco, Giorgio Krstulovic. Intermittency of Velocity Circulation in Quantum Turbulence. Physical Review X, American Physical Society, 2021, 11 (1), ⟨10.1103/PhysRevX.11.011053⟩. ⟨insu-03198834⟩
Record views | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.826195478439331, "perplexity": 1681.4169122459784}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588244.55/warc/CC-MAIN-20211027212831-20211028002831-00025.warc.gz"} |
http://tex.stackexchange.com/questions/1512/pause-messes-up-the-page-layout/73729 | # \pause messes up the page layout
I'm having a frame in beamer which compiles just right when I do not use pauses (\pause). However, when I pause the different list items, the last items do not appear on the frame anymore (actually, they are outside the frame viewable part). It seems in some way beamer has some problem calculating how to fit the different items on the page when pauses are included.
Any idea how to avoid this problem?
EDIT : Some source code exhibiting the problem :
\documentclass[slidetop,11pt]{beamer}
\begin{document}
\begin{frame}{Kubo-Greenwood Transport Formalism : Derivation}
Mott Method :
\begin{itemize}
\pause \item Electric field :
\footnotesize
\begin{equation*}
E(t) = E_0 cos(\omega t) u_x
\end{equation*}
\normalsize
\pause \item Coulomb gauge ($E=\delta A / \delta t$) :
\footnotesize
\begin{equation*}
A(t) = -\frac{E_0}{2 i \omega} (e^{i \omega t} - e^{-i \omega t}) u_x
\end{equation*}
\normalsize
\pause \item First order perturbation of H :
\footnotesize
\begin{equation*}
\delta \widehat{H} (t) = \frac{2e \widehat{P}.A(t)}{2 m} = e \widehat{V}.A(t) = -\frac{e E_0}{2 i \omega}(e^{i\omega t} - e^{-i \omega t}) \widehat{V}_x
\end{equation*}
\normalsize
\pause \item Transition from a state at t=0 to a state at t :
\footnotesize
\begin{equation*}
p_{nm} (t) = \frac{1}{\hbar^2} \left |\int_0^t d\tau e^{i(E_m-E_n) \tau / \hbar} \langle m|\delta \widehat{H}(\tau)|n \rangle \right |^2
\end{equation*}
\normalsize
\pause \item At long times :
\footnotesize
\begin{equation*}
\frac{p_{nm}(t)}{t} = \frac{2 \pi}{\hbar} \left(\frac{e2E_0}{2 \omega}\right)^2 \langle m|\widehat{V}_x|n \rangle \left[ \delta(E_m-E_n+\hbar \omega) + \delta(E_m-E_n-\hbar \omega)\right]
\end{equation*}
\normalsize
\end{itemize}
\end{frame}
\end{document}
And actually, thanks to your comment vanden to give a minimal amount of packages and comments, I managed to find the cause to this compilation error. It is the "\linespread{1.2}" command that messes things up when using \pause. If no fix available, I'll just comment it out I guess.
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Could you post some minimal compilable code that exhibits the problem? (I.e., just enough code that someone else can run it and observe your issue, with all packages and content not needed to make the issue occur removed.) – vanden Aug 11 '10 at 2:25
I edited as asked. And thanks for adding the pause tag, I tried but did not have enough reputation to create a new tag... – Nigu Aug 11 '10 at 3:00
There is special syntax for item's - I've never tried pause with lists for that reason, but my guess is that it's causing trouble. Try removing all the pauses and replace \begin{itemize} with
\begin{itemize}[<+->]
This causes each item to be uncovered one by one. For more fine-grained control, instead of the above change, use e.g.
\item<3->
To make an item appear on slides 3 and above. There are other variants, see the Beamer user guide.
-
Tested this, and it seems to fix it. – Neil Olver Aug 11 '10 at 4:59
Thank you. I heart of this syntax, but never used it... – Nigu Aug 11 '10 at 5:13
That's some curious behaviour you observed! There's nothing inherently wrong in the syntax you use – I'll explain below why the output goes awry nevertheless. Neil's suggestion to use \begin{itemize}[<+->] is a great alternative to \pause in your example. If you want to use \pause all the same, then there's an easy fix: adding an empty line (or a \par) before the offending \pauses will remove the additional vertical space, i.e., with
\pause\item
everything will be alright!
So, what causes the unwanted vertical space, and why on earth does an additional empty line remove the space? The problem is the combination of the displayed equation before and the \item after the \pause: after the display, TeX goes into horizontal mode, ready to build a new line of text. (This means that \lastskip is the last horizontal skip, which is 0pt; see below.) The \pause puts some \pdfliterals onto that line, and the \item ends it with a \par. This already gives one \baselineskip additional vertical space. On top of that, the \item adds an \itemsep (since \lastskip is 0pt after the \par, see also below).
Without the \pause, these vertical spaces do not appear: the line following the displayed equation remains empty, so the \par doesn't add a \baselineskip. Moreover, the last vertical skip \lastskip is now \belowdisplayskip (or \belowdisplayshortskip), which is greater than an \itemsep, and \item is designed to not add \itemsep in this case.
And why does an empty line (i.e., a \par) before the \pause help? It ends the line that TeX started after the display, bringing TeX into vertical mode. That line is still empty, so no \baselineskip is added! Moreover, in vertical mode, \lastskip is again the last vertical skip \belowdisplay(short)skip. Now \pause does some \unskip magic so that the \pdfliterals don't influence the \lastskip. Then \item issues another \par, but this doesn't do anything since TeX is already in vertical mode. Finally, \lastskip is still the same as without the \pause, so the \item doesn't add \itemsep, either.
In summary: \pause may go awry in horizontal mode (when TeX builds lines and paragraphs), but it's safe to use in vertical mode¹. That's why, a \par before a \pause can help in certain circumstances.
Just for the fun of it, here's a redefinition of \pause that looks ahead and inserts the \par automatically if it sees an \item (or a \par):
\makeatletter
\AtBeginDocument{%
\let\saved@pause\pause
\renewcommand\pause{\futurelet\pause@next@char\pause@i}%
\newcommand\pause@i{%
\ifx\pause@next@char\par\par\fi
\ifx\pause@next@char\item\par\fi
\saved@pause
}%
}
\makeatother
¹However, at the top of a \vtop box, when TeX is in internal vertical mode, \pause can cause problems.
- | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9892981052398682, "perplexity": 3754.046348454736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510273012.22/warc/CC-MAIN-20140728011753-00373-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://computergraphics.stackexchange.com/questions/12420/subsurface-scatteringreflection-from-layered-surfaces-due-to-subsurface-scatte | [Subsurface Scattering]Reflection from Layered Surfaces due to Subsurface Scattering
Recently, I am doing some research about subsurface scattering. i am a little confused about the backscattered radiance mentioned in this paper Reflection from Layered Surfaces due to Subsurface Scattering. I understand the light transfer equation, but i just cannot figure out why it has to be that form.
I don't know Why does it has to be ,there is a picture which can describe the radiance clearly:
Does anyone who have read that paper? I need some help
The factor $$e^{-\tau_d (1/\cos \theta_i + 1/\cos \theta_r)}$$ represents the attenuation of backscattered light due to the path it takes through the layer.
Imagine for a moment a layer of thickness 1. A ray passing through this layer from top to bottom at angle $$\theta$$ will then have a length of $$1/\cos \theta$$, which you can see by drawing a right triangle. This applies to both the incident and reflected rays, so the total path length of the ray within this layer is $$1/\cos \theta_i + 1/\cos\theta_r$$.
Multiply this by the optical thickness of the layer, $$\tau_d$$, and you have the optical thickness of the whole ray path; thus $$e^{-\tau_d (1/\cos \theta_i + 1/\cos \theta_r)}$$ is the attenuation factor along that path.
The other cosine factors out front and the $$1 -$$ in front of the exponential term, I'm guessing, probably arise from doing an integral over the depth of the layer, to account for scattering events at any depth in the layer. This often shows up when integrating exponentials: $$\int_0^{\tau_d} e^{-\tau \cdot \text{stuff}}\,d\tau = \frac{1}{\text{stuff}} \bigl(1 - e^{-\tau_d \cdot \text{stuff}} \bigr)$$ as long as the $$\text{stuff}$$ is independent of depth. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8483124375343323, "perplexity": 258.7317562083751}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300616.11/warc/CC-MAIN-20220117182124-20220117212124-00569.warc.gz"} |
https://www.physicsforums.com/threads/expand-integration-and-undesirable-points.213498/ | # Expand integration and undesirable points
1. Feb 6, 2008
### husseinshimal
The purpose behinde this post is an attempt to expand integration space to include functions with undesirable points where the function could be undefined.I need help to understand if this post makes sense.The main question here, is this way could be more general than using the measurement set theory to expand the integration?
Assume the function F(x),
F:[a,b]→R
We will put the interval[a,b] as acombination of subsets, UGk,
UGk=GNUGQUGQ̀....etc.(U,here stands for combination symbol) which stands for natural set,rational set ,irrational set,….etc.
Lets define the subsets,
өi={gk:F(xi)≥gk≥0},
xiЄ[a,b],
Let,(pi) be apartitoning of Gk in [a,b] and (pөi) apartitioning of(өi),
(Mөi=SUPөi), and (mөi=infөi),
(UFөi,pi)= Σi Mөi(xi-xi-1), (UFөi,pi)=upper darboux sum.
(LFөi,pi)= Σi mөi(xi-xi-1),(LFөi,pi)=lowe darboux sum.
(UFөi,pi,Pөi)=inf{UFөi:piPөi,(Pөi) partioning of(өi), (pi) partitioning of (Gk)},
(LFөi,pi,Pөi)=sup{LFөi:piPөi,(Pөi) partioning of(өi),(pi) partitioning (Gk)},
now, we put the integration in the form,
∫Fөi,over,Gk={0,UFөi}={0,LFөi}=the subsets,sөi,
∫F,over,[a,b]=Usөi
for example;
f(x):[0,1]→R,
f(x)=x , xЄ irrational numbers=Q̀, within[0,1],
f(x)=1,xЄ rational numbers=Q, within[0,1],
∫F,over,[o,1]={0,1\2}Q̀,U{0,1}Q={0,1\2}R,U,{1\2,1}Q , ,i.e,the integration would involve the real numbers within {0,1\2} plus the rational numbers within {1\2,1},(Q̀,Q and,R,are suffixes her and, U, stands for combination symbol.)
one might say it seems to be similar to the difference between Riemann integration and Lebesgue integration.
in Lebesgue integration,the above example would be, μ(0,1\2)inQ`set+μ(0,1)inQset=1\2+0=1\2,iam suggesting to keep integration in form of combination of subsets regardless they were countable or not.wouldnot this be more genral?
2. Feb 6, 2008
### HallsofIvy
Frankly, I'm not at all clear what you are doing. You seem to be staying with intervals with the exception of "undesirable points". If so, your integration is much weaker than Lebesque integration in which we can integrate over all measurable sets. Other than the fact that all countable sets have measure 0 and so are trivial in Lebesque integration, I don't see what "countable or not" has to do with it.
The Lebesque integral of your f (f(x)= x if x is irrational, 0 if rational, 0< x< 1) is trivially 1/2. I have no idea why you would worry about any "undesirable points".
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http://mathhelpforum.com/trigonometry/208259-trigonometric-hyperbolic-identities-print.html | # Trigonometric and Hyperbolic identities
• November 23rd 2012, 02:23 PM
boza100
Trigonometric and Hyperbolic identities
Question is as follows:-
Hence solve for t for values in the range 0 ≤ t ≤ 2 π rad:
5.5 Cos t + 7.8 Sin t = 4.5
Any help would be greatful, thanks
• November 23rd 2012, 03:10 PM
topsquark
Re: Trigonometric and Hyperbolic identities
Quote:
Originally Posted by boza100
Question is as follows:-
Hence solve for t for values in the range 0 ≤ t ≤ 2 π rad:
5.5 Cos t + 7.8 Sin t = 4.5
Any help would be greatful, thanks
Well it's a bit ugly but one approach would be to recall that $cos(t) = \sqrt{1 - sin^2(t)}$ and plug that in...
$5.5~\sqrt{1 - sin^2(t)} + 7.8~sin(t) = 4.5$
Isolate the radical and square it. This will give you a quadratic in sin(t) which you can solve using the quadratic formula. Check for extra, but not valid, solutions.
Also since in reality $cos(t) = \pm \sqrt{1 - sin^2(t)}$ you should also work through the negative solution as well. And again check your solutions with the original equation.
-Dan
• November 23rd 2012, 03:18 PM
MarkFL
Re: Trigonometric and Hyperbolic identities
Another approach would be to use a linear combination identity to write the equation as:
$\sqrt{5.5^2+7.8^2}\sin\left(t+\tan^{-1}\left(\frac{5.5}{7.8} \right) \right)=4.5$
$\sin\left(t+\tan^{-1}\left(\frac{55}{78} \right) \right)=\frac{45}{\sqrt{9109}}$
Now, after finding the quadrant IV solution, use the identity $\sin(\pi-x)=\sin(x)$ to get the quadrant III solution. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8556411862373352, "perplexity": 1196.0023881841375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678702045/warc/CC-MAIN-20140313024502-00012-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://brilliant.org/problems/an-algebra-problem-by-ayushi-gupta/ | # An algebra problem by ayushi gupta
Algebra Level pending
Marbles of diameter 1.4cm are dropped into a cylindrical beaker of diameter 7cm containing some water.Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm.
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http://math.stackexchange.com/questions/75807/how-do-i-prove-that-the-orthocenter-of-a-triangle-is-barycentre-of-its-vertices | # How do I prove that the orthocenter of a triangle is barycentre of its vertices?
Let's say I have a triangle $ABC$, the middle of the sides are called $A'$, $B'$ and $C'$.
I have proved that $\Omega$, the orthocenter of $ABC$, is the barycentre of $A'B'C'$ with masses $\tan \alpha$, $\tan \beta$ and $\tan \gamma$ on $A'$, $B'$ and $C'$. Now I have to deduce from this that $\Omega$ is also the barycentre of $A$, $B$ and $C$ with masses $a$, $b$ and $c$. I want to find $a, b, c$ so that $\Omega$ is the barycentre of $ABC$.
Thank you in advance!
-
I think this question is rather unclear as to what is being asked. Is my comment on the answer below essentially what is intended? If so the question needs to be modified accordingly. – Mark Bennet Oct 25 '11 at 18:21
I edited it, is that clearer like this ? – Skydreamer Oct 25 '11 at 18:43
It's not true that the orthocentre of $ABC$ is the barycentre of $A'B'C'$ with masses $\tan\alpha$, $\tan\beta$ and $\tan\gamma$. In a right triangle, the orthocentre is at the corner $C$ with the right angle, whereas that barycentre would be at $C'$, since $\tan\gamma$ goes to infinity. More generally, as long as all angles are acute, that barycentre would be within $A'B'C'$, wheras the orthocentre of $ABC$ doesn't have to be.
If your result were correct, it would be straightforward to obtain a corresponding mass distribution on $A$, $B$ and $C$: Move half the mass on the midpoints to each of the adjacent corners; that moves all the mass to the corners without moving the barycentre. So the result would be masses of $(\tan\alpha+\tan\beta)/2$ on $C$ etc.
For the correct barycentric coordinates of the orthocentre, see this Wikipedia section.
-
By what I recall, if $\omega$ is the orthocenter of a triangle and its barycenter, then, by $lal$, that the triangle is equilateral.
I think OP means that if there are masses $\tan \alpha$ etc at the vertices $A', B', C'$ then the barycentre of these is the orthocentre of triangle ABC, and wants to know what masses should be placed at A, B, C (up to a factor) so that the barycentre of those masses is also the orthocentre, using what he has already established. I think ... but the question is rather unclear, and I was going to post much the same as you. – Mark Bennet Oct 25 '11 at 18:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9589329361915588, "perplexity": 182.56061949345144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776440271.67/warc/CC-MAIN-20140707234040-00062-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://www.preprints.org/manuscript/201906.0046/v1 | Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed
# Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines
Version 1 : Received: 4 June 2019 / Approved: 5 June 2019 / Online: 5 June 2019 (16:10:07 CEST)
A peer-reviewed article of this Preprint also exists.
Jauch, C.; Gloe, A. Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines. Energies 2019, 12, 3013. Jauch, C.; Gloe, A. Simultaneous Inertia Contribution and Optimal Grid Utilization with Wind Turbines. Energies 2019, 12, 3013.
Journal reference: Energies 2019, 12, 3013
DOI: 10.3390/en12153013
## Abstract
This paper presents findings of a study on continuous feed-in management and continuous synthetic inertia contribution with wind turbines. A realistic case study, based on real measurements, is outlined. A wind turbine feeds into a weak feeder, such that its power has to be adapted to the permissible loading of this feeder. At the same time the wind turbine is to provide inertia to the grid by applying the previously published variable inertia constant controller. It is discussed that optimal grid utilisation and simultaneous inertia contribution are mandatory for the frequency control in power systems that are heavily penetrated with renewable energies. The study shows that continuous feed-in management can be combined well with continuous inertia provision. There are hardly any negative consequences for the wind turbine. The benefits for the grid are convincing, both in terms of increased system utilisation and in terms of provided inertia. It is concluded that wind turbines can enhance angular stability in a power system to a larger extent than conventional power plants.
## Keywords
feed-in management; frequency domain; inertial energy; inertial response; power control; synthetic inertia; wind turbine
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https://www.varsitytutors.com/hotmath/hotmath_help/topics/matrix-dimensions.html | # Dimensions of a Matrix
The dimensions of a matrix are the number of rows by the number of columns. If a matrix has $a$ rows and $b$ columns, it is an $a×b$ matrix. For example, the first matrix shown below is a $2×2$ matrix; the second one is a $1×4$ matrix; and the third one is a $3×3$ matrix.
$\left[\begin{array}{rr}\hfill 3& \hfill 5\\ \hfill 99& \hfill -0.5\end{array}\right]$
$\left[\begin{array}{rrrr}\hfill \frac{1}{3}& \hfill 7& \hfill \frac{2}{3}& \hfill 6\end{array}\right]$
$\left[\begin{array}{rrr}\hfill x& \hfill 0& \hfill 0\\ \hfill 0& \hfill 4x& \hfill 0\\ \hfill 0& \hfill 0& \hfill y\end{array}\right]$
When you add and subtract matrices , their dimensions must be the same; when you multiply them, their dimensions must be compatible . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8164119124412537, "perplexity": 177.56880257594136}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659340.1/warc/CC-MAIN-20190117204652-20190117230652-00293.warc.gz"} |
https://scicomp.stackexchange.com/tags/parabolic-pde/hot?filter=all | Tag Info
14
The CFL condition states that the "mathematical domain of dependence" must be (asymptotically) contained in the numerical domain of dependence. For hyperbolic problems, this provides a bound $\Delta t < C \Delta x$ that is useful at all resolutions. For a parabolic problem, it merely requires that $\Delta t \in o(\Delta x)$ in the limit $\Delta x \to 0$. ...
10
This phenomenon is often called "ringing" and plagues methods that are not $L$-stable. This can be seen in this motivating example from Hairer & Wanner (1999) "Stiff differential equations solved by Radau methods". Consider the equation $$\dot y = -50 (y - \cos t)$$ and apply explicit Euler with time step near the stability limit, implicit midpoint ...
10
The best way to do this is (as you said) to just use the definition of periodic boundary conditions and set up your equations correctly from the start using the fact that $u(0)=u(1)$. In fact, even more strongly, periodic boundary conditions identify $x=0$ with $x=1$. For this reason, you should only have one of these points in your solution domain. An open ...
8
This makes no sense. Let us assume that $g(z)=0$ has exactly one solution $z=z^\ast$, then your boundary condition $g(u|_\Gamma)=0$ is equivalent to $u|_\Gamma=z^\ast$, i.e., a linear Dirichlet condition. On the other hand, if there are multiple solutions of $g(z)=0$, then you are saying that the value $u|_\Gamma$ could have multiple values, but this does ...
6
I'm going to write this as an answer although it doesn't directly answer the question. Plugging the second equation and the third equation into the first, and plugging the third into the second, together give: \begin{align} \frac{\partial^2 c}{\partial t^2} &= \frac{\partial^2}{\partial x^2}\frac{\partial c}{\partial t} + \frac{\partial b}{\partial ... 6 A two-point flux like this is not convergent if the mesh is not "orthogonal", in the sense that the edge/face between two cells is orthogonal to the line segment joining the cell centroids. If your mesh is orthogonal, you would use the distance between centroids for h_{ij} above. If you would like a method to work on more general meshes within the cell-... 6 The solutions for the equation are in\psi \in \mathbb{C}^{3M}\times\mathbb{R}^+ \enspace .$$If the number of electrons is small enough you can just use any traditional method. Like a domain discretization method (Finite Difference, Finite Element, Boundary Element), or a pseudospectral method. Since solving this equation is not more difficult than ... 6 Such problems (sometimes called lateral Cauchy problems) are in general not well-posed (meaning they either lack a solution, or there are infinitely many of them, or the solution is unstable under perturbations of the boundary conditions). For parabolic (or dissipative) equations, it makes sense to study the stationary limit (simply omit the term u_t in ... 5 I get u''=-n^2 u, and the condition holds with K=0. By the way, Kreiss' conclusion holds for any linear operator; no ellipticity must be assumed. 5 As Jed says, limiters are not usually an efficient approach for parabolic/elliptic problems. WENO is much more expensive than simple piecewise-polynomial interpolation, so I would first try vanilla interpolation and see if you actually have oscillations. WENO is really designed for situations in which the solution is discontinuous; yours is not. In case ... 5 The sources you are looking at are all looking at hyperbolic problems. The issues are different for elliptic problems and "limiters" are generally not the preferred tool. I outlined some of the methods and tradeoffs in this answer. As for time integration, L-stability is the important property to prevent bad overshoots for parabolic systems. ... 5 A nice reference for this is Chapter 10 of LeVeque's finite difference book. Of course, it only covers basic finite difference approaches, and there are plenty of others (all within the method of lines framework). The method of lines is indeed applicable in multiple dimensions, and two-dimensional problems are discussed in the reference just given. Most ... 5 On your first question: I assume that by "usual discretization matrix" you mean either the 3-point finite difference discretization in 1d, or what you get using linear finite elements. In either case, it's not actually the Crank-Nicolson scheme that determines this. It's true that for the two spatial discretizations mentioned above, the spatial error is O(h^... 5 Parabolic PDE's such as those in the book can usually be solved using the Method of Lines. First you create some mesh for the x direciton. I will assume that you used some uniform spacing since the plots don't show any characteristics that show the need of non-uniformity. Next you recast your equations with only the time derviative on the left hand side ... 5 Don't worry about programming skills, everyone's a beginner at some point. It's a good start actually. I'm just going to give some hints assuming that this is an exercise. Actually, choward's answer is complete, this is just a rephrasing of his suggestions in, I hope, a more beginner friendly language. So, if you do accept an answer it should be his ;) Your ... 5 First off, the PDE can be rewritten instead as$$\frac{\partial C}{\partial t} = \frac{\partial}{\partial x}C\frac{\partial C}{\partial x}$$or, by applying the product rule in reverse again, as$$\frac{\partial C}{\partial t} = \frac{1}{2}\frac{\partial^2}{\partial x^2}C^2.$$This equation is often referred to as the porous medium equation or the slow ... 4 Let$$A = \left(\begin{array}{ccccc} -2 & 1 \\ 1 & -2 & 1 \\ &&\ddots\\ &&1 & -2 & 1\\&&&1&-2\end{array}\right)$$be the standard Laplacian matrix. Your system can be written in traditional time-stepping form as$$u^{n+1} = \left(I + \frac{h}{(h')^2}A\right)u^n \doteq Mu^n,$$where$$u^n = \left(\begin{...
4
As Hui pointed out above, to apply Neumann boundary conditions correctly you should utilize ghost points and extend your $n^{th}$ order discretisation stencil to your domain boundaries. Utilising forward/backward difference or extrapolation at the boundary will degrade your solution. Assuming a $2^{nd}$ order central difference scheme the Neuman boundary ...
4
The two problems you mention indeed have different roots. The first one is a consequence of numerical dispersion and the other one of numerical instability. Let me elaborate a little: Problem #1: The PDE in question is non-dispersive, i.e. waves of any frequency and wavenumber will travel equally fast - at speed $a$. However, after discretisation, this is ...
4
You would need to linearize the problem. I prefer to do it before discretization but it's possible to do also after discretization. (I'm a bit skeptical of linearization after discretization because I have never looked into the details. In general, discretization and linearization steps do not commute.) In the following I assume that the equation is actually ...
3
I think that one key point to understand the answers is that, with the parabolic PDE that you wrote, we have some control on the "quantity of $u$", i.e. $\int_{\Omega} u$: If you integrate the PDE, you have $$\int_{\Omega} u_t = \int_{\Omega} \Delta u + \int_{\Omega} f(x,t) = \int_{\Omega} f(x,t)$$ because $\int_{\Omega} \Delta u = \int_{\partial \Omega} \... 3 Providing a whole detailed solution is out of the scope of this site, but asking for references is on-topic, so here is what I would suggest to get started: There are many good books on finite difference methods (for instance, "Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems" by LeVeque, or ... 3 You want to solve for 3 to 10 particle systems (3D per particle)? As far as I am aware, mean field theories do not work especially well for so few particles, but it seems there has been DFT work on diatomic molecules. Is this a system where Born-Oppenheimer is valid? If so, I might be inclined to expand the electronic wavefunction using a linear combination ... 3 The Crank-Nicolson discretization of this equation will read $$\frac{T^n-T^{n-1}}{\Delta t} = \frac 12 \left[ \partial_x \left((T^n)^{5/2} \partial_x T^n\right) + \partial_x \left((T^{n-1})^{5/2} \partial_x T^{n-1}\right) \right]$$ which is a nonlinear, time-independent, elliptic partial differential equation in$T^n$. The way to solve such ... 3 It depends on how you define "projection" and what scheme you are using. But let's investigate the backward Euler method. There, you need to solve the following discrete problem in every time step: $$(v_h,U_h^n) + \Delta t (\nabla v_h, \nabla u_h^n) = (v_h, U_h^{n-1}).$$ The question is what to use in the first time step: Either$$(v_h,U_h^1) + \... 3 Yes, with Dirichlet boundary conditions you always have exponential convergence to the staedy state. Any PDE book will have a proof. For a nice explanation from a numerical perspective, see chapter 2 of LeVeque's FDM book. 3 The confusion was the misleading variables$F_{j-1/2}$and$F_{j+1/2}$with f_left and f_right, which are completely different. f_left and f_right are the interpolated fluxes at a one single face. They must be then upwinded using the advection speed to compute the Flux at a specific cell face. Which means if$C>0$we take f_left, otherwise we take ... 3 So after browsing the paper a bit, I think that the answer is essentially what Christian Clason stated in his comment. It seems that the original question refers to the statement just above Equation (3) in the article linked by kwesi : There, the authors say that the advection-diffusion equation (Equation (1) in the paper)$\frac{\partial c}{\partial t} + \...
3
You really don't want to solve the heat equation with an explicit time stepping scheme. You need to choose the time step so incredibly small that you won't make any progress towards the end time. (Explanation in lecture 27: http://www.math.tamu.edu/~bangerth/videos.html .)
3
While i agree with Wolfgang that its best to choose Crank-Nicolson time stepping, i think it is incorrect to assert explicit time stepping results in 'incredibly small' time steps or even to suggest your script is not functioning because of explicit time stepping. You can make it work just fine, but you need to get your discretization correct and to ...
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https://gateoverflow.in/699/gate2001-1-6?show=27448 | 4.3k views
Given an arbitrary non-deterministic finite automaton (NFA) with $N$ states, the maximum number of states in an equivalent minimized DFA at least
1. $N^2$
2. $2^N$
3. $2N$
4. $N!$
edited | 4.3k views
0
if NFA has $N$ states then DFA can have $M$ states where $1\leq M \leq 2^N$
Answer is (B) $2^N$.
In DFA any subset of the $N$ states (for $N$ element set $2^N$ subsets possible) can become a new state and they can remain even when the DFA is minimized. So, maximum we can get $2^N$ states for the minimized DFA. (at least in question must be a typo for at most).
by Loyal (8.1k points)
edited
0
In DFA any subset of the N states
This should be "In NFA any subset of the N states..."
Example DFA-> 3rs symbol from right is x.
https://gateoverflow.in/544/gate1991_17-b
Here you have to use 2^3 symbols.
nth symbol from right is x , this DFA will have 2^n state.s
by Boss (41.4k points)
by Active (2.4k points)
Ans: B
by Loyal (7.2k points) | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8561301231384277, "perplexity": 3627.7808888403874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668712.57/warc/CC-MAIN-20191115195132-20191115223132-00217.warc.gz"} |
http://mathhelpforum.com/algebra/167335-assistance-required-what-seems-basic-simplification.html | # Thread: Assistance required with what seems a basic simplification.
1. ## Assistance required with what seems a basic simplification.
My expression is -3=[(-x*pi)/(sqrt(1-x^2))]
An online equation solver gave a solution of x=3/[sqrt(9+pi^2)] or x=.690621 but does not show the working.
I have spent hours on this but am positively stuck!
Can anyone help?
Regards.
2. Hello!
Use LaTeX in future for writing equations.
$-3=\frac{-\pi x}{\sqrt{1-x^2}}$
Hint:
$(-3)^2=(\frac{-\pi x}{\sqrt{1-x^2}})^2$
3. $\displaystyle -3 = \frac{-x\times \pi}{\sqrt{1-x^2}}$
$\displaystyle -3 \sqrt{1-x^2}= -x\times \pi$
$\displaystyle 3 \sqrt{1-x^2}= x\times \pi$
$\displaystyle 3^2 (1-x^2)= x^2\times \pi^2$
$\displaystyle 9-9x^2= x^2\times \pi^2$
$\displaystyle 9-9x^2- \pi^2x^2=0$
$\displaystyle 9-(9+ \pi^2)x^2 =0$
$\displaystyle (9+ \pi^2)x^2 =9$
$\displaystyle x^2 =\frac{9}{9+ \pi^2}$
$\displaystyle x =\sqrt{\frac{9}{9+ \pi^2}}$
4. Thank you very much for your replies - that one was seriously haunting me!
Regards.
5. I am curious to know - what rule tells me I cannot touch the terms under the square root?
To me sqrt(9+x^2) is 3+x but this is clearly not the case in this instance.
Some further clarification would be much appreciated.
Regards.
6. $\displaystyle \sqrt{9+x^2} \neq 3+x$
I'm not sure I follow what you are saying.
7. Obviously I am a bit rusty with my laws of powers etc. I thought sqrt(9+x^2) = sqrt(9) + sqrt(x^2) = 3 +x.
As I said - a bit rusty. Further reading necessary.
Regards.
8. You may be confused with
$\displaystyle \sqrt{a\times b } = \sqrt{a}\sqrt{b}$
$\displaystyle \sqrt{a+ b } \neq \sqrt{a}+\sqrt{b}$
9. In your second line did you mean sqrt{a+b }?
I apologise - not only am I rusty at powers but am new to Latex.
10. Generally speaking, you can only simplify a radical expression that is in factored form.
$\sqrt{9x^2}$ for example CAN be simplified to $3x$
The expression $\sqrt{x^2 + 9}$ on the other hand cannot be simplfied as-is.
This is especially apparent when you recall that $(a + b)^2 \neq a^2 + b^2$, because the square root would be the same as $(a + b)^{\frac{1}{2}}$, which by the same token, is not equal to $a^{\frac{1}{2}} + b^{\frac{1}{2}}$.
11. Great information. Thank you.
Makes me think of BOMDAS - brackets first, then powers.
Regards. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 21, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9143347144126892, "perplexity": 1143.6952113828524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345769117/warc/CC-MAIN-20131218054929-00065-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/need-help-with-flow-physics.155862/ | # Need help with flow physics
1. Feb 12, 2007
### wat
i need your urgent help in the following :
I have a cylindrical tank :
- inner diameter is 2 m
- capacity 50 m3
- hight over ground 0.5 m (50 cm) from ground to tank bottom
- the tank is 60% full of liqued and 40% gas , the pressure inside
the tank is 3 bar :
What is the drain size (diameter) that allow to get 2.8 m3/h of the liquid , without using any pumps , just by the pressure force inside the tank ?
2. Feb 12, 2007
### quark
That is a funny tank, in practice. (16 m height / 2m dia.) Is it horizontal or vertical?
Just go to the link below and do some trials and error.
http://www.efunda.com/formulae/fluids/draining_tank.cfm#calc
Consider 3 bar as 30 meters head approximately. 60% liquid adds about 9 meters and initially the head will be 39 meters. As the tank gets emptied, the head will be 30 meters. The average of these two flow readings gives you the average flowrate.
The diameter is approximately 0.2mm
Use a rather conservative discharge coefficient of 0.85
3. Feb 12, 2007
### wat
flow
the tank is horizontal , attached drawing is cross section in tank
and what is the effect of liquid viscosity ?
thanks again
#### Attached Files:
• ###### tank.jpg
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https://www.physicsforums.com/threads/calculating-the-optimal-day-to-observe-an-object-given-the-ra-and-dec.766736/ | # Archived Calculating the optimal day to observe an object given the RA and dec
1. Aug 20, 2014
### pondzo
1. The problem statement, all variables and given/known data
OmegaCen is a Globular Cluster which lies at coordinates: R.A. = 13h26m45.89s,
Dec = −47°28′36.7′′ (J2000.0) estimate the optimal day on which to observe
this object.
2. Relevant equations
3. The attempt at a solution
We are to interpret optimal as 12 am midnight directly overhead
since this is 12 hrs after noon you subtract 12hrs RA = 1hr26m45.89sec
which is ≈ 1.446 hrs RA and this is due to the monthly RA shift
2 hrs of RA shift per month so, 30/1.446 ≈ 20.75 days
so 20.75 days after the vernal equinox, which is april the 10.75 th
im not quite sure how to interpret the 10.75, do i say its on the 10th of april or the 11th ? and the observation is meant to be at 12 am midnight so would you say its on the 11th april? (at the very beginning). Thank you!
2. Feb 4, 2016
### Staff: Mentor
The vernal equinox probably won't happen exactly at midnight, but that depends on the time zone... April 11th should be fine.
Draft saved Draft deleted
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http://openstudy.com/updates/53476406e4b01730eeaf9f2f | Here's the question you clicked on:
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## ethaned 11 months ago Find the average value of f(x) =-t^2 + 10t + 50 on the interval [2,8] Delete Cancel Submit
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find the area under the curve. The average value of f(x) will be the y-value of a rectangle with the same width as your region (i.e. 8-2= 6 units), and same area as your region. in other words $f_{avg}= \frac{1}{6} \int_2^8 -x^2 + 10x + 50 \ dx$
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9876222014427185, "perplexity": 4328.545058148844}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131299261.59/warc/CC-MAIN-20150323172139-00194-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://scicomp.stackexchange.com/questions/33676/low-rank-update-of-qr-of-inverse | # Low rank update of QR of inverse
I am in a situation where as part of a sort of inverse power method scheme, I want to very often perform the following step:
1. Apply a symmetric rank one update $$uu^\top$$ to my inverse matrix $$A^{-1}$$
2. Compute the QR decomposition of my updated inverse
Right now, I'm using Sherman-Morrison-Woodbury formula to update my inverse:
1. Update $$A^{-1}$$ with Sherman-Morrison-Woodbury:
• Let $$a = 1 / (1 + u^\top A^{-1} u)$$
• Update $$A^{-1} \gets A^{-1} - a A^{-1} u u^\top A^{-1}$$
and then I'm recomputing the QR from scratch:
1. Recompute QR: $$QR = A^{-1}$$.
However, I'm aware that it's possible to efficiently update a QR decomposition with a low-rank update. Unfortunately, as we can see above the Sherman-Morrison update looks to be full rank, so we can't make use of the QR update.
I'm doubtful, but maybe there is some approach I am missing that can avoid the hit of recomputing the whole QR?
(Also: there are a lot of other questions here about low rank updates of different factorizations here, and I didn't see anything along these lines. Also, I have looked through Matrix Computations without success.)
The update on the inverse is actually rank-one. You can group the terms as $$(A^{-1}u)(A^{-1}u)^T$$ because of the symmetry of $$A$$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8227881193161011, "perplexity": 523.7498609109643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886706.29/warc/CC-MAIN-20200704201650-20200704231650-00119.warc.gz"} |
http://mathonline.wikidot.com/the-continuity-of-composite-functions-on-metric-spaces | The Continuity of Composite Functions on Metric Spaces
# The Continuity of Composite Functions on Metric Spaces
Recall from the Continuity of Functions on Metric Spaces page that if $(S, d_S)$ and $(T, d_T)$ are metric spaces and $f : S \to T$ then $f$ is said to be continuous at the point $p \in S$ if for all $\epsilon > 0$ there exists a $\delta > 0$ such that if $d_S(x, p) < \delta$ then $d_T(f(x), f(p)) < \epsilon$.
Equivalently, we said that $f$ is continuous at $p$ if for all $\epsilon > 0$ there exists a $\delta > 0$ such that:
(1)
\begin{align} \quad f(B_S(p, \delta)) \subseteq B_T(f(p), \epsilon) \end{align}
On the Sequential Criterion for the Continuity of a Function on Metric Spaces page we also proved a very important theorem which said that $f$ is continuous at $p$ if and only if for all sequences $(x_n)_{n=1}^{\infty}$ from $S$ that converge to $p$ we have that the sequence $(f(x_n))_{n=1}^{\infty}$ converges to $f(p)$.
We will now continue in looking at what can be said about the continuity of functions. Let $(S, d_S)$, $(T, d_T)$, and $(U, d_U)$ all be metric spaces and let $f : S \to T$ and $g : T \to U$. We can obtain a composite function $g \circ f : S \to U$ defined for all $x \in S$ by:
(2)
\begin{align} \quad (g \circ f)(x) = g(f(x)) \end{align}
In the following theorem we will see how the continuity
Theorem 1: Let $(S, d_S)$, $(T, d_T)$, and $(U, d_U)$ be metric spaces and let $f : S \to T$ and $g : T \to U$. If $f$ is continuous at $p$ and $g$ is continuous at $f(p)$ then $g \circ f$ is continuous at $p$.
• Proof: To show that $h$ is continuous at $p$ we must show that for all $\epsilon > 0$ there exists a $\delta > 0$ such that if $d_S(x, p) < \delta$ that then:
(3)
\begin{align} \quad d_U(g(f(x)), g(f(p))) < \epsilon \end{align}
• Since $g$ is continuous at $f(p)$ we have that for all $\epsilon > 0$ there exists a $\hat{\delta} > 0$ such that if $d_T(f(x), f(p)) < \hat{\delta}$ $(***)$ then:
(4)
\begin{align} \quad d_U(g(f(x)), g(f(p))) < \epsilon (****) \end{align}
• Also, since $f$ is continuous at $p$ we have that for all $\delta$ ($> 0$) that there exists a $\bar{\delta} > 0$ such that if $d_S(x, p) < \bar{\delta}$ $(*)$ then:
(5)
\begin{align} \quad d_T(f(x), f(p)) < \hat{\delta} (**) \end{align}
• So then for any given $\epsilon > 0$, take $\delta = \bar{\delta}$. Then if $(*)$ holds then $(**)$ holds and by $(***)$ we then have that $(****)$ holds.
• Hence, for all $\epsilon > 0$ there exists a $\delta = \bar{\delta} > 0$ such that if $d_S(x, p) < \delta$ then $d_U(g(f(x)), g(f(p)) < \epsilon$, so $g \circ f$ is continuous at $p$. $\blacksquare$ | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995408058166504, "perplexity": 66.1149370422889}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315329.55/warc/CC-MAIN-20190820113425-20190820135425-00510.warc.gz"} |
http://revoltinthedesert.blogspot.com/2006/12/birth-five-hypotheses-for-meister.html | ## Monday, December 24, 2007
### birth: five propositions for meister eckhart on christmas (the struggle, part 8)
Arthur Hughes, "The Nativity" (1858)
mary gave birth to Truth so that the Truth might be made universally incarnate in us.
until the event of Truth is universally incarnate as History, nothing is Whole (adorno: "the whole is the false").
Truth must be realized in order to be Whole, therefore we must give birth to Truth.
mary is the last moment before the initial realization of Truth. mary realized that she was nothing and thus she was set free to be the event of the birth of Truth: the one whose heart had the fecundity of virginity and the purity of motherhood. but beyond mary's insight, one must realize that the consummation of the nothing is Truth and that the Truth is not-other to the nothing. this is incarnation.
today, we too fail to grasp the possibility of the Whole-of-History (Peace). but perhaps like mary we can realize that we are nothing ("let it be done to me as you will") and thus be the site in which Truth is born. therefore let us be the nothing out of which the Truth creates History.
-LoA
Suroor said...
"... we can realize that we are nothing ("let it be done to me as you will") and thus be the site in which Truth is born. therefore let us be the nothing out of which the Truth creates History."
Perfectly said!
Lawrence of Arabia said...
creation, salvation, revelation...you can't really pull them apart can you?
best wishes,
LoA.
thekingpin68 said...
creation, salvation, revelation...you can't really pull them apart can you?
A good point. Merry Christmas, Lawrence.
darvish said...
Amen! That is the goal of the Sufi path also :)
Merry Christmas and a Happy New Year to you and your family :)
Peace and Many Blessings!
Ya Haqq!
Lawrence of Arabia said...
darvish,
i think there probably are many points of convergence between the great neoplatonic tradition within xty, represented here by meister eckhart, and sufism.
happy new year to you as well.
LoA. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8267311453819275, "perplexity": 3918.302374870646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535922763.3/warc/CC-MAIN-20140909041744-00039-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/319197/normal-idempotent-operator-implies-self-adjointness | # Normal, idempotent operator implies self-adjointness.
I have been trying to solve this problem for quite a while. I am still unsure of whether any of the avenues I have pursued have been of any use. Any advice will be much appreciated.
Question:
Let $V$ be a finite-dimensional inner product space, and let $E$ be an idempotent linear operator on $V$. Prove that if $EE^* = E^*E$ then $E$ is self-adjoint.
-
Well, if you want to use a big hammer, the spectral theorem says that normal operators are unitarily diagonalizable. So it suffices to consider the case where $E$ is diagonal, which should be pretty easy. – Nate Eldredge Mar 3 '13 at 5:32
@NateEldredge Is there a smaller hammer? – providence Mar 3 '13 at 5:49
If $E$ is normal, $\| E x \| = \|E^* x \|$ for all $x$. Similarly, $I-E$ is normal, so $\|(I-E) x\| = \|(I - E^*)x \|$. In particular, since $(I-E)Ex = 0$, $(I-E^*)Ex = 0$, i.e. $E^* E = E$, and similarly since $E(I-E)x = 0$, $E^*(I-E)x = 0$, i.e. $E^* E = E^*$. But those together say $E = E^*$.
The equality $EE^\ast=E^\ast E$ implies that $(E+E^\ast-I)(E-E^\ast)=0$. If you can show that $E+E^\ast-I$ is invertible, you are done.
Suppose $(E+E^\ast -I)v=0$. Left-mulitply the equation by $E^\ast$, we get $E^\ast Ev=0$. Hence show that $Ev=0$. Since $EE^\ast=E^\ast E$, similarly, show that $E^\ast v=0$. Now, consider the equation $(E+E^\ast -I)v=0$ again and show that $E+E^\ast -I$ is invertible.
How do you get $Ev=0$? I don't see that... – user59083 Jun 5 '14 at 0:10
@5space $E^\ast Ev=0\Rightarrow v^\ast E^\ast Ev=0$. – user1551 Jun 5 '14 at 9:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.993191659450531, "perplexity": 119.6804290003588}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783404405.88/warc/CC-MAIN-20160624155004-00007-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://mathforum.org/mathimages/index.php/Pappus_Chain | # Pappus Chain
Pappus Chain
Pappus chain consists of all the black circles in the pink region.
# Basic Description
A chain of inscribed circles is called a Pappus Chain when its first circle $C_1$ is tangent to the three semicircles forming the Arbelos, and all the subsequent circles $C_n$ are tangent to one another and to the boundaries of the arbelos. The Pappus Chain is named after Pappus of Alexandria, a great Greek mathematician who studied and wrote about it in the 4th century A.D.
The figure above shows all of the three variations of the chain: leftward, rightward, and downward. The default position is the one that extends to the right.
# A More Mathematical Explanation
Note: understanding of this explanation requires: *Geometry
## Properties
### Height
Figure 5-Height
In the Papp [...]
## Properties
### Height
Figure 5-Height
In the Pappus Chain, the height of the center of the nth circle is n times the diameter of that circle.
The proof Pappus gave is long and complicated, containing Euclidean geometry, similar triangles, and the Pythagorean Theorem. We won’t list his proof here. Instead, here’s a simpler, more modern proof using the concept of inversion:
It’s fine if you don't know much about “circle inversion.” Basically, "inversion is a type of transformation that moves points from the inside of a circle to the outside and from the outside of a circle to the inside using a specific rule" [1]. The basic properties of inversion are as follows. Go to Inversion to get a more complete understanding.
• The inverse of a line not passing through the center of the circle is a circle;
• The inverse of a circle not passing through the center of the circle is a circle;
• The inverse of a circle passing through the center of the circle is a line.
We want to prove that the height of the center of the nth circle above $AB$ is n times the diameter of that circle, so we are inverting over the nth circle in the chain. To do this, first invert circle $AC$ and circle $BC$ with respect to a circle centered at $C$. Because both circle $AC$ and circle $BC$ pass through the center of the circle $C$, they become two vertical lines according to the third property listed above (see the figure on the left). Circle $BC$ inverts to the left line because when $BC$ has a smaller radius than $AC$, it inverts to a further line. To help you understand it better, treat the circle centered at $C$ as a mirror. If the circle is closer to the center point $C$, it will be reflected further away.
Second, invert the nth circle in the Pappus Chain and the two circles that are tangent to it. The inverse of the nth circle is itself. The inverse of the subsequent circles inscribed in the chain are circles tangent to the two parallel, vertical lines below or above the nth circle. Because the subsequent circles are tangent to circle $AC$ and $BC$, it makes sense that they are still tangent to the inverse of the two circles.
Now we are done with the inversions. Let's take a look at the right figure. Since those inversed circle are identical, it is not hard to conclude that the height of the center of the nth circle is n times the diameter of that circle. For example, $EF = 4r = 2d$ for the second circle.
### Ellipse
Figure 6-Ellipse
The centers of all the circles $C_n$ in the Pappus Chain lie on an ellipse.
Let $M$ be the center of circle $AC, N$ be the center of the circle $BC, C_n$ represent the centers of all of the circles in the Pappus Chain, and $r_n$ represent the radii of those circles.
In order to prove this property, the first thing to do is to know the definition of an ellipse. In what conditions will a point lie on an ellipse in two-dimensions? First, the sum of the distances from a point on the ellipse to two fixed points is a constant. Second, the constant is greater than the distance between the two fixed points.
We need to show that all of the centers of the circles in the Pappus Chain satisfy the two conditions. The two fixed points are $M, N$.
Because
$C_n M = MD - C_n D =\frac{1}{2} - r_n$
and
$C_n N= C_n E + EN = r_n + \frac{1- r}{2}$,
we get
$C_n M + C_n N = (\frac{1}{2} - r_n) + (r_n + \frac{1- r}{2})= 1 - \frac{r}{2}= constant.$
For the reason that $MN = MC - NC = \frac{1}{2} - \frac{1- r}{2} = \frac{r}{2} < 1 - \frac{r}{2}$ (because $r < 1$ )
Thus, the centers of all the circles $C_n$ in the Pappus Chain lie on an ellipse.
## Pappus Chain and Steiner Chain
The Pappus Chain is also a Steiner Chain (see Steiner's Porism), a chain formed by circles that are tangent to two circles, one inscribed within the other.
# References
[1] van Lamoen, Floor and Weisstein, Eric W. Pappus Chain. From MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/PappusChain.html.
1. More mathematical explanation about Pappus Chain
2. Add "Why is this interesting" section
3. A more interesting main image if possible. . | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 29, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.857795774936676, "perplexity": 291.9773766854202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921957.9/warc/CC-MAIN-20140901014521-00104-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://www.jstage.jst.go.jp/article/bpb/43/2/43_b19-00538/_article | Biological and Pharmaceutical Bulletin
Online ISSN : 1347-5215
Print ISSN : 0918-6158
ISSN-L : 0918-6158
Regular Articles
A Pilot Clinical Study on Thiamine Hydrochloride as a New Mosquito Repellent: Determination of the Minimum Effective Dose on Human Skin
Author information
JOURNAL FREE ACCESS FULL-TEXT HTML
2020 Volume 43 Issue 2 Pages 284-288
Details
Abstract
Thiamine hydrochloride has been suggested as a natural, safe yet effective alternative for chemical insect repellents. However, there is a demand for a reassessment of the minimum required dose that is sufficient to perform a topical repellency on the human skin. Therefore, the purpose of the current work is to establish a dose–response curve from which the effective dose (ED) is calculated. A series of increasing concentrations of thiamine hydrochloride were applied to the forearm of adult volunteers, the number of bites was counted and the percent repellency calculated accordingly. Data of percent repellency were converted to probit values which were plotted against log doses. A linear relation was obtained from the dose–response curve with an r2 = 0.958. Statistical validation of the equation was tested through linear regression analysis, where the slope and intercept were found significant from zero. No significant difference was shown between observed and expected responses (p > 0.05). ED 50 and 99.9% were computed from the linear equation and found to be 4.57 and 344 mg, respectively. This finding can be supported by future works in which a proper formulation of thiamine hydrochloride in the respective doses would be presented. One can get prolonged safe protection against insect bites.
Graphical Abstract Fullsize Image
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© 2020 The Pharmaceutical Society of Japan
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https://www.physicsforums.com/threads/self-inductance-question.271669/ | # Self Inductance Question
1. Nov 13, 2008
### TFM
1. The problem statement, all variables and given/known data
Give a definition of (self) inductance. Suppose a battery, which supplies a constant EMF ϵ_0 is connected to a circuit of resistance R and inductance L at t = 0. Find an expression for the current as a function of time.
2. Relevant equations
V = IR
$$V = -L\frac{dI}{dt} [/tex 3. The attempt at a solution I am assuming that this is to be treated as a Kirchoff Loop, thus the total voltage = 0 Voltage providers: Inductor Battery Users: Resistor Thus I have the equation: [tex] \epsilon - L\frac{dI}{dt} - IR = 0$$
and thus:
$$\epsilon - L\frac{dI}{dt} = IR$$
treating like a differential equation:
$$\epsilon - L\frac{dI}{dt} = IR$$
$$\epsilon dt - L dI = IR dt$$
rearrange:
$$\frac{L}{IR} dI = -dt + \epsilon dt$$
Gives:
$$\frac{1}{L}ln(IR) dI = -t + \epsilon t$$
multiply by L
$$ln(IR) = -Lt + \epsilon t [/tex take exponentials: [tex] IR = e^{-Lt} + e^{\epsilon t}$$
Does this look right so far?
TFM
#### Attached Files:
• ###### LR Circuit.jpg
File size:
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2. Nov 14, 2008
### alphysicist
Hi TFM,
This equation does not follow from the previous one.
3. Nov 14, 2008
### TFM
No it doesn't
so:
$$\epsilon dt - L dI = IR dt$$
see, I have to rearrange to get I onto the left side.
does this look better:
$$\epsilon dt - L dI = IR dt$$
$$- L dI = IR dt - \epsilon dt$$
$$- L dI = (IR - \epsilon) dt$$
$$- \frac{L}{IR - \epsilon} dI = dt$$
so and so:
$$- \frac{1}{L}ln(IR - \epsilon) = t$$
Does this look better?
TFM
4. Nov 14, 2008
### alphysicist
I think this part looks okay.
This isn't quite right. The integration is not right (if you take the derivative of the left side with respect to I you don't get the left side of the previous equation). Also remember that these are definite integrals, so you have to evaluate the limits.
5. Nov 14, 2008
### TFM
Would the limits be for I between 0 and I and for t between 0 and t?
I am not sure how to integrate this, because I thought when you integrated:
$$\frac{1}{x} dx$$
you got:
$$ln(x)$$
and for:
$$\frac{b}{x}$$
where b is a constant, you got:
$$\frac{1}{b}lnx$$
???
TFM
6. Nov 14, 2008
### alphysicist
No, the integral
$$\int \frac{b}{x} dx \to b \ln x$$
(plus a constant) because in that case the b can come out of the integral (it is not affected by the integration process at all). However, you do have to take into account that the R is multiplying the I.
$$- L\left( \int\limits_0^I \frac{1}{IR - \epsilon} dI \right) = \int\limits_0^t dt$$
7. Nov 14, 2008
### TFM
Okay, so:
$$- L\left( \int\limits_0^I \frac{1}{IR - \epsilon} dI \right) = \int\limits_0^t dt$$
$$-L(ln(IR - \epsilon) - (0R - \epsilon)) = t - 0$$
$$-L(ln(IR - \epsilon - - \epsilon)) = t$$
$$-L(ln(IR)) = t$$
???
TFM
8. Nov 14, 2008
### alphysicist
The R has to be handled like this:
$$\int \frac{1}{IR-\epsilon}\ dI \to \frac{\ln(IR-\epsilon)}{R}$$
(plus the constant).
Also when you go to apply limits,
$$\ln (x)\Big|_{x_0}^{x_f} \neq \ln (x_f - x_0)$$
$$\ln (x)\Big|_{x_0}^{x_f} = \ln (x_f) - \ln(x_0)$$
9. Nov 14, 2008
### TFM
Okay, so:
$$- L\left( \int\limits_0^I \frac{1}{IR - \epsilon} dI \right) = \int\limits_0^t dt$$
This will integrate to:
$$-L\left[\frac{ln(IR - \epsilon)}{R}\right]^I_0 = t$$
$$-L \left(\frac{IR - \epsilon}{R} - \frac{0R - \epsilon}{R}\right) = t$$
$$-L \left(\frac{IR - \epsilon}{R} - \frac{- \epsilon}{R}\right) = t$$
does this look better?
???
TFM
10. Nov 14, 2008
### alphysicist
You seemed to have dropped your $\ln$'s when you put in the limits.
11. Nov 14, 2008
### TFM
Sorry, copied through typo
It should be:
$$-L\left[\frac{ln(IR - \epsilon)}{R}\right]^I_0 = t$$
$$-L \left(\frac{ln(IR - \epsilon)}{R} - \frac{ln(0R - \epsilon)}{R}\right) = t$$
$$-L \left(\frac{ln(IR - \epsilon)}{R} - \frac{ln(- \epsilon)}{R}\right) = t$$
???
TFM
12. Nov 15, 2008
### TFM
Does this look correct
???
TFM
13. Nov 15, 2008
### alphysicist
What does that give for I?
14. Nov 15, 2008
### TFM
Well, if we rearrange it:
$$-L \left(\frac{ln(IR - \epsilon)}{R} - \frac{ln(- \epsilon)}{R}\right) = t$$
$$\left(\frac{ln(IR - \epsilon)}{R} - \frac{ln(- \epsilon)}{R}\right) = -\frac{t}{L}$$
Multiply by R:
$$ln(IR - \epsilon) - ln(-\epsilon) = -\frac{Rt}{L}$$
take exponentials:
$$IR - \epsilon + \epsilon = e^{-\frac{Rt}{L}}$$
$$IR = e^{-\frac{Rt}{L}}$$
$$I = \frac{^{-\frac{Rt}{L}}}{R}$$
Does this look correct?
TFM
15. Nov 15, 2008
### alphysicist
This line is not correct, because:
$$\exp \left\{ \ln x + \ln y\right\} \neq x + y$$
Before you take the exponential of both sides, you just want a single natural log on the left . That is, you want the left side to be just:
ln(something)
16. Nov 15, 2008
### TFM
so:
$$ln(IR - \epsilon) - ln(-\epsilon) = -\frac{Rt}{L}$$
isn't $$ln(a) - ln(b) = ln(\frac{a}{b})$$
???
If so:
$$ln(IR - \epsilon) - ln(-\epsilon) \equiv ln\left(\frac{IR - \epsilon}{-\epsilon} \right)$$
giving:
$$ln\left(\frac{IR - \epsilon}{-\epsilon} \right) = \frac{-Rt}{L}$$
taking exponentials:
$$\frac{IR - \epsilon}{-\epsilon} = e^{\frac{-Rt}{L}}$$
Does this look better?
TFM
17. Nov 15, 2008
### alphysicist
Yes.
18. Nov 16, 2008
### TFM
Excellent. So:
$$\frac{IR - \epsilon}{-\epsilon} = e^{\frac{-Rt}{L}}$$
$$IR - \epsilon = \epsilon e^{\frac{-Rt}{L}}$$
$$IR = \epsilon - \epsilon e^{\frac{-Rt}{L}}$$
factorise out:
$$IR = \epsilon \left(1 - e^{\frac{-Rt}{L}} \right)$$
divide by R:
$$I = \frac{\epsilon}{R} \left(1 - e^{\frac{-Rt}{L}} \right)$$
Does this look correct?
TFM
19. Nov 16, 2008
### alphysicist
That looks right to me. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9540966153144836, "perplexity": 3940.602353722235}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170741.49/warc/CC-MAIN-20170219104610-00388-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/16739/what-is-force-times-angle/16740 | # What is force times angle?
I'm looking at an explanation of pendulums, and the following is said:
What I don't understand is where it says "if restoring force is given by $mg\theta$..." - conceptually, what is a force times an angle? Never being one to simply commit something to memory for the sake of it, I really want to understand this...
Any help greatly appreciated!
Tim.
EDIT:
-
Because an angle is dimensionless, its force. The exact value is mgsin(theta), but for small angles sin is identical to the angle (in radians). For that mgsin(theta) imagine the forces on that pendulum at some point. – Georg Nov 9 '11 at 11:00
Your edit should be a second question. – Colin K Nov 10 '11 at 2:46
Colin, you're right - have fixed that up. Cheers. – nulliusinverba Nov 10 '11 at 3:13
As @Georg puts it, the force is $mg\sin{\theta}$, but then for small $\theta$ one can assume $\sin{\theta} = \theta$.
So, the force becomes, $mg\theta$.
And regarding the dimensions, $\sin{\theta}$ and $\theta$ are dimension less quantities.
So dimensionally, $mg$ and $mg\sin{\theta}$ are same $\left[ kg \cdot m \cdot s^{-2} \right]$. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8848252892494202, "perplexity": 863.8006028999397}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645195983.63/warc/CC-MAIN-20150827031315-00346-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/140915 | Infoscience
Journal article
# Gauge factor of thick-film resistors: Outcomes of the variable-range-hopping model
Despite a large amount of data and numerous theoretical proposals, the microscopic mechanism of ransport in thick-film resistors remains unclear. However, recent low-temperature measurements point toward a possible variable-range-hopping mechanism of transport. Here, we examine how such a mechanism affects the gauge factor of thick-film resistors. We find that at sufficiently low temperatures T, for which the resistivity follows the Mott’s law R(T);exp(T0 /T)1/4, the gauge factor GF! is proportional to (T0 /T)1/4. Moreover, the inclusion of Coulomb gap effects leads to GF;(T08/T)1/2 at lower temperatures. In addition, we study a simple model which generalizes the variable-range-hopping mechanism by taking into account the finite mean intergrain spacing. Our results suggest a possible experimental verification of the validity of the variable-range hopping in thick-film resistors. | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9792707562446594, "perplexity": 2961.193194625312}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720468.71/warc/CC-MAIN-20161020183840-00370-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://digitalscholarship.unlv.edu/physastr_fac_articles/550/ | ## Physics & Astronomy Faculty Publications
#### Title
A Redshifted Inner Disk Atmosphere and Transient Absorbers in the Ultracompact Neutron Star X-Ray Binary 4U 1916–053
Article
8-11-2020
#### Publication Title
The Astrophysical Journal Letters
899
1
1
12
#### Abstract
The very small accretion disks in ultracompact X-ray binaries are special laboratories in which to study disk accretion and outflows. We report on three sets of new (250 ks total) and archival (50 ks) Chandra/HETG observations of the "dipping" neutron star X-ray binary 4U 1916–053, which has an orbital period of P sime 50 minutes. We find that the bulk of the absorption in all three spectra originates in a disk atmosphere that is redshifted by v sime 220–290 km s−1, corresponding to the gravitational redshift at a radius of R ~ 1200 GM/c2. This shift is present in the strongest, most highly ionized lines (Si xiv and Fe xxvi), with a significance of 5σ. Absorption lines observed during dipping events (typically associated with the outermost disk) instead display no velocity shifts and serve as a local standard of rest, suggesting that the redshift is intrinsic to an inner disk atmosphere and not due to radial motion in the galaxy or a kick. In two spectra, there is also evidence of a more strongly redshifted component that would correspond to a disk atmosphere at R ~ 70 GM/c2; this component is significant at the 3σ level. Finally, in one spectrum, we find evidence of a disk wind with a blueshift of $v=-{1700}_{-1200}^{+1700}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. If real, this wind would require magnetic driving.
#### Keywords
Accretion; Neutron Stars; High Energy Astrophysics
#### Disciplines
Astrophysics and Astronomy | Physical Sciences and Mathematics | Stars, Interstellar Medium and the Galaxy
English
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