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https://www.coursehero.com/file/26217297/AP-PHYSICS-C-Desc-2015doc/	# AP PHYSICS C Desc 2015.doc - AP PHYSICS C MECHANICS COURSE... • Notes • 9 This preview shows page 1 - 3 out of 9 pages. AP PHYSICS C: MECHANICS COURSE SYLLABUS COURSE: AP Physics C: Mechanics TEACHER: Mr. Schwarz TEXTS: Fundamentals of Physics, Halliday & Resnick 10 th Edition COURSE DESCRIPTION: AP Physics C: Mechanics is taught according to Keyport High School’s “A-B Block” schedule. Classes are 80 minutes per day, every other day for the full duration of the school year. Labs will be performed once every two calendar weeks, or once out of every five class periods. Unit exams will follow the format of the AP exam, with a timed multiple choice section and free response section. These exams will be scored in the same manner as the AP exam. COURSE CONTENT: AP Physics C: Mechanics is an Advanced Placement science course equivalent to an introductory college physics course that uses a calculus approach to study the topics in Newtonian Mechanics of kinematics, Newton's Laws, energy, momentum, gravitation and rotation. Methods of calculus are used wherever appropriate in formulating physical principles and in applying them to physical problems. This course is designed for students aspiring to be physics or engineering majors. All enrolled students must have previously earned a minimum average of 88 in physics and be concurrently enrolled in calculus. A teacher recommendation is also required. OUTLINE OF TOPICS a. Kinematics – 5.5 weeks i. Measurement ii. Motion in one dimension iii. Motion in two dimensions iv. Test b. Newton’s Laws of Motion – 6 weeks i. Static equilibrium ii. Dynamics of a single particle iii. Systems of two or more bodies iv. Friction v. Test c. Work, Energy, Power – 4 weeks i. Work and work-energy theorem ii. Conservative forces and potential energy iii. Conservation of energy iv. Power v. Test d. Systems of particles, linear momentum – 3.5 weeks i. Center of mass ii. Impulse and Momentum iii. Conservation of Linear Momentum, collisions iv. Test e. Circular Motion – 5.5 weeks i. Uniform circular motion ii. Torque and rotational statics iii. Rotational kinematics and dynamics iv. Angular momentum and its conservation v. Test f. Oscillations and Gravitation – 5.5 weeks i. Simple harmonic motion (dynamics and energy relationships) ii. Mass on a spring iii. Pendulum and other oscillations iv. Newton’s law of gravitation v. Orbits of planets and other bodies vi. Test g. Review and AP Exam – 3 weeks h. Final Project – 6 weeks COURSE REQUIREMENTS This is the method on how your final marking period grade will be determined. - Major Assignments (50%) - Minor Assignments (35%) - Homework (15%) 1. AP EXAM – The AP Physics C: Mechanics exam is scheduled for May 9, 2016 at Noon. It is required that you take the AP Physics exam. You have signed up to take an AP course so you should take the AP exam. Generally, a score of three, or higher on the AP exam can translate into college credit.	{"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": 0.805363118648529, "perplexity": 2095.684044473469}, "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/1631780057882.56/warc/CC-MAIN-20210926144658-20210926174658-00407.warc.gz"}
http://aimpl.org/l2invariantsgroups/1/	$\newcommand{\Cat}{{\rm Cat}}$ $\newcommand{\A}{\mathcal A}$ $\newcommand{\freestar}{ \framebox[7pt]{\star} }$ ## 1. Approximation of $L_2$-torsion. 1. Let $M$ be a closed Riemannian manifold and let $$\Gamma=\pi_1(M)>\Gamma_1>\Gamma_2>\ldots$$ be a decreasing sequence of finite index normal subgroups of $\Gamma$ with $\bigcap\Gamma_n=1$. Let $\tilde{M}$ be the universal cover of $M$ and let $M_n=\tilde{M}/\Gamma_n$. In addition, suppose that $M$ is aspherical with $\dim M=2k+1$ and $\beta_j^{(2)}=0$ for every $j$. #### Problem 1.1. [Wolfgang Lück] Do we have $$\rho^{(2)}(\tilde{M})=(-1)^k\lim \frac{\log(\|tors (H_k(M_n))\|)}{\|\Gamma:\Gamma_n\|}?$$ 1. Remark. Note that, if $M$ is a hyperbolic $3$-manifold then $\rho^{(2)}(\tilde{M})=-\frac{1}{6\pi}vol(M)$. Moreover, if $\Gamma$ has an elementary amenable normal subgroup, then Question holds for $\Gamma$. • Remark. Note that, the question is true for groups that are limits of left-orderable amenable groups. Also for groups where every non-trivial finitely generated subgroup surjects on $\Z$). • Let $M$ be a closed Riemannian manifold and let $$\Gamma=\pi_1(M)>\Gamma_1>\Gamma_2>\ldots$$ be a decreasing sequence of finite index normal subgroups of $\Gamma$ with $\bigcap\Gamma_n=1$. Let $\tilde{M}$ be the universal cover of $M$ and let $M_n=\tilde{M}/\Gamma_n$. #### Problem 1.2. [Wolfgang Lück] Is $$\rho^{(2)}(\tilde{M})=\lim\limits_n \frac{\rho(M_n)}{\|\Gamma:\Gamma_n\|}?$$ Here $\rho$ is the Ray-Singer torsion and $\rho^{(2)}$ is $L_2$-version of it. • The following is equivalent to the previous problem. #### Problem 1.3. Let $A\in M_l(\mathbb{Z} \Gamma)$, denote $A_k=A/\Gamma_k$. Is it true that $$tr_{L\Gamma}(\log A^A)=\lim \frac{tr(\log A_k^A_k)}{\|\Gamma:\Gamma_k\|}?$$ Here $tr_{L\Gamma}$ is the canonical trace on the group von Neumann algebra $L\Gamma$. • #### Problem 1.4. Is $$\lim \frac{b_{F_p}(\Gamma_n)}{\|\Gamma : \Gamma_n\|}=\lim \frac{rk(\Gamma_n)}{\|\Gamma:\Gamma_n\|}$$ for any (not necessarily finitely generated) group? • Let $\Gamma$ be a finitely presented residually $p$-group. Let $\Gamma_n$ be a normal $p$-chain with $\bigcap \Gamma_n=1$, then $$\lim \frac{b_{\mathbb{Q}}(\Gamma_n)}{\|\Gamma:\Gamma_n\|}\leq \lim \frac{b_{F_p}}{\|\Gamma: \Gamma_n\|}\leq \lim \frac{rk(\Gamma_n)}{\|\Gamma:\Gamma_n\|}$$ #### Problem 1.5. [Misha Ershov] Can these inequalities be strict? Cite this as: AimPL: $L^2$ invariants for finitely generated groups, available at http://aimpl.org/l2invariantsgroups.	{"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": 2, "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": 0.9979787468910217, "perplexity": 275.1380027100603}, "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/1500549436316.91/warc/CC-MAIN-20170728002503-20170728022503-00583.warc.gz"}
https://physics.stackexchange.com/questions/76640/how-do-you-show-from-the-index-notation-that-the-change-of-frame-formula-for-a-m	# How do you show from the index notation that the change of frame formula for a metric must involve the transpose? Let $x^\mu$ and $x^{'\mu}$ be two coordinate systems related by $$dx^{'\mu}~=~S^\mu{}_\nu~ dx^\mu.$$ In index notation the metric in both systems are related by: $$g'_{\rho\sigma}~=~g_{\mu\nu}~(S^{-1})^\mu{}_\rho~(S^{-1})^\nu{}_\sigma.$$ In matrix form this is $$g'~=~(S^{-1})^Tg(S^{-1}).$$ How is it clear from the index notation that the matrix form must involve the transpose matrix? Repeated indices will be summed throughout. Recall that given any two matrices $A = (A_{ij})$ and $B = (B_{ij})$, the matrix product is a new matrix $AB = (C_{ij})$ defined as follows: \begin{align} C_{ij} = A_{ik}B_{kj} \end{align} In particular, if we think of the first index as the row index and the second index as the column index, then we see that in the matrix product, the column index of the first matrix factor (matrix $A$) is being summed with the row index of the second factor (matrix $B$). Now, recall that for $A$ given as above, its transpose is defined by $(A^T)_{ij} = A_{ji}$, so we would have \begin{align} (A^TB)_{ij} = (A^T)_{ik}B_{kj} = A_{ki}B_{kj} \end{align} In other words, when we multiply the transpose of a matrix $A$ with another matrix $B$, in index notation this corresponds to summing over the row indices of both factors $A$ and $B$. Given these observations, and using the standard convention that the left-most index is the row index (regardless of whether it's up or down) and the right-most index is the column index, we see that in the expression \begin{align} (S^{-1})^\mu_{\phantom\mu\rho} g_{\mu\nu}(S^{-1})^\nu_{\phantom\nu\sigma} \end{align} the row index of the first $S^{-1}$ factor is being summed with the row index of $g$; so the first two factors involve the product of $(S^{-1})^T$ and $g$. joshphysics's answer addresses how to convert between the index and matrix notations. Here's something I use to avoid mistakenly converting it to $(S^{-1}gS^{-1})$, which might happen because the two appreances of $S$ in the index notation look symmetric: notice that the expression $$g_{\mu\nu}~(S^{-1})^\mu{}_\rho~(S^{-1})^\nu{}_\sigma$$ is unchanged when we swap $\rho$ with $\sigma$, which means that it represents a symmetric tensor. The expression $$(S^{-1})^Tg(S^{-1})$$ is also symmetric, which we can see by taking the transpose.	{"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": 3, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9832397103309631, "perplexity": 191.0918322028641}, "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-2020-10/segments/1581875148163.71/warc/CC-MAIN-20200228231614-20200229021614-00527.warc.gz"}
https://brilliant.org/problems/trignometrysummation/	# Trignometry+Summation Calculus Level 5 The sum $$\displaystyle \sum _{ n=1 }^{ 50 }{ \tan ^{ -1 }{ \left( \frac { 2n }{ { n }^{ 4 }-{ n }^{ 2 }+1 } \right) } }$$ can be expressed as $$\tan^{-1} k$$. Find the value of $$k$$. ×	{"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": 0.9378113150596619, "perplexity": 1790.0455187061964}, "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-2017-13/segments/1490218187113.46/warc/CC-MAIN-20170322212947-00638-ip-10-233-31-227.ec2.internal.warc.gz"}
https://orinanobworld.blogspot.com/2015/02/flagging-specific-variable-value.html	## Monday, February 2, 2015 ### Flagging a Specific Variable Value A recent question on a web forum, one I've seen asked elsewhere, was the following: in a mathematical programming model, how does one constrain a binary variable to take the value 1 if another variable takes a specific (predefined) value, and 0 otherwise? If the binary variable is $x$, the other variable is $y$, and the target value is $m$, then what we want is \begin{eqnarray}y = m & \implies & x = 1 \\ y \neq m & \implies & x = 0.\end{eqnarray}I hinted at the answer to this at the end of a previous post (Indicator Implies Relation), but perhaps a bit more detail is in order. We will need $y$ to be bounded, say $L\le y \le U$. The easy case is when $y$ is integer valued, in which case $y\neq m$ means either $y \le m-1$ or $y \ge m+1$. One approach (I don't claim it's the only one) is to introduce two new binary variables, $z_1$ and $z_2$. Essentially, $z_1$ will be an indicator for $y\le m-1$, $z_2$ will be an indicator for $y \ge m+1$, and $x$ remains an indicator for $y=m$. To do this, we add the constraints \begin{eqnarray} y & \le & (m-1)z_1 + mx + Uz_2 \\ y & \ge & Lz_1 + mx + (m+1)z_2 \\ z_1 + x + z_2 & = & 1. \end{eqnarray} Life gets trickier if $y$ is continuous. For any given choice of values for the discrete variables, we need the projection of the feasible region onto the subspace of continuous variables to be closed, which rules out strict inequalities. In other words, we can't say $y > m$ or $y < m$ when $x = 0$. The best we can do is pick a small positive parameter $\epsilon > 0$ and treat any value of $y$ in $(m-\epsilon, m+\epsilon)$ as if it were $m$. The resulting inequalities are as above, but with $m \pm 1$ changed to $m \pm \epsilon$: \begin{eqnarray} y & \le & (m-\epsilon)z_1 + mx + Uz_2 \\ y & \ge & Lz_1 + mx + (m+\epsilon)z_2 \\ z_1 + x + z_2 & = & 1. \end{eqnarray}Note that this precludes $y \in (m-\epsilon, m) \cup (m, m+\epsilon)$, i.e., the only value between $m-\epsilon$ and $m+\epsilon$ that $y$ can take is $m$. As a practical matter, you should be careful not to pick $\epsilon$ too small. It's tempting to think in terms of the smallest positive double-precision number known to your compiler, but that could result in $x = 0$ when theoretically $y = m$ but actually the computed value of $y$ contains a bit of rounding error.	{"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": 0.9875016212463379, "perplexity": 201.36836906693134}, "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/1539583513548.72/warc/CC-MAIN-20181021010654-20181021032154-00128.warc.gz"}
https://arxiv.org/abs/1812.07577	astro-ph.CO (what is this?) # Title:Using a Primordial Gravitational Wave Background to Illuminate New Physics Abstract: A primordial spectrum of gravitational waves serves as a backlight to the relativistic degrees of freedom of the cosmological fluid. Any change in the particle physics content, due to a change of phase or freeze-out of a species, will leave a characteristic imprint on an otherwise featureless primordial spectrum of gravitational waves and indicate its early-Universe provenance. We show that a gravitational wave detector such as the Laser Interferometer Space Antenna would be sensitive to physics near 100 TeV in the presence of a sufficiently strong primordial spectrum. Such a detection could complement searches at newly proposed 100 km circumference accelerators such as the Future Circular Collider at CERN and the Super Proton-Proton Collider in China, thereby providing insight into a host of beyond Standard Model issues, including the hierarchy problem, dark matter, and baryogenesis. Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph) Cite as: arXiv:1812.07577 [astro-ph.CO] (or arXiv:1812.07577v1 [astro-ph.CO] for this version) ## Submission history From: Devin Walker [view email] [v1] Tue, 18 Dec 2018 19:00:01 UTC (94 KB)	{"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": 0.800254225730896, "perplexity": 3113.7326042890522}, "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-2019-04/segments/1547583657907.79/warc/CC-MAIN-20190116215800-20190117001800-00506.warc.gz"}
http://math.stackexchange.com/questions/406394/fubini-theorem-for-measure-zero	# Fubini Theorem for measure zero I know Fubini Theorem in calculus, but the measure zero version does not make sense to me: $n=k+1$, and $V_c$ is the "vertical slice" {c}$\times R_l$. Let $A$ be a closed subset of $R^n$ such that $A \cap V_c$ has measure zero in $V_c$ for all $c \in R^k$. Then $A$ has measure zero in $R^n$. Could someone help me explain what does this mean, and how it relates to the Fubini Theorem in calculus? Thank you very much! - Can you explain what the $V_c$ are? – Rookatu May 30 '13 at 5:55 Hi @Rookatu thank you very much for your reminder. $V_c$ is the "vertical slice" {c}$\times R_l$. Also, $n=k+1$. – 1LiterTears May 30 '13 at 6:55 Let $\chi_A$ be the characteristic function of $A$: that is, $\chi_A(x)=1$ when $x\in A$ and $0$ otherwise. The integral of $\chi_A$ with respect to whatever measure is equal to the measure of $A$. This is why the characteristic function is used to make the transition from measures to integrals and back. Fubini's theorem is about integrals. Applied to $\chi_A$, it says that the integral of $\chi_A$ can be found by integrating over each vertical slice first, and then integrating over $c$. Well, if every slice has measure zero, then the integral over every slice is zero. Then $\int 0\,dc =0$, and the conclusion is that $A$ has measure zero.	{"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": 0.9976816773414612, "perplexity": 146.10005762660063}, "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/1454701145751.1/warc/CC-MAIN-20160205193905-00052-ip-10-236-182-209.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/limit-of-a-function.120137/	# Homework Help: Limit of a function 1. May 8, 2006 ### Unskilled could anyone tell me if this have a limit: lim ((exp(x)-1-x)^2)/(x^2 - ln(x^2+1))) x->0 My conclusion is that this doesn't have a limit. Tried everything, this is an problem that i run into. Last edited: May 8, 2006 2. May 8, 2006 ### daveb Have you tried applying L'Hospital's? 3. May 9, 2006 ### VietDao29 Have you tried using Maclaurin Series to solve this problem? :) Hint: The expansion of exp(x) arround x = 0 is: $$e ^ x = 1 + x + \frac{x ^ 2}{2} + ...$$ The expansion of ln(x + 1) arround x = 0 is: $$\ln (x + 1) = x - \frac{x ^ 2}{2} + ...$$ So what's the expansion of ln(x2 + 1) arround x = 0? Can you go from here? :)	{"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": 0.8896098732948303, "perplexity": 3348.830670093929}, "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/1537267159359.58/warc/CC-MAIN-20180923114712-20180923135112-00291.warc.gz"}
https://www.physicsforums.com/threads/force-applied-at-centre-of-mass.188917/	# Force applied at centre of mass 1. Oct 4, 2007 ### chandran If a force is applied at centre of mass the object will only translate and not rotate. Can anyone proove this mathematically? 2. Oct 4, 2007 ### Zorodius Torque is the cross product of the vector from the center of mass to the point where the force is applied (r), and the force. If r is zero, or r is parallel to the force, there will be no torque, and so no rotational force.	{"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": 0.9146230816841125, "perplexity": 518.4179706498877}, "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/1539583510932.57/warc/CC-MAIN-20181017002502-20181017024002-00099.warc.gz"}
http://mathhelpforum.com/advanced-statistics/119981-moment-generating-expected-value.html	# Math Help - Moment-Generating and Expected Value 1. ## Moment-Generating and Expected Value a) Suppose the height of a rectangle is twice its width and the width is a uniform distribution over [0,6]. Find the expected area of the rectangle. b) Let X have m.g.f. of Mx(t) = (1-5t)^-2 for t<1/5. Find the Var(X) 2. a) $A=HW=2W^2$ SO $E(A)=2E(W^2)={1\over 3}\int_0^6 w^2dw$ b) you can differentiate twice and let t=0 to get the first two moments From that you can get the variance. However this is a gamma and you can obtain the variance by inspection.	{"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": 2, "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": 0.9972874522209167, "perplexity": 1154.4848030544513}, "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/1408500832662.33/warc/CC-MAIN-20140820021352-00421-ip-10-180-136-8.ec2.internal.warc.gz"}
https://biust.pure.elsevier.com/en/publications/on-the-chaotic-pole-of-attraction-for-hindmarsh-rose-neuron-dynam/	# On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input Emile Franck Doungmo Goufo, Conrad B. Tabi Research output: Contribution to journalArticlepeer-review 7 Citations (Scopus) ## Abstract Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1, the nerve cell’s behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic. Original language English 023104 1-9 9 Chaos (Woodbury, N.Y.) 29 Published - 2019	{"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": 0.9169382452964783, "perplexity": 2410.9684855444066}, "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/1606141176922.14/warc/CC-MAIN-20201124170142-20201124200142-00034.warc.gz"}
https://worldwidescience.org/topicpages/w/wave+dragon+wave.html	#### Sample records for wave dragon wave 1. Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter; Sørensen, H. C. 1998-01-01 This paper concerns with the development of the wave energy converter (WEC) Wave Dragon. This WEC is based on the overtopping principle. An overview of the performed research done concerning the Wave Dragon over the past years is given, and the results of one of the more comprehensive studies......, concerning a hydraulic evaluation and optimisation of the geometry of the Wave Dragon, is presented. Furthermore, the plans for the future development projects are sketched.... 2. Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter; Friis-Madsen, Erik 2008-01-01 Since March 2003 a prototype of Wave Dragon has been tested in an inland sea in Denmark. This has been a great success with all subsystems tested and improved through working in an offshore environment. The project has proved the Wave Dragon device and has enabled the next stage, a production sized... 3. Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter; Friis-Madsen, Erik; 2008-01-01 Since March 2003 a prototype of Wave Dragon has been tested in an inland sea in Denmark. This has been a great success with all subsystems tested and improved through working in an offshore environment. The project has proved the Wave Dragon device and has enabled the next stage, a production sized... 4. Wave Dragon DEFF Research Database (Denmark) Kramer, Morten; Frigaard, Peter På foranledning af Löwenmark F.R.I, er der udført numeriske beregninger af Wave Dragons (herefter WD) armes effektivitet for forskellige geometriske udformninger. 5 geometriske modeller, hvor WD's arme er forkortet/forlænget er undersøgt for 3 forskellige drejninger af armene. I alt er 15... 5. Wave Dragon DEFF Research Database (Denmark) Kramer, Morten; Frigaard, Peter På foranledning af Löwenmark F.R.I, er der udført numeriske beregninger af Wave Dragons (herefter WD) armes effektivitet for forskellige geometriske udformninger. 5 geometriske modeller, hvor WD's arme er forkortet/forlænget er undersøgt for 3 forskellige drejninger af armene. I alt er 15... 6. Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter; Knapp, W. 2006-01-01 Wave Dragon is a floating wave energy converter working by extracting energy principally by means of overtopping of waves into a reservoir. A 1:4.5 scale prototype has been sea tested for 20 months. This paper presents results from testing, experiences gained and developments made during...... this extended period. The prototype is highly instrumented. The overtopping characteristic and the power produced are presented here. This has enabled comparison between the prototype and earlier results from both laboratory model and computer simulation. This gives the optimal operating point and the expected... 7. Impact of Wave Dragon on Wave Climate DEFF Research Database (Denmark) Andersen, Thomas Lykke; Tedd, James; Kramer, Morten This report is an advisory paper for use in determining the wave dragon effects on hydrography, by considering the effect on the wave climate in the region of a wave dragon. This is to be used in the impact assessment for the Wave Dragon pre-commercial demonstrator.......This report is an advisory paper for use in determining the wave dragon effects on hydrography, by considering the effect on the wave climate in the region of a wave dragon. This is to be used in the impact assessment for the Wave Dragon pre-commercial demonstrator.... 8. The Wave Dragon DEFF Research Database (Denmark) Sørensen, H. C.; Hansen, R.; Friis-Madsen, E. 2000-01-01 The Wave Dragon is an offshore wave energy converter of the overtopping type, utilizing a patented wave reflector design to focus the waves towards a ramp, and the overtopping is used for electricity production through a set of Kaplan/propeller hydro turbines. During the last 2 years, excessive...... design an testing has been performed on a scale 1:50 model of the Wave Dragon, and on a scale 1:3:5 model turbine. Thus survivability, overtopping, hydraulic response, turbine performance and feasibility have been verified.... 9. Wave Dragon MW DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter Wave Dragon is a wave energy converter of the overtopping type. The device has been thoroughly tested on a 1:51.8 scale model in wave laboratories and a 1:4.5 scale model deployed in Nissum Bredning, a large inland waterway in Denmark. Based on the experience gained a full scale, multi MW prototype... 10. Wave Dragon MW DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter Wave Dragon is a wave energy converter of the overtopping type. The device has been thoroughly tested on a 1:51.8 scale model in wave laboratories and a 1:4.5 scale model deployed in Nissum Bredning, a large inland waterway in Denmark. Based on the experience gained a full scale, multi MW prototype... 11. Wave Dragon Buoyancy Regulation Study DEFF Research Database (Denmark) Jakobsen, Jens; Kofoed, Jens Peter Wave Dragon is a wave energy converter, which was deployed offshore at Nissum Bredning in Denmark in 2003. The experience gained from operating Wave Dragon during 2003 and 2004 has shown that the buoyancy regulation system can be improved in a number of ways. This study describes the current... 12. Wave Overtopping Characteristics of the Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter Simulation work has been used extensively with the Wave dragon and other overtopping devices to analyse the power production performance of them and to optimise the structural design and the control strategy. A time domain approach to this is well documented in Jakobsen & Frigaard 1999. Using...... measurements taken from the Wave Dragon Nissum Bredning prototype, some of the previous assumptions have been slightly modified and improved upon, so that the simulation method better represents the reality of what is occurring.... 13. Wave Overtopping Characteristics of the Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter Simulation work has been used extensively with the Wave dragon and other overtopping devices to analyse the power production performance of them and to optimise the structural design and the control strategy. A time domain approach to this is well documented in Jakobsen & Frigaard 1999. Using...... measurements taken from the Wave Dragon Nissum Bredning prototype, some of the previous assumptions have been slightly modified and improved upon, so that the simulation method better represents the reality of what is occurring.... 14. Model testing of Wave Dragon Energy Technology Data Exchange (ETDEWEB) NONE 2001-07-01 Previous to this project a scale model 1:50 of the wave energy converter (WEC) Wave Dragon was built by the Danish Maritime Institute and tested in a wave tank at Aalborg University (AAU). The test programs investigated the movements of the floating structure, mooring forces and forces in the reflectors. The first test was followed by test establishing the efficiency in different sea states. The scale model has also been extensively tested in the EU Joule Craft project JOR-CT98-7027 (Low-Pressure Turbine and Control Equipment for Wave Energy Converters /Wave Dragon) at University College Cork, Hydraulics and Maritime Research Centre, Ireland. The results of the previous model tests have formed the basis for a redesign of the WEC. In this project a reconstruction of the scale 1:50 model and sequential tests of changes to the model geometry and mass distribution parameters will be performed. AAU will make the modifications to the model based on the revised Loewenmark design and perform the tests in their wave tank. Grid connection requirements have been established. A hydro turbine with no movable parts besides the rotor has been developed and a scale model 1:3.5 tested, with a high efficiency over the whole head range. The turbine itself has possibilities for being used in river systems with low head and variable flow, an area of interest for many countries around the world. Finally, a regulation strategy for the turbines has been developed, which is essential for the future deployment of Wave Dragon.The video includes the following: 1. Title, 2. Introduction of the Wave Dragon, 3. Model test series H, Hs = 3 m, Rc = 3 m, 4. Model test series H, Hs = 5 m, Rc = 4 m, 5. Model test series I, Hs = 7 m, Rc = 1.25 m, 6. Model test series I, Hs = 7 m, Rc = 4 m, 7. Rolling title. On this VCD additional versions of the video can be found in the directory 'addvideo' for playing the video on PC's. These versions are: Model testing of Wave Dragon, DVD version 15. Wave Dragon Buoyancy Regulation Study DEFF Research Database (Denmark) Jakobsen, Jens; Kofoed, Jens Peter Wave Dragon is a wave energy converter, which was deployed offshore at Nissum Bredning in Denmark in 2003. The experience gained from operating Wave Dragon during 2003 and 2004 has shown that the buoyancy regulation system can be improved in a number of ways. This study describes the current situ...... situation, and proposes a number of activities in order to improve the buoyancy regulation system. This work was performed under EU ENERGIE contract no. ENK5-CT-2002-00603, and is a contribution to WP 2.3/2.4 and D40/D41.... 16. Wave Dragon Wave Energy Converters Used as Coastal Protection DEFF Research Database (Denmark) Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Kofoed, Jens Peter 2011-01-01 This paper deals with wave energy converters used to reduce the wave height along shorelines. For this study the Wave Dragon wave energy converter is chosen. The wave height reduction from a single device has been evaluated from physical model tests in scale 1:51.8 of the 260 x 150 m, 24 kW/m model...... Spain, to evaluate the potential for reducing wave heights close the shore by means of Wave Dragons.... 17. Wave Dragon Wave Energy Converters Used as Coastal Protection DEFF Research Database (Denmark) Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Kofoed, Jens Peter 2011-01-01 This paper deals with wave energy converters used to reduce the wave height along shorelines. For this study the Wave Dragon wave energy converter is chosen. The wave height reduction from a single device has been evaluated from physical model tests in scale 1:51.8 of the 260 x 150 m, 24 kW/m model... 18. Prototype Testing of the Wave Energy Converter Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter; Friis-Madsen, Erik 2006-01-01 The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power. In the period...... from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57!27 m wide and 237 tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world’s first offshore wave energy... 19. Prototype Testing of the Wave Energy Converter Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter Bak; Friis-Madsen, Erik 2004-01-01 The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power. In the period...... from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57 x 27 m wide and 237 tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world's first offshore wave energy... 20. Design of the Wave Dragon Mooring System DEFF Research Database (Denmark) Parmeggiani, Stefano This report is part of the project “Wave Dragon 1.5 MW North Sea Demonstrator”, funded by the Danish Energy Agency under the EUDP program (J.no. 64010-0405). In phase 1 of the project the hydrodynamic characterization of Wave Dragon was carried out through numerical analysis with a model calibrated...... storm conditions typical of the DanWEC location. The most desirable mooring configuration has also been better defined in terms of horizontal compliance. In phase 3 results from phase 1 shall be used to setup a numerical model for time-domain analysis of the composite system Wave Dragon + moorings... 1. Hydraulic Response of the Wave Energy Converter Wave Dragon in Nissum Bredning DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter This report deals with the hydraulic performance of the wave energy converter Wave Dragon, Nissum Bredning prototype.......This report deals with the hydraulic performance of the wave energy converter Wave Dragon, Nissum Bredning prototype.... 2. Testing, Analysis and Control of Wave Dragon, Wave Energy Converter DEFF Research Database (Denmark) Tedd, James of a textbook, a submitted journal paper and three peer-reviewed conference papers. The content can be broadly divided into four topics: experiences gained with the Wave Dragon prototype device; power-production verification; overtopping analysis; and improvements in control. A comprehensive record...... the expected performance. Other sources of generation are presented, including development and tank testing of a novel power absorbing joint. Wave Dragon belongs in the family of overtopping wave energy converters. The energy is captured by waves running up a ramp and overtopping the crest into a reservoir... 3. Advanced Control Techniques for WEC Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter; Jasinski, M.; 2007-01-01 This paper presents the ongoing work on control of the Wave Dragon wave energy converter. Research is being conducted in and between several centers across Europe. This is building upon the knowledge gained in the prototype project, and will enable much better performance of the future deployment... 4. Experimental Overtopping Investigation for the Wave Dragon DEFF Research Database (Denmark) Borgarino, Bruno; Kofoed, Jens Peter; Tedd, James The present report displays the results from overtopping tests carried on the 1:51.8 Wave Dragon model in September 2007. This tests have been carried on by Bruno Borgarino, James Tedd and Jens Peter Kofoed in the wave tank facilities of Aalborg University. The objective was to provide an updated... 5. Hydraulic Model Tests on Modified Wave Dragon DEFF Research Database (Denmark) Hald, Tue; Lynggaard, Jakob A floating model of the Wave Dragon (WD) was built in autumn 1998 by the Danish Maritime Institute in scale 1:50, see Sørensen and Friis-Madsen (1999) for reference. This model was subjected to a series of model tests and subsequent modifications at Aalborg University and in the following...... are found in Hald and Lynggaard (2001). Model tests and reconstruction are carried out during the phase 3 project: ”Wave Dragon. Reconstruction of an existing model in scale 1:50 and sequentiel tests of changes to the model geometry and mass distribution parameters” sponsored by the Danish Energy Agency... 6. Prototype testing of the wave energy converter wave dragon Energy Technology Data Exchange (ETDEWEB) Kofoed, Jens Peter; Frigaard, Peter [Hydraulics and Coastal Engineering Laboratory, Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, Aalborg 9000 (Denmark); Friis-Madsen, Erik [Loewenmark F.R.I., Copenhagen (Denmark); Soerensen, Hans Chr. [SPOK, Copenhagen (Denmark) 2006-02-01 The Wave Dragon is an offshore wave energy converter of the overtopping type. It consists of two wave reflectors focusing the incoming waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power. In the period from 1998 to 2001 extensive wave tank testing on a scale model was carried at Aalborg University. Then, a 57x27m wide and 237tonnes heavy (incl. ballast) prototype of the Wave Dragon, placed in Nissum Bredning, Denmark, was grid connected in May 2003 as the world's first offshore wave energy converter. The prototype is fully equipped with hydro turbines and automatic control systems, and is instrumented in order to monitor power production, wave climate, forces in mooring lines, stresses in the structure and movements of the Wave Dragon. In the period May 2003 to January 2005 an extensive measuring program has been carried out, establishing the background for optimal design of the structure and regulation of the power take off system. Planning for deployment of a 4MW power production unit in the Atlantic by 2007 is in progress. (author) 7. Investigation of Wave Transmission from a Floating Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Nørgaard, Jørgen Harck; Andersen, Thomas Lykke 2012-01-01 This paper focuses on the calibration of the MIKE21BW model against the measured wave height reduction behind a 24 kW/m Wave Dragon (WD) wave energy converter. A numerical model is used to determine the wave transmission through the floating WD in varying wave conditions. The transmission obtained... 8. Overtopping Measurements on the Wave Dragon Nissum Bredning Prototype DEFF Research Database (Denmark) Frigaard, Peter; Kofoed, Jens Peter; Rasmussen, Michael R. 2004-01-01 The paper describes the methods used to estimate (calculated from some indirect measurements) the overtopping of the wave energy converter Wave Dragon placed in a real sea environment. The wave energy converter in quistion is the 237-tonne heavy Wave Dragon Nissum Bredning Prototype. Comparisons... 9. Hydraulic behaviour of the floating wave energy converter Wave Dragon Energy Technology Data Exchange (ETDEWEB) NONE 2002-07-01 The objective of the project is to establish a scale 1:4.5 test model of the floating offshore wave energy converter - Wave Dragon - for testing at 5 m water depth in the Inlet Nissum Bredning. The test model will be equipped with an existing diameter 340 mm model turbine plus additional outlet tubes simulating the resistance from 1 - 16 turbines. The model will be designed to stay afloat even with a total loss of air pressure in the open bottom buoyancy chambers. The test series will primarily focus on measurements of hydraulic response, forces in the mooring system and overtopping quantities. Also data such as head, rotational speed and power production from the turbine will be monitored during the whole test period. The project will verify the effect of the pressured air buoyancy system, which cannot be scaled correctly in laboratory scale models. The test results will allow for an evaluation of the Wave Dragon power production as a function of sea state and freeboard height, in order to calibrate the existing WD-power simulation software. The model can be utilized for further testing of turbine regulation and stress and strain in the structure, establishing the necessary knowledge base for deploying a full-scale demonstration plant. This CD-ROM contains various videos, reports, notes, conference papers and Power Point presentations on the making of the wave energy converter Wave Dragon. (BA) 10. CFD study of the overtopping discharge of the Wave Dragon wave energy converter DEFF Research Database (Denmark) Eskilsson, K.; Palm, J.; Kofoed, Jens Peter 2015-01-01 The Wave Dragon is a floating Wave Energy Converter (WEC) working by the overtopping principle. The overtopping discharge has been determined by model scale experiments in wave basins. In the present study we numerically simulate the overtopping behavior of the Wave Dragon device using a VOFbased... 11. Survivability mode and extreme loads on the mooring lines of the Wave Dragon Wave Energy Converter Energy Technology Data Exchange (ETDEWEB) Parmeggiani, S.; Kofoed, J.P. 2010-11-15 This report is a product of the cooperation agreement between Wave Dragon and Aalborg University regarding phase 2 of the development of the Wave Dragon Wave Energy Converter. The research is carried out by testing the 1:51.8 scale model of the Wave Dragon, aiming at the assessment of the survivability of the device in extreme waves and evaluation of the design loads for the mooring component. The outcome of the research will be used as input for future research work aimed at the design of the mooring system and the certification of the structural design for the full scale Wave Dragon demonstrator. (Author) 12. Evaluation of Hydraulic Response of the Wave Dragon DEFF Research Database (Denmark) Frigaard, Peter; Kofoed, Jens Peter The present study investigates the hydraulic response of the wave energy converter Wave Dragon. This is done by peforming model tests in a wave tank in the Hydraulics & Coastal Engineering Laboratory at Aalborg University. In the model tests a floating scale model (length scale 1:50) of the Wave...... Dragon is subjected to irregular, long crested irregular and short crested sea conditions corresponding to typical situations under which the Wave Dragon will produce power. Furthermore two situations corresponding to extreme storm conditions are tested. The objective of the study is to determine...... the wave induced forces in the moorings and in the junction between the reflectors and the reservoir part, and motions of the Wave Dragon situated in different sea conditions.... 13. Evaluation of Hydraulic Response of the Wave Dragon DEFF Research Database (Denmark) Frigaard, Peter; Kofoed, Jens Peter The present study investigates the hydraulic response of the wave energy converter Wave Dragon. This is done by peforming model tests in a wave tank in the Hydraulics & Coastal Engineering Laboratory at Aalborg University. In the model tests a floating scale model (length scale 1:50) of the Wave...... Dragon is subjected to irregular, long crested irregular and short crested sea conditions corresponding to typical situations under which the Wave Dragon will produce power. Furthermore two situations corresponding to extreme storm conditions are tested. The objective of the study is to determine...... the wave induced forces in the moorings and in the junction between the reflectors and the reservoir part, and motions of the Wave Dragon situated in different sea conditions.... 14. Investigation of Wave Transmission from a Floating Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Nørgaard, Jørgen Harck; Andersen, Thomas Lykke 2012-01-01 This paper focuses on the calibration of the MIKE21BW model against the measured wave height reduction behind a 24 kW/m Wave Dragon (WD) wave energy converter. A numerical model is used to determine the wave transmission through the floating WD in varying wave conditions. The transmission obtained...... from the MIKE21BW model is compared to results from a simpler model, based on the integration of wave energy flux. The conclusion is that the simplified approach provides results similar to the transmission obtained from the numerical model, both for a single WD and a farm of multiple WDs.... 15. The wave dragon. Now ready for test in real sea Energy Technology Data Exchange (ETDEWEB) Soerensen, H..; Hansen, R.; Friis-Madsen, E. (and others) 2001-07-01 The Wave Dragon is an offshore wave energy converter of the overtopping type, utilizing a patented wave reflector design to focus the waves towards a ramp, and the overtopping is used for electricity production through a set of Kaplan/propeller hydro turbines. During the last 2 years, excessive design and testing has been performed on a scale 1:50 model of the Wave Dragon, and on a scale 1:3.5 model turbine. The survivability, overtopping, hydraulic response, turbine performance and feasibility have been verified. Furthermore regulation strategy, grid connection technology, generator technology, and mooring systems have been accommodated to the Wave Dragon. The main conclusions from this work are elaborated, and the future plans for, and expectations to, the technology is described. (au) 16. Evaluation of hydraulic response of the Wave Dragon Energy Technology Data Exchange (ETDEWEB) NONE 1999-02-01 The present study investigates the hydraulic response of the wave energy converter Wave Dragon. This is done by performing model tests in a wave tank in the Hydraulics and Coastal Engineering Laboratory at Aalborg University. In the model tests a floating scale model (length scale 1:50) of the Wave Dragon is subjected to irregular long crested irregular and short crested sea conditions corresponding to typical situations under which the Wave Dragon will produce power. Furthermore two situations corresponding to extreme storm conditions are tested. The objective of the study is to determine the wave induced forces in the moorings and in the junction between the reflectors and the reservoir part, and motions of the Wave Dragon situated in different sea conditions. On the background of the performed model tests and evaluation of the investigated concept is given. The floating model of Wave Dragon demonstrated a good behaviour and was able to collect water in all sea conditions. Motions in seas with up to 5 m significant wave height were reasonable. Though, the heave motion and the pitch motion seemed to be rather large. wave Dragon survived tests in very severe sea conditions with significant wave heights between 10 m and 15 m. This was the case for long crested waves and short crested as well. Some problems were seen while adjusting the crest freeboard to the different sea conditions. The maximum force in the instrumented junction between the reflector and the reservoir part was found to be approximately 30 MN (3.000 ton). Maximum forces in the mooring system were found to be 20 MN, 30 MN and 140 MN, respectively, giving stresses in the order of 1.000 MPa to 4.000 MPa in the pre-designed wires. (au) 17. Slow waves, sharp waves, ripples, and REM in sleeping dragons. Science.gov (United States) Shein-Idelson, Mark; Ondracek, Janie M; Liaw, Hua-Peng; Reiter, Sam; Laurent, Gilles 2016-04-29 Sleep has been described in animals ranging from worms to humans. Yet the electrophysiological characteristics of brain sleep, such as slow-wave (SW) and rapid eye movement (REM) activities, are thought to be restricted to mammals and birds. Recording from the brain of a lizard, the Australian dragon Pogona vitticeps, we identified SW and REM sleep patterns, thus pushing back the probable evolution of these dynamics at least to the emergence of amniotes. The SW and REM sleep patterns that we observed in lizards oscillated continuously for 6 to 10 hours with a period of ~80 seconds. The networks controlling SW-REM antagonism in amniotes may thus originate from a common, ancient oscillator circuit. Lizard SW dynamics closely resemble those observed in rodent hippocampal CA1, yet they originate from a brain area, the dorsal ventricular ridge, that has no obvious hodological similarity with the mammalian hippocampus. 18. Experimental Modeling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter; Friis-Madsen, Erik 2011-01-01 The Wave Dragon Wave Energy Converter is currently facing a precommercial phase. At this stage of development a reliable overtopping model is highly required, in order to predict the performance of the device at possible deployment locations. A model formulation derived for an overtopping device...... with general geometry has been used so far. The paper presents an updated formulation drawn through the tank testing of a scaled model the Wave Dragon. The sensitivity analysis of the main features influencing the overtopping flow led to an updated model formulation which can be specifically suited...... for the Wave Dragon.... 19. Experimental Modeling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter; Friis-Madsen, Erik 2011-01-01 The Wave Dragon Wave Energy Converter is currently facing a precommercial phase. At this stage of development a reliable overtopping model is highly required, in order to predict the performance of the device at possible deployment locations. A model formulation derived for an overtopping device...... with general geometry has been used so far. The paper presents an updated formulation drawn through the tank testing of a scaled model the Wave Dragon. The sensitivity analysis of the main features influencing the overtopping flow led to an updated model formulation which can be specifically suited...... for the Wave Dragon.... 20. Data Obtained from Prototype Wave Dragon in Nissum Bredning DEFF Research Database (Denmark) Tedd, James William; Curie, Marie; Kofoed, Jens Peter This report is a product of the Project: Sea Testing and Optimisation of Power Production on a Scale 1:4.5 Test Rig of the Offshore Wave Energy Converter Wave Dragon. This report aims to provide access for the project partners to the raw data obtained from the testing period in Nissum Bredning... 1. Data Obtained from Prototype Wave Dragon in Nissum Bredning DEFF Research Database (Denmark) Tedd, James William; Curie, Marie; Kofoed, Jens Peter This report is a product of the Project: Sea Testing and Optimisation of Power Production on a Scale 1:4.5 Test Rig of the Offshore Wave Energy Converter Wave Dragon. This report aims to provide access for the project partners to the raw data obtained from the testing period in Nissum Bredning... 2. Experimental Update of the Overtopping Model Used for the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter; Friis-Madsen, Erik 2013-01-01 An overtopping model specifically suited for Wave Dragon is needed in order to improve the reliability of its performance estimates. The model shall be comprehensive of all relevant physical processes that affect overtopping and flexible to adapt to any local conditions and device configuration....... An experimental investigation is carried out to update an existing formulation suited for 2D draft-limited, low-crested structures, in order to include the effects on the overtopping flow of the wave steepness, the 3D geometry of Wave Dragon, the wing reflectors, the device motions and the non-rigid connection...... of which can be measured in real-time. Instead of using new fitting coefficients, this approach allows a broader applicability of the model beyond the Wave Dragon case, to any overtopping WEC or structure within the range of tested conditions. Predictions reliability of overtopping over Wave Dragon... 3. Experimental Modelling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter The Wave Dragon is a floating slack-moored Wave Energy Converter (WEC) of the overtopping type. Oncoming waves are focused by two wing reflectors towards the ramp of the device, surge-up and overtop into a reservoir placed at a higher level than the surface of the sea. The energy production takes...... place as the water is led back to the sea through a set of low-head hydro-turbines. After many years of development, Wave Dragon (WD) is now facing the phase of pre-commercial demonstration. In this phase it is very important to be able to use the available data to predict the performances of the device...... at different scales and locations. A flexible and comprehensive modelling tool is therefore highly required. Wave Dragon produces power through different steps of energy conversion: 1. Primary energy conversion: overtopping – The energy content of the wave (partly in the kinetic and partly in the potential... 4. Modelling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Pecher, Arthur; Kofoed, Jens Peter 2010-01-01 The Wave Dragon is a floating slack-moored Wave Energy Converter of the overtopping type, which is facing now the last phase of development before the commercial exploitation: the deployment of a full-scale demonstrator. In this phase a modelling tool allowing for accurate predictions of the perf......The Wave Dragon is a floating slack-moored Wave Energy Converter of the overtopping type, which is facing now the last phase of development before the commercial exploitation: the deployment of a full-scale demonstrator. In this phase a modelling tool allowing for accurate predictions... 5. Measurements of Overtopping Flow Time Series on the Wave Dragon, Wave Energy Converter DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter 2009-01-01 A study of overtopping flow series on the Wave Dragon prototype, a low crested device designed to maximise flow, in a real sea, is presented. This study aims to fill the gap in the literature on time series of flow overtopping low crested structures. By comparing to a simulated flow the character......A study of overtopping flow series on the Wave Dragon prototype, a low crested device designed to maximise flow, in a real sea, is presented. This study aims to fill the gap in the literature on time series of flow overtopping low crested structures. By comparing to a simulated flow...... the characteristics of the overtopping flow are discussed and the simulation algorithm is tested. Measured data is shown from a storm build up in October 2006, from theWave Dragon prototype situated in an inland sea in Northern Denmark. This wave energy converter extracts energy from the waves, by funnelling them... 6. Renovation of the Wave Dragon Nissum Bredning Prototype DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter; Friis-Madsen, Erik 2006-01-01 This paper presents developments of the Wave Dragon, a large offshore wave energy converter. A prototype has been tested in a real sea environment for over 20 months. During 2005 the plant has been in harbor for a major overhaul of several of its components. The motivation for the upgrades......, the laboratory testing procedure and the design and manufacture are described. The modifications are complete and the prototype is scheduled to be deployed at a higher energy site in December 2005.... 7. Wave Dragon. Test to evaluate hydraulic response. Report phase A Energy Technology Data Exchange (ETDEWEB) 1999-02-01 Danish Maritime Institute has in the spring 1998 built a model in scale 1:50 of the wave energy converter Wave Dragon. The scale model is based on calculations performed by the inventor Erik Friis-Madsen from the consultant Loewenmark F.R.I. The scale model is tested in the wave tank at Aalborg University, the Hydraulic and Coastal Engineering Laboratory. This report deals with the results from this test (phase A of the test program). The objective of the test series was to get a judgement of the viability of Wave Dragon in extreme sea conditions in the Danish part of the North Sea at a water depth of 30 meters. The test series had to document: The viability of the Wave Dragon in extreme sea conditions up to 100-year waves; the hydraulic response in 7 different sea conditions where forces and movements have been registered. The main findings are: Wave Dragon has the expected behavior, i.e. the converter is able to survive a 100-year storm; An adjustment of the pitch of the converter could improve the energy efficiency; The forces in the mooring system and the junction between wave reflectors and the platform are acceptable. The forces and the movements are registered at 7 different sea conditions. Video recording has been taken during the test. Five of the sea conditions correspond to 'normal' waves in which power will be produced. Two sea conditions correspond to extreme wave situations. The duration of the registration in each sea conditions was approximately 1/2 an hour, i.e. 3.5 hours in scale 1:1. The conclusion is: The planned test series to evaluate the energy performance can start up (phase B of the test program); The energy efficiency is expected to be improved by a slight modification in the geometry of the Wave Dragon. The modifications can include the geometry of the front and the stabilising wing at the rear end of the platform. Further on changes are possible in the stiffness of the junction between the wave reflectors and the platform and 8. Numerical Simulation of Wake Effects in the Lee of a Farm of Wave Dragon Wave Energy Converters DEFF Research Database (Denmark) Beels, C.; Troch, P.; De Visch, K.; 2009-01-01 . In this paper wake effects in the lee of a single Wave Dragon WEC and multiple Wave Dragon WECs are studied in a time-dependent mild-slope equation model. The Wave Dragon WEC is a floating offshore converter of the overtopping type. The water volume of overtopped waves is first captured in a basin above mean...... sea level and then drains back to the sea through hydro turbines. The wake dimensions behind a single Wave Dragon WEC are investigated for uni- and multidirectional waves. An increasing directional spreading results in a faster wave redistribution behind the WEC. The power absorption of a farm of five...... Wave Dragon WECs, installed in a staggered grid, is calculated for varying inbetween distances. It is observed that an in-between distance of 2D is preferred, when taking spatial and safety considerations into account.... 9. Specification of Instrumentation of Multi MW Wave Dragon Offshore Wave Energy Converter DEFF Research Database (Denmark) Gilling, Lasse; Kofoed, Jens Peter Wave Dragon is a wave energy converter of the overtopping type and is described e.g. in Tedd et. al. (2006). The device has been thoroughly tested on a 1:51.8 scale model in wave laboratories and a 1:4.5 scale model deployed in Nissum Bredning, a large inland waterway in Denmark. Based on the exp......Wave Dragon is a wave energy converter of the overtopping type and is described e.g. in Tedd et. al. (2006). The device has been thoroughly tested on a 1:51.8 scale model in wave laboratories and a 1:4.5 scale model deployed in Nissum Bredning, a large inland waterway in Denmark. Based... 10. Extreme Loads on the Mooring Lines and Survivability Mode for the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter; Friis-Madsen, E. 2011-01-01 One of the main challenges Wave Energy Converters have to face on the road towards commercialization is to ensure survivability in extreme condition at a reasonable capital costs. For a floating device like the Wave Dragon, a reliable mooring system is essential. The control strategy of the Wave...... by approximately 20-30% by lowering the crest level and balancing the device to lean a little towards the front.... 11. Development of the Wave Energy Converter -Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter; Sørensen, Hans Christian; 2000-01-01 2Over the years wave energy has gradually been brought into focus, as it has become clear that the fossil energy resources are limited, and cause large environmental problems, e.g. CO2 pollution. On this background a number of different wave energy converters have been proposed. In Denmark...... the government have decided to appropriate 20 mill. DKK (approx. 2,7 mill. EUR) to the development of wave energy devices over two years, 1998-1999, and the European Community (EC) also supports the development through the JOULECRAFT program.... 12. Experimental Update of the Overtopping Model Used for the Wave Dragon Wave Energy Converter Energy Technology Data Exchange (ETDEWEB) Parmeggiani, Stefano [Wave Dragon Ltd., London (United Kingdom); Kofoed, Jens Peter [Aalborg Univ. (Denmark). Department of Civil Engineering; Friis-Madsen, Erik [Wave Dragon Ltd., London (United Kingdom) 2013-04-15 An overtopping model specifically suited for Wave Dragon is needed in order to improve the reliability of its performance estimates. The model shall be comprehensive of all relevant physical processes that affect overtopping and flexible to adapt to any local conditions and device configuration. An experimental investigation is carried out to update an existing formulation suited for 2D draft-limited, low-crested structures, in order to include the effects on the overtopping flow of the wave steepness, the 3D geometry of Wave Dragon, the wing reflectors, the device motions and the non-rigid connection between platform and reflectors. The study is carried out in four phases, each of them specifically targeted at quantifying one of these effects through a sensitivity analysis and at modeling it through custom-made parameters. These are depending on features of the wave or the device configuration, all of which can be measured in real-time. Instead of using new fitting coefficients, this approach allows a broader applicability of the model beyond the Wave Dragon case, to any overtopping WEC or structure within the range of tested conditions. Predictions reliability of overtopping over Wave Dragon increased, as the updated model allows improved accuracy and precision respect to the former version. 13. Experimental Update of the Overtopping Model Used for the Wave Dragon Wave Energy Converter Directory of Open Access Journals (Sweden) 2013-04-01 Full Text Available An overtopping model specifically suited for Wave Dragon is needed in order to improve the reliability of its performance estimates. The model shall be comprehensive of all relevant physical processes that affect overtopping and flexible to adapt to any local conditions and device configuration. An experimental investigation is carried out to update an existing formulation suited for 2D draft-limited, low-crested structures, in order to include the effects on the overtopping flow of the wave steepness, the 3D geometry of Wave Dragon, the wing reflectors, the device motions and the non-rigid connection between platform and reflectors. The study is carried out in four phases, each of them specifically targeted at quantifying one of these effects through a sensitivity analysis and at modeling it through custom-made parameters. These are depending on features of the wave or the device configuration, all of which can be measured in real-time. Instead of using new fitting coefficients, this approach allows a broader applicability of the model beyond the Wave Dragon case, to any overtopping WEC or structure within the range of tested conditions. Predictions reliability of overtopping over Wave Dragon increased, as the updated model allows improved accuracy and precision respect to the former version. 14. Power Production Experience from Wave Dragon Prototype Testing in Nissum Bredning DEFF Research Database (Denmark) Frigaard, Peter; Kofoed, Jens Peter The first Wave Dragon prototype power production testing started May 2003 and ended temporarily primo 2005. In the mentioned period Wave Dragon was situated in a corner of Nissum Bredning with relative little amount of wave energy. Main purpose of the tests was demonstration of survivability... 15. Model Testing of Forces in the Reflector Joint and Mooring Forces on Wave Dragon DEFF Research Database (Denmark) Gilling, Lasse; Kofoed, Jens Peter; Tedd, James This report aims to present the results of a test series analysing the forces in the redesigned reflector joint and the forces in the main mooring link. The resluts presented are intended to be used by WD project partners, for the design and construction of the joint on the prototype Wave Dragon...... at Nissum Bredning and for future North Sea scale Wave Dragon. Lengths, forces and other dimentions presented are scaled to the North sea Wave Dragon unless otherwise specified.... 16. Model Testing of Forces in the Reflector Joint and Mooring Forces on Wave Dragon DEFF Research Database (Denmark) Gilling, Lasse; Kofoed, Jens Peter; Tedd, James This report aims to present the results of a test series analysing the forces in the redesigned reflector joint and the forces in the main mooring link. The resluts presented are intended to be used by WD project partners, for the design and construction of the joint on the prototype Wave Dragon...... at Nissum Bredning and for future North Sea scale Wave Dragon. Lengths, forces and other dimentions presented are scaled to the North sea Wave Dragon unless otherwise specified.... 17. The Wave Dragon: tests on a modified model Energy Technology Data Exchange (ETDEWEB) Martinelli, Luca; Frigaard, Peter 1999-09-01 A modified floating model of the Wave Dragon was tested for movements, overtopping and forces on critical positions. The modifications and consequent testing of the model are part of a R and D programme. 18 tests (repetitions included) were carried out during May 1999. Forces in 7 different positions and movements for three degrees of freedom (heave, pitch and surge) were recorded for 7 wave situations. Total overtopping was measured for 5 different wave situations. Furthermore influence of crest freeboard was tested. Sensitivity to the energy spreading in multidirectional seas was investigated. A typical exponential equation describing overtopping was fitted to the data in case of frequent wave conditions. The formula is compared to the present tests. (au) 18. Wave Induced Stresses Measured at the Wave Dragon Nissum Bredning Prototype DEFF Research Database (Denmark) Corona, L.; Kofoed, Jens Peter 2006-01-01 The paper describes the wave induced loading on the overtopping based wave energy converter Wave Dragon. Focus is put on the junction between the main body and the reflector, also called the "shoulder part", where large cross sectional forces and bending moments acts. There are two main objectives...... for this paper, first to verify the FEM results obtained by Niras, Danish society in charge of the finite element modelling and structural design, and then to make a first experimental fatigue analysis of a particular part of the Wave Dragon. This last part shall be considered as an exercise for the further work...... that is to be done for the fatigue analysis, and which is not part of this paper.... 19. Preliminary Results from Second Phase Sea Testing of the Wave Dragon Prototype Wave Energy Converter DEFF Research Database (Denmark) Soerensen, Hans Chr.; Tedd, James; Friis-Madsen, Erik; 2006-01-01 In March 2006 the prototype Wave Dragon has been redeployed to a more energetic site in Nissum Bredning an inland sea in Western Denmark. This has followed a period of renovation of many aspects of the device which have resulted in 20% higher energy output. This paper describes the preliminary re... 20. Preliminary Results from Second Phase Sea Testing of the Wave Dragon Prototype Wave Energy Converter DEFF Research Database (Denmark) Soerensen, Hans Chr.; Tedd, James; Friis-Madsen, Erik 2006-01-01 In March 2006 the prototype Wave Dragon has been redeployed to a more energetic site in Nissum Bredning an inland sea in Western Denmark. This has followed a period of renovation of many aspects of the device which have resulted in 20% higher energy output. This paper describes the preliminary... 1. Low-pressure hydro turbines and control equipment for wave energy converters (Wave Dragon). Final report Energy Technology Data Exchange (ETDEWEB) Soerensen, H.C.; Hansen, R. 2001-06-01 The Wave Dragon is a 4 MW floating offshore wave energy converter of the overtopping type. Through performing tests on a scale 1:50 model of the Wave Dragon, real-time overtopping time series were provided. These allowed the development of a feasible turbine and regulation strategy for handling the varying heads and flows occurring in the reservoir. A model turbine with a runner diameter of 340 mm was designed, and tested in a conventional turbine test stand. The results revealed very high efficiencies (91.3% peak efficiency), and more importantly a very flat performance curve yielding high turbine efficiency for the complete range of heads available at the Wave Dragon. A suitable power take-off and grid connection system was developed, addressing power quality issues, as well as more practical issues of flexible cabling solutions. It was concluded that feasible solutions to the technical barriers envisioned prior to the project had been found. Also means for improving the overtopping characteristics of the device were put forward. The feasibility of the Wave Dragon at original 1st generation design was investigated and key performance figures were given as net annual power production of 5.1-3.1 GWh/year, 2,775-3,150 Euro/kW in construction costs and a power production price of 0.19-0.27 Euro/kWh. The figures includes availability losses, all losses in the power train, and losses from restricted freedom of movement for two of the scenarios, with a wave energy potential of 16 and 24 kW/m wave front respectively. Significant scope for improvement, especially from enhanced overtopping from improved design, mass production and learning effects were also identified. Through implementing the known technical improvements to the Wave Dragon design identified through the project an annual net power production of 8.9 GWh/year and a production price of 0.12 Euro/kWh is foreseen for a 24 kW/m wave potential. With additional technical improvements, mass production benefits and 2. Model Testing of Hydraulic Damping of the Reflector Joint on Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter Further development of the Wave Dragon wave energy converter in preparation for full-scale demonstration in the North Sea, PHASE A. FU4305, A4305 & ENS j.nr. 7903-030......Further development of the Wave Dragon wave energy converter in preparation for full-scale demonstration in the North Sea, PHASE A. FU4305, A4305 & ENS j.nr. 7903-030... 3. Model Testing of Hydraulic Damping of the Reflector Joint on Wave Dragon DEFF Research Database (Denmark) Tedd, James; Kofoed, Jens Peter Further development of the Wave Dragon wave energy converter in preparation for full-scale demonstration in the North Sea, PHASE A. FU4305, A4305 & ENS j.nr. 7903-030......Further development of the Wave Dragon wave energy converter in preparation for full-scale demonstration in the North Sea, PHASE A. FU4305, A4305 & ENS j.nr. 7903-030... 4. Calibration and validation of measurement system. Wave Dragon, Nissum Bredning Energy Technology Data Exchange (ETDEWEB) Kofoed, J.P-; Riemann, S.; Knapp, W. 2004-03-01 This report deals with the calibration of the measuring equipment on board the Wave Dragon, Nissum Bredning (WD-NB) prototype. The report covers the following instruments on board WD-NB: 1) Pressure transducers. 2) Force transducers. 3) Accelerometers. 4) Displacement sensors. 5) Strain gauges. 6) Inclinometers. All of these instruments are connected to the HBM MGC+ amplifier and data acquisition unit. In the following the calibration will be dealt with individually. Furthermore, a preliminary calibration of the siphon and dummy turbines has been carried out and this is also described in the following. (au) 5. Hydraulic model tests on modified Wave Dragon. Phase 3 Energy Technology Data Exchange (ETDEWEB) Hald, T.; Lynggaard, J. 2002-11-01 The purpose of this report is to describe the model tests conducted with a new designed 2. generation WD model as well as obtained model test results. Tests are conducted as sequential reconstruction followed by physical model tests. All details concerning the reconstruction are found in Hald and Lynggaard (2001). Model tests and reconstruction are carried out during the phase 3 project: 'Wave Dragon. Reconstruction of an existing model in scale 1:50 and sequential tests of changes to the model geometry and mass distribution parameters' sponsored by the Danish Energy Agency (DEA) wave energy programme. The tests will establish a well documented basis for the development of a 1:4.5 scale prototype planned for testing Nissum Bredning, a sea inlet on the Danish West Coast. (au) 6. Experimental modelling of the overtopping flow on the Wave Dragon Wave Energy Converter Energy Technology Data Exchange (ETDEWEB) Parmeggiani, S.; Kofoed, J.P. 2010-11-15 The Wave Dragon is a floating slack-moored Wave Energy Converter (WEC) of the overtopping type. Oncoming waves are focused by two wing reflectors towards the ramp of the device, surge-up and overtop into a reservoir placed at a higher level than the surface of the sea. The energy production takes place as the water is led back to the sea through a set of low-head hydro-turbines. After many years of development, Wave Dragon (WD) is now facing the phase of pre-commercial demonstration. In this phase it is very important to be able to use the available data to predict the performances of the device at different scales and locations. A flexible and comprehensive modelling tool is therefore highly required. Wave Dragon produces power through different steps of energy conversion: 1. Primary energy conversion: overtopping - The energy content of the wave (partly in the kinetic and partly in the potential form) is transferred to the device in the form of volumes of water coming into the reservoir. These volumes are stored at a higher level than the surrounding sea, being a stock of potential energy. 2. Secondary energy conversion: turbines - The potential energy stored in the reservoir is transformed into mechanical energy as the water flows back to the sea, activating the lowhead hydro-turbines. 3. Tertiary energy conversion step: generators - The turbines shaft rotation activates the permanent magnet generators, converting mechanical energy into electrical energy. 4. Grid connection and delivery of the power - The electricity produced is delivered to the grid at the right frequency, by means of a frequency converter. The present research is focused on the overtopping. Being the primary energy conversion mechanism of the WD, the overtopping is indeed the stage where the performances of the device are influenced by local conditions and the geometric features of the set-up. This makes it the right step where to account for these features through an accurate modelling 7. Survivability Mode and Extreme Loads on the Mooring Lines of the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter of the survivability of the device in extreme waves and evaluation of the design loads for the mooring component. The testing has been carried out in October 2010 by PhD student Stefano Parmeggiani and Master students Giovanna Bevilacqua and Giacomo Girardi Ferruzza at the Hydraulic and Coastal Laboratories...... of the department of Civil Engineering at Aalborg University. The outcome of the research will be used as input for future research work aimed at the design of the mooring system and the certification of the structural design for the full scale Wave Dragon demonstrator.... 8. Description of the Power Take-off System on board the Wave Dragon Prototype DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter; Knapp, Wilfried 2005-01-01 The paper describes the power take-off system of the overtopping based wave energy converter Wave Dragon (WD). Focus is put on the hydro turbine arrangement used for the extraction of the potential energy in the water obtained by wave overtopping of the ramp into the reservoir.......The paper describes the power take-off system of the overtopping based wave energy converter Wave Dragon (WD). Focus is put on the hydro turbine arrangement used for the extraction of the potential energy in the water obtained by wave overtopping of the ramp into the reservoir.... 9. Measurements of overtopping flow time series on the Wave Dragon, wave energy converter Energy Technology Data Exchange (ETDEWEB) Tedd, James; Peter Kofoed, Jens [Department of Civil Engineering, Aalborg University, Sohngaardhomsvej 57, Aalborg 9000 (Denmark) 2009-03-15 A study of overtopping flow series on the Wave Dragon prototype, a low crested device designed to maximise flow, in a real sea, is presented. This study aims to fill the gap in the literature on time series of flow overtopping low crested structures. By comparing to a simulated flow the characteristics of the overtopping flow are discussed and the simulation algorithm is tested. Measured data is shown from a storm build up in October 2006, from the Wave Dragon prototype situated in an inland sea in Northern Denmark. This wave energy converter extracts energy from the waves, by funnelling them to run-up a ramp and overtop into a reservoir. This water is stored at a higher level than the average sea surface, before being discharged through hydro turbines. The waves, device sea handling and overtopping flow are measured by pressure transducers ahead of, beneath and in the device. Comparisons of the distribution and correlation show that the measurements support the use of the algorithm for generating a simulated flow. (author) 10. Application of the Time-Dependent Mild-Slope Equations for the Simulation of Wake Effects in the Lee of a Farm of Wave Dragon Wave Energy Converters DEFF Research Database (Denmark) Beels, Charlotte; Troch, Peter; Visch, Kenneth De; 2010-01-01 in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus...... and reservoir) are simulated as porous structures, exhibiting the same reflection, respectively absorption characteristics as obtained for the prototype Wave Dragon WEC. The wake effects behind a single Wave Dragon WEC are studied in detail for uni- and multidirectional waves. The shadow zone indicating...... the wake effect is decreasing with increasing directional spreading. The wake in the lee of a farm of five Wave Dragon WECs, installed in a staggered grid (3 WECs in the first row and 2 WECs in the second row), is calculated for three in-between distances of respectively D, 2D and 3D, with D the distance... 11. Experimental Modelling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter The Wave Dragon is a floating slack-moored Wave Energy Converter (WEC) of the overtopping type. Oncoming waves are focused by two wing reflectors towards the ramp of the device, surge-up and overtop into a reservoir placed at a higher level than the surface of the sea. The energy production takes...... place as the water is led back to the sea through a set of low-head hydro-turbines. After many years of development, Wave Dragon (WD) is now facing the phase of pre-commercial demonstration. In this phase it is very important to be able to use the available data to predict the performances of the device...... form) is transferred to the device in the form of volumes of water coming into the reservoir. These volumes are stored at a higher level than the surrounding sea, being a stock of potential energy. 2. Secondary energy conversion: turbines – The potential energy stored in the reservoir is transformed... 12. Modelling of the Overtopping Flow on the Wave Dragon Wave Energy Converter DEFF Research Database (Denmark) Parmeggiani, Stefano; Pecher, Arthur; Kofoed, Jens Peter 2010-01-01 The Wave Dragon is a floating slack-moored Wave Energy Converter of the overtopping type, which is facing now the last phase of development before the commercial exploitation: the deployment of a full-scale demonstrator. In this phase a modelling tool allowing for accurate predictions of the perf......The Wave Dragon is a floating slack-moored Wave Energy Converter of the overtopping type, which is facing now the last phase of development before the commercial exploitation: the deployment of a full-scale demonstrator. In this phase a modelling tool allowing for accurate predictions...... of the performance of the device at different scaling ratios and locations of interest is strongly required. The overtopping, depending on the local conditions of the deployment site, is identified as the right stage to be considered in the modelling. The existing formulation of the overtopping model needs...... to be updated in order to represent more accurately the effects of the geometrical features and stability of the device and of the local conditions and nonscalable parameters on the overtopping flow. The paper analyses the conditions at which the present formulation has been established and proposes a strategy... 13. Influence of Buoyancy Control Performance on Power Production by the Wave Dragon Nissum Bredning Prototype DEFF Research Database (Denmark) Kofoed, Jens Peter; Tedd, James; Friis-Madsen, E. 2007-01-01 This paper reports on the real sea performance of the buoyancy control system of Wave Dragon, a floating wave energy converter using the overtopping principle. The device operates with the full independent control system which has been tested during three years of operation. The impact of the buo......This paper reports on the real sea performance of the buoyancy control system of Wave Dragon, a floating wave energy converter using the overtopping principle. The device operates with the full independent control system which has been tested during three years of operation. The impact... 14. Modelling and Testing of Wave Dragon Wave Energy Converter Towards Full Scale Deployment DEFF Research Database (Denmark) Parmeggiani, Stefano -commercial stage in which it has proven difficult to secure the necessary funding for the deployment of a full-scale demonstrator unit. The work presented aims at easing this process, by increasing public and scientific knowledge of the device, as well as by showing the latest progress in its development. Research....... This is mainly due to the development of an updated overtopping model specifically suited to Wave Dragon, which allows greater quality to predictions of the primary energy absorption of the device compared to previous versions. At the same time an equitable approach has been described and used in the performance......, the research has also provided a deeper insight into the physics of the overtopping process by individually assessing the influence of related device configuration and wave features, which goes beyond the present application and may be used for other overtopping WECs as well. Comprehensive analysis... 15. Performance Assessment of the Wave Dragon Wave Energy Converter Based on the EquiMar Methodology DEFF Research Database (Denmark) Parmeggiani, Stefano; Chozas, Julia Fernandez; Pecher, Arthur 2011-01-01 At the present pre-commercial phase of the wave energy sector, device developers are called to provide reliable estimates on power performance and production at possible deployment locations. The EU EquiMar project has proposed a novel approach, where the performance assessment is based mainly...... on experimental data deriving from sea trials rather than solely on numerical predictions. The study applies this methodology to evaluate the performance of Wave Dragon at two locations in the North Sea, based on the data acquired during the sea trials of a 1:4.5 scale prototype. Indications about power...... performance and production of the device at the target locations, as well as on the applicability of the methodology, are provided.... 16. Development of Wave Dragon from Scale 1:50 to Prototype DEFF Research Database (Denmark) Soerensen, H. C.; Friis-Madsen, E.; Panhauser, W.; 2003-01-01 The Wave Dragon is a 4 to 11 MW offshore wave energy converter of the overtopping type. It basically consists of two wave reflectors focusing the waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power......’s first offshore wave energy converter. During the coming 2 years an extensive measuring program will establish the background for optimal design of the structure and regulation of the power take off system. Planning for full scale deployment of a 7 MW unit within the next 2-3 years is in progress.... 17. Application of the time-dependent mild-slope equations for the simulation of wake effects in the lee of a farm of Wave Dragon wave energy converters Energy Technology Data Exchange (ETDEWEB) Beels, Charlotte; Troch, Peter; De Visch, Kenneth; De Backer, Griet [Ghent University, Department of Civil Engineering, Technologiepark 904, B-9052 Zwijnaarde (Belgium); Kofoed, Jens Peter [Aalborg University, Department of Civil Engineering, Sohngaardsholmsvej 57, DK-9000 Aalborg (Denmark) 2010-08-15 Time-dependent mild-slope equations have been extensively used to compute wave transformations near coastal and offshore structures for more than 20 years. Recently the wave absorption characteristics of a Wave Energy Converter (abbreviated as WEC) of the overtopping type have been implemented in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus the incident wave power towards a ramp. The focussed waves run up the ramp and overtop in a water reservoir above mean sea level. The obtained potential energy is converted into electricity when the stored water drains back to the sea through hydro turbines. The wave reflectors and the main body (ramp and reservoir) are simulated as porous structures, exhibiting the same reflection, respectively absorption characteristics as obtained for the prototype Wave Dragon WEC. The wake effects behind a single Wave Dragon WEC are studied in detail for uni- and multidirectional waves. The shadow zone indicating the wake effect is decreasing with increasing directional spreading. The wake in the lee of a farm of five Wave Dragon WECs, installed in a staggered grid (3 WECs in the first row and 2 WECs in the second row), is calculated for three in-between distances of respectively D, 2D and 3D, with D the distance between the tips of the wave reflectors of a single WEC. As a result, a farm of five Wave Dragon WECs installed in a staggered grid with an in-between distance of 2D is preferred, when taking cost and spatial considerations into account. (author) 18. The environmental impact of a Wave Dragon array operating in the Black Sea. Science.gov (United States) Diaconu, Sorin; Rusu, Eugen 2013-01-01 The present work describes a study related to the influence on the shoreline dynamics of a wave farm consisting of Wave Dragon devices operating in the western side of the Black Sea. Based on historical data analysis of the wave climate, the most relevant environmental conditions that could occur were defined, and for these cases, simulations with SWAN spectral phase averaged wave model were performed. Two situations were considered for the most representative patterns: model simulations without any wave energy converter and simulations considering a wave farm consisting of six Wave Dragon devices. Comparisons of the wave model outputs have been carried out in both geographical and spectral spaces. The results show that although a significant influence appears near the wave farm, this gradually decreases to the coast line level. In order to evaluate the influence of the wave farm on the longshore currents, a nearshore circulation modeling system was used. In relative terms, the longshore current velocities appear to be more sensitive to the presence of the wave farm than the significant wave height. Finally, the possible impact on the marine flora and fauna specific to the target area was also considered and discussed. 19. The Environmental Impact of a Wave Dragon Array Operating in the Black Sea Directory of Open Access Journals (Sweden) Sorin Diaconu 2013-01-01 Full Text Available The present work describes a study related to the influence on the shoreline dynamics of a wave farm consisting of Wave Dragon devices operating in the western side of the Black Sea. Based on historical data analysis of the wave climate, the most relevant environmental conditions that could occur were defined, and for these cases, simulations with SWAN spectral phase averaged wave model were performed. Two situations were considered for the most representative patterns: model simulations without any wave energy converter and simulations considering a wave farm consisting of six Wave Dragon devices. Comparisons of the wave model outputs have been carried out in both geographical and spectral spaces. The results show that although a significant influence appears near the wave farm, this gradually decreases to the coast line level. In order to evaluate the influence of the wave farm on the longshore currents, a nearshore circulation modeling system was used. In relative terms, the longshore current velocities appear to be more sensitive to the presence of the wave farm than the significant wave height. Finally, the possible impact on the marine flora and fauna specific to the target area was also considered and discussed. 20. The Environmental Impact of a Wave Dragon Array Operating in the Black Sea Science.gov (United States) Rusu, Eugen 2013-01-01 The present work describes a study related to the influence on the shoreline dynamics of a wave farm consisting of Wave Dragon devices operating in the western side of the Black Sea. Based on historical data analysis of the wave climate, the most relevant environmental conditions that could occur were defined, and for these cases, simulations with SWAN spectral phase averaged wave model were performed. Two situations were considered for the most representative patterns: model simulations without any wave energy converter and simulations considering a wave farm consisting of six Wave Dragon devices. Comparisons of the wave model outputs have been carried out in both geographical and spectral spaces. The results show that although a significant influence appears near the wave farm, this gradually decreases to the coast line level. In order to evaluate the influence of the wave farm on the longshore currents, a nearshore circulation modeling system was used. In relative terms, the longshore current velocities appear to be more sensitive to the presence of the wave farm than the significant wave height. Finally, the possible impact on the marine flora and fauna specific to the target area was also considered and discussed. PMID:23844401 1. Design of a 1.5MW Wave Dragon DEFF Research Database (Denmark) Soerensen, H. C.; Friis-Madsen, E.; Parmeggiani, Stefano 2013-01-01 The paper discusses results of regular wave tests conducted at the University of Naples “Federico II” with the purpose of investigating the qualitative features and the magnitude of the wave pressures acting onto the front face of a Seawave Slot-Cone Generator (SSG). Various wave conditions have... 2. Design of a 1.5MW Wave Dragon DEFF Research Database (Denmark) Soerensen, H. C.; Friis-Madsen, E.; Parmeggiani, Stefano 2013-01-01 The paper discusses results of regular wave tests conducted at the University of Naples “Federico II” with the purpose of investigating the qualitative features and the magnitude of the wave pressures acting onto the front face of a Seawave Slot-Cone Generator (SSG). Various wave conditions have ... 3. Forces and overtopping on 2. generation Wave Dragon for Nissum Bredning. Phase 3 Energy Technology Data Exchange (ETDEWEB) Hald, T.; Frigaard, P. 2001-11-01 The purpose of this report is to summarize forcing and overtopping on the redesigned Wave Dragon model. The results will establish a basis for the development of the 1:4.5 scale prototype planned for testing in Nissum Bredning, a sea inlet on the Danish West Coast. For comparison also results obtained using the 1. generation are referred in this report. (au) 4. 3 Years Experience with Energy Production on the Nissum Bredning Wave Dragon Prototype DEFF Research Database (Denmark) Frigaard, Peter; Tedd, James; Kofoed, Jens Peter 2006-01-01 Wave Dragon is a floating wave energy converter working by extracting energy principally by means of overtopping of waves into a reservoir. A 1:4.5 scale prototype has been sea tested for 20 months. This paper presents results from testing, experiences gained and developments made during...... this extended period. The prototype is highly instrumented. The overtopping characteristic and the power produced are presented here. This has enabled comparison between the prototype and earlier results from both laboratory model and computer simulation. This gives the optimal operating point and the expected... 5. The Wave Dragon: 3D overtopping tests on a floating model Energy Technology Data Exchange (ETDEWEB) Martinelli, Luca; Frigaard, Peter 1999-05-01 In order to investigate the overtopping likely to occur in the Wave Dragon (WD), some tests were carried out measuring the total overtopping volumes on a floating 1:50 model for 5 selected wave conditions. The model set-up and the tests are first described. The aim of the tests is to measure all the water overtopping the crest freeboard and, if possible, to obtain some elements to enhance the WD efficiency. A typical exponential equation describing overtopping has been fitted to the data. Tests results are then given and compared to previous tests performed in a 2D non-floating model of the structure. (au) 6. Wave DEFF Research Database (Denmark) Ibsen, Lars Bo 2008-01-01 Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many t... 7. Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Petersen, Anne-Louise S. 2004-01-01 Udvikling og produktion af vindmøller har været en af de største danske erhvervssucceser gennem de sidste 10 år. Nu er det næste danske bud på en vedvarende energikilde under udvikling havets bølger skal fanges, og deres energi skal tappes.... 8. Wave Dragon DEFF Research Database (Denmark) Kofoed, Jens Peter; Petersen, Anne-Louise S. 2004-01-01 Udvikling og produktion af vindmøller har været en af de største danske erhvervssucceser gennem de sidste 10 år. Nu er det næste danske bud på en vedvarende energikilde under udvikling havets bølger skal fanges, og deres energi skal tappes.......Udvikling og produktion af vindmøller har været en af de største danske erhvervssucceser gennem de sidste 10 år. Nu er det næste danske bud på en vedvarende energikilde under udvikling havets bølger skal fanges, og deres energi skal tappes.... 9. Automatic control of freeboard and turbine operation. Wave Dragon, Nissum Bredning Energy Technology Data Exchange (ETDEWEB) Kofoed, Jens Peter; Frigaard, P. [Aalborg Univ. (Denmark); Friis-Madsen, Erik [Wave Dragon ApS (Denmark); Nimskov, M. [Balslev (Denmark) 2004-02-01 This report deals with the modules for automatic control of freeboard and turbine operation on board the Wave Dragon, Nissum Bredning (WD-NB) prototype, and covers what has been going on up to ultimo 2003. The modules have been implemented on board WD-NB by means of a Siemens PLC. The control and monitoring of the PLC is achieved through a SCADA software package (SIMATIC WinCC V6) running on a Windows 2000 PC situated on board. A preliminary Users manual is available (Nimskov, 2003). The two modules for automatic control of freeboard and turbine operation are denoted 'Buoyancy' and 'Generators', respectively, in the SCADA system. The 'Buoyancy' part controls the freeboard by blowing air into or letting air out of air chambers underneath the structure, and thereby raise or lower it. The 'generator' part controls the generators, and thereby the turbines, by switching them on and of in order to maintain the water level in the reservoir within the specified work span. Furthermore, the generators are controlled by frequency converters, so the rotational speed for each turbine is achieved, corresponding to the optimal operation point. (au) 10. Comparison of Mooring Loads in Survivability Mode on the Wave Dragon Wave Energy Converter Obtained by a Numerical Model and Experimental Data DEFF Research Database (Denmark) Parmeggiani, Stefano; Muliawan, Made Jaya; Gao, Zhen; 2012-01-01 to be carried out numerically, through coupled analyses of alternative solutions. The present study deals with the preliminary hydrodynamic characterization of Wave Dragon needed in order to calibrate the numerical model to be used for the mooring design. A hydrodynamic analysis of the small scale model......, with experimental results derived from tank tests of a small scale model. Due to the complex geometry of the device, a sensitivity analysis is performed to discuss the influence of the mean position on the quality of the numerical predictions. Good correspondence is achieved between the experimental and numerical...... model. The numerical model is hence considered reliable for future design applications.... 11. Experimental Study Related to the Mooring Design for the 1.5 MW Wave Dragon WEC Demonstrator at DanWEC DEFF Research Database (Denmark) Parmeggiani, Stefano; Kofoed, Jens Peter; Friis-Madsen, Erik 2013-01-01 The paper presents the results of an experimental study identifying the response of a 1.5 MW Wave Dragon to extreme conditions typical of the DanWEC test center. The best strategies allowing for a reduction in the extreme mooring tension have also been investigated, showing that this is possible... 12. Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena Science.gov (United States) Peng, Huai-Wu; Li, Rui-Qu; Chen, Song-Ze; Li, Cun-Biao 2008-02-01 This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency. The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam. Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities (the same as the surface elevation), i.e. Iω ~ ω-3.5. The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of 'narrowband pumping' for a direct cascade of energy. Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage. 13. Correlation dimension analysis and capillary wave turbulence in Dragon-Wash phenomena Institute of Scientific and Technical Information of China (English) Peng Huai-Wu; Li Rui-Qu; Chen Song-Ze; Li Cun-Biao 2008-01-01 This paper describes the evolution of surface capillary waves of deep water excited by gradually increasing the lateral external force at a single frequency.The vertical velocities of the water surface are measured by using a Polytec Laser Vibrometer with a thin layer of aluminium powder scattering on the surface to reflect the laser beam.Nonlinear interaction processes result in a stationary Fourier spectrum of the vertical surface velocities (the same as the surface elevation),i.e.Iω～ω-3.5.The observed spectrum can be interpreted as a wave-turbulent Kolmogorov spectrum for the case of 'narrowband pumping' for a direct cascade of energy.Correlation dimension analysis of the whole development process reveals four distinct stages during the wave structure development and identifies the wave turbulence stage. 14. Development of Wave Energy Devices: The Danish Case / The Dragon of Nissum Bredning DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter 2009-01-01 The paper presents the Danish case of development of wave energy devices and outlines the established best practice. A brief overview of international standardization efforts is given and the Danish involvement in this described. The developed Danish best practice, which is being carried over to ... 15. Development of Wave Energy Devices: The Danish Case / The Dragon of Nissum Bredning DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter 2009-01-01 The paper presents the Danish case of development of wave energy devices and outlines the established best practice. A brief overview of international standardization efforts is given and the Danish involvement in this described. The developed Danish best practice, which is being carried over to ... 16. The Wave Energy Device DEFF Research Database (Denmark) Frigaard, Peter; Kofoed, Jens Peter; Tedd, James William 2006-01-01 The Wave Dragon is a 4 to 11 MW offshore wave energy converter of the overtopping type. It basically consists of two wave reflectors focusing the waves towards a ramp, a reservoir for collecting the overtopping water and a number of hydro turbines for converting the pressure head into power......'s first offshore wave energy converter. During this period an extensive measuring program has established the background for optimal design of the structure and regulation of the power take off system. Planning for full scale deployment of a 7 MW unit within the next 2 years is in progress. The prototype....... In the period from 1998 to 2001 extensive testing on a scale 1:50 model was carried at Aalborg University. During the last two years, testing has started on a prototype of the Wave Dragon in Nissum Bredning, Denmark (scale 1:4.5 of the North Sea). The prototype was grid connected in May 2003 as the world... 17. Key Aspects of Wave Energy DEFF Research Database (Denmark) Margheritini, Lucia; Nørgaard, Jørgen Harck 2012-01-01 . By collecting the experience from mainly three different wave energy developers, the possible alternative functions (other than energy production) of the devices are describe: Wave Dragon can be effectively used to reduce coastline erosion and/or as mussel farm; the Sea wave Slot cone Generator (SSG) can... 18. Sea testing and optimisation of power production on a scale 1:4.5 test rig of the offshore wave energy converter wave dragon. Summary of final technical report Energy Technology Data Exchange (ETDEWEB) 2006-06-15 The 4-11 MW Wave Dragon is a slack moored device that can be deployed in large parks wherever a sufficient wave climate and a water depth of more than 20 m is found--typically this is the case in the North Sea and in the Atlantic, offering significant economic and environmental benefits for the EU. The primary objective of the project was to establish the scientific knowledge base needed for deploying a full-scale prototype of the overtopping wave energy converter Wave Dragon. This has been obtained through long-term field-testing on a test rig with all systems installed. The scale 1:4.5 prototype has an installed power of 20 kW corresponding to 4 MW in full-scale with full-turbine deployment and is grid connected. The scale 1:4.5 prototype has been designed based on the conclusions from a previous EU Craft project. The basic test rig construction is provided through a project sponsored by the Danish Energy Authority. The test site is in protected waters in Nissum Bredning, Denmark, where the wave climate resembles North Sea conditions (scale 1:4.5) which in accordance with model law resembles a power scale of 1:200. The test results after more than 20,000 hours of operation cover: Long-term field testing of turbine operation, control strategy testing and optimisation, power monitoring and evaluation, stress and strain measurements and analysis, and mooring and cable systems analysis. The model tools developed in the previous EU Craft project have been validated and slightly modified based on the measured data. A Life Cycle Analysis and Finite Element Modelling have been performed. A report on market analysis, economic risk assessment and job creation potential has also been carried out. The project has established the necessary scientific and technical knowledge base for engaging in the establishment of a full-scale prototype in exposed waters. This includes the existence of a well-established design basis and documentation of technical viability through long 19. Experimental Study Related to the Mooring Design for the 1.5 MW Wave Dragon WEC Demonstrator at DanWEC Energy Technology Data Exchange (ETDEWEB) Parmeggiani, Stefano [Wave Dragon Ltd., London (United Kingdom); Kofoed, Jens Peter [Aalborg Univ. (Denmark). Department of Civil Engineering; Friis-Madsen, Erik [Wave Dragon Ltd., London (United Kingdom) 2013-04-15 The paper presents the results of an experimental study identifying the response of a 1.5 MW Wave Dragon to extreme conditions typical of the Danish Wave Energy Centre (DanWEC) test center. The best strategies allowing for a reduction in the extreme mooring tension have also been investigated, showing that this is possible by increasing the surge natural period of the system. The most efficient strategy in doing this is to provide the mooring system with a large horizontal compliance (typically in the order of 100 s), which shall be therefore assumed as design configuration. If this is not possible, it can also be partly achieved by lowering the floating level to a minimum (survivability mode) and by adopting a negative trim position. The adoption of the design configuration would determine in a 100-year storm extreme mooring tensions in the order of 0.9 MN, 65% lower than the worst case experienced in the worst case configuration. At the same time it would lead to a reduction in the extreme motion response, resulting in heave and pitch oscillation heights of 7 m and 19 deg and surge excursion of 12 m. Future work will numerically identify mooring configurations that could provide the desired compliance. 20. Electromagnetic Waves DEFF Research Database (Denmark) This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis... 1. Experimental Study Related to the Mooring Design for the 1.5 MW Wave Dragon WEC Demonstrator at DanWEC Directory of Open Access Journals (Sweden) Jens Peter Kofoed 2013-04-01 Full Text Available The paper presents the results of an experimental study identifying the response of a 1.5 MW Wave Dragon to extreme conditions typical of the DanWEC test center. The best strategies allowing for a reduction in the extreme mooring tension have also been investigated, showing that this is possible by increasing the surge natural period of the system. The most efficient strategy in doing this is to provide the mooring system with a large horizontal compliance (typically in the order of 100 s, which shall be therefore assumed as design configuration. If this is not possible, it can also be partly achieved by lowering the floating level to a minimum (survivability mode and by adopting a negative trim position. The adoption of the design configuration would determine in a 100-year storm extreme mooring tensions in the order of 0.9 MN, 65% lower than the worst case experienced in the worst case configuration. At the same time it would lead to a reduction in the extreme motion response, resulting in heave and pitch oscillation heights of 7 m and 19° and surge excursion of 12 m. Future work will numerically identify mooring configurations that could provide the desired compliance. 2. Plasma waves CERN Document Server Swanson, DG 1989-01-01 Plasma Waves discusses the basic development and equations for the many aspects of plasma waves. The book is organized into two major parts, examining both linear and nonlinear plasma waves in the eight chapters it encompasses. After briefly discussing the properties and applications of plasma wave, the book goes on examining the wave types in a cold, magnetized plasma and the general forms of the dispersion relation that characterize the waves and label the various types of solutions. Chapters 3 and 4 analyze the acoustic phenomena through the fluid model of plasma and the kinetic effects. Th 3. Heat Waves Science.gov (United States) Heat Waves Dangers we face during periods of very high temperatures include: Heat cramps: These are muscular pains and ... having trouble with the heat. If a heat wave is predicted or happening… - Slow down. Avoid strenuous ... 4. Wave Star DEFF Research Database (Denmark) Kramer, Morten; Brorsen, Michael; Frigaard, Peter Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star.......Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star.... 5. Electromagnetic Waves DEFF Research Database (Denmark) This book is dedicated to various aspects of electromagnetic wave theory and its applications in science and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis......, material characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, etc.... 6. Wave phenomena CERN Document Server Towne, Dudley H 1988-01-01 This excellent undergraduate-level text emphasizes optics and acoustics, covering inductive derivation of the equation for transverse waves on a string, acoustic plane waves, boundary-value problems, polarization, three-dimensional waves and more. With numerous problems (solutions for about half). ""The material is superbly chosen and brilliantly written"" - Physics Today. Problems. Appendices. 7. Development of the Wave Energy Converter DEFF Research Database (Denmark) Kofoed, Jens Peter; Frigaard, Peter; Sørensen, Hans Christian 2000-01-01 The development of the wave energy converter Wave Dragon (WD) is presented. The WD is based on the overtopping principle. Initially a description of the WD is given. Then the development over time in terms of the various research and development projects working with the concept is described... 8. Design and testing for novel joint for wave reflectors Energy Technology Data Exchange (ETDEWEB) Tedd, J. [SPOK ApS, Copenhagen (Denmark); Friis-Madsen, E. [Loewenmark, Copenhagen (Denmark); Frigaard, P. [Aalborg Univ., Aalborg (Denmark) 2005-07-01 Construction of a novel joint between the main platform and the wave reflectors of the Wave Dragon has begun. This paper describes the design and testing process behind this. Tests conducted in the facilities at Aalborg University highlighted large motions, and similar force magnitudes to the previous design. This testing has influenced the design and allowed construction to begin on refitting the joint to the 1:4.5 scale prototype Wave Dragon. (au) 9. Denmark's clean energy future from waves Energy Technology Data Exchange (ETDEWEB) Lund, G. [Nova Pro, CADDET Danish National Team, Toelloese (Denmark) 1999-10-01 This article presents a brief overview of Denmark's wave energy programme which aims to develop wave energy plants to supply 15% of Denmark's energy consumption. Details are given of the Wave Dragon deep water floating wave power plant, the Swan DK3 backward bend duct buoy, the point absorber float, and the WavePlane floating device. The step by step development approach for projects accepted by the wave energy programme, and future options are discussed. (UK) 10. Making waves Science.gov (United States) Kruse, Karsten 2017-01-01 Traveling waves propagating along surfaces play an important role for intracellular organization. Such waves can appear spontaneously in reaction-diffusion systems, but only few general criteria for their existence are known. Analyzing the dynamics of the Min proteins in Escherichia coli, Levine and Kessler (2016 New J. Phys. 18 122001) now identified a new mechanism for the emergence of traveling waves that relies on conservation laws. From their analysis one can expect traveling waves to be a generic feature of systems made of proteins that have a cytoplasmic and a membrane-bound state. 11. Janus Waves OpenAIRE 2016-01-01 We show the existence of a family of waves that share a common interesting property affecting the way they propagate and focus. These waves are a superposition of twin waves, which are conjugate to each other under inversion of the propagation direction. In analogy to holography, these twin "real" and "virtual" waves are related respectively to the converging and the diverging part of the beam and can be clearly visualized in real space at two distinct foci under the action of a focusing lens... 12. Wave Star DEFF Research Database (Denmark) Kramer, Morten; Brorsen, Michael; Frigaard, Peter Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star.......Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star.... 13. Wave Solutions CERN Document Server Christov, Ivan C 2012-01-01 In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be understood as a specific type of solution of an appropriate mathematical equation modeling the underlying physics. Typical models consist of partial differential equations that exhibit certain general properties, e.g., hyperbolicity. This, in turn, leads to the possibility of wave solutions. Various analytical techniques (integral transforms, complex variables, reduction to ordinary differential equations, etc.) are available to find wave solutions of linear partial differential equations. Furthermore, linear hyperbolic equations with higher-order derivatives provide the mathematical underpinning of the phenomenon of dispersion, i.e., the dependence of a wave's phase speed on its wavenumber. For systems of nonlinear first-order hyperbolic equations, there also exists a general ... 14. Waves, damped wave and observation CERN Document Server Phung, Kim Dang 2009-01-01 We consider the wave equation in a bounded domain (eventually convex). Two kinds of inequality are described when occurs trapped ray. Applications to control theory are given. First, we link such kind of estimate with the damped wave equation and its decay rate. Next, we describe the design of an approximate control function by an iterative time reversal method. 15. Gravity waves Science.gov (United States) Fritts, David 1987-02-01 Gravity waves contributed to the establishment of the thermal structure, small scale (80 to 100 km) fluctuations in velocity (50 to 80 m/sec) and density (20 to 30%, 0 to peak). Dominant gravity wave spectrum in the middle atmosphere: x-scale, less than 100 km; z-scale, greater than 10 km; t-scale, less than 2 hr. Theorists are beginning to understand middle atmosphere motions. There are two classes: Planetary waves and equatorial motions, gravity waves and tidal motions. The former give rise to variability at large scales, which may alter apparent mean structure. Effects include density and velocity fluctuations, induced mean motions, and stratospheric warmings which lead to the breakup of the polar vortex and cooling of the mesosphere. On this scale are also equatorial quasi-biennial and semi-annual oscillations. Gravity wave and tidal motions produce large rms fluctuations in density and velocity. The magnitude of the density fluctuations compared to the mean density is of the order of the vertical wavelength, which grows with height. Relative density fluctuations are less than, or of the order of 30% below the mesopause. Such motions may cause significant and variable convection, and wind shear. There is a strong seasonal variation in gravity wave amplitude. Additional observations are needed to address and quantify mean and fluctuation statistics of both density and mean velocity, variability of the mean and fluctuations, and to identify dominant gravity wave scales and sources as well as causes of variability, both temporal and geographic. 16. Turbine Control Strategy using Wave Prediction to Optimise Power Take Off of Overtopping Wave Energy Converters DEFF Research Database (Denmark) Tedd, James; Knapp, Wilfried; Frigaard, Peter; 2005-01-01 This paper presents the control strategy used on Wave Dragon overtopping wave energy converter. The nature of overtopping requires that for optimum performance the water level in the reservoir must be controlled by controlling the turbine outflows. A history of the simulations performed is included... 17. Janus Waves CERN Document Server Papazoglou, Dimitris G; Tzortzakis, Stelios 2016-01-01 We show the existence of a family of waves that share a common interesting property affecting the way they propagate and focus. These waves are a superposition of twin waves, which are conjugate to each other under inversion of the propagation direction. In analogy to holography, these twin "real" and "virtual" waves are related respectively to the converging and the diverging part of the beam and can be clearly visualized in real space at two distinct foci under the action of a focusing lens. Analytic formulas for the intensity distribution after focusing are derived, while numerical and experimental demonstrations are given for some of the most interesting members of this family, the accelerating Airy and ring-Airy beams. 18. Short term wave forecasting, using digital filters, for improved control of Wave Energy Converters DEFF Research Database (Denmark) Tedd, James; Frigaard, Peter 2007-01-01 experimentally. Results are shown form measurements taken on the Wave Dragon prototype device, a floating overtopping device situated in Northern Denmark. In this case the method is able to accurately predict the surface elevation at the device 11.2 seconds before the measurement is made. This is sufficient......This paper presents a Digital Filter method for real time prediction of waves incident upon a Wave Energy device. The method transforms waves measured at a point ahead of the device, to expected waves incident on the device. The relationship between these incident waves and power capture is derived... 19. Wave Star DEFF Research Database (Denmark) Kramer, Morten; Frigaard, Peter Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star.... 20. Wave Star DEFF Research Database (Denmark) Kramer, Morten; Andersen, Thomas Lykke Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star.... 1. Blast Waves CERN Document Server Needham, Charles E 2010-01-01 The primary purpose of this text is to document many of the lessons that have been learned during the author’s more than forty years in the field of blast and shock. The writing therefore takes on an historical perspective, in some sense, because it follows the author’s experience. The book deals with blast waves propagating in fluids or materials that can be treated as fluids. It begins by distinguishing between blast waves and the more general category of shock waves. It then examines several ways of generating blast waves, considering the propagation of blast waves in one, two and three dimensions as well as through the real atmosphere. One section treats the propagation of shocks in layered gases in a more detailed manner. The book also details the interaction of shock waves with structures in particular reflections, progressing from simple to complex geometries, including planar structures, two-dimensional structures such as ramps or wedges, reflections from heights of burst, and three-dimensional st... 2. Modeling the Buoyancy System of a Wave Energy Power Plant DEFF Research Database (Denmark) Pedersen, Tom S.; Nielsen, Kirsten M. 2009-01-01 A nonlinear dynamic model of the buoyancy system in a wave energy power plant is presented. The plant ("Wave Dragon") is a floating device using the potential energy in overtopping waves to produce power. A water reservoir is placed on top of the WD, and hydro turbines lead the water to the sea... 3. Modeling the Buoyancy System of a Wave Energy Power Plant DEFF Research Database (Denmark) Pedersen, Tom S.; Nielsen, Kirsten M. 2009-01-01 A nonlinear dynamic model of the buoyancy system in a wave energy power plant is presented. The plant ("Wave Dragon") is a floating device using the potential energy in overtopping waves to produce power. A water reservoir is placed on top of the WD, and hydro turbines lead the water to the sea... 4. Wave Generation Theory DEFF Research Database (Denmark) Frigaard, Peter; Høgedal, Michael; Christensen, Morten The intention of this manual is to provide some formulas and techniques which can be used for generating waves in hydraulic laboratories. Both long crested waves (2-D waves) and short crested waves (3-D waves) are considered.... 5. Wave Generation Theory OpenAIRE Frigaard, Peter; Høgedal, Michael; Christensen, Morten 1993-01-01 The intention of this manual is to provide some formulas and techniques which can be used for generating waves in hydraulic laboratories. Both long crested waves (2-D waves) and short crested waves (3-D waves) are considered. 6. Nonlinear wave-wave interactions and wedge waves Institute of Scientific and Technical Information of China (English) Ray Q.Lin; Will Perrie 2005-01-01 A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction. 7. Worlds Largest Wave Energy Project 2007 in Wales DEFF Research Database (Denmark) Christensen, Lars; Friis-Madsen, Erik; Kofoed, Jens Peter 2006-01-01 a large number of fundamentally different technologies are utilised to harvest wave energy. The Wave Dragon belongs to the wave overtopping class of converters and the paper describes the fundamentals and the technical solutions used in this wave energy converter. An offshore floating WEC like the Wave......This paper introduces world largest wave energy project being developed in Wales and based on one of the leading wave energy technologies. The background for the development of wave energy, the total resource ands its distribution around the world is described. In contrast to wind energy turbines...... Dragon has to be scaled in accordance with the wave climate at the deployment site, which makes the Welch demonstrator device the worlds largest WEC so far with a total width of 300 meters. The project budget, the construction methods and the deployment site are also given.... 8. Shallow Water Waves and Solitary Waves CERN Document Server Hereman, Willy 2013-01-01 Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow Water Wave Equations of Geophysical Fluid Dynamics; Computation of Solitary Wave Solutions; Numerical Methods; Water Wave Experiments and Observations; Future Directions, and Bibliography. 9. Waves & vibrations OpenAIRE Nicolas, Maxime 2016-01-01 Engineering school; This course is designed for students of Polytech Marseille, engineering school. It covers first the physics of vibration of the harmonic oscillator with damping and forcing, coupled oscillators. After a presentation of the wave equation, the vibration of strings, beams and membranes are studied. 10. Relativistic spherical plasma waves Science.gov (United States) Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P. 2012-02-01 Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking. 11. Gravitational waves CERN Document Server Ciufolini, I; Moschella, U; Fre, P 2001-01-01 Gravitational waves (GWs) are a hot topic and promise to play a central role in astrophysics, cosmology, and theoretical physics. Technological developments have led us to the brink of their direct observation, which could become a reality in the coming years. The direct observation of GWs will open an entirely new field: GW astronomy. This is expected to bring a revolution in our knowledge of the universe by allowing the observation of previously unseen phenomena, such as the coalescence of compact objects (neutron stars and black holes), the fall of stars into supermassive black holes, stellar core collapses, big-bang relics, and the new and unexpected.With a wide range of contributions by leading scientists in the field, Gravitational Waves covers topics such as the basics of GWs, various advanced topics, GW detectors, astrophysics of GW sources, numerical applications, and several recent theoretical developments. The material is written at a level suitable for postgraduate students entering the field. 12. Wave Star DEFF Research Database (Denmark) Kramer, Morten; Frigaard, Peter; Brorsen, Michael Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004.......Nærværende rapport beskriver foreløbige hovedkonklusioner på modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star i perioden 13/9 2004 til 12/11 2004.... 13. Wave Propagation CERN Document Server Ferrarese, Giorgio 2011-01-01 Lectures: A. Jeffrey: Lectures on nonlinear wave propagation.- Y. Choquet-Bruhat: Ondes asymptotiques.- G. Boillat: Urti.- Seminars: D. Graffi: Sulla teoria dell'ottica non-lineare.- G. Grioli: Sulla propagazione del calore nei mezzi continui.- T. Manacorda: Onde nei solidi con vincoli interni.- T. Ruggeri: "Entropy principle" and main field for a non linear covariant system.- B. Straughan: Singular surfaces in dipolar materials and possible consequences for continuum mechanics 14. Shock Waves CERN Document Server Jiang, Z 2005-01-01 The International Symposium on Shock Waves (ISSW) is a well established series of conferences held every two years in a different location. A unique feature of the ISSW is the emphasis on bridging the gap between physicists and engineers working in fields as different as gas dynamics, fluid mechanics and materials sciences. The main results presented at these meetings constitute valuable proceedings that offer anyone working in this field an authoritative and comprehensive source of reference. 15. Making Waves: Seismic Waves Activities and Demonstrations Science.gov (United States) Braile, S. J.; Braile, L. W. 2011-12-01 The nature and propagation of seismic waves are fundamental concepts necessary for understanding the exploration of Earth's interior structure and properties, plate tectonics, earthquakes, and seismic hazards. Investigating seismic waves is also an engaging approach to learning basic principles of the physics of waves and wave propagation. Several effective educational activities and demonstrations are available for teaching about seismic waves, including the stretching of a spring to demonstrate elasticity; slinky wave propagation activities for compressional, shear, Rayleigh and Love waves; the human wave activity to demonstrate P- and S- waves in solids and liquids; waves in water in a simple wave tank; seismic wave computer animations; simple shake table demonstrations of model building responses to seismic waves to illustrate earthquake damage to structures; processing and analysis of seismograms using free and easy to use software; and seismic wave simulation software for viewing wave propagation in a spherical Earth. The use of multiple methods for teaching about seismic waves is useful because it provides reinforcement of the fundamental concepts, is adaptable to variable classroom situations and diverse learning styles, and allows one or more methods to be used for authentic assessment. The methods described here have been used effectively with a broad range of audiences, including K-12 students and teachers, undergraduate students in introductory geosciences courses, and geosciences majors. 16. Geometrical vs wave optics under gravitational waves CERN Document Server Angélil, Raymond 2015-01-01 We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely null geodesics and Maxwell's equations, or, geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics, rather than solving Maxwell's equations directly for the fields, as in most previous approaches, we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic... 17. CMS-Wave Science.gov (United States) 2014-10-27 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE CMS -Wave 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward-marching, finite...difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction, diffraction, reflection 18. Efficient Wave Energy Amplification with Wave Reflectors DEFF Research Database (Denmark) Kramer, Morten Mejlhede; Frigaard, Peter Bak 2002-01-01 Wave Energy Converters (WEC's) extract wave energy from a limited area, often a single point or line even though the wave energy is generally spread out along the wave crest. By the use of wave reflectors (reflecting walls) the wave energy is effectively focused and increased to approximately 130......-140%. In the paper a procedure for calculating the efficiency and optimizing the geometry of wave reflectors are described, this by use of a 3D boundary element method. The calculations are verified by laboratory experiments and a very good agreement is found. The paper gives estimates of possible power benifit...... for different geometries of the wave reflectors and optimal geometrical design parameters are specified. On this basis inventors of WEC's can evaluate whether a specific WEC possible could benefit from wave reflectors.... 19. Smooth sandwich gravitational waves CERN Document Server Podolsky, J 1999-01-01 Gravitational waves which are smooth and contain two asymptotically flat regions are constructed from the homogeneous pp-waves vacuum solution. Motion of free test particles is calculated explicitly and the limit to an impulsive wave is also considered. 20. The physics of waves CERN Document Server Georgi, Howard 1993-01-01 The first complete introduction to waves and wave phenomena by a renowned theorist. Covers damping, forced oscillations and resonance; normal modes; symmetries; traveling waves; signals and Fourier analysis; polarization; diffraction. 1. Calculation of the Wave Conditions in Nissum Bredning DEFF Research Database (Denmark) Svendsen, Rasmus; Frigaard, Peter For the purpose of determining the optimal position in Nissum Bredning for placement of wave dragon, the wave energy flux in Nissum Bredning has been calculated. It has not been posible to retrieve satisfactory measured wavedata for Nissum Bredning, therefor the calculations are based on the SPM-......-method1. By this method the significant wave height, Hs, and the peak period, Tp, are calculated from the fetch, F, and wind stress factor, Ua.... 2. Short term wave forecasting, using digital filters, for improved control of Wave Energy Converters Energy Technology Data Exchange (ETDEWEB) Tedd, J.; Frigaard, P. [Department of Civil Engineering, Aalborg University, Aalborg (Denmark) 2007-07-01 This paper presents a Digital Filter method for real time prediction of waves incident upon a Wave Energy device. The method transforms waves measured at a point ahead of the device, to expected waves incident on the device. The relationship between these incident waves and power capture is derived experimentally. Results are shown form measurements taken on the Wave Dragon prototype device, a floating overtopping device situated in Northern Denmark. In this case the method is able to accurately predict the surface elevation at the device 11.2 seconds before the measurement is made. This is sufficient to allow advanced control systems to be developed using this knowledge to significantly improve power capture. 3. WaveNet Science.gov (United States) 2015-10-30 generates wave and wind roses and histograms of directional wave data required to define the wave climate for Corps projects. Five published technical...on the CIRP wiki: http://cirpwiki.info/wiki/Main_Page Application of Products Projected Benefits Documentation Points of Contact CIRP Website Figure 2. Display of time series of wave height ( blue ) and wind speed (red) 4. Waves in inhomogeneous media NARCIS (Netherlands) Gerritsen, S. 2007-01-01 In this thesis we study wave propagation in inhomogeneous media. Examples of the classical (massless) waves we consider are acoustic waves (sound) and electromagnetic waves (light, for example). Interaction with inhomogeneities embedded in a reference medium alter the propagation direction, velocity 5. A Simple Wave Driver Science.gov (United States) Temiz, Burak Kagan; Yavuz, Ahmet 2015-01-01 This study was done to develop a simple and inexpensive wave driver that can be used in experiments on string waves. The wave driver was made using a battery-operated toy car, and the apparatus can be used to produce string waves at a fixed frequency. The working principle of the apparatus is as follows: shortly after the car is turned on, the… 6. Waves in inhomogeneous media NARCIS (Netherlands) Gerritsen, S. 2007-01-01 In this thesis we study wave propagation in inhomogeneous media. Examples of the classical (massless) waves we consider are acoustic waves (sound) and electromagnetic waves (light, for example). Interaction with inhomogeneities embedded in a reference medium alter the propagation direction, velocity 7. Linear Rogue waves CERN Document Server Yuce, C 2015-01-01 We predict the existence of linear discrete rogue waves. We discuss that Josephson effect is the underlying reason for the formation of such waves. We study linear rogue waves in continuous system and present an exact analytical rogue wave solution of the Schrodinger-like equation. 8. Finsler p p -waves Science.gov (United States) Fuster, Andrea; Pabst, Cornelia 2016-11-01 In this work we present Finsler gravitational waves. These are a Finslerian version of the well-known p p -waves, generalizing the very special relativity line element. Our Finsler p p -waves are an exact solution of Finslerian Einstein's equations in vacuum and describe gravitational waves propagating in an anisotropic background. 9. Studies on seismic waves Institute of Scientific and Technical Information of China (English) 张海明; 陈晓非 2003-01-01 The development of seismic wave study in China in the past four years is reviewed. The discussion is divided into several aspects, including seismic wave propagation in laterally homogeneous media, laterally heterogeneous media, anisotropic and porous media, surface wave and seismic wave inversion, and seismic wave study in prospecting and logging problems. Important projects in the current studies on seismic wave is suggested as the development of high efficient numerical methods, and applying them to the studies of excitation and propagation of seismic waves in complex media and strong ground motion, which will form a foundation for refined earthquake hazard analysis and prediction. 10. Wave Data Analysis DEFF Research Database (Denmark) Alikhani, Amir; Frigaard, Peter; Burcharth, Hans F. 1998-01-01 The data collected over the course of the experiment must be analysed and converted into a form suitable for its intended use. Type of analyses range from simple to sophisticated. Depending on the particular experiment and the needs of the researcher. In this study three main part of irregular wave...... data analyses are presented e.g. Time Domain (Statistical) Analyses, Frequency Domain (Spectral) Analyses and Wave Reflection Analyses. Random wave profile and definitions of representative waves, distributions of individual wave height and wave periods and spectra of sea waves are presented.... 11. A Comparison of Nature Waves and Model Waves with Special Reference to Wave Grouping DEFF Research Database (Denmark) Burcharth, Hans F. This paper represents a comparative analyses of the occurrence of wave grouping in field storm waves and laboratory waves with similar power spectra and wave height distribution.......This paper represents a comparative analyses of the occurrence of wave grouping in field storm waves and laboratory waves with similar power spectra and wave height distribution.... 12. Stochastic wave propagation CERN Document Server Sobczyk, K 1985-01-01 This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media. 13. Sources of localized waves OpenAIRE Chatzipetros, Argyrios Alexandros 1994-01-01 The synthesis of two types of Localized Wave (L W) pulses is considered; these are the 'Focus Wave Model (FWM) pulse and the X Wave pulse. First, we introduce the modified bidirectional representation where one can select new basis functions resulting in different representations for a solution to the scalar wave equation. Through this new representation, we find a new class of focused X Waves which can be extremely localized. The modified bidirectional decomposition is applied... Science.gov (United States) 2014-10-27 ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18. NUMBER OF PAGES 2 19a. NAME...upgrades the Coastal Modeling System’s ( CMS ) wave model CMS -Wave, a phase-averaged spectral wave model, and BOUSS-2D, a Boussinesq-type nonlinear wave...provided by this work unit address these critical needs of the Corps’ navigation mission. Description Issue Addressed CMS -Wave application at Braddock 15. Relativistic spherical plasma waves CERN Document Server Bulanov, S S; Schroeder, C B; Zhidkov, A G; Esarey, E; Leemans, W P 2011-01-01 Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena. 16. Wave-Ice interaction Institute of Scientific and Technical Information of China (English) 沈奚海莉 2001-01-01 The growth and movement of sea ice cover are influenced by the presence of wave field. Inturn, the wave field is influenced by the presence of ice cover. Their interaction is not fully understood.In this paper, we discuss some current understanding on wave attenuation when it propagates through frag-mented ice cover, ice drift due to the wave motion, and the growth characteristics of ice cover in wave field. 17. Comparison and Sensitivity Investigations of a CALM and SALM Type Mooring System for Wave Energy Converters National Research Council Canada - National Science Library Arthur Pecher; Aligi Foglia; Jens Peter Kofoed 2014-01-01 ...) of 2000 kN and a water depth of 30 m. This reference scenario seems to be representative for large WECs operating in intermediate water depths, such as Weptos, Wave Dragon and many others, including reasonable design safety factors... 18. Freak waves in counterpropagating wave systems Science.gov (United States) Støle-Hentschel, Susanne; Rye, Lisa; Raustøl, Anne; Trulsen, Karsten 2016-04-01 The kurtosis of unimodal and counterpropagating bimodal wave systems is compared by means of laboratory experiments and simulations. Both give strong evidence that a bimodal wave system with waves travelling in opposite directions has reduced kurtosis compared to the corresponding unidirectional case. We thus anticipate reduced probability of freak waves in counterpropagating waves. The laboratory tests were performed with a JONSWAP wavefield in a long and narrow flume. The unimodal case was run with a damping beach in one end, while the bimodality was created by inserting a reflecting wall. The simulations were carried out with a numerical wave tank based on a Higher order spectral method employing partially or non-reflecting boundary conditions. 19. Long Waves Associated with Bichromatic Waves Institute of Scientific and Technical Information of China (English) DONG Guohai(董国海); YE Wenya(叶文亚); Nicholas Dodd 2001-01-01 A numerical model of low frequency waves is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called Weighted-Average Flux (WAF) method withTime-Operator-Splitting (TOS) used for the treatment of the source terms. This method allows a small number ofcomputational points to be used, and is particularly efficient in modeling wave setup. The short wave (or primary wave)energy equation is solved with a traditional Lax-Wendroff technique. A nonlinear wave theory is introduced. The modeldescribed in this paper is found to be satisfactory in modeling low frequency waves associated with incident bichromaticwaves. 20. Robust Wave Resource Estimation DEFF Research Database (Denmark) Lavelle, John; Kofoed, Jens Peter 2013-01-01 An assessment of the wave energy resource at the location of the Danish Wave Energy test Centre (DanWEC) is presented in this paper. The Wave Energy Converter (WEC) test centre is located at Hanstholm in the of North West Denmark. Information about the long term wave statistics of the resource...... is necessary for WEC developers, both to optimise the WEC for the site, and to estimate its average yearly power production using a power matrix. The wave height and wave period sea states parameters are commonly characterized with a bivariate histogram. This paper presents bivariate histograms and kernel...... density estimates of the PDF as a function both of Hm0 and Tp, and Hm0 and T0;2, together with the mean wave power per unit crest length, Pw, as a function of Hm0 and T0;2. The wave elevation parameters, from which the wave parameters are calculated, are filtered to correct or remove spurious data... 1. Fracture channel waves Science.gov (United States) Nihei, Kurt T.; Yi, Weidong; Myer, Larry R.; Cook, Neville G. W.; Schoenberg, Michael 1999-03-01 The properties of guided waves which propagate between two parallel fractures are examined. Plane wave analysis is used to obtain a dispersion equation for the velocities of fracture channel waves. Analysis of this equation demonstrates that parallel fractures form an elastic waveguide that supports two symmetric and two antisymmetric dispersive Rayleigh channel waves, each with particle motions and velocities that are sensitive to the normal and tangential stiffnesses of the fractures. These fracture channel waves degenerate to shear waves when the fracture stiffnesses are large, to Rayleigh waves and Rayleigh-Lamb plate waves when the fracture stiffnesses are low, and to fracture interface waves when the fractures are either very closely spaced or widely separated. For intermediate fracture stiffnesses typical of fractured rock masses, fracture channel waves are dispersive and exhibit moderate to strong localization of guided wave energy between the fractures. The existence of these waves is examined using laboratory acoustic measurements on a fractured marble plate. This experiment confirms the distinct particle motion of the fundamental antisymmetric fracture channel wave (A0 mode) and demonstrates the ease with which a fracture channel wave can be generated and detected. 2. NEW WIND WAVE GROWTH RELATIONS Institute of Scientific and Technical Information of China (English) WU Shu-ping; HOU Yi-jun; YIN Bao-shu 2004-01-01 In the present paper combining the relationship between wave steepness and wave age with the significant wave energy balance equation for wind wave,a new wind wave growth relation is presented.Comparisons with the other existing wind wave growth relations show that the results in present paper accord better with the wind wave growth process. 3. THEORY?OF?WATER?WAVES?IN?AN?ELASTIC?VESSEL Institute of Scientific and Technical Information of China (English) D.Y.Hsieh 2000-01-01 Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential apillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the onset of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and numerical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation. 4. Wave Meteorology and Soaring Science.gov (United States) Wiley, Scott 2008-01-01 This viewgraph document reviews some mountain wave turbulence and operational hazards while soaring. Maps, photographs, and satellite images of the meteorological phenomena are included. Additionally, photographs of aircraft that sustained mountain wave damage are provided. 5. Coronal Waves and Oscillations Directory of Open Access Journals (Sweden) Nakariakov Valery M. 2005-07-01 Full Text Available Wave and oscillatory activity of the solar corona is confidently observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands, and interpreted in terms of magnetohydrodynamic (MHD wave theory. The review reflects the current trends in the observational study of coronal waves and oscillations (standing kink, sausage and longitudinal modes, propagating slow waves and fast wave trains, the search for torsional waves, theoretical modelling of interaction of MHD waves with plasma structures, and implementation of the theoretical results for the mode identification. Also the use of MHD waves for remote diagnostics of coronal plasma - MHD coronal seismology - is discussed and the applicability of this method for the estimation of coronal magnetic field, transport coefficients, fine structuring and heating function is demonstrated. 6. Electromagnetic ultrasonic guided waves CERN Document Server Huang, Songling; Li, Weibin; Wang, Qing 2016-01-01 This book introduces the fundamental theory of electromagnetic ultrasonic guided waves, together with its applications. It includes the dispersion characteristics and matching theory of guided waves; the mechanism of production and theoretical model of electromagnetic ultrasonic guided waves; the effect mechanism between guided waves and defects; the simulation method for the entire process of electromagnetic ultrasonic guided wave propagation; electromagnetic ultrasonic thickness measurement; pipeline axial guided wave defect detection; and electromagnetic ultrasonic guided wave detection of gas pipeline cracks. This theory and findings on applications draw on the author’s intensive research over the past eight years. The book can be used for nondestructive testing technology and as an engineering reference work. The specific implementation of the electromagnetic ultrasonic guided wave system presented here will also be of value for other nondestructive test developers. 7. Viscothermal wave propagation NARCIS (Netherlands) Nijhof, Marten Jozef Johannes 2010-01-01 In this work, the accuracy, efficiency and range of applicability of various (approximate) models for viscothermal wave propagation are investigated. Models for viscothermal wave propagation describe thewave behavior of fluids including viscous and thermal effects. Cases where viscothermal effects a 8. Detonation Wave Profile Energy Technology Data Exchange (ETDEWEB) Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2015-12-14 The Zel’dovich-von Neumann-Doering (ZND) profile of a detonation wave is derived. Two basic assumptions are required: i. An equation of state (EOS) for a partly burned explosive; P(V, e, λ). ii. A burn rate for the reaction progress variable; d/dt λ = R(V, e, λ). For a steady planar detonation wave the reactive flow PDEs can be reduced to ODEs. The detonation wave profile can be determined from an ODE plus algebraic equations for points on the partly burned detonation loci with a specified wave speed. Furthermore, for the CJ detonation speed the end of the reaction zone is sonic. A solution to the reactive flow equations can be constructed with a rarefaction wave following the detonation wave profile. This corresponds to an underdriven detonation wave, and the rarefaction is know as a Taylor wave. 9. Controlling spiral wave with target wave in oscillatory systems Institute of Scientific and Technical Information of China (English) Liu Fu-Cheng; Wang Xiao-Fei; Li Xue-Chen; Dong Li-Fang 2007-01-01 Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied. 10. Explosive Line Wave Generators Science.gov (United States) 2013-12-01 curvature produced by each line wave generator. Piezoelectric pins were used for an additional assessment of the explosive lens design...to a visual assessment of the wave curvature from the high speed camera images, the explosive lens design was also evaluated using piezoelectric pins...High Explosive Firing Complex (HEFC). The various explosive line wave generators were taped vertically on a supporting board and the detonation wave 11. Surface water waves interaction in a circular vessel with oscillating walls. Science.gov (United States) Denissenko, Petr; Hsieh, Din-Yu 1998-11-01 Surface water waves appeared in a circular elastic vessel (modelled after the Chinese antique "Dragon Wash") are studied experimentally. Interaction of different wave modes are investigated. For small amplitude of wall oscillations, only the axisymmetric capillary wave mode, which is hardly visible to naked eyes, exists. When the amplitude is increased, half-frequency circumferential wave appears. Further increase of amplitude leads to chaotic behavior of surface waves. For large amplitudes, water drops jumping from edge regions are observed. Then, excitation of different modes of low frequency axisymmetric gravity waves may be obtained. Conditions for appearance of these gravity waves are investigated. Optical methods were applied for water surface diagnostics. 12. The Wave Energy Sector DEFF Research Database (Denmark) 2017-01-01 This Handbook for Ocean Wave Energy aims at providing a guide into the field of ocean wave energy utilization. The handbook offers a concise yet comprehensive overview of the main aspects and disciplines involved in the development of wave energy converters (WECs). The idea for the book has been ... 13. Wave turbulence in annular wave tank Science.gov (United States) Onorato, Miguel; Stramignoni, Ettore 2014-05-01 We perform experiments in an annular wind wave tank at the Dipartimento di Fisica, Universita' di Torino. The external diameter of the tank is 5 meters while the internal one is 1 meter. The tank is equipped by two air fans which can lead to a wind of maximum 5 m/s. The present set up is capable of studying the generation of waves and the development of wind wave spectra for large duration. We have performed different tests including different wind speeds. For large wind speed we observe the formation of spectra consistent with Kolmogorv-Zakharov predictions. 14. Physics of waves CERN Document Server Elmore, William C 1985-01-01 Because of the increasing demands and complexity of undergraduate physics courses (atomic, quantum, solid state, nuclear, etc.), it is often impossible to devote separate courses to the classic wave phenomena of optics, acoustics, and electromagnetic radiation. This brief comprehensive text helps alleviate the problem with a unique overview of classical wave theory in one volume.By examining a sequence of concrete and specific examples (emphasizing the physics of wave motion), the authors unify the study of waves, developing abstract and general features common to all wave motion. The fundam 15. Design of the Wave Dragon Mooring System DEFF Research Database (Denmark) Parmeggiani, Stefano with experimental data, derived from tank tests of the 2nd generation scaled model of the device. In phase 2 further tank testing has been carried out on a novel 3rd generation scaled model to assess the design loads in the mooring system and the extreme response of the device in surge, heave and pitch to extreme....... Alternative mooring configurations have to be assessed in order to identify the most cost-effective, real configurations allowing the desired compliance to the system, as shown by the results of phase 2. The numerical model used is part of the commercial software package SESAM, developed by DNV together... CERN Document Server Engelbrecht, Jüri 2015-01-01 This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity. 17. 4-wave dynamics in kinetic wave turbulence CERN Document Server Chibbaro, Sergio; Rondoni, Lamberto 2016-01-01 A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function $Z$ is obtained within an "interaction representation" and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for $Z$. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the $N$-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. 18. Cycloidal Wave Energy Converter Energy Technology Data Exchange (ETDEWEB) Stefan G. Siegel, Ph.D. 2012-11-30 This program allowed further advancing the development of a novel type of wave energy converter, a Cycloidal Wave Energy Converter or CycWEC. A CycWEC consists of one or more hydrofoils rotating around a central shaft, and operates fully submerged beneath the water surface. It operates under feedback control sensing the incoming waves, and converts wave power to shaft power directly without any intermediate power take off system. Previous research consisting of numerical simulations and two dimensional small 1:300 scale wave flume experiments had indicated wave cancellation efficiencies beyond 95%. The present work was centered on construction and testing of a 1:10 scale model and conducting two testing campaigns in a three dimensional wave basin. These experiments allowed for the first time for direct measurement of electrical power generated as well as the interaction of the CycWEC in a three dimensional environment. The Atargis team successfully conducted two testing campaigns at the Texas A&M Offshore Technology Research Center and was able to demonstrate electricity generation. In addition, three dimensional wave diffraction results show the ability to achieve wave focusing, thus increasing the amount of wave power that can be extracted beyond what was expected from earlier two dimensional investigations. Numerical results showed wave cancellation efficiencies for irregular waves to be on par with results for regular waves over a wide range of wave lengths. Using the results from previous simulations and experiments a full scale prototype was designed and its performance in a North Atlantic wave climate of average 30kW/m of wave crest was estimated. A full scale WEC with a blade span of 150m will deliver a design power of 5MW at an estimated levelized cost of energy (LCOE) in the range of 10-17 US cents per kWh. Based on the new results achieved in the 1:10 scale experiments these estimates appear conservative and the likely performance at full scale will 19. Life cycle assessment of the wave energy converter: Wave Dragon DEFF Research Database (Denmark) Hans Chr., Sørensen; Stefan, Naef; Stefan, Anderberg Any power production technology should be able to demonstrate that it's able to comply with current and future environmental regulation and that it demonstrates a considerable surplus in the energy balance being a part of the entire power system. This means that the energy used throughout all...... the lifecycle stages; from provision of materials over manufacturing of components and assembly, to deployment and use and eventually the disposal stage, is considerably less than the energy produced by the devise during its use/production stage.... 20. Analysis of Waves DEFF Research Database (Denmark) Frigaard, Peter; Andersen, Thomas Lykke The present book describes the most important aspects of wave analysis techniques applied to physical model tests. Moreover, the book serves as technical documentation for the wave analysis software WaveLab 3, cf. Aalborg University (2012). In that respect it should be mentioned that supplementary...... to the present technical documentation exists also the online help document describing the WaveLab software in detail including all the inputs and output fields. In addition to the two main authors also Tue Hald, Jacob Helm-Petersen and Morten Møller Jakobsen have contributed to the note. Their input is highly...... acknowledged. The outline of the book is as follows: • Chapter 2 and 3 describes analysis of waves in time and frequency domain. • Chapter 4 and 5 describes the separation of incident and reflected waves for the two-dimensional case. • Chapter 6 describes the estimation of the directional spectra which also... 1. Waves and compressible flow CERN Document Server Ockendon, Hilary 2016-01-01 Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications. New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises. Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, ... 2. MHD waves in sunspots CERN Document Server Sych, Robert 2015-01-01 The review addresses the spatial frequency morphology of sources of sunspot oscillations and waves, including their localization, size, oscillation periods, height localization with the mechanism of cut-off frequency that forms the observed emission variability. Dynamic of sunspot wave processes, provides the information about the structure of wave fronts and their time variations, investigates the oscillation frequency transformation depending on the wave energy is shown. The initializing solar flares caused by trigger agents like magnetoacoustic waves, accelerated particle beams, and shocks are discussed. Special attention is paid to the relation between the flare reconnection periodic initialization and the dynamics of sunspot slow magnetoacoustic waves. A short review of theoretical models of sunspot oscillations is provided. 3. Five Waves of Innovation DEFF Research Database (Denmark) Østergaard, Claus Møller; Rosenstand, Claus Andreas Foss; Gertsen, Frank 2012-01-01 Building on previous well-argued work by Jon Sundbo (1995a), on how innovation has evolved in three phases or waves since 1880, this paper’s contribution is extending the historical line, by offering arguments and explanations for two additional waves of innovation that explain the most recent...... developments. The paper also adds new interpretations of the previous work by Sundbo (1995a) in suggesting that the waves are triggered by societal and economic crisis. The result is a new theoretical and historical framework, proposing five waves of innovation triggered by societal and economic crises....... The innovation within each wave is constituted by different drivers of innovation: Cost-driven, development-driven, market-driven, user-driven, and remains of these waves are accumulated to form the complex character of today’s network-driven innovation.... 4. Shock wave reflection phenomena CERN Document Server Ben-dor, Gabi 2007-01-01 This book provides a comprehensive state-of-the-knowledge description of the shock wave reflection phenomena from a phenomenological point of view. The first part is a thorough introduction to oblique shock wave reflections, presenting the two major well-known reflection wave configurations, namely, regular (RR) and Mach (MR) reflections, the corresponding two- and three-shock theories, their analytical and graphical solution and the proposed transition boundaries between these two reflection-wave configurations. The second, third and fourth parts describe the reflection phenomena in steady, pseudo-steady and unsteady flows, respectively. Here, the possible specific types of reflection wave configurations are described, criteria for their formation and termination are presented and their governing equations are solved analytically and graphically and compared with experimental results. The resolution of the well-known von Neumann paradox and a detailed description of two new reflection-wave configurations - t... 5. Gravitational wave astronomy CERN Document Server CERN. Geneva 2016-01-01 In the past year, the LIGO-Virgo Collaboration announced the first secure detection of gravitational waves. This discovery heralds the beginning of gravitational wave astronomy: the use of gravitational waves as a tool for studying the dense and dynamical universe. In this talk, I will describe the full spectrum of gravitational waves, from Hubble-scale modes, through waves with periods of years, hours and milliseconds. I will describe the different techniques one uses to measure the waves in these bands, current and planned facilities for implementing these techniques, and the broad range of sources which produce the radiation. I will discuss what we might expect to learn as more events and sources are measured, and as this field matures into a standard part of the astronomical milieu. 6. Near Shore Wave Processes Science.gov (United States) 2016-06-07 the alongshore current, and a full non linear bottom shear stress. Contributions from the alongshore wind stress are mostly evident offshore and over...fraction) profiles measured on a day with offshore wave height of 1.6m, and 10 ms-1 wind speed. The one hour mean void fraction profiles are measured in a...given the offshore wave conditions. OBJECTIVES We hypothesize that the wave-induced kinematic, sediment and morphologic processes are nonlinearly 7. Dyakonov surface waves DEFF Research Database (Denmark) Takayama, Osamu; Crasovan, Lucian Cornel; Johansen, Steffen Kjær; 2008-01-01 The interface of two semi-infinite media, where at least one of them is a birefringent crystal, supports a special type of surface wave that was predicted theoretically by D'yakonov in 1988. Since then, the properties of such waves, which exist in transparent media only under very special......, the existence of these surface waves in specific material examples is analyzed, discussing the challenge posed by their experimental observation.... 8. Spheroidal wave functions CERN Document Server Flammer, Carson 2005-01-01 Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates.Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical Bessel function products. Additional subje 9. Making Wave Concept Tangible OpenAIRE Bülbül, Mustafa Şahin 2012-01-01 This study includes efficiency of some designed materials and activities for the students with special needs (blind students) about wave concept. In 9th grade Turkish High School Physics Curriculum, all the students have to learn wave concept because physics course is compulsory and wave concept was prepared as a unit. Generally, blind students only memorize some definitions about period, frequency and amplitude in that unit. This seems the easiest way for both teacher and students. Observing... 10. Non-diffractive waves CERN Document Server Hernandez-Figueroa, Hugo E; Recami, Erasmo 2013-01-01 This continuation and extension of the successful book ""Localized Waves"" by the same editors brings together leading researchers in non-diffractive waves to cover the most important results in their field and as such is the first to present the current state.The well-balanced presentation of theory and experiments guides readers through the background of different types of non-diffractive waves, their generation, propagation, and possible applications. The authors include a historical account of the development of the field, and cover different types of non-diffractive waves, including Airy 11. Propagation of waves CERN Document Server David, P 2013-01-01 Propagation of Waves focuses on the wave propagation around the earth, which is influenced by its curvature, surface irregularities, and by passage through atmospheric layers that may be refracting, absorbing, or ionized. This book begins by outlining the behavior of waves in the various media and at their interfaces, which simplifies the basic phenomena, such as absorption, refraction, reflection, and interference. Applications to the case of the terrestrial sphere are also discussed as a natural generalization. Following the deliberation on the diffraction of the "ground? wave around the ear 12. The Wave Energy Sector DEFF Research Database (Denmark) 2017-01-01 This Handbook for Ocean Wave Energy aims at providing a guide into the field of ocean wave energy utilization. The handbook offers a concise yet comprehensive overview of the main aspects and disciplines involved in the development of wave energy converters (WECs). The idea for the book has been...... shaped by the development, research, and teaching that we have carried out at the Wave Energy Research Group at Aalborg University over the past decades. It is our belief and experience that it would be useful writing and compiling such a handbook in order to enhance the understanding of the sector... DEFF Research Database (Denmark) Burcharth, H. F.; Frigaard, Peter 1989-01-01 Wave loads may be defined as time varying forces on a body resulting from the wave induced flow fields which surrounds the body in whole or in part. Such unsteady fluid forces are the net result of pressure and shear forces integrated over the instantaneous wetted area.......Wave loads may be defined as time varying forces on a body resulting from the wave induced flow fields which surrounds the body in whole or in part. Such unsteady fluid forces are the net result of pressure and shear forces integrated over the instantaneous wetted area.... 14. Wave groups in uni-directional surface-wave models NARCIS (Netherlands) Groesen, van E. 1998-01-01 Uni-directional wave models are used to study wave groups that appear in wave tanks of hydrodynamic laboratories; characteristic for waves in such tanks is that the wave length is rather small, comparable to the depth of the layer. In second-order theory, the resulting Nonlinear Schrödinger (NLS) eq 15. Exitation of Whistler Waves by a Helical Wave Structure DEFF Research Database (Denmark) Balmashnov, A. A.; Lynov, Jens-Peter; Michelsen, Poul 1981-01-01 The excitation of whistler waves in a radial inhomogeneous plasma is investigated experimentally, using a slow-wave structure consisting of a helix of variable length surrounding the plasma column. The excited waves were observed to have a wave-vector parallel to the external magnetic field....... The possibility of exciting the waves in different radial regions is demonstrated.... 16. Reflectors to Focus Wave Energy DEFF Research Database (Denmark) Kramer, Morten; Frigaard, Peter 2005-01-01 Wave Energy Converters (WEC’s) extract wave energy from a limited area, often a single point or line even though the wave energy is generally spread out along the wave crest. By the use of wave reflectors (reflecting walls) the wave energy is effectively focused and increased by approximately 30......-50%. Clearly longer wave reflectors will focus more wave energy than shorter wave reflectors. Thus the draw back is the increased wave forces for the longer wave reflectors. In the paper a procedure for calculating the energy efficiency and the wave forces on the reflectors are described, this by use of a 3D...... boundary element method. The calculations are verified by laboratory experiments and a very good agreement is found. The paper gives estimates of possible power benefit for different wave reflector geometries and optimal geometrical design parameters are specified. On this basis inventors of WEC’s can... 17. Wave Mechanics or Wave Statistical Mechanics Institute of Scientific and Technical Information of China (English) 2007-01-01 By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics. 18. EMS wave logger data processing NARCIS (Netherlands) Verhagen, H.J. 2013-01-01 Waves can be measured in several ways. One way of measuring waves is by measuring the wave pressure at a certain depth using a pressure sensor and calculate the wave information from the pressure record. The EMS wave logger uses a Honeywell MLH 050 PGP 06A pressure sensor. The information is stored 19. Making waves: visualizing fluid flows NARCIS (Netherlands) Zweers, Wout; Zwart, Valerie; Bokhove, Onno 2013-01-01 We explore the visualization of violent wave dynamics and erosion by waves and jets in laser-cut reliefs, laser engravings, and three-dimensional printing. For this purpose we built table-top experiments to cast breaking waves, and also explored the creation of extreme or rogue waves in larger wave 20. Developing de Broglie Wave Directory of Open Access Journals (Sweden) Zheng-Johansson J. X. 2006-10-01 Full Text Available The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity v, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed c between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength Λd=vcΛ and phase velocity c2/v+v which resembles directly L. de Broglie’s hypothetic phase wave. This phase wave in terms of transmitting the particle mass at the speed v and angular frequency Ωd= 2πv/Λd, with Λd and Ωd obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schrödinger equation of an identical system. 1. Slow frictional waves Science.gov (United States) Viswanathan, Koushik; Sundaram, Narayan; Chandrasekar, Srinivasan Stick-slip, manifest as intermittent tangential motion between two dry solid surfaces, is a friction instability that governs diverse phenomena from automobile brake squeals to earthquakes. We show, using high-speed in situ imaging of an adhesive polymer interface, that low velocity stick-slip is fundamentally of three kinds, corresponding to passage of three different surface waves -- separation pulses, slip pulses and the well-known Schallamach waves. These waves, traveling much slower than elastic waves, have clear distinguishing properties. Separation pulses and Schallamach waves involve local interface separation, and propagate in opposite directions while slip pulses are characterized by a sharp stress front and do not display any interface detachment. A change in the stick-slip mode from separation to slip pulse is effected simply by increasing the normal force. Together, these three waves constitute all possible stick-slip modes in adhesive friction and are shown to have direct analogues in muscular locomotory waves in soft bodied invertebrates. A theory for slow wave propagation is also presented which is capable of explaining the attendant interface displacements, velocities and stresses. 2. [Shock waves in orthopedics]. Science.gov (United States) Haupt, G 1997-05-01 Extracorporeal shock waves have revolutionized urological stone treatment. Nowadays shock waves are widely used in orthopedics, too. This article reviews the applications of extracorporeal shock waves on bone and adjacent soft tissue. The osteoneogenetic effect of extracorporeal shock waves has been proven and can be used to treat pseudarthrosis with a success rate of around 75%. Shock waves have a positive effect in tennis and golfer's elbow, calcaneal spur, and the complex called "periarthritis humero-scapularis." The mechanism for this is not yet known, and results from large prospective and randomized studies are still lacking. However, the treatment has been performed many thousands of times. In patients in whom conservative treatment has failed surgery used to be the only choice, but its success rate barely exceeds that of shock wave therapy and surgery can still be done if shock wave therapy fails. Extracorporeal shock waves will have an impact on orthopedics comparable to its effect in urology. Scientific evaluations, professional certifications, quality assurance and reimbursement issues present great challenges. 3. Wave Reflection Model Tests DEFF Research Database (Denmark) Burcharth, H. F.; Larsen, Brian Juul The investigation concerns the design of a new internal breakwater in the main port of Ibiza. The objective of the model tests was in the first hand to optimize the cross section to make the wave reflection low enough to ensure that unacceptable wave agitation will not occur in the port. Secondly... 4. Ship bow waves Institute of Scientific and Technical Information of China (English) NOBLESSE Francis; DELHOMMEAU Gerard; LIU Hua; WAN De-cheng; YANG Chi 2013-01-01 The bow wave generated by a ship hull that advances at constant speed in calm water is considered.The bow wave only depends on the shape of the ship bow (not on the hull geometry aft of the bow wave).This basic property makes it possible to determine the bow waves generated by a canonical family of ship bows defined in terms of relatively few parameters.Fast ships with fine bows generate overturning bow waves that consist of detached thin sheets of water,which are mostly steady until they hit the main free surface and undergo turbulent breaking up and diffusion.However,slow ships with blunt bows create highly unsteady and turbulent breaking bow waves.These two alternative flow regimes are due to a nonlinear constraint related to the Bernoulli relation at the free surface.Recent results about the overturning and breaking bow wave regimes,and the boundary that divides these two basic flow regimes,are reviewed.Questions and conjectures about the energy of breaking ship bow waves,and free-surface effects on flow circulation,are also noted. 5. The Relativistic Wave Vector Science.gov (United States) 2009-01-01 The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the… 6. Dyakonov surface waves DEFF Research Database (Denmark) Takayama, Osamu; Crasovan, Lucian Cornel; Johansen, Steffen Kjær 2008-01-01 The interface of two semi-infinite media, where at least one of them is a birefringent crystal, supports a special type of surface wave that was predicted theoretically by D'yakonov in 1988. Since then, the properties of such waves, which exist in transparent media only under very special conditi... 7. Gravitational waves from inflation Science.gov (United States) Guzzetti, M. C.; Bartolo, N.; Liguori, M.; Matarrese, S. 2016-09-01 The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio r and tensor spectral index nT. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized. 8. Ion Acoustic Waves in the Presence of Electron Plasma Waves DEFF Research Database (Denmark) Michelsen, Poul; Pécseli, Hans; Juul Rasmussen, Jens 1977-01-01 Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave.......Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave.... 9. Project GlobWave Science.gov (United States) Busswell, Geoff; Ash, Ellis; Piolle, Jean-Francois; Poulter, David J. S.; Snaith, Helen; Collard, Fabrice; Sheera, Harjit; Pinnock, Simon 2010-12-01 The ESA GlobWave project is a three year initiative, funded by ESA and CNES, to service the needs of satellite wave product users across the globe. Led by Logica UK, with support from CLS, IFREMER, SatOC and NOCS, the project will provide free access to satellite wave data and products in a common format, both historical and in near real time, from various European and American SAR and altimeter missions. Building on the successes of similar projects for Sea Surface Temperature and ocean colour, the project aims to stimulate increased use and analysis of satellite wave products. In addition to common-format satellite data the project will provide comparisons with in situ measurements, interactive data analysis tools and a pilot spatial wave forecast verification scheme for operational forecast production centres. The project will begin operations in January 2010, with direction from regular structured user consultation. 10. Wave Reflection Coefficient Spectrum Institute of Scientific and Technical Information of China (English) 俞聿修; 邵利民; 柳淑学 2003-01-01 The wave reflection coefficient frequency spectrum and directional spectrum for concrete face slope breakwaters and rubble mound breakwaters are investigated through physical model tests in the present study. The reflection coefficients of oblique irregular waves are analyzed by the Modified Two-Point Method (MTPM) proposed by the authors. The results show that the wave reflection coefficient decreases with increasing wave frequency and incident angle or decreasing structure slope. The reflection coefficient frequency spectrum and its variation with Iribarren number are given in this paper. The paper also suggests an empirical 3-dimensional reflection coefficient spectrum, i.e. reflection coefficient directional spectrum, which can be used to illustrate quantitatively the variation of reflection coefficient with the incident angle and the Iribarren number for oblique irregular waves. 11. Gravitational waves from inflation CERN Document Server Guzzetti, Maria Chiara; Liguori, Michele; Matarrese, Sabino 2016-01-01 The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power-spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between t... 12. Electromagnetic wave energy converter Science.gov (United States) Bailey, R. L. (Inventor) 1973-01-01 Electromagnetic wave energy is converted into electric power with an array of mutually insulated electromagnetic wave absorber elements each responsive to an electric field component of the wave as it impinges thereon. Each element includes a portion tapered in the direction of wave propagation to provide a relatively wideband response spectrum. Each element includes an output for deriving a voltage replica of the electric field variations intercepted by it. Adjacent elements are positioned relative to each other so that an electric field subsists between adjacent elements in response to the impinging wave. The electric field results in a voltage difference between adjacent elements that is fed to a rectifier to derive dc output power. 13. Parabolic Wave Equation for Surface Water Waves. Science.gov (United States) 1986-11-01 extended to wave propagation problems in other fields of physical sciences, such as nonlinear optics ( Svelto , 1974), plasma physics (Karpman, 1975...34 Journal of Fluid Mechanics, Vol. 72, pp. 373-384. Svelto , 0., 1974, Progress in Optics, North-Holland Pub., Chapter 1, pp. 1-51. Tappert, F.D., 1977, "The 14. Elimination of Spiral Waves and Competition between Travelling Wave Impulses and Spiral Waves Institute of Scientific and Technical Information of China (English) YUAN Guo-Yong; ZHANG Guang-Cai; WANG Guang-Rui; CHEN Shi-Gang; SUN Peng 2005-01-01 @@ The interaction between travelling wave impulses and spiral waves is studied and the results of their competition are related to the exciting period. From the results, it is known that the formation and development of spiral waves in cardiac tissue depend on the period by which the travelling wave impulses are excited. A method is proposed to eliminate spiral waves, which is easily operated. 15. Abnormal Waves Modelled as Second-order Conditional Waves DEFF Research Database (Denmark) Jensen, Jørgen Juncher 2005-01-01 The paper presents results for the expected second order short-crested wave conditional of a given wave crest at a specific point in time and space. The analysis is based on the second order Sharma and Dean shallow water wave theory. Numerical results showing the importance of the spectral density......, the water depth and the directional spreading on the conditional mean wave profile are presented. Application of conditional waves to model and explain abnormal waves, e.g. the well-known New Year Wave measured at the Draupner platform January 1st 1995, is discussed. Whereas the wave profile can be modelled...... quite well by the second order conditional wave including directional spreading and finite water depth the probability to encounter such a wave is still, however, extremely rare. The use of the second order conditional wave as initial condition to a fully non-linear three-dimensional analysis... 16. Wave phenomena in sunspots Science.gov (United States) Löhner-Böttcher, Johannes 2016-03-01 Context: The dynamic atmosphere of the Sun exhibits a wealth of magnetohydrodynamic (MHD) waves. In the presence of strong magnetic fields, most spectacular and powerful waves evolve in the sunspot atmosphere. Allover the sunspot area, continuously propagating waves generate strong oscillations in spectral intensity and velocity. The most prominent and fascinating phenomena are the 'umbral flashes' and 'running penumbral waves' as seen in the sunspot chromosphere. Their nature and relation have been under intense discussion in the last decades. Aims: Waves are suggested to propagate upward along the magnetic field lines of sunspots. An observational study is performed to prove or disprove the field-guided nature and coupling of the prevalent umbral and penumbral waves. Comprehensive spectroscopic observations at high resolution shall provide new insights into the wave characteristics and distribution across the sunspot atmosphere. Methods: Two prime sunspot observations were carried out with the Dunn Solar Telescope at the National Solar Observatory in New Mexico and with the Vacuum Tower Telescope at the Teide Observatory on Tenerife. The two-dimensional spectroscopic observations were performed with the interferometric spectrometers IBIS and TESOS. Multiple spectral lines are scanned co-temporally to sample the dynamics at the photospheric and chromospheric layers. The time series (1 - 2.5 h) taken at high spatial and temporal resolution are analyzed according to their evolution in spectral intensities and Doppler velocities. A wavelet analysis was used to obtain the wave power and dominating wave periods. A reconstruction of the magnetic field inclination based on sunspot oscillations was developed. Results and conclusions: Sunspot oscillations occur continuously in spectral intensity and velocity. The obtained wave characteristics of umbral flashes and running penumbral waves strongly support the scenario of slow-mode magnetoacoustic wave propagation along the 17. Stress wave focusing transducers Energy Technology Data Exchange (ETDEWEB) Visuri, S.R., LLNL 1998-05-15 Conversion of laser radiation to mechanical energy is the fundamental process behind many medical laser procedures, particularly those involving tissue destruction and removal. Stress waves can be generated with laser radiation in several ways: creation of a plasma and subsequent launch of a shock wave, thermoelastic expansion of the target tissue, vapor bubble collapse, and ablation recoil. Thermoelastic generation of stress waves generally requires short laser pulse durations and high energy density. Thermoelastic stress waves can be formed when the laser pulse duration is shorter than the acoustic transit time of the material: {tau}{sub c} = d/c{sub s} where d = absorption depth or spot diameter, whichever is smaller, and c{sub s} = sound speed in the material. The stress wave due to thermoelastic expansion travels at the sound speed (approximately 1500 m/s in tissue) and leaves the site of irradiation well before subsequent thermal events can be initiated. These stress waves, often evolving into shock waves, can be used to disrupt tissue. Shock waves are used in ophthalmology to perform intraocular microsurgery and photodisruptive procedures as well as in lithotripsy to fragment stones. We have explored a variety of transducers that can efficiently convert optical to mechanical energy. One such class of transducers allows a shock wave to be focused within a material such that the stress magnitude can be greatly increased compared to conventional geometries. Some transducer tips could be made to operate regardless of the absorption properties of the ambient media. The size and nature of the devices enable easy delivery, potentially minimally-invasive procedures, and precise tissue- targeting while limiting thermal loading. The transducer tips may have applications in lithotripsy, ophthalmology, drug delivery, and cardiology. 18. Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude OpenAIRE Geyer, Anna 2016-01-01 Following a general principle introduced by Ehrnstr\\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves. 19. Symmetric waves are traveling waves for a shallow water equation for surface waves of moderate amplitude OpenAIRE Geyer, Anna 2016-01-01 Following a general principle introduced by Ehrnstr\\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves. 20. Demonstration of Shear Waves, Lamb Waves, and Rayleigh Waves by Mode Conversion. Science.gov (United States) Leung, W. P. 1980-01-01 Introduces an experiment that can be demonstrated in the classroom to show that shear waves, Rayleigh waves, and Lamb waves can be easily generated and observed by means of mode conversion. (Author/CS) 1. A relationship between wave steepness and wave age for wind waves in deep water Institute of Scientific and Technical Information of China (English) LIU Bin; DING Yun; GUAN Changlong 2007-01-01 Studying the relationship between wave steepness and wave age is import ant for describing wind wave growth with energy balance equation of significant waves. After invoking the dispersion relation of surface gravity wave in deep water, a new relationship between wave steepness and wave age is revealed based on the "3/2-power law" (Toba, 1972), in which wave steepness is a function of wave age with a drag coefficient as a parameter. With a given wave age, a larger drag coefficient would lead to larger wave steepness. This could be interpreted as the result of interaction between wind and waves.Comparing with previous relationships, the newly proposed one is more consistent with observational data in field and laboratory. 2. Spin wave confinement CERN Document Server 2008-01-01 This book presents recent scientific achievements in the investigation of magnetization dynamics in confined magnetic systems. Introduced by Bloch as plane waves of magnetization in unconfined ferromagnets, spin waves currently play an important role in the description of very small magnetic systems ranging from microelements, which form the basis of magnetic sensors, to magnetic nano-contacts. The spin wave confinement effect was experimentally discovered in the 1990s in permalloy microstripes. The diversity of systems where this effect is observed has been steadily growing since then, and 3. Violent breaking wave impacts DEFF Research Database (Denmark) Bredmose, Henrik; Peregrine, D.H.; Bullock, G.N. 2009-01-01 for a homogeneous mixture of incompressible liquid and ideal gas. This enables a numerical description of both trapped air pockets and the propagation of pressure shock waves through the aerated water. An exact Riemann solver is developed to permit a finite-volume solution to the flow model with smallest possible...... local error. The high pressures measured during wave impacts on a breakwater are reproduced and it is shown that trapped air can be compressed to a pressure of several atmospheres. Pressure shock waves, reflected off nearby surfaces such as the seabed, can lead to pressures comparable with those... 4. Waves in the seas Digital Repository Service at National Institute of Oceanography (India) Varkey, M.J. or change. If ini- tially, only a thin layer of air close to the water surface matters in the mo- mentum transfer from wind to water, afterwards with strong winds, a layer of air upto say 15 to 30 metres comes Small sand waves formed on a seashore due... it breaks with a heading wind or on a beach). Consider an open sea of say 1000 square kilometres wherein billions of 'pushes' and 'pulls' happen over tens of hours, causing uncountable number of waves and wave groups of various types moving in different... 5. Mathieu Progressive Waves Institute of Scientific and Technical Information of China (English) Andrei B. Utkin 2011-01-01 A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type. 6. Vibrations and waves CERN Document Server Kaliski, S 2013-01-01 This book gives a comprehensive overview of wave phenomena in different media with interacting mechanical, electromagnetic and other fields. Equations describing wave propagation in linear and non-linear elastic media are followed by equations of rheological models, models with internal rotational degrees of freedom and non-local interactions. Equations for coupled fields: thermal, elastic, electromagnetic, piezoelectric, and magneto-spin with adequate boundary conditions are also included. Together with its companion volume Vibrations and Waves. Part A: Vibrations this work provides a wealth 7. Relativistic wave mechanics CERN Document Server Corinaldesi, Ernesto 1963-01-01 Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat 8. Chiral Shock Waves CERN Document Server Sen, Srimoyee 2016-01-01 We study shock waves in relativistic chiral matter. We argue that the conventional Rankine- Hugoinot relations are modified due to the presence of chiral transport phenomena. We show that the entropy discontinuity in a weak shock wave is linearly proportional to the pressure discontinuity when the effect of chiral transport becomes sufficiently large. We also show that rarefaction shock waves, which do not exist in usual nonchiral fluids, can appear in chiral matter. These features are exemplified by shock propagation in dense neutrino matter in the hydrodynamic regime. 9. Ocean wave energy conversion CERN Document Server McCormick, Michael E 2007-01-01 This volume will prove of vital interest to those studying the use of renewable resources. Scientists, engineers, and inventors will find it a valuable review of ocean wave mechanics as well as an introduction to wave energy conversion. It presents physical and mathematical descriptions of the nine generic wave energy conversion techniques, along with their uses and performance characteristics.Author Michael E. McCormick is the Corbin A. McNeill Professor of Naval Engineering at the U.S. Naval Academy. In addition to his timely and significant coverage of possible environmental effects associa 10. Spin Waves in Terbium DEFF Research Database (Denmark) Jensen, J.; Houmann, Jens Christian Gylden; Bjerrum Møller, Hans 1975-01-01 The energies of spin waves propagating in the c direction of Tb have been studied by inelastic neutron scattering, as a function of a magnetic field applied along the easy and hard directions in the basal plane, and as a function of temperature. From a general spin Hamiltonian, consistent...... with the symmetry, we deduce the dispersion relation for the spin waves in a basal-plane ferromagnet. This phenomenological spin-wave theory accounts for the observed behavior of the magnon energies in Tb. The two q⃗-dependent Bogoliubov components of the magnon energies are derived from the experimental results... 11. Water wave scattering CERN Document Server Mandal, Birendra Nath 2015-01-01 The theory of water waves is most varied and is a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers, and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special configurations that are of interest to ocean engineers. Unfortunately, even the apparently simple problems appear to be difficult to tackle mathematically unless some simplified assumptions are made. Fortunately, one can assume water to be an incompressible, in viscid and homogeneous 12. Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin Institute of Scientific and Technical Information of China (English) LIU Shu-xue; Keyyong HONG 2005-01-01 An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distribution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced by wave directionality and that the breaking criteria for directional waves are distinctly different from those for unidirectional waves. 13. Wave Dissipation and Balance - NOPP Wave Project Science.gov (United States) 2014-09-30 interactions between them, and it is not clear how to transform each type of measurement into a clear constraint for the functional form and magnitude of...white with a uniform current U = 0.15 m/s towards the trigonometric angle 99 degrees. The white dashed line marks approximately the separation between...A. Roland, A. van der Westhuysen, P. Queffeulou, J.-M. Lefevre, L. Aouf, and F. Collard. Semi-empirical dissipation source functions for wind-wave 14. Island-trapped Waves, Internal Waves, and Island Circulation Science.gov (United States) 2015-09-30 Island-trapped waves , internal waves , and island circulation T. M. Shaun Johnston Scripps Institution of Oceanography University of California...topography. As strong flows encounter small islands, points, and submarine ridges, it is expected that wakes, eddies, and arrested internal lee waves ...form drag, lee waves , eddy generation) over small-scale topographic features and (ii) fundamentally nonlinear processes (turbulent island wakes 15. Traveling-wave photodetector Science.gov (United States) Hietala, Vincent M.; Vawter, Gregory A. 1993-01-01 The traveling-wave photodetector of the present invention combines an absorptive optical waveguide and an electrical transmission line, in which optical absorption in the waveguide results in a photocurrent at the electrodes of the electrical transmission line. The optical waveguide and electrical transmission line of the electrically distributed traveling-wave photodetector are designed to achieve matched velocities between the light in the optical waveguide and electrical signal generated on the transmission line. This velocity synchronization provides the traveling-wave photodetector with a large electrical bandwidth and a high quantum efficiency, because of the effective extended volume for optical absorption. The traveling-wave photodetector also provides large power dissipation, because of its large physical size. 16. Sound wave transmission (image) Science.gov (United States) When sounds waves reach the ear, they are translated into nerve impulses. These impulses then travel to the brain where they are interpreted by the brain as sound. The hearing mechanisms within the inner ear, can ... 17. Theory of Gravitational Waves CERN Document Server Tiec, Alexandre Le 2016-01-01 The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein's equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein's quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds a... 18. NOAA NDBC SOS - waves Data.gov (United States) National Oceanic and Atmospheric Administration, Department of Commerce — The NOAA NDBC SOS server is part of the IOOS DIF SOS Project. The stations in this dataset have waves data. Because of the nature of SOS requests, requests for data... 19. Global Coronal Waves CERN Document Server Chen, P F 2016-01-01 After the {\\em Solar and Heliospheric Observatory} ({\\em SOHO}) was launched in 1996, the aboard Extreme Ultraviolet Imaging Telescope (EIT) observed a global coronal wave phenomenon, which was initially named "EIT wave" after the telescope. The bright fronts are immediately followed by expanding dimmings. It has been shown that the brightenings and dimmings are mainly due to plasma density increase and depletion, respectively. Such a spectacular phenomenon sparked long-lasting interest and debates. The debates were concentrated on two topics, one is about the driving source, and the other is about the nature of this wavelike phenomenon. The controversies are most probably because there may exist two types of large-scale coronal waves that were not well resolved before the {\\em Solar Dynamics Observatory} ({\\em SDO}) was launched: one is a piston-driven shock wave straddling over the erupting coronal mass ejection (CME), and the other is an apparently propagating front, which may correspond to the CME frontal... 20. Acoustics waves and oscillations CERN Document Server Sen, S.N. 2013-01-01 Parameters of acoustics presented in a logical and lucid style Physical principles discussed with mathematical formulations Importance of ultrasonic waves highlighted Dispersion of ultrasonic waves in viscous liquids explained This book presents the theory of waves and oscillations and various applications of acoustics in a logical and simple form. The physical principles have been explained with necessary mathematical formulation and supported by experimental layout wherever possible. Incorporating the classical view point all aspects of acoustic waves and oscillations have been discussed together with detailed elaboration of modern technological applications of sound. A separate chapter on ultrasonics emphasizes the importance of this branch of science in fundamental and applied research. In this edition a new chapter ''Hypersonic Velocity in Viscous Liquids as revealed from Brillouin Spectra'' has been added. The book is expected to present to its readers a comprehensive presentation of the subject matter... 1. Magnetoresistive waves in plasmas Science.gov (United States) Felber, F. S.; Hunter, R. O., Jr.; Pereira, N. R.; Tajima, T. 1982-10-01 The self-generated magnetic field of a current diffusing into a plasma between conductors can magnetically insulate the plasma. Propagation of magnetoresistive waves in plasmas is analyzed. Applications to plasma opening switches are discussed. 2. Waving in the rain CERN Document Server Cavaleri, Luigi; Bidlot, Jean-Raymond 2015-01-01 We consider the effect of rain on wind wave generation and dissipation. Rain falling on a wavy surface may have a marked tendency to dampen the shorter waves in the tail of the spectrum, the related range increasing with the rain rate. Following the coupling between meteorological and wave models, we derive that on the whole this should imply stronger wind and higher waves in the most energetic part of the spectrum. This is supported by numerical experiments. However, a verification based on the comparison between operational model results and measured data suggests that the opposite is true. This leads to a keen analysis of the overall process, in particular on the role of the tail of the spectrum in modulating the wind input and the white-capping. We suggest that the relationship between white-capping and generation by wind is deeper and more implicative than presently generally assumed. 3. Turbulence generation by waves Energy Technology Data Exchange (ETDEWEB) Kaftori, D.; Nan, X.S.; Banerjee, S. [Univ. of California, Santa Barbara, CA (United States) 1995-12-31 The interaction between two-dimensional mechanically generated waves, and a turbulent stream was investigated experimentally in a horizontal channel, using a 3-D LDA synchronized with a surface position measuring device and a micro-bubble tracers flow visualization with high speed video. Results show that although the wave induced orbital motion reached all the way to the wall, the characteristics of the turbulence wall structures and the turbulence intensity close to the wall were not altered. Nor was the streaky nature of the wall layer. On the other hand, the mean velocity profile became more uniform and the mean friction velocity was increased. Close to the free surface, the turbulence intensity was substantially increased as well. Even in predominantly laminar flows, the introduction of 2-D waves causes three dimensional turbulence. The turbulence enhancement is found to be proportional to the wave strength. 4. Wave Equation Inversion of Skeletonized SurfaceWaves KAUST Repository Zhang, Zhendong 2015-08-19 We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method. 5. The wave of the future - Searching for gravity waves Energy Technology Data Exchange (ETDEWEB) Goldsmith, D. 1991-04-01 Research on gravity waves conducted by such scientists as Gamov, Wheeler, Weber and Zel'dovich is discussed. Particular attention is given to current trends in the theoretical analysis of gravity waves carried out by theorists Kip Thorne and Leonid Grishchuk. The problems discussed include the search for gravity waves; calculation of the types of gravity waves; the possibility of detecting gravity waves from localized sources, e.g., from the collision of two black holes in a distant galaxy or the collapse of a star, through the Laser Interferometer Gravitational Wave Observatory; and detection primordial gravity waves from the big bang. 6. The wave of the future - Searching for gravity waves Science.gov (United States) Goldsmith, Donald 1991-04-01 Research on gravity waves conducted by such scientists as Gamov, Wheeler, Weber and Zel'dovich is discussed. Particular attention is given to current trends in the theoretical analysis of gravity waves carried out by theorists Kip Thorne and Leonid Grishchuk. The problems discussed include the search for gravity waves; calculation of the types of gravity waves; the possibility of detecting gravity waves from localized sources, e.g., from the collision of two black holes in a distant galaxy or the collapse of a star, through the Laser Interferometer Gravitational Wave Observatory; and detection primordial gravity waves from the big bang. 7. Caustics for Spherical Waves CERN Document Server de Rham, Claudia 2016-01-01 We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the Galileon and the DBI-Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global galilean symmetry or a global relativistic galilean symmetry. 8. Electromagnetic van Kampen waves Energy Technology Data Exchange (ETDEWEB) Ignatov, A. M., E-mail: [email protected] [Russian Academy of Sciences, Prokhorov General Physics Institute (Russian Federation) 2017-01-15 The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed. 9. Heisenberg's wave packet reconsidered OpenAIRE Grabbe, J. Orlin 2005-01-01 This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing Heisenberg's restrictions leads to a more general formulation of the uncertainty principle. This reformulation shows quantum uncertainty can exist at a macroscopic level. These modifications also give rise to a new form of Schrodinger's wave equation as the... 10. Wave Dissipation by Vegetation Science.gov (United States) 2011-09-01 Coastal and Hydraulics Engineering Technical Note (CHETN) provides a literature review of wave dissipation by vegetation. INTRODUCTION: Flooding...coastal mangrove forests of Vietnam (Quartel et al. 2007, Mazda et al. 2006, Mazda et al. 1997), salt marshes of the United States (Bradley and...et al. 2007, Mazda et al. 2006, Cooper 2005, Möller and Spencer 2002, Möller et al. 1999). A year-long study by Cooper (2005) found that wave 11. Sound Waves Levitate Substrates Science.gov (United States) Lee, M. C.; Wang, T. G. 1982-01-01 System recently tested uses acoustic waves to levitate liquid drops, millimeter-sized glass microballoons, and other objects for coating by vapor deposition or capillary attraction. Cylindrical contactless coating/handling facility employs a cylindrical acoustic focusing radiator and a tapered reflector to generate a specially-shaped standing wave pattern. Article to be processed is captured by the acoustic force field under the reflector and moves as reflector is moved to different work stations. 12. Wind generated rogue waves in an annular wave flume CERN Document Server Toffoli, A; Salman, H; Monbaliu, J; Frascoli, F; Dafilis, M; Stramignoni, E; Forza, R; Manfrin, M; Onorato, M 2016-01-01 We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves, where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an {\\it unlimited-fetch} condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment. 13. Wind Generated Rogue Waves in an Annular Wave Flume. Science.gov (United States) Toffoli, A; Proment, D; Salman, H; Monbaliu, J; Frascoli, F; Dafilis, M; Stramignoni, E; Forza, R; Manfrin, M; Onorato, M 2017-04-07 We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment. 14. Exact solitary wave solutions of nonlinear wave equations Institute of Scientific and Technical Information of China (English) 2001-01-01 The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions. 15. Traveling-Wave Tubes Science.gov (United States) Kory, Carol L. 1998-01-01 The traveling-wave tube (TWT) is a vacuum device invented in the early 1940's used for amplification at microwave frequencies. Amplification is attained by surrendering kinetic energy from an electron beam to a radio frequency (RF) electromagnetic wave. The demand for vacuum devices has been decreased largely by the advent of solid-state devices. However, although solid state devices have replaced vacuum devices in many areas, there are still many applications such as radar, electronic countermeasures and satellite communications, that require operating characteristics such as high power (Watts to Megawatts), high frequency (below 1 GHz to over 100 GHz) and large bandwidth that only vacuum devices can provide. Vacuum devices are also deemed irreplaceable in the music industry where musicians treasure their tube-based amplifiers claiming that the solid-state and digital counterparts could never provide the same "warmth" (3). The term traveling-wave tube includes both fast-wave and slow-wave devices. This article will concentrate on slow-wave devices as the vast majority of TWTs in operation fall into this category. 16. On conformally related -waves Varsha Daftardar-Gejji 2001-05-01 Brinkmann [1] has shown that conformally related distinct Ricci flat solutions are -waves. Brinkmann's result has been generalized to include the conformally invariant source terms. It has been shown that [4] if $g_{ik}$ and $\\overline{g}_{ik}$ ($=^{-2}g_{ik}$, : a scalar function), are distinct metrics having the same Einstein tensor, $G_{ik}=\\overline{G}_{ik}$, then both represent (generalized) $pp$-waves and $_{i}$ is a null convariantly constant vector of $g_{ik}$. Thus $pp$-waves are the only candidates which yield conformally related nontrivial solutions of $G_{ik}=T_{ik}=\\overline{G}_{ik}$, with $T_{ik}$ being conformally invariant source. In this paper the functional form of the conformal factor for the conformally related $pp$-waves/generalized $pp$-waves has been obtained. It has been shown that the most general $pp$-wave, conformally related to ${\\rm d}s^{2}=-2{\\rm d}u[{\\rm d}v-m{\\rm d}y+H{\\rm d}u]+P^{-2}[{\\rm d}y^{2}+{\\rm d}z^{2}]$, turns out to the $(au+b)^{-2}{\\rm d}s^{2}$, where , are constants. Only in the special case when $m=0$, $H=1$, and $P=P(y,z)$, the conformal factor is $(au+b)^{-2}$ or $(a(u+v)+b)^{-2}$. 17. Undamped electrostatic plasma waves CERN Document Server Valentini, F; Califano, F; Pegoraro, F; Veltri, P; Morrison, P J; O'Neil, T M 2015-01-01 Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\\omega_{_R})$ plane ($\\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existenc... 18. Rain waves-wind waves interaction application to scatterometry Science.gov (United States) Kharif, C.; Giovanangeli, J. P.; Bliven, L. 1989-01-01 Modulation of a rain wave pattern by longer waves has been studied. An analytical model taking into account capillarity effects and obliquity of short waves has been developed. Modulation rates in wave number and amplitude have been computed. Experiments were carried out in a wave tank. First results agree with theoretical models, but higher values of modulation rates are measured. These results could be taken into account for understanding the radar response from the sea surface during rain. 19. Predictability of the Power Output of Three Wave Energy Technologies in the Danish North Sea DEFF Research Database (Denmark) Chozas, Julia Fernandez; Jensen, N. E. Helstrup; Sørensen, H. C.; 2011-01-01 of the study is to provide an indication on the accuracy of the forecast of i) wave parameters, ii) the normalised theoretical power productions from each of the selected technologies (Pelamis, Wave Dragon and Wavestar), and iii) the normalised theoretical power production of a combination of the three devices...... of the normalised theoretical power outputs of Pelamis, Wave Dragon and Wavestar are 44%, 52% and 62%, respectively. The best compromise between forecast accuracy and mean power production results when considering the combined production of the three devices.......The paper addresses an important challenge ahead the integration of the electricity generated by wave energy conversion technologies into the electric grid. Particularly, it looks into the role of wave energy within the day-ahead electricity market. For that the predictability of the theoretical... 20. Partnership for Wave Power - Roadmaps DEFF Research Database (Denmark) Nielsen, Kim; Krogh, Jan; Brodersen, Hans Jørgen; This Wave Energy Technology Roadmap is developed by the Partnership for Wave Power including nine Danish wave energy developers. It builds on to the strategy [1] published by the Partnership in 2012, a document that describes the long term vision of the Danish Wave Energy sector: “By 2030... 1. Nonlinear surface waves over topography NARCIS (Netherlands) Janssen, T.T. 2006-01-01 As ocean surface waves radiate into shallow coastal areas and onto beaches, their lengths shorten, wave heights increase, and the wave shape transforms from nearsinusoidal to the characteristic saw-tooth shapes at the onset of breaking; in the ensuing breaking process the wave energy is cascaded to 2. Near Shore Wave Modeling and applications to wave energy estimation Science.gov (United States) Zodiatis, G.; Galanis, G.; Hayes, D.; Nikolaidis, A.; Kalogeri, C.; Adam, A.; Kallos, G.; Georgiou, G. 2012-04-01 The estimation of the wave energy potential at the European coastline is receiving increased attention the last years as a result of the adaptation of novel policies in the energy market, the concernsfor global warming and the nuclear energy security problems. Within this framework, numerical wave modeling systems keep a primary role in the accurate description of wave climate and microclimate that is a prerequisite for any wave energy assessment study. In the present work two of the most popular wave models are used for the estimation of the wave parameters at the coastline of Cyprus: The latest parallel version of the wave model WAM (ECMWF version), which employs new parameterization of shallow water effects, and the SWAN model, classically used for near shore wave simulations. The results obtained from the wave models near shores are studied by an energy estimation point of view: The wave parameters that mainly affect the energy temporal and spatial distribution, that is the significant wave height and the mean wave period, are statistically analyzed,focusing onpossible different aspects captured by the two models. Moreover, the wave spectrum distribution prevailing in different areas are discussed contributing, in this way, to the wave energy assessmentin the area. This work is a part of two European projects focusing on the estimation of the wave energy distribution around Europe: The MARINA platform (http://www.marina-platform.info/ index.aspx) and the Ewave (http://www.oceanography.ucy.ac.cy/ewave/) projects. 3. SCALAR WAVES AND WIRELESS POWER Directory of Open Access Journals (Sweden) Trunev A. P. 2013-11-01 Full Text Available It is established that in the classical electrodynamics with Lorenz gauge there are solutions in the form of waves of scalar and vector potential at zero magnetic and electric field. It is shown that wave scalar and vector potential can interact with the substance, causing ionization of the atoms and molecules. The analogue of scalar waves in electrodynamics and sound waves in gas dynamics is discussed. Proposed technical application of the waves of scalar and vector potential similar to acoustic waves. Discusses Tesla invented electrical device capable of generating and receiving scalar waves 4. SOME PROBLEMS ABOUT SHIP WAVES Institute of Scientific and Technical Information of China (English) Liu Min-jia 2003-01-01 Several problems about ship waves were discussed in the dissertation:(1) Transient ship waves from calmness to the generation of steady-state ship waves were described. (2) The procedure of the formation of the V-shaped steady-state ship waves were clearly shown, and the difference of ship waves on an inviscid fluid and on a viscous fluid was exmined. (3) With the Lighthill two-stage scheme, the algebraic expression for ship waves on a viscous fluid of finite depth was obtained.(4) Singularity on the two boundaries of the ship waves was treated. 5. On the Draupner freak wave CERN Document Server Fedele, Francesco 2015-01-01 In this paper, we revisit extreme wave statistics related to the 1993's Draupner freak wave event drawing on ERA-interim reanalysis data. In particular, we study the influence of nonlinear wave-wave interactions and space-time variability of the wave field on the predictions of the maximum wave and crest heights expected at the Draupner site. According to Janssen's (2003) theory, in realistic oceanic storms characterized by short-crested seas the wave field forgets its initial conditions and adjusts to a non-Gaussian state dominated by second order bound nonlinearities on time scales t\\gg t_{c}\\approx0.13T_{0}/\ 6. Metamaterials, from electromagnetic waves to water waves, bending waves and beyond KAUST Repository Dupont, G. 2015-08-04 We will review our recent work on metamaterials for different types of waves. Transposition of transform optics to water waves and bending waves on plates will be considered with potential applications of cloaking to water waves protection and anti-vibrating systems. 7. Stability of Solitary Waves for Three Coupled Long Wave - Short Wave Interaction Equations OpenAIRE Borluk, H.; Erbay, S. 2009-01-01 In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods. 8. Nonstationary distributions of wave intensities in wave turbulence Science.gov (United States) Choi, Yeontaek; Jo, Sanggyu; Kwon, Young-Sam; Nazarenko, Sergey 2017-09-01 We obtain a general solution for the probability density function (PDF) of wave intensities in non-stationary wave turbulence. The solution is expressed in terms of the initial PDF and the wave action spectrum satisfying the wave-kinetic equation. We establish that, in the absence of wave breaking, the wave statistics converge to a Gaussian distribution in forced-dissipated wave systems while approaching a steady state. Also, we find that in non-stationary systems, if the statistic is Gaussian initially, it will remain Gaussian for all time. Generally, if the statistic is not initially Gaussian, it will remain non-Gaussian over the characteristic nonlinear evolution time of the wave spectrum. In freely decaying wave turbulence, substantial deviations from Gaussianity may persist infinitely long. 9. Infragravity Waves Produced by Wave Groups on Beaches Institute of Scientific and Technical Information of China (English) 邹志利; 常梅 2003-01-01 The generation of low frequency waves by a single or double wave groups incident upon two plane beaches with the slope of 1/40 and 1/100 is investigated experimentally and numerically. A new type of wave maker signal is used to generate the groups, allowing the bound long wave (set-down) to be included in the group. The experiments show that the low frequency wave is generated during breaking and propagation to the shoreline of the wave group. This process of generation and propagation of low frequency waves is simulated numerically by solving the short-wave averaged mass and momentum conservation equations. The computed and measured results are in good agreement. The mechanism of generation of low frequency waves in the surf zone is examined and discussed. 10. Reflection and Refraction of Acoustic Waves by a Shock Wave Science.gov (United States) Brillouin, J. 1957-01-01 The presence of sound waves in one or the other of the fluid regions on either side of a shock wave is made apparent, in the region under superpressure, by acoustic waves (reflected or refracted according to whether the incident waves lie in the region of superpressure or of subpressure) and by thermal waves. The characteristics of these waves are calculated for a plane, progressive, and uniform incident wave. In the case of refraction, the refracted acoustic wave can, according to the incidence, be plane, progressive, and uniform or take the form of an 'accompanying wave' which remains attached to the front of the shock while sliding parallel to it. In all cases, geometrical constructions permit determination of the kinematic characteristics of the reflected or refractive acoustic waves. The dynamic relationships show that the amplitude of the reflected wave is always less than that of the incident wave. The amplitude of the refracted wave, whatever its type, may in certain cases be greater than that of the incident wave. 11. Rupture, waves and earthquakes Science.gov (United States) UENISHI, Koji 2017-01-01 Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but “extraordinary” phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable. PMID:28077808 12. Ion Acoustic Travelling Waves CERN Document Server Webb, G M; Ao, X; Zank, G P 2013-01-01 Models for travelling waves in multi-fluid plasmas give essential insight into fully nonlinear wave structures in plasmas, not readily available from either numerical simulations or from weakly nonlinear wave theories. We illustrate these ideas using one of the simplest models of an electron-proton multi-fluid plasma for the case where there is no magnetic field or a constant normal magnetic field present. We show that the travelling waves can be reduced to a single first order differential equation governing the dynamics. We also show that the equations admit a multi-symplectic Hamiltonian formulation in which both the space and time variables can act as the evolution variable. An integral equation useful for calculating adiabatic, electrostatic solitary wave signatures for multi-fluid plasmas with arbitrary mass ratios is presented. The integral equation arises naturally from a fluid dynamics approach for a two fluid plasma, with a given mass ratio of the two species (e.g. the plasma could be an electron pr... 13. Bent Marshak Waves Energy Technology Data Exchange (ETDEWEB) Hurricane, O A; Hammer, J H 2005-10-11 Radiation driven heat waves (Marshak Waves) are ubiquitous in astrophysics and terrestrial laser driven high energy density plasma physics (HEDP) experiments. Generally, the equations describing Marshak waves are so nonlinear, that solutions involving more than one spatial dimension require simulation. However, in this paper we show how one may analytically solve the problem of the two-dimensional nonlinear evolution of a Marshak wave, bounded by lossy walls, using an asymptotic expansion in a parameter related to the wall albedo and a simplification of the heat front equation of motion. Three parameters determine the nonlinear evolution, a modified Markshak diffusion constant, a smallness parameter related to the wall albedo, and the spacing of the walls. The final nonlinear solution shows that the Marshak wave will be both slowed and bent by the non-ideal boundary. In the limit of a perfect boundary, the solution recovers the original diffusion-like solution of Marshak. The analytic solution will be compared to a limited set of simulation results and experimental data. 14. Rupture, waves and earthquakes. Science.gov (United States) Uenishi, Koji 2017-01-01 Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but "extraordinary" phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable. 15. Tango waves in a bidomain model of fertilization calcium waves Science.gov (United States) Li, Yue-Xian 2003-12-01 Fertilization of an egg cell is marked by one or several Ca 2+ waves that travel across the intra-cellular space, called fertilization Ca 2+ waves. Patterns of Ca 2+ waves observed in mature or immature oocytes include traveling fronts and pulses as well as concentric and spiral waves. These patterns have been studied in other excitable media in physical, chemical, and biological systems. Here, we report the discovery of a new wave phenomenon in the numerical study of a bidomain model of fertilization Ca 2+ waves. This wave is a front that propagates in a back-and-forth manner that resembles the movement of tango dancers, thus is called a tango wave. When the medium is excitable, a forward-moving tango wave can generate traveling pulses that propagate down the space without reversal. The study shows that the occurrence of tango waves is related to spatial inhomogeneity in the local dynamics. This is tested and confirmed by simulating similar waves in a medium with stationary spatial inhomogeneity. Similar waves are also obtained in a FitzHugh-Nagumo system with a linear spatial ramp. In both the bidomain model of Ca 2+ waves and the FitzHugh-Nagumo system, the front is stable when the slope of a linear ramp is large. As the slope decreases beyond a critical value, front oscillations occur. The study shows that tango waves facilitate the dispersion of localized Ca 2+. Key features of the bidomain model underlying the occurrence of tango waves are revealed. These features are commonly found in egg cells of a variety of species. Thus, we predict that tango waves can occur in real egg cells provided that a slowly varying inhomogeneity does occur following the sperm entry. The observation of tango wave-like waves in nemertean worm and ascidian eggs seems to support such a prediction. 16. Experimental Study on the WavePiston Wave Energy Converter DEFF Research Database (Denmark) Pecher, Arthur; Kofoed, Jens Peter; Angelelli, E. This report presents the results of an experimental study of the power performance of the WavePiston wave energy converter. It focuses mainly on evaluating the power generating capabilities of the device and the effect of the following issues: Scaling ratios PTO loading Wave height and wave period...... dependency Oblique incoming waves Distance between plates During the study, the model supplied by the client, WavePiston, has been rigorously tested as all the anticipated tests have been done thoroughly and during all tests, good quality data has been obtained from all the sensors.... 17. Dynamics of coupled light waves and electron-acoustic waves. Science.gov (United States) Shukla, P K; Stenflo, L; Hellberg, M 2002-08-01 The nonlinear interaction between coherent light waves and electron-acoustic waves in a two-electron plasma is considered. The interaction is governed by a pair of equations comprising a Schrödinger-like equation for the light wave envelope and a driven (by the light pressure) electron-acoustic wave equation. The newly derived nonlinear equations are used to study the formation and dynamics of envelope light wave solitons and light wave collapse. The implications of our investigation to space and laser-produced plasmas are pointed out. 18. Conversion from surface wave to surface wave on reflection DEFF Research Database (Denmark) Novitsky, Andrey 2010-01-01 We discuss the reflection and transmission of an incident surface wave to a pure surface wave state at another interface. This is allowed only for special media parameters: at least one of the media must be magnetic. We found such material characteristics that the obliquely incident surface wave...... can be transmitted without changing its direction (nevertheless the amplitude varies). For other media parameters, only normally incident surface waves can be converted to surface waves. We propose applications of the predicted conversion as a beam splitter and polarization filter for surface waves.... 19. Piezoelectric wave motor Science.gov (United States) Yerganian, Simon Scott 2001-07-17 A piezoelectric motor having a stator in which piezoelectric elements are contained in slots formed in the stator transverse to the desired wave motion. When an electric field is imposed on the elements, deformation of the elements imposes a force perpendicular to the sides of the slot, deforming the stator. Appropriate frequency and phase shifting of the electric field will produce a wave in the stator and motion in a rotor. In a preferred aspect, the piezoelectric elements are configured so that deformation of the elements in direction of an imposed electric field, generally referred to as the d.sub.33 direction, is utilized to produce wave motion in the stator. In a further aspect, the elements are compressed into the slots so as to minimize tensile stresses on the elements in use. 20. IR Hot Wave Energy Technology Data Exchange (ETDEWEB) Graham, T. B. 2010-04-01 The IR Hot Wave{trademark} furnace is a breakthrough heat treatment system for manufacturing metal components. Near-infrared (IR) radiant energy combines with IR convective heating for heat treating. Heat treatment is an essential process in the manufacture of most components. The controlled heating and cooling of a metal or metal alloy alters its physical, mechanical, and sometimes chemical properties without changing the object's shape. The IR Hot Wave{trademark} furnace offers the simplest, quickest, most efficient, and cost-effective heat treatment option for metals and metal alloys. Compared with other heat treatment alternatives, the IR Hot Wave{trademark} system: (1) is 3 to 15 times faster; (2) is 2 to 3 times more energy efficient; (3) is 20% to 50% more cost-effective; (4) has a {+-}1 C thermal profile compared to a {+-}10 C thermal profile for conventional gas furnaces; and (5) has a 25% to 50% smaller footprint. 1. Waves in continuous media CERN Document Server Gavrilyuk, S L; Sukhinin, S V 2017-01-01 Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations. 2. Nonlinear Water Waves CERN Document Server 2016-01-01 This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the... 3. Extremal periodic wave profiles Directory of Open Access Journals (Sweden) E. van Groesen 2007-01-01 Full Text Available As a contribution to deterministic investigations into extreme fluid surface waves, in this paper wave profiles of prescribed period that have maximal crest height will be investigated. As constraints the values of the momentum and energy integrals are used in a simplified description with the KdV model. The result is that at the boundary of the feasible region in the momentum-energy plane, the only possible profiles are the well known cnoidal wave profiles. Inside the feasible region the extremal profiles of maximal crest height are "cornered" cnoidal profiles: cnoidal profiles of larger period, cut-off and periodically continued with the prescribed period so that at the maximal crest height a corner results. 4. Quantum wave packet revivals CERN Document Server Robinett, R W 2004-01-01 The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet (minipackets' or clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities. We review the theoretical machinery of quantum w... 5. The Juno Waves Investigation Science.gov (United States) Kurth, W. S.; Hospodarsky, G. B.; Kirchner, D. L.; Mokrzycki, B. T.; Averkamp, T. F.; Robison, W. T.; Piker, C. W.; Sampl, M.; Zarka, P. 2017-07-01 Jupiter is the source of the strongest planetary radio emissions in the solar system. Variations in these emissions are symptomatic of the dynamics of Jupiter's magnetosphere and some have been directly associated with Jupiter's auroras. The strongest radio emissions are associated with Io's interaction with Jupiter's magnetic field. In addition, plasma waves are thought to play important roles in the acceleration of energetic particles in the magnetosphere, some of which impact Jupiter's upper atmosphere generating the auroras. Since the exploration of Jupiter's polar magnetosphere is a major objective of the Juno mission, it is appropriate that a radio and plasma wave investigation is included in Juno's payload. This paper describes the Waves instrument and the science it is to pursue as part of the Juno mission. 6. Magnetohydrodynamic Shearing Waves CERN Document Server Johnson, B M 2006-01-01 I consider the nonaxisymmetric linear theory of an isothermal magnetohydrodynamic (MHD) shear flow. The analysis is performed in the shearing box, a local model appropriate for a thin disk geometry. Linear perturbations in this model can be decomposed in terms of shearing waves (shwaves), which appear spatially as plane waves in a frame comoving with the shear. The time dependence of these waves cannot in general be expressed in terms of a frequency eigenvalue as in a normal mode decomposition, and numerical integration of a set of first-order amplitude equations is required for a complete characterization of their behavior. Their generic time dependence, however, is oscillatory with slowly-varying frequency and amplitude, and one can construct accurate analytic solutions by applying the Wentzel-Kramers-Brillouin method to the full set of amplitude equations. For the bulk of wavenumber space, therefore, the shwaves are well-approximated as modes with time-dependent frequencies and amplitudes. The incompressiv... 7. Solar system plasma waves Science.gov (United States) Gurnett, Donald A. 1995-01-01 An overview is given of spacecraft observations of plasma waves in the solar system. In situ measurements of plasma phenomena have now been obtained at all of the planets except Mercury and Pluto, and in the interplanetary medium at heliocentric radial distances ranging from 0.29 to 58 AU. To illustrate the range of phenomena involved, we discuss plasma waves in three regions of physical interest: (1) planetary radiation belts, (2) planetary auroral acceleration regions and (3) the solar wind. In each region we describe examples of plasma waves that are of some importance, either due to the role they play in determining the physical properties of the plasma, or to the unique mechanism involved in their generation. 8. Communication at millimeter waves Science.gov (United States) Kamal, A. K.; Christopher, P. F. The advantage and disadvantages of millimeter waves for terrestrial and satellite communications are enumerated. Atmospheric attenuation is discussed in detail, with brief attention given to signal loss in particulates, sandstorms, snow, hail, and fog. Short closed forms are then found for gaseous attenuation on ground-satellite paths. An exponential rain loss probability density function is used in generating atmospheric loss at arbitrary required availability. It is pointed out that this loss (as a function of frequency) can be used to pick optimum carrier frequencies as a function of location, required availability, elevation angle, and system cost. An estimate is made of the rate-of-change of millimeter wave device availability. Special attention is given to GaAs FETs, not only because they will be useful, but because one phase of their millimeter wave performance is predictable: their noise performance as a function of frequency can be estimated with the aid of a Fukui equation. 9. Nonlinear elastic waves in materials CERN Document Server Rushchitsky, Jeremiah J 2014-01-01 The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional... 10. GEODYNAMIC WAVES AND GRAVITY Directory of Open Access Journals (Sweden) A. V. Vikulin 2015-09-01 Full Text Available Gravity phenomena related to the Earth movements in the Solar System and through the Galaxy are reviewed. Such movements are manifested by geological processes on the Earth and correlate with geophysical fields of the Earth. It is concluded that geodynamic processes and the gravity phenomena (including those of cosmic nature are related. The state of the geomedium composed of blocks is determined by stresses with force moment and by slow rotational waves that are considered as a new type of movements [Vikulin, 2008, 2010]. It is shown that the geomedium has typical rheid properties [Carey, 1954], specifically an ability to flow while being in the solid state [Leonov, 2008]. Within the framework of the rotational model with a symmetric stress tensor, which is developed by the authors [Vikulin, Ivanchin, 1998; Vikulin et al., 2012a, 2013], such movement of the geomedium may explain the energy-saturated state of the geomedium and a possibility of its movements in the form of vortex geological structures [Lee, 1928]. The article discusses the gravity wave detection method based on the concept of interactions between gravity waves and crustal blocks [Braginsky et al., 1985]. It is concluded that gravity waves can be recorded by the proposed technique that detects slow rotational waves. It is shown that geo-gravitational movements can be described by both the concept of potential with account of gravitational energy of bodies [Kondratyev, 2003] and the nonlinear physical acoustics [Gurbatov et al., 2008]. Based on the combined description of geophysical and gravitational wave movements, the authors suggest a hypothesis about the nature of spin, i.e. own moment as a demonstration of the space-time ‘vortex’ properties. 11. On the generation of internal wave modes by surface waves Science.gov (United States) Harlander, Uwe; Kirschner, Ian; Maas, Christian; Zaussinger, Florian 2016-04-01 Internal gravity waves play an important role in the ocean since they transport energy and momentum and the can lead to mixing when they break. Surface waves and internal gravity waves can interact. On the one hand, long internal waves imply a slow varying shear current that modifies the propagation of surface waves. Surface waves generated by the atmosphere can, on the other hand, excite internal waves by nonlinear interaction. Thereby a surface wave packet consisting of two close frequencies can resonate with a low frequency internal wave (Phillips, 1966). From a theoretical point of view, the latter has been studied intensively by using a 2-layer model, i.e. a surface layer with a strong density contrast and an internal layer with a comparable weak density contrast (Ball, 1964; Craig et al., 2010). In the present work we analyse the wave coupling for a continuously stratified fluid using a fully non-linear 2D numerical model (OpenFoam) and compare this with laboratory experiments (see Lewis et al. 1974). Surface wave modes are used as initial condition and the time development of the dominant surface and internal waves are studied by spectral and harmonic analysis. For the simple geometry of a box, the results are compared with analytical spectra of surface and gravity waves. Ball, F.K. 1964: Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465. Craig, W., Guyenne, P., Sulem, C. 2010: Coupling between internal and surface waves. Natural Hazards 57, 617-642. Lewis, J.E., Lake, B.M., Ko, D.R.S 1974: On the interaction of internal waves and surfacr gravity waves, J. Fluid Mech. 63, 773-800. Phillips, O.M. 1966: The dynamics of the upper ocean, Cambridge University Press, 336pp. 12. Piecewise flat gravitational waves Energy Technology Data Exchange (ETDEWEB) Van de Meent, Maarten, E-mail: [email protected] [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, PO Box 80.195, 3508 TD Utrecht (Netherlands) 2011-04-07 We examine the continuum limit of the piecewise flat locally finite gravity model introduced by 't Hooft. In the linear weak field limit, we find the energy-momentum tensor and metric perturbation of an arbitrary configuration of defects. The energy-momentum turns out to be restricted to satisfy certain conditions. The metric perturbation is mostly fixed by the energy-momentum except for its lightlike modes which reproduce linear gravitational waves, despite no such waves being present at the microscopic level. 13. Metamaterials and wave control CERN Document Server Lheurette, Eric 2013-01-01 Since the concept was first proposed at the end of the 20th Century, metamaterials have been the subject of much research and discussion throughout the wave community. More than 10 years later, the number of related published articles is increasing significantly. Onthe one hand, this success can be attributed to dreams of new physical objects which are the consequences of the singular properties of metamaterials. Among them, we can consider the examples of perfect lensing and invisibility cloaking. On other hand,metamaterials also provide new tools for the design of well-known wave functions s 14. Hysteretic Faraday Waves CERN Document Server Périnet, Nicolas; Chergui, Jalel; Juric, Damir; Shin, Seungwon 2016-01-01 We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate towards highly nonlinear ones, with twice their amplitude. We propose a simple phenomenological model which can describe the observed bifurcation. We relate this hysteresis with the change of shear stress using a simple stress balance, in agreement with numerical results. 15. Tsunami wave energy CERN Document Server Dutykh, Denys 2008-01-01 In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallow-water equations with an energy equation. It is shown that dispersive effects only appear at higher order in the energy budget. Then we solve the Cauchy-Poisson problem of tsunami generation for the linearized water wave equations. Exchanges between potential and kinetic energies are clearly revealed. 16. Thermoplastic waves in magnetars CERN Document Server Beloborodov, Andrei M 2014-01-01 Magnetar activity is generated by shear motions of the neutron star surface, which relieve internal magnetic stresses. An analogy with earthquakes and faults is problematic, as the crust is permeated by strong magnetic fields, which greatly constrain crustal displacements. We describe a new deformation mechanism that is specific to strongly magnetized neutron stars. The magnetically stressed crust begins to move because of a thermoplastic instability, which launches a wave that shears the crust and burns its magnetic energy. The propagating wave front resembles the deflagration front in combustion physics. We describe the conditions for the instability, the front structure and velocity, and discuss implications for observed magnetar activity. 17. THERMOPLASTIC WAVES IN MAGNETARS Energy Technology Data Exchange (ETDEWEB) Beloborodov, Andrei M. [Physics Department and Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street New York, NY 10027 (United States); Levin, Yuri, E-mail: [email protected], E-mail: [email protected] [Monash Center for Astrophysics and School of Physics, Monash University, Clayton, VIC 3800 (Australia) 2014-10-20 Magnetar activity is generated by shear motions of the neutron star surface, which relieve internal magnetic stresses. An analogy with earthquakes and faults is problematic, as the crust is permeated by strong magnetic fields which greatly constrain crustal displacements. We describe a new deformation mechanism that is specific to strongly magnetized neutron stars. The magnetically stressed crust begins to move because of a thermoplastic instability, which launches a wave that shears the crust and burns its magnetic energy. The propagating wave front resembles the deflagration front in combustion physics. We describe the conditions for the instability, the front structure, and velocity, and discuss implications for observed magnetar activity. 18. Mechanics, Waves and Thermodynamics Science.gov (United States) Ranjan Jain, Sudhir 2016-05-01 Figures; Preface; Acknowledgement; 1. Energy, mass, momentum; 2. Kinematics, Newton's laws of motion; 3. Circular motion; 4. The principle of least action; 5. Work and energy; 6. Mechanics of a system of particles; 7. Friction; 8. Impulse and collisions; 9. Central forces; 10. Dimensional analysis; 11. Oscillations; 12. Waves; 13. Sound of music; 14. Fluid mechanics; 15. Water waves; 16. The kinetic theory of gases; 17. Concepts and laws of thermodynamics; 18. Some applications of thermodynamics; 19. Basic ideas of statistical mechanics; Bibliography; Index. 19. Cyclotron waves in plasma CERN Document Server Lominadze, D G 2013-01-01 Cyclotron Waves in Plasma is a four-chapter text that covers the basic physical concepts of the theory of cyclotron waves and cyclotron instabilities, brought about by the existence of steady or alternating plasma currents flowing perpendicular to the magnetic field.This book considers first a wide range of questions associated with the linear theory of cyclotron oscillations in equilibrium plasmas and in electron plasmas in metals and semiconductors. The next chapter deals with the parametric excitation of electron cyclotron oscillations in plasma in an alternating electric field. A chapter f 20. Leapfrogging Kelvin waves CERN Document Server Hietala, N; Salman, H; Barenghi, C F 2016-01-01 Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simpified model that provides an analytical approximation developed for nearly parallel vortices. Our results are also relevant to thin-cored helical vortices in classical fluids. 1. Leapfrogging Kelvin waves Science.gov (United States) Hietala, N.; Hänninen, R.; Salman, H.; Barenghi, C. F. 2016-12-01 Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simplified model that provides an analytical approximation developed for nearly parallel vortices. Our results are also relevant to thin-cored helical vortices in classical fluids. 2. TSUNAMI WAVE PROPAGATION ALONG WAVEGUIDES Directory of Open Access Journals (Sweden) Andrei G. Marchuk 2009-01-01 Full Text Available This is a study of tsunami wave propagation along the waveguide on a bottom ridge with flat sloping sides, using the wave rays method. During propagation along such waveguide the single tsunami wave transforms into a wave train. The expression for the guiding velocities of the fastest and slowest signals is defined. The tsunami wave behavior above the ocean bottom ridges, which have various model profiles, is investigated numerically with the help of finite difference method. Results of numerical experiments show that the highest waves are detected above a ridge with flat sloping sides. Examples of tsunami propagation along bottom ridges of the Pacific Ocean are presented. 3. Relationship between wave steepness and wave age in the course of wind wave growth Institute of Scientific and Technical Information of China (English) WU Shuping; HOU Yijun; YIN Baoshu; SONG Jinbao; ZHAO Xixi 2004-01-01 It is traditionally assumed that the relationship between wave steepness and wave age is independent of the wind wave growth state. In fact, the traditional relationship can not describe the whole course of wind wave growth. This paper assumes that the relationship between wave steepness and wave age changes with the variety of dimensionless fetch. Based on the relationship proposed by Hou and Wen (1990), a new relationship in the course of wind wave growth is revealed. Comparisons between the present study and other previous relationships show that this new relationship explains better the observations than the other existing relationships. In the case of small fetch, wave age value increases more quickly than other models while it is in opposition to that in the case of large fetch. The result in present paper can clearly reflect the whole course of wind wave growth, it is an improvement for traditional results. 4. Localized coherence of freak waves Science.gov (United States) Latifah, Arnida L.; van Groesen, E. 2016-09-01 This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave. 5. Directional Ocean Wave Spectra Science.gov (United States) 1991-01-01 rpecra. Dil terent wkas e wind forecasts and thle adecomn of water \\ aport for the models used tl the toreca~st icenters arid anah’.ed at The release of...Goda, Y., "On Wave Groups," in An International Conference on the Be-4 Watson , K. MI., and West, B. J., "A Transport Equation Desciption of Non- honiour 6. Third wave development expertise NARCIS (Netherlands) Byskov, Morten 2017-01-01 In this paper I offer a normative account of development expertise. Although extending expertise beyond the traditional development experts to include local stakeholders, this normative account aims to delimit legitimate forms of expertise. I label this normative view third wave development expertis 7. SUPERSYMMETRIC STRING WAVES NARCIS (Netherlands) BERGSHOEFF, EA; KALLOSH, R; ORTIN, T 1993-01-01 We present plane-wave-type solutions of the lowest-order superstring effective action which have unbroken space-time supersymmetries. They are given by a stringy generalization of the Brinkmann metric, dilaton, axion, and gauge fields. Some conspiracy between the metric and the axion field is requir 8. SUPERSYMMETRIC STRING WAVES NARCIS (Netherlands) BERGSHOEFF, E 1994-01-01 We present plane-wave-type solutions to the superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a generalization of the Brinkmann metric. A crucial property of the solutions is a conspiracy between the metric and the axion fie 9. "Hearing" Electromagnetic Waves Science.gov (United States) Rojo, Marta; Munoz, Juan 2014-01-01 In this work, an educational experience is described in which a microwave communication link is used to make students aware that all electromagnetic waves have the same physical nature and properties. Experimental demonstrations are linked to theoretical concepts to increase comprehension of the physical principles underlying electromagnetic… 10. "Hearing" Electromagnetic Waves Science.gov (United States) Rojo, Marta; Munoz, Juan 2014-01-01 In this work, an educational experience is described in which a microwave communication link is used to make students aware that all electromagnetic waves have the same physical nature and properties. Experimental demonstrations are linked to theoretical concepts to increase comprehension of the physical principles underlying electromagnetic… 11. Oblique dust density waves Science.gov (United States) Piel, Alexander; Arp, Oliver; Menzel, Kristoffer; Klindworth, Markus 2007-11-01 We report on experimental observations of dust density waves in a complex (dusty) plasma under microgravity. The plasma is produced in a radio-frequency parallel-plate discharge (argon, p=15Pa, U=65Vpp). Different sizes of dust particles were used (3.4 μm and 6.4μm diameter). The low-frequency (f 11Hz) dust density waves are naturally unstable modes, which are driven by the ion flow in the plasma. Surprisingly, the wave propagation direction is aligned with the ion flow direction in the bulk plasma but becomes oblique at the boundary of the dust cloud with an inclination of 60^o with respect to the plasma boundary. The experimental results are compared with a kinetic model in the electrostatic approximation [1] and a fluid model [2]. Moreover, the role of dust surface waves is discussed. [1] M. Rosenberg, J. Vac. Sci. Technol. A 14, 631 (1996) [2] A. Piel et al, Phys. Rev. Lett. 97, 205009 (2006) 12. Fission waves can oscillate CERN Document Server Osborne, Andrew G 2016-01-01 Under the right conditions, self sustaining fission waves can form in fertile nuclear materials. These waves result from the transport and absorption of neutrons and the resulting production of fissile isotopes. When these fission, additional neutrons are produced and the chain reaction propagates until it is poisoned by the buildup of fission products. It is typically assumed that fission waves are soliton-like and self stabilizing. However, we show that in uranium, coupling of the neutron field to the 239U->239Np->239Pu decay chain can lead to a Hopf bifurcation. The fission reaction then ramps up and down, along with the wave velocity. The critical driver for the instability is a delay, caused by the half-life of 239U, between the time evolution of the neutron field and the production of 239Pu. This allows the 239Pu to accumulate and burn out in a self limiting oscillation that is characteristic of a Hopf bifurcation. Time dependent results are obtained using a numerical implementation of a reduced order r... 13. Fast Deflagration Waves. Science.gov (United States) 1980-07-01 Fendell (1970) to finite Mach numbers, and uncovered the existence of very slow deflagration waves. JI.. -2- 2. The governing equations The governing...FlapmSI, Cambridge University Press. 2. Buckmaster, J. 1976. The quenching of deflagration vaves. Combust. Flme. 26, 151-162. 3. Bush, W.B. & Fendell , F.E 14. Deflagration Wave Profiles Energy Technology Data Exchange (ETDEWEB) Menikoff, Ralph [Los Alamos National Laboratory 2012-04-03 Shock initiation in a plastic-bonded explosives (PBX) is due to hot spots. Current reactive burn models are based, at least heuristically, on the ignition and growth concept. The ignition phase occurs when a small localized region of high temperature (or hot spot) burns on a fast time scale. This is followed by a growth phase in which a reactive front spreads out from the hot spot. Propagating reactive fronts are deflagration waves. A key question is the deflagration speed in a PBX compressed and heated by a shock wave that generated the hot spot. Here, the ODEs for a steady deflagration wave profile in a compressible fluid are derived, along with the needed thermodynamic quantities of realistic equations of state corresponding to the reactants and products of a PBX. The properties of the wave profile equations are analyzed and an algorithm is derived for computing the deflagration speed. As an illustrative example, the algorithm is applied to compute the deflagration speed in shock compressed PBX 9501 as a function of shock pressure. The calculated deflagration speed, even at the CJ pressure, is low compared to the detonation speed. The implication of this are briefly discussed. 15. Electron-Cyclotron Waves NARCIS (Netherlands) Westerhof, E. 1994-01-01 The essential elements of the theory of electron cyclotron waves are reviewed, The two main electro-magnetic modes of propagation are identified and their dispersion and absorption properties are discussed. The importance of the use of the relativistic resonance condition is stressed. 16. SSG Wave Energy Converter DEFF Research Database (Denmark) Margheritini, Lucia; Vicinanza, Diego; Frigaard, Peter 2008-01-01 head hydroturbines are converting the potential energy of the stored water into power. A key to success for the SSG will be the low cost of the structure and its robustness. The construction of the pilot plant is scheduled and this paper aims to describe the concept of the SSG wave energy converter...... and the studies behind the process that leads to its construction. The pilot plant is an on-shore full scale module in 3 levels with an expected power production of 320 MWh/y in the North Sea. Location, wave climate and laboratory tests results will be used here to describe the pilot plant and its characteristics.......The SSG (Sea Slot-cone Generator) is a wave energy converter of the overtopping type. The structure consists of a number of reservoirs one on the top of each others above the mean water level, in which the water of incoming waves is stored temporary. In each reservoir, expressively designed low... 17. Breaking the Waves DEFF Research Database (Denmark) Christensen, Poul Rind; Kirketerp, Anne 2006-01-01 The paper shortly reveals the history of a small school - the KaosPilots - dedicated to educate young people to carriers as entrepreneurs. In this contribution we want to explore how the KaosPilots managed to break the waves of institutionalised concepts and practices of teaching entrepreneurship... 18. Real time wave measurements and wave hindcasting in deep waters Digital Repository Service at National Institute of Oceanography (India) Anand, N.M.; Mandal, S.; SanilKumar, V.; Nayak, B.U. Deep water waves off Karwar (lat. 14~'45.1'N, long. 73~'34.8'E) at 75 m water depth pertaining to peak monsoon period have been measured using a Datawell waverider buoy. Measured wave data show that the significant wave height (Hs) predominantly... 19. Numerical Modelling of Wave Run-Up: Regular Waves DEFF Research Database (Denmark) Ramirez, Jorge; Frigaard, Peter; Andersen, Thomas Lykke; 2011-01-01 Wave loads are important in problems related to offshore structure, such as wave run-up, slamming. The computation of such wave problems are carried out by CFD models. This paper presents one model, NS3, which solve 3D Navier-Stokes equations and use Volume of Fluid (VOF) method to treat the free... 20. Numerical Modelling of Wave Run-Up: Regular Waves DEFF Research Database (Denmark) Ramirez, Jorge; Frigaard, Peter; Andersen, Thomas Lykke 2011-01-01 Wave loads are important in problems related to offshore structure, such as wave run-up, slamming. The computation of such wave problems are carried out by CFD models. This paper presents one model, NS3, which solve 3D Navier-Stokes equations and use Volume of Fluid (VOF) method to treat the free... 1. Active Absorption Wave Maker System for Irregular Waves Institute of Scientific and Technical Information of China (English) 柳淑学; 王先涛; 李木国; 郭美谊 2003-01-01 The key problem in physical model tests with highly reflective structures is to prevent the multiple reflections between the reflective structures and the wave maker. An active absorption wave maker system is described and the representative frequency method for irregular waves is proposed in this paper. Physical model tests are conducted to verify the effectiveness of the proposed method. 2. Quantum wave packet revivals Energy Technology Data Exchange (ETDEWEB) Robinett, R.W 2004-03-01 The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet ('minipackets' or 'clones') is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities. We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems. 3. Quantum wave packet revivals Science.gov (United States) Robinett, R. W. 2004-03-01 The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially localized quantum states which have a short-term, quasi-classical time evolution, which then can spread significantly over several orbits, only to reform later in the form of a quantum revival in which the spreading reverses itself, the wave packet relocalizes, and the semi-classical periodicity is once again evident. Relocalization of the initial wave packet into a number of smaller copies of the initial packet (‘minipackets’ or ‘clones’) is also possible, giving rise to fractional revivals. Systems exhibiting such behavior are a fundamental realization of time-dependent interference phenomena for bound states with quantized energies in quantum mechanics and are therefore of wide interest in the physics and chemistry communities. We review the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as discussing how information on the classical period and revival time is encoded in the energy eigenvalue spectrum. We discuss a number of one-dimensional model systems which exhibit revival behavior, including the infinite well, the quantum bouncer, and others, as well as several two-dimensional integrable quantum billiard systems. Finally, we briefly review the experimental evidence for wave packet revivals in atomic, molecular, and other systems, and related revival phenomena in condensed matter and optical systems. 4. Estimation of directional wave spreading Digital Repository Service at National Institute of Oceanography (India) Mandal, S.; Bhat, S.S.; Anand, N.M.; Nayak, B.U. Directional properties of ocean waves are of great economic interest. The knowledge of wave directionality is important for the design of maritime structures and offshore operations. Two main aspects are considered for this study for the data... 5. Wave propagation in electromagnetic media CERN Document Server Davis, Julian L 1990-01-01 This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessi... 6. Energy Wave Model of Atom Institute of Scientific and Technical Information of China (English) 伍细如 2015-01-01 proton emits energy wave, electron could sits any position away from nucleus, but be the most stable just when it sits at the trough of energy wave, and this position accords with Bohr radius and Schr?dinger equation. 7. Transformation method and wave control Science.gov (United States) Chang, Zheng; Hu, Jin; Hu, Geng-Kai 2010-12-01 Transformation method provides an efficient way to control wave propagation by materials. The transformed relations for field and material during a transformation are essential to fulfill this method. We propose a systematic method to derive the transformed relations for a general physic process, the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier's equation for elastodynamics, Helmholtz's equation for acoustic wave and Maxwell's equation for electromagnetic wave, the corresponding transformed relations are derived, which can be used in the framework of transformation method for wave control. We show that contrary to electromagnetic wave, the transformed relations are not uniquely determined for elastic wave and acoustic wave, so we have a freedom to choose them differently. Using the obtained transformed relations, we also provide some examples for device design, a concentrator for elastic wave, devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations. 8. Gravitational Waves: The Evidence Mounts Science.gov (United States) Wick, Gerald L. 1970-01-01 Reviews the work of Weber and his colleagues in their attempts at detecting extraterrestial gravitational waves. Coincidence events recorded by special detectors provide the evidence for the existence of gravitational waves. Bibliography. (LC) 9. Diurnal variation of mountain waves Directory of Open Access Journals (Sweden) R. M. Worthington 2006-11-01 Full Text Available Mountain waves could be modified as the boundary layer varies between stable and convective. However case studies show mountain waves day and night, and above e.g. convective rolls with precipitation lines over mountains. VHF radar measurements of vertical wind (1990–2006 confirm a seasonal variation of mountain-wave amplitude, yet there is little diurnal variation of amplitude. Mountain-wave azimuth shows possible diurnal variation compared to wind rotation across the boundary layer. 10. Observed Statistics of Extreme Waves Science.gov (United States) 2006-12-01 9 Figure 5. An energy stealing wave as a solution to the NLS equation . (From: Dysthe and...shown that nonlinear interaction between four colliding waves can produce extreme wave behavior. He utilized the NLS equation in his numerical ...2000) demonstrated the formation of extreme waves using the Korteweg de Vries ( KdV ) equation , which is valid in shallow water. It was shown in the 11. Rogue waves in a wave tank: experiments and modeling Directory of Open Access Journals (Sweden) A. Lechuga 2013-07-01 Full Text Available In past decades theoretical studies have been carried out with the double aim of improving the knowledge of rogue wave main characteristics and of attempting to predict its sudden appearance. As an effort on this topic we tried the generation of rogue waves in a water wave tank using a symmetric spectrum (Akhmediev et al., 2011a as input on the wave maker. To go on further the next step has been to apply a theoretical model to the envelope of these waves. After some considerations the best model has been an analogue of the Ginzburg–Landau equation. 12. Conceptual Design of Wave Plane DEFF Research Database (Denmark) Frigaard, Peter; Trewers, Andrew; Kofoed, Jens Peter; The Wave Plane is a patented Wave Energy device of the overtopping type, designed to capture potential as well as kinetic energy. This is as such different to other overtopping devices, who usually only focus on potential energy. If Wave Plane A/S can deliver the turbine technology to utilize both... 13. An Extented Wave Action Equation Institute of Scientific and Technical Information of China (English) 左其华 2003-01-01 Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given. 14. Energy in a String Wave Science.gov (United States) Ng, Chiu-king 2010-01-01 When one end of a taut horizontal elastic string is shaken repeatedly up and down, a transverse wave (assume sine waveform) will be produced and travel along it. College students know this type of wave motion well. They know when the wave passes by, each element of the string will perform an oscillating up-down motion, which in mechanics is termed… 15. Comparison and sensitivity investigations of a CALM and SALM type mooring system for wave energy converters DEFF Research Database (Denmark) Pecher, Arthur; Foglia, Aligi; Kofoed, Jens Peter 2014-01-01 , such as Weptos, Wave Dragon and many others, including reasonable design safety factors. Around this reference scenario, the main influential parameters were modified in order to investigate their impact on the specifications of the mooring system, e.g. the water depth, the horizontal design load, and a mooring... 16. Generation of long subharmonic internal waves by surface waves Science.gov (United States) Tahvildari, Navid; Kaihatu, James M.; Saric, William S. 2016-10-01 A new set of Boussinesq equations is derived to study the nonlinear interactions between long waves in a two-layer fluid. The fluid layers are assumed to be homogeneous, inviscid, incompressible, and immiscible. Based on the Boussinesq equations, an analytical model is developed using a second-order perturbation theory and applied to examine the transient evolution of a resonant triad composed of a surface wave and two oblique subharmonic internal waves. Wave damping due to weak viscosity in both layers is considered. The Boussinesq equations and the analytical model are verified. In contrast to previous studies which focus on short internal waves, we examine long waves and investigate some previously unexplored characteristics of this class of triad interaction. In viscous fluids, surface wave amplitudes must be larger than a threshold to overcome viscous damping and trigger internal waves. The dependency of this critical amplitude as well as the growth and damping rates of internal waves on important parameters in a two-fluid system, namely the directional angle of the internal waves, depth, density, and viscosity ratio of the fluid layers, and surface wave amplitude and frequency is investigated. 17. Wave energy power take off system control and simulation Energy Technology Data Exchange (ETDEWEB) Zhoul, Z.; Holland, P.M.; Igic, P. [Swansea Univ., Swansea, Wales (United Kingdom). School of Engineering; Knapp, W. [Technische Univ. Muenchen, Munich (Germany); MacEnri, J. [ESB International, Dublin (Ireland); Srensen, H.Ch.; Friis-Madsen, E. [Wave Dragon APS and LTD, Copenhagen (Denmark) 2008-07-01 The generation of electric power from wave energy using an offshore wave energy take-off system has received global interest. Several different wave energy take off techniques have been suggested. Among these, the Wave Dragon is one of the most efficient wave energy conversion systems. This paper presented a wave energy power take off system control and simulation scheme. The characteristics of low pressure hydro turbine were described. A variable speed control scheme using IGBT alternating current/direct current converter for low-head hydro-turbine was described in order to achieve maximum efficiency. The electrical system configuration, operation and grid connection issues were presented. Last, in order to investigate the long electro-mechanical process, a simulation model was developed for simulating the generator-turbine starting-stop process. The simulated parameters included the effects of the water head on the torque, speed and output power. Simulation results were presented and discussed. It was concluded that the proposed model is suitable for investigating the overall performance of a wave energy power take off system. 12 refs., 14 figs. 18. Resonance wave pumping: wave mass transport pumping Science.gov (United States) Carmigniani, Remi; Violeau, Damien; Gharib, Morteza 2016-11-01 It has been previously reported that pinching at intrinsic resonance frequencies a valveless pump (or Liebau pump) results in a strong pulsating flow. A free-surface version of the Liebau pump is presented. The experiment consists of a closed tank with a submerged plate separating the water into a free-surface and a recirculation section connected through two openings at each end of the tank. A paddle is placed at an off-centre position at the free-surface and controlled in a heaving motion with different frequencies and amplitudes. Near certain frequencies identified as resonance frequencies through a linear potential theory analysis, the system behaves like a pump. Particle Image Velocimetry (PIV) is performed in the near free surface region and compared with simulations using Volume of Fluid (VOF) method. The mean eulerian mass flux field (ρ) is extracted. It is observed that the flow is located in the vicinity of the surface layer suggesting Stokes Drift (or Wave Mass Transport) is the source of the pumping. A model is developped to extend the linear potential theory to the second order to take into account these observations. The authors would like to acknowledge the Gordon and Betty Moore Foundation for their generous support. 19. Surface Acoustic Wave Devices DEFF Research Database (Denmark) Dühring, Maria Bayard of a Mach-Zehnder interferometer (MZI). This is an optical device consisting if one waveguide that is split into two waveguide arms which are assembled again later on. By applying the mechanical field from a SAW the light in the two arms can be modulated and interfere constructively and destructively......The work of this project is concerned with the simulation of surface acoustic waves (SAW) and topology optimization of SAW devices. SAWs are elastic vibrations that propagate along a material surface and are extensively used in electromechanical filters and resonators in telecommunication. A new...... application is modulation of optical waves in waveguides. This presentation elaborates on how a SAW is generated by interdigital transducers using a 2D model of a piezoelectric, inhomogeneous material implemented in the high-level programming language Comsol Multiphysics. The SAW is send through a model... 20. Dimensions and Gravitational Waves Science.gov (United States) van Haasteren, Rutger 2014-10-01 High-precision timing of Galactic millisecond pulsars with radio telescopes holds great promise for the detection of astrophysical gravitational-waves in frequency range 10--100 nHz. Modern Bayesian data analysis methods rely mostly on Markov Chain Monte Carlo (MCMC) to explore the model parameter space when searching for signals in the pulsar timing data. Current challenges involve parameter spaces with large dimensionality, and linear algebra of high-dimensional systems. I will present sampling methods (taken from the Planck analysis team), and rank-reduction methods for large linear systems, that have enabled us to decrease the dimensionality of such problems. These methods are now being used to search for gravitational-waves in pulsar timing array projects. Especially our rank-reduction techniques are useful for any data analysis problem that involve large linear least-squares systems. 1. Electromagnetic fields and waves CERN Document Server Iskander, Magdy F 2013-01-01 The latest edition of Electromagnetic Fields and Waves retains an authoritative, balanced approach, in-depth coverage, extensive analysis, and use of computational techniques to provide a complete understanding of electromagnetic—important to all electrical engineering students. An essential feature of this innovative text is the early introduction of Maxwell's equations, together with the quantifying experimental observations made by the pioneers who discovered electromagnetics. This approach directly links the mathematical relations in Maxwell's equations to real experiments and facilitates a fundamental understanding of wave propagation and use in modern practical applications, especially in today's wireless world. New and expanded topics include the conceptual relationship between Coulomb's law and Gauss's law for calculating electric fields, the relationship between Biot-Savart's and Ampere's laws and their use in calculating magnetic fields from current sources, the development of Faraday's law from e... 2. Shock waves & explosions CERN Document Server Sachdev, PL 2004-01-01 Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. Offering an introductory review of historic research, Shock Waves and Explosions brings analytic and computational methods to a wide audience in a clear and thorough way. Beginning with an overview of the research on combustion and gas dynamics in the 1970s and 1980s, the author brings you up to date by covering modeling techniques and asymptotic and perturbative methods and ending with a chapter on computational methods.Most of the book deals with the mathematical analysis of explosions, but computational results are also included wherever they are available. Historical perspectives are provided on the advent of nonlinear science, as well as on the mathematical study of the blast wave phenomenon, both when visualized as a point explosion and when simulated as the expansion of a high-pressure ... 3. When Shock Waves Collide CERN Document Server Hartigan, P; Frank, A; Hansen, E; Yirak, K; Liao, A S; Graham, P; Wilde, B; Blue, B; Martinez, D; Rosen, P; Farley, D; Paguio, R 2016-01-01 Supersonic outflows from objects as varied as stellar jets, massive stars and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures and therefore a higher-excitation spectrum than an oblique one does. In this paper we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and ... 4. Snell's Law for Spin Waves Science.gov (United States) Stigloher, J.; Decker, M.; Körner, H. S.; Tanabe, K.; Moriyama, T.; Taniguchi, T.; Hata, H.; Madami, M.; Gubbiotti, G.; Kobayashi, K.; Ono, T.; Back, C. H. 2016-07-01 We report the experimental observation of Snell's law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves. We use a thickness step as the interface between two media with different dispersion relations. Since the dispersion relation for magnetostatic waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25 ° with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications. 5. Phonon creation by gravitational waves CERN Document Server Sabín, Carlos; Ahmadi, Mehdi; Fuentes, Ivette 2014-01-01 We show that gravitational waves create phonons in a Bose-Einstein condensate (BEC). A traveling spacetime distortion produces particle creation resonances that correspond to the dynamical Casimir effect in a BEC phononic field contained in a cavity-type trap. We propose to use this effect to detect gravitational waves. The amplitude of the wave can be estimated applying recently developed relativistic quantum metrology techniques. We provide the optimal precision bound on the estimation of the wave's amplitude. Finally, we show that the parameter regime required to detect gravitational waves with this technique is within experimental reach. 6. Gravitational Wave - Gauge Field Oscillations CERN Document Server Caldwell, R R; Maksimova, N A 2016-01-01 Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multi-dimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields. 7. Introduction to THz wave photonics CERN Document Server Zhang, X-C 2009-01-01 Introduction to THz Wave Photonics examines the science and technology related to terahertz wave technologies, taking a dual approach between presenting the field 's history while simultaneously providing an overview of existing technology. The latest research in developing THz areas such as electromagnetic waves are presented, along with an introduction to continuous wave THz technology. Authors X.-C. Zhang and Jingzhou Xu place particular emphasis on pulsed THz technology, among many other facets of THz technology including: Complete coverage of THz wave spectroscopy and imagingA discussion 8. Spatiotemporal chaos involving wave instability Science.gov (United States) Berenstein, Igal; Carballido-Landeira, Jorge 2017-01-01 In this paper, we investigate pattern formation in a model of a reaction confined in a microemulsion, in a regime where both Turing and wave instability occur. In one-dimensional systems, the pattern corresponds to spatiotemporal intermittency where the behavior of the systems alternates in both time and space between stationary Turing patterns and traveling waves. In two-dimensional systems, the behavior initially may correspond to Turing patterns, which then turn into wave patterns. The resulting pattern also corresponds to a chaotic state, where the system alternates in both space and time between standing wave patterns and traveling waves, and the local dynamics may show vanishing amplitude of the variables. 9. Efficient Generation of Freak Waves in Laboratory Institute of Scientific and Technical Information of China (English) 2007-01-01 In the present study, Kriebel's method is improved to generate freak waves in laboratory. The improved method superposes a random wave train with two transient wave trains to simulate freak wave events in a wave tank. The freak waves are more nonlinear than what generated with Kriebel's method of the same energy. It can also generate freak waves to satisfy all the qualifications of the adopted definition with less energy than Kriebel's and can hardly influence the significant wave height. 10. Fractional Electromagnetic Waves CERN Document Server Gómez, J F; Bernal, J J; Tkach, V I; Guía, M 2011-01-01 In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\\gamma<1. A new parameter \\sigma, is introduced which characterizes the existence of the fractional components in the system. We analyze the fractional derivative with respect to time and space, for \\gamma = 1 and \\gamma = 1/2 cases. 11. Assimilation of Wave Imaging Radar Observations for Real-time Wave-by-Wave Forecasting Energy Technology Data Exchange (ETDEWEB) Simpson, Alexandra [Oregon State Univ., Corvallis, OR (United States); Haller, Merrick; Walker, David [SRI International, Menlo Park, CA (United States); Lynett, Pat [Univ. of Southern California, Los Angeles, CA (United States) 2017-08-29 This project addressed Topic 3: “Wave Measurement Instrumentation for Feed Forward Controls” under the FOA number DE-FOA-0000971. The overall goal of the program was to develop a phase-resolving wave forecasting technique for application to the active control of Wave Energy Conversion (WEC) devices. We have developed an approach that couples a wave imaging marine radar with a phase-resolving linear wave model for real-time wave field reconstruction and forward propagation of the wave field in space and time. The scope of the project was to develop and assess the performance of this novel forecasting system. Specific project goals were as follows: Develop and verify a fast, GPU-based (Graphical Processing Unit) wave propagation model suitable for phase-resolved computation of nearshore wave transformation over variable bathymetry; Compare the accuracy and speed of performance of the wave model against a deep water model in their ability to predict wave field transformation in the intermediate water depths (50 to 70 m) typical of planned WEC sites; Develop and implement a variational assimilation algorithm that can ingest wave imaging radar observations and estimate the time-varying wave conditions offshore of the domain of interest such that the observed wave field is best reconstructed throughout the domain and then use this to produce model forecasts for a given WEC location; Collect wave-resolving marine radar data, along with relevant in situ wave data, at a suitable wave energy test site, apply the algorithm to the field data, assess performance, and identify any necessary improvements; and Develop a production cost estimate that addresses the affordability of the wave forecasting technology and include in the Final Report. The developed forecasting algorithm (“Wavecast”) was evaluated for both speed and accuracy against a substantial synthetic dataset. Early in the project, performance tests definitively demonstrated that the system was capable of 12. Downscattering of Diocotron Wave Action Science.gov (United States) Smerdyakov, K.; Mattor, Nathan; Mitchell, Travis B. 1996-11-01 Here we present a quantitative theory of resonant downscattering of diocotron waves in a non-neutral plasma (or Kelvin waves in a 2D fluid), in which wave action is transferred between two normal modes via a resonance of the beat wave with the ambient fluid. This phenomenon is a fluid analogue of nonlinear wave-particle-wave scattering in a plasma. (J. D. Crawford and T. M. O'Neil, Phys. Fluids 30,) 2076 (1987), and T. S. Hahm Phys. Fluids B, 4, 2801 (1992). The analytic treatment consists of a weak turbulence expansion of the 2D Euler equation, which results in a wave kinetic equation. The principal new result is a quantitative prediction of the scattering rate, which is compared with the rates measured in a recent experiment which observed this phenomenon. (T. B. Mitchell and C. F. Driscoll, Phys. Rev. Lett. 73,) 2196 (1994). 13. Tamm-Langmuir surface waves Science.gov (United States) Golenitskii, K. Â. Yu.; Koshelev, K. Â. L.; Bogdanov, A. Â. A. 2016-10-01 In this work we develop a theory of surface electromagnetic waves localized at the interface of periodic metal-dielectric structures. We have shown that the anisotropy of plasma frequency in metal layers lifts the degeneracy of plasma oscillations and opens a series of photonic band gaps. This results in appearance of surface waves with singular density of states—we refer to them as Tamm-Langmuir waves. Such naming is natural since we have found that their properties are very similar to the properties of both bulk Langmuir and surface Tamm waves. Depending on the anisotropy parameters, Tamm-Langmuir waves can be either forward or backward waves. Singular density of states and high sensitivity of the dispersion to the anisotropy of the structure makes Tamm-Langmuir waves very promising for potential applications in nanophotonics and biosensing. 14. Surface-wave photonic quasicrystal CERN Document Server Gao, Zhen; Zhang, Youming; Xu, Hongyi; Zhang, Baile 2016-01-01 In developing strategies of manipulating surface electromagnetic waves, it has been recently recognized that a complete forbidden band gap can exist in a periodic surface-wave photonic crystal, which has subsequently produced various surface-wave photonic devices. However, it is not obvious whether such a concept can be extended to a non-periodic surface-wave system that lacks translational symmetry. Here we experimentally demonstrate that a surface-wave photonic quasicrystal that lacks periodicity can also exhibit a forbidden band gap for surface electromagnetic waves. The lower cutoff of this forbidden band gap is mainly determined by the maximum separation between nearest neighboring pillars. Point defects within this band gap show distinct properties compared to a periodic photonic crystal for the absence of translational symmetry. A line-defect waveguide, which is crafted out of this surface-wave photonic quasicrystal by shortening a random row of metallic rods, is also demonstrated to guide and bend sur... 15. Residual Liquefaction under Standing Waves DEFF Research Database (Denmark) Kirca, V.S. Ozgur; Sumer, B. Mutlu; Fredsøe, Jørgen 2012-01-01 This paper summarizes the results of an experimental study which deals with the residual liquefaction of seabed under standing waves. It is shown that the seabed liquefaction under standing waves, although qualitatively similar, exhibits features different from that caused by progressive waves....... The experimental results show that the buildup of pore-water pressure and the resulting liquefaction first starts at the nodal section and spreads towards the antinodal section. The number of waves to cause liquefaction at the nodal section appears to be equal to that experienced in progressive waves for the same...... wave height. Recommendations are made as to how to assess liquefaction potential in standing waves. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE).... 16. WAVE ASSIMILATION AND NUMERICAL PREDICTION Institute of Scientific and Technical Information of China (English) 2000-01-01 An adjoint variational method for wave data assimilation in the LAGFD-WAM wave model is proposed. The adjoint equation of the wavenumber energy spectrum balance equation is derived. And fortunately, its characteristic equations are the same as those in the LAGFD-WAM wave model. Simple experiments on the functional optimization and assimilation effectiveness during the prediction period indicated that the adjoint variational method is effective for wave assimilation and that the initial optimization of the wave model is important for the short-range wave prediction. All of this is under the assumption that the wind field is accurate, the method is the important first step for combined wind and wave data assimilation systems. 17. Tamm-Langmuir surface waves CERN Document Server Golenitskii, K U; Bogdanov, A A 2016-01-01 In this work we develop a theory of surface electromagnetic waves localized at the interface of periodic metal-dielectric structures. We have shown that the anisotropy of plasma frequency in metal layers lifts the degeneracy of plasma oscillations and opens a series of photonic band gaps. This results in appearance of surface waves with singular density of states - we refer to them as Tamm-Langmuir waves. Such naming is natural since we have found that their properties are very similar to the properties of both bulk Langmuir and surface Tamm waves. Depending on the anisotropy parameters, Tamm-Langmuir waves can be either forward or backward waves. Singular density of states and high sensitivity of the dispersion to the anisotropy of the structure makes Tamm-Langmuir waves very promising for potential applications in nanophotonics and biosensing. 18. Assessing wave energy effects on biodiversity: the wave hub experience. Science.gov (United States) Witt, M J; Sheehan, E V; Bearhop, S; Broderick, A C; Conley, D C; Cotterell, S P; Crow, E; Grecian, W J; Halsband, C; Hodgson, D J; Hosegood, P; Inger, R; Miller, P I; Sims, D W; Thompson, R C; Vanstaen, K; Votier, S C; Attrill, M J; Godley, B J 2012-01-28 Marine renewable energy installations harnessing energy from wind, wave and tidal resources are likely to become a large part of the future energy mix worldwide. The potential to gather energy from waves has recently seen increasing interest, with pilot developments in several nations. Although technology to harness wave energy lags behind that of wind and tidal generation, it has the potential to contribute significantly to energy production. As wave energy technology matures and becomes more widespread, it is likely to result in further transformation of our coastal seas. Such changes are accompanied by uncertainty regarding their impacts on biodiversity. To date, impacts have not been assessed, as wave energy converters have yet to be fully developed. Therefore, there is a pressing need to build a framework of understanding regarding the potential impacts of these technologies, underpinned by methodologies that are transferable and scalable across sites to facilitate formal meta-analysis. We first review the potential positive and negative effects of wave energy generation, and then, with specific reference to our work at the Wave Hub (a wave energy test site in southwest England, UK), we set out the methodological approaches needed to assess possible effects of wave energy on biodiversity. We highlight the need for national and international research clusters to accelerate the implementation of wave energy, within a coherent understanding of potential effects-both positive and negative. 19. Shear wave speed recovery in sonoelastography using crawling wave data. Science.gov (United States) Lin, Kui; McLaughlin, Joyce; Renzi, Daniel; Thomas, Ashley 2010-07-01 The crawling wave experiment, in which two harmonic sources oscillate at different but nearby frequencies, is a development in sonoelastography that allows real-time imaging of propagating shear wave interference patterns. Previously the crawling wave speed was recovered and used as an indicator of shear stiffness; however, it is shown in this paper that the crawling wave speed image can have artifacts that do not represent a change in stiffness. In this paper, the locations and shapes of some of the artifacts are exhibited. In addition, a differential equation is established that enables imaging of the shear wave speed, which is a quantity strongly correlated with shear stiffness change. The full algorithm is as follows: (1) extract the crawling wave phase from the spectral variance data; (2) calculate the crawling wave phase wave speed; (3) solve a first-order PDE for the phase of the wave emanating from one of the sources; and (4) compute and image the shear wave speed on a grid in the image plane. 20. Generation of rogue waves in a wave tank Science.gov (United States) Lechuga, A. 2012-04-01 Rogue waves have been reported as causing damages and ship accidents all over the oceans of the world. For this reason in the past decades theoretical studies have been carried out with the double aim of improving the knowledge of their main characteristics and of attempting to predict its sudden appearance. As an effort on this line we are trying to generate them in a water tank. The description of the procedure to do that is the objective of this presentation. After Akhmediev et al. (2011) we use a symmetric spectrum as input on the wave maker to produce waves with a rate(Maximun wave height/ significant wave height) of 2.33 and a kurtosis of 4.77, clearly between the limits of rogue waves. As it was pointed out by Janssen (2003), Onorato et al. (2006) and Kharif, Pelinovsky and Slunyaev (2009) modulation instability is enhanced when waves depart from Gaussian statistics (i.e. big kurtosis) and therefore both numbers enforce the criterion that we are generating genuine rogue waves. The same is confirmed by Shemer (2010) and Dudley et al.(2009) from a different perspective. If besides being symmetrical the spectrum is triangular, following Akhmediev(2011),the generated waves are even more conspicuously rogue waves. 1. Study of Novel Slow Wave Circuit for Miniaturized Millimeter Wave Helical Traveling Wave Tube Science.gov (United States) Li, Bin; Zhu, Xiaofang; Liao, Li; Yang, Zhonghai; Zeng, Baoqing; Yao, Lieming 2006-07-01 Two kinds of novel helical slow wave circuit, supported by Chemical Vapor Deposition (CVD) diamond, are presented. They are applying in miniaturized millimeter wave helical traveling wave tube. Cold test characteristic of these circuits are simulated by MAFIA code. Higher performances are achieved with smaller size, compared with conventional circuit supported by BeO rods. The nonlinear analysis is implemented by Beam and Wave Interaction (BWI) module, which is a part of TWTCAD Integrated Framework. Results have been found to be consistent with the expectation. It should be wider apply in microwave and millimeter wave vacuum electronic devices. 2. Waves in geophysical fluids tsunamis, rogue waves, internal waves and internal tides CERN Document Server Schneider, Wilhelm; Trulsen, Karsten 2006-01-01 Waves in Geophysical Fluids describes: the forecasting and risk evaluation of tsunamis by tectonic motion, land slides, explosions, run-up, and maps the tsunami sources in the world's oceans; stochastic Monte-Carlo simulations and focusing mechanisms for rogue waves, nonlinear wave models, breather formulas, and the kinematics of the Draupner wave; the full story about the discovery of the very large oceanic internal waves, how the waves are visible from above through the signatures on the sea surface, and how to compute them; observations of energetic internal tides and hot spots from several field campaigns in all parts of the world's oceans, with interpretation of spectra. An essential work for students, scientists and engineers working with the fundamental and applied aspects of ocean waves. 3. Skeletonized wave equation of surface wave dispersion inversion KAUST Repository Li, Jing 2016-09-06 We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media. 4. A Wave Modulation Model of Ripples over Long Surface Waves Institute of Scientific and Technical Information of China (English) CONG Peixiu; ZHENG Guizhen 2011-01-01 A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modulation model is proposed. In this model, the wind surface stress modulation is related to the modulation of tipple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the tipple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves. 5. Numerical Wave Flume Study on Wave Motion Around Submerged Plates Institute of Scientific and Technical Information of China (English) 齐鹏; 侯一筠 2003-01-01 Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters. 6. Shock wave treatment in medicine S K Shrivastava; Kailash 2005-03-01 Extracorporeal shock wave therapy in orthopedics and traumatology is still a young therapy method. Since the last few years the development of shock wave therapy has progressed rapidly. Shock waves have changed the treatment of urolithiasis substantially. Today shock waves are the first choice to treat kidney and urethral stones. Urology has long been the only medical field for shock waves in medicine. Meanwhile shock waves have been used in orthopedics and traumatology to treat insertion tendinitis, avascular necrosis of the head of femur and other necrotic bone alterations. Another field of shock wave application is the treatment of tendons, ligaments and bones on horses in veterinary medicine. In the present paper we discuss the basic theory and application of shock waves and its history in medicine. The idea behind using shock wave therapy for orthopedic diseases is the stimulation of healing in tendons, surrounding tissue and bones. This is a completely different approach compared to urology where shock waves are used for disintegration. 7. Scattering and Depolarization of Electromagnetic Waves--Full Wave Solutions. Science.gov (United States) 1984-01-01 Analysis," Proceedings of the International Union of Radio Science URSI Conference at Ciudad Universitaria , Madrid, August 1983, in press. . . 13...rough land and seat3 J. The full wave approach was also used to determine the scattering and depolarization of radio waves in irregular spheroidal struc...Full Wave Solutions," Radio Science, Vol. 17, No. 5, September-October 1982, pp. 1055-1066. 4. "Scattering and Depolarization by Rough Surfaces: Full 8. From bell-shaped solitary wave to W/M-shaped solitary wave solutions in an integrable nonlinear wave equation Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang 2010-01-01 The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained. 9. Helical localized wave solutions of the scalar wave equation. Science.gov (United States) Overfelt, P L 2001-08-01 A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch. 10. Skeletonized wave-equation Qs tomography using surface waves KAUST Repository Li, Jing 2017-08-17 We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy. 11. Wave-equation Qs Inversion of Skeletonized Surface Waves KAUST Repository Li, Jing 2017-02-08 We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy. 12. Waves in complex systems Science.gov (United States) Xie, Hang The theme of this thesis is the study of wave phenomena in complex systems. In particular, the following three topics constitute the foci of my research. The first topic involves the generalization of an electronic transport mechanism commonly observed in disordered media, fluctuation induced tunneling conduction, by considering tunneling through not just insulating potential barriers, but also narrow conducting channels. Here the wave nature of the electron implies that a narrow conduction channel can act as an electronic waveguide, with a cutoff transverse dimension that is half the Fermi wavelength. My research involves the study of electronic transport through finite-length conducting channels with transverse dimensions below the cutoff. Such narrow conduction channel may be physically realized by chains of single conducting atoms, for example. At small voltage bias across the conduction channel, only tunneling transport is possible at zero temperature. But at finite temperatures some of the electrons with energies above the Fermi level can ballistically transport across the channel. By considering both tunneling and thermal activation mechanisms, with thermally-generated (random) voltage bias across the narrow channel, we obtained a temperature-dependent conductivity behavior that is in good agreement with the measured two-lead conductance of RuO2 and IrO2 nanowires. Furthermore, by considering high applied voltage across the nano conduction channels, our model predicts interesting electronic Fabry-Perot behavior whose experimental verification is presently underway. The second topic involves the study of the Hall effect in mesoscopic samples. In particular, we are interested in the possibility of enhancing the Hall effect by nano-patterning samples of 2D electron gas. Through numerical solution of the Schrodinger equation in the presence of a magnetic field, mesoscopic transport behavior is obtained for samples with given geometric patterns of the 13. Electromagnetic waves and photons CERN Document Server Hofmann, Ralf 2015-01-01 We explore how the thermal ground states of two mixing and pure SU(2) Yang-Mills theories, SU(2)$_{\\tiny\\mbox{CMB}}$ of scale $\\Lambda_{\\tiny\\mbox{CMB}}\\sim 10^{-4}\\,$eV and SU(2)$_{e}$ of scale $\\Lambda_{e}\\sim 5\\times 10^5\\,$eV, associate either wave or particle aspects to electromagnetic disturbances during thermalisation towards the photon gas of a blackbody, in realising the photoelectric effect, and through the frequency dependence of the monochromatic, nonthermal beam structure in Thomson/Compton scattering. 14. Gravitational-Wave Astronomy Science.gov (United States) Kelly, Bernard J. 2010-01-01 Einstein's General Theory of Relativity is our best classical description of gravity, and informs modern astronomy and astrophysics at all scales: stellar, galactic, and cosmological. Among its surprising predictions is the existence of gravitational waves -- ripples in space-time that carry energy and momentum away from strongly interacting gravitating sources. In my talk, I will give an overview of the properties of this radiation, recent breakthroughs in computational physics allowing us to calculate the waveforms from galactic mergers, and the prospect of direct observation with interferometric detectors such as LIGO and LISA. 15. Holographic Magnetisation Density Waves CERN Document Server Donos, Aristomenis 2016-01-01 We numerically construct asymptotically $AdS$ black brane solutions of $D=4$ Einstein theory coupled to a scalar and two $U(1)$ gauge fields. The solutions are holographically dual to $d=3$ CFTs in a constant external magnetic field along one of the $U(1)$'s. Below a critical temperature the system's magnetisation density becomes inhomogeneous, leading to spontaneous formation of current density waves. We find that the transition can be of second order and that the solutions which minimise the free energy locally in the parameter space of solutions have averaged stressed tensor of a perfect fluid. 16. Models of wave memory CERN Document Server Kashchenko, Serguey 2015-01-01 This monograph examines in detail models of neural systems described by delay-differential equations. Each element of the medium (neuron) is an oscillator that generates, in standalone mode, short impulses also known as spikes. The book discusses models of synaptic interaction between neurons, which lead to complex oscillatory modes in the system. In addition, it presents a solution to the problem of choosing the parameters of interaction in order to obtain attractors with predetermined structure. These attractors are represented as images encoded in the form of autowaves (wave memory). The target audience primarily comprises researchers and experts in the field, but it will also be beneficial for graduate students. 17. Elementary wave optics CERN Document Server Webb, Robert H 2005-01-01 This undergraduate textbook presents thorough coverage of the standard topics of classical optics and optical instrument design; it also offers significant details regarding the concepts of modern optics. Its survey of the mathematical tools of optics grants students insights into the physical principles of quantum mechanics.Two principal concepts occur throughout: a treatment of scattering from real scatterers (leading to Huygens' principles, diffraction theory, the index of refraction, and related topics); and the difference between coherent and noncoherent wave phenomena. Examinations of su 18. Holographic charge density waves CERN Document Server Donos, Aristomenis 2013-01-01 We show that strongly coupled holographic matter at finite charge density can exhibit charge density wave phases which spontaneously break translation invariance while preserving time-reversal and parity invariance. We show that such phases are possible within Einstein-Maxwell-dilaton theory in general spacetime dimensions. We also discuss related spatially modulated phases when there is an additional coupling to a second vector field, possibly with non-zero mass. We discuss how these constructions, and others, should be associated with novel spatially modulated ground states. 19. Holographic charge density waves Science.gov (United States) Donos, Aristomenis; Gauntlett, Jerome P. 2013-06-01 We show that strongly coupled holographic matter at finite charge density can exhibit charge density wave phases which spontaneously break translation invariance while preserving time-reversal and parity invariance. We show that such phases are possible within Einstein-Maxwell-dilaton theory in general spacetime dimensions. We also discuss related spatially modulated phases when there is an additional coupling to a second vector field, possibly with nonzero mass. We discuss how these constructions, and others, should be associated with novel spatially modulated ground states. 20. Waves of information technology OpenAIRE Case, Donald O. 2009-01-01 This is a history of the various concepts and technologies of a public information utility. The first “wave” existed from about 1900 to 1945, and was centered on the idea of microfilm as an access mechanism to the world’s information. The advocates included Paul Otlet (1934) of Belgium, Englishman H.G. Wells’ vision of a “World Brain” (1938), and American Vanevar Bush and his “Memex” device (1945). The second wave consisted of the development of computers and their networks, which eventual... 1. Exploring Beneath the Waves Institute of Scientific and Technical Information of China (English) 2010-01-01 A China-made manned submersible has reached a depth of 3,759 meters The first China-designed and developed manned submersible Jiaolong has successfully completed its work in manned tests,diving to 3,000 meters under the waves,the Ministry of Science and Technology and the State Oceanic Administration(SOA) said at a press conference on August 26. With a deepest dive to 3,759 meters,Jiaolong surpassed the average ocean depth,3,682 meters.It also established a record by operating underwater for 9 hours and 3 minutes. 2. Exploring Beneath the Waves Institute of Scientific and Technical Information of China (English) YU LINTAO 2010-01-01 @@ The first China-designed and developed manned submersible Jiaolong has successfully completed its work in manned tests, diving to 3,000 meters under the waves, the Ministry of Science and Technology and the State Oceanic Administration (SOA) said at a press confer-ence on August 26. With a deepest dive to 3,759 meters, Jiaolong surpassed the aver-age ocean depth, 3,682 meters. It also estab-lished a record by operating underwater for 9 hours and 3 minutes. 3. Breaking the Waves DEFF Research Database (Denmark) Christensen, Poul Rind; Kirketerp, Anne 2006-01-01 The paper shortly reveals the history of a small school - the KaosPilots - dedicated to educate young people to carriers as entrepreneurs. In this contribution we want to explore how the KaosPilots managed to break the waves of institutionalised concepts and practices of teaching entrepreneurship....... Following the so-called 'Dogma' concept developed by Danish filmmakers, this contribution aim to explore the key elements making up the recipes guiding the entrepreneurship training program exercised by the school. Key factors forming a community of learning practice are outlined as well as the critical...... pedagogical elements on which the education in entrepreneurship rests.... 4. Spin Waves in Terbium DEFF Research Database (Denmark) Jensen, J.; Houmann, Jens Christian Gylden 1975-01-01 The selection rules for the linear couplings between magnons and phonons propagating in the c direction of a simple basal-plane hcp ferromagnet are determined by general symmetry considerations. The acoustic-optical magnon-phonon interactions observed in the heavy-rare-earth metals have been expl...... by Liu. The coupled magnon—transverse-phonon system for the c direction of Tb is analyzed in detail, and the strengths of the couplings are deduced as a function of wave vector by combining the experimental studies with the theory.... 5. Predictability of the Power Output of Three Wave Energy Technologies in the Danish North Sea DEFF Research Database (Denmark) Chozas, Julia Fernandez; Jensen, N. E. Helstrup; Sørensen, H. C. 2011-01-01 The paper addresses an important challenge ahead the integration of the electricity generated by wave energy conversion technologies into the electric grid. Particularly, it looks into the role of wave energy within the day-ahead electricity market. For that the predictability of the theoretical...... of the study is to provide an indication on the accuracy of the forecast of i) wave parameters, ii) the normalised theoretical power productions from each of the selected technologies (Pelamis, Wave Dragon and Wavestar), and iii) the normalised theoretical power production of a combination of the three devices......, during a very energetic time period. Results show that for the 12 to 36 hours time horizon forecast, the accuracy in the predictions (in terms of scatter index) of the significant wave height, zero crossing period and wave power are 22%, 11% and 68%, respectively; and the accuracy in the predictions... 6. Oscillating nonlinear acoustic shock waves DEFF Research Database (Denmark) Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth 2016-01-01 We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined.... 7. Bipolar-rogue-wave structures Science.gov (United States) Ding, Yingchun; Zhang, Bin; Feng, Qi; Tang, Xin; Liu, Zhongxuan; Chen, Zhaoyang; Lin, Chengyou 2017-01-01 The formation of extreme localization structures in nonlinear dispersive media (water or optical fibres) can be explained and described by the focusing nonlinear Schrödinger equation (NLSE). The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We have studied theoretically SCB solutions solved with the dressing method. A class of bipolar-rogue-wave structures that are constructed by collisions between elementary SCB or bipolar solitonic solutions was found. Besides, we have also found a new class of regular bright solitonic rogue waves that are originated from the collision between two bipolar-rogue-wave structures. The bipolar-rogue-wave structures can be considered to provide a new prototype for rogue-waves dynamics modeling. Our results extend previous studies in the area of rogue waves and may be important in the study of oceanography and optics. 8. Quantitative wave-particle duality Science.gov (United States) Qureshi, Tabish 2016-07-01 The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is here described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these characteristics, known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student. 9. A simple electron plasma wave Energy Technology Data Exchange (ETDEWEB) Brodin, G., E-mail: [email protected] [Department of Physics, Umeå University, SE-901 87 Umeå (Sweden); Stenflo, L. [Department of Physics, Linköping University, SE-581 83 Linköping (Sweden) 2017-03-18 Considering a class of solutions where the density perturbations are functions of time, but not of space, we derive a new exact large amplitude wave solution for a cold uniform electron plasma. This result illustrates that most simple analytical solutions can appear even if the density perturbations are large. - Highlights: • The influence of large amplitude electromagnetic waves on electrostatic oscillations is found. • A generalized Mathieu equation is derived. • Anharmonic wave profiles are computed numerically. 10. Wave energy: a Pacific perspective. Science.gov (United States) Paasch, Robert; Ruehl, Kelley; Hovland, Justin; Meicke, Stephen 2012-01-28 This paper illustrates the status of wave energy development in Pacific rim countries by characterizing the available resource and introducing the region's current and potential future leaders in wave energy converter development. It also describes the existing licensing and permitting process as well as potential environmental concerns. Capabilities of Pacific Ocean testing facilities are described in addition to the region's vision of the future of wave energy. 11. Coriolis effect on water waves OpenAIRE Benjamin, Melinand 2015-01-01 This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness theorem for the water waves equations with vorticity and Coriolis force, taking into account the dependence on various physical parameters and we justify rigorously the shallow water model. We also consider a possible non constant pr... 12. Precession resonance in water waves CERN Document Server Lucas, Dan; Perlin, Marc 2016-01-01 We describe the theory and present numerical evidence for a new type of nonlinear resonant interaction between gravity waves on the surface of deep water. The resonance constitutes a generalisation of the usual 'exact' resonance as we show that exchanges of energy between the waves can be enhanced when the interaction is three-wave rather than four and the linear frequency mismatch, or detuning, is non-zero i.e. $\\omega_1\\pm\\omega_2\\pm\\omega_3 \ 13. Tropical Cyclogenesis in a Tropical Wave Critical Layer: Easterly Waves Science.gov (United States) Dunkerton, T. J.; Montgomery, M. T.; Wang, Z. 2009-01-01 The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a dividing streamline separates air within the cat's eye from air outside. 14. When Shock Waves Collide Science.gov (United States) Hartigan, P.; Foster, J.; Frank, A.; Hansen, E.; Yirak, K.; Liao, A. S.; Graham, P.; Wilde, B.; Blue, B.; Martinez, D.; Rosen, P.; Farley, D.; Paguio, R. 2016-06-01 Supersonic outflows from objects as varied as stellar jets, massive stars, and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures, and therefore a higher-excitation spectrum than does an oblique shock. In this paper, we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations and can regrow if the intersection angle changes to become more favorable. The experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in Hubble Space Telescope images at the intersections of some bow shocks in stellar jets. 15. Wave mixing spectroscopy Energy Technology Data Exchange (ETDEWEB) Smith, R.W. 1980-08-01 Several new aspects of nonlinear or wave mixing spectroscopy were investigated utilizing the polarization properties of the nonlinear output field and the dependence of this field upon the occurrence of multiple resonances in the nonlinear susceptibility. First, it is shown theoretically that polarization-sensitive detection may be used to either eliminate or controllably reduce the nonresonant background in coherent anti-Stokes Raman spectroscopy, allowing weaker Raman resonances to be studied. The features of multi-resonant four-wave mixing are examined in the case of an inhomogeneously broadened medium. It is found that the linewidth of the nonlinear output narrows considerably (approaching the homogeneous width) when the quantum mechanical expressions for the doubly- and triply-resonant susceptibilities are averaged over a Doppler or strain broadened profile. Experimental studies of nonlinear processes in Pr/sup +3/:LaF/sub 3/ verify this linewidth narrowing, but indicate that this strain broadened system cannot be treated with a single broadening parameter as in the case of Doppler broadening in a gas. Several susceptibilities are measured from which are deduced dipole matrix elements and Raman polarizabilities related to the /sup 3/H/sub 4/, /sup 3/H/sub 6/, and /sup 3/P/sub 0/ levels of the praseodymium ions. 16. Delaying vortex breakdown by waves Science.gov (United States) Yao, M. F.; Jiang, L. B.; Wu, J. Z.; Ma, H. Y.; Pan, J. Y. 1989-03-01 The effect of spiral waves on delaying vortex breakdown in a tube is studied experimentally and theoretically. When a harmonic oscillation was imposed on one of guiding vanes in the tube, the breakdown was observed to be postponed appreciately. According to the generalized Lagrangian mean theory, proper forcing spiral waves may produce an additional streaming momentum, of which the effect is favorable and similar to an axial suction at downstream end. The delayed breakdown position is further predicted by using nonlinear wave theory. Qualitative agreement between theory and experiment is obtained, and experimental comparison of the effects due to forcing spiral wave and axial suction is made. 17. Google Wave Up and Running CERN Document Server Ferrate, Andres 2010-01-01 Catch Google Wave, the revolutionary Internet protocol and web service that lets you communicate and collaborate in realtime. With this book, you'll understand how Google Wave integrates email, instant messaging (IM), wiki, and social networking functionality into a powerful and extensible platform. You'll also learn how to use its features, customize its functions, and build sophisticated extensions with Google Wave's open APIs and network protocol. Written for everyone -- from non-techies to ninja coders -- Google Wave: Up and Running provides a complete tour of this complex platform. You' 18. Wave motion in elastic solids CERN Document Server Graff, Karl F 1991-01-01 This highly useful textbook presents comprehensive intermediate-level coverage of nearly all major topics of elastic wave propagation in solids. The subjects range from the elementary theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. The book is designed not only for a wide audience of engineering students, but also as a general reference for workers in vibrations and acoustics. Chapters 1-4 cover wave motion in the simple structural shapes, namely strings, longitudinal rod motion, beams and membranes, plates and (cylindrical) shells. Chapter 19. Wave Manipulation by Topology Optimization DEFF Research Database (Denmark) Andkjær, Jacob Anders Sound and light propagate as waves and are scattered, reflected and change direction when encountering other media and obstacles. By optimizing the spatial placement and distribution of the media, which the waves encounter, one can obtain useful and interesting effects. This thesis describes how...... topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable... 20. Wave-equation dispersion inversion KAUST Repository Li, Jing 2016-12-08 We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves. 1. Newnes short wave listening handbook CERN Document Server Pritchard, Joe 2013-01-01 Newnes Short Wave Listening Handbook is a guide for starting up in short wave listening (SWL). The book is comprised of 15 chapters that discuss the basics and fundamental concepts of short wave radio listening. The coverage of the text includes electrical principles; types of signals that can be heard in the radio spectrum; and using computers in SWL. The book also covers SWL equipment, such as receivers, converters, and circuits. The text will be of great use to individuals who want to get into short wave listening. 2. Traveling waves in rapid solidification Directory of Open Access Journals (Sweden) Karl Glasner 2000-02-01 Full Text Available We analyze rigorously the one-dimensional traveling wave problem for a thermodynamically consistent phase field model. Existence is proved for two new cases: one where the undercooling is large but not in the hypercooled regime, and the other for waves which leave behind an unstable state. The qualitative structure of the wave is studied, and under certain restrictions monotonicity of front profiles can be obtained. Further results, such as a bound on propagation velocity and non-existence are discussed. Finally, some numerical examples of monotone and non-monotone waves are provided. 3. Wigner functions of s waves DEFF Research Database (Denmark) Dahl, Jens Peder; Varro, S.; Wolf, A. 2007-01-01 We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle.... 4. Electromagnetic waves in stratified media CERN Document Server Wait, James R; Fock, V A; Wait, J R 2013-01-01 International Series of Monographs in Electromagnetic Waves, Volume 3: Electromagnetic Waves in Stratified Media provides information pertinent to the electromagnetic waves in media whose properties differ in one particular direction. This book discusses the important feature of the waves that enables communications at global distances. Organized into 13 chapters, this volume begins with an overview of the general analysis for the electromagnetic response of a plane stratified medium comprising of any number of parallel homogeneous layers. This text then explains the reflection of electromagne 5. Experiments on the WavePiston, Wave Energy Converter DEFF Research Database (Denmark) Angelelli, E.; Zanuttigh, B.; Kofoed, Jens Peter 2011-01-01 This paper analyses the performance of a new Wave Energy Converter (WEC) of the Oscillating Water Column type (OWC), named WavePiston. This near-shore floating device is composed of plates (i.e. energy collectors) sliding around a cylinder, that is placed perpendicular to the shore. Tests... 6. Solitary Wave and Wave Front as Viewed From Curvature Institute of Scientific and Technical Information of China (English) LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; LIANG Fu-Ming; XIN Guo-Jun 2004-01-01 The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometri cally, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s), which varies with arc length s. For solitary wave when s →±∞, then its curvature c(s) approaches zero, and when s = 0, the curvature c(s) reaches its maximum. For wave front, when s →±∞, then its curvature c(s) approaches zero, and when s = 0, the curvature c(s) is still zero, but c'(s) ≠ 0. That is, s = 0 is a turning point. When c(s) is given, the variance at some point (x, y) in stream line with arc length s satisfies a 2-order linear variable-coefficient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front. 7. Short wave breaking effects on low frequency waves NARCIS (Netherlands) Daly, C.; Roelvink, J.A.; Van Dongeren, A.; Van Thiel de Vries, J.S.M.; McCall, R.T. 2010-01-01 The effect of short wave breaking on low frequency waves is investigated using two breaker formulations implemented in a time-dependent numerical model (XBeach): (1) an advective-deterministic approach (ADA) and (2) the probabilistic breaker formulation of Roelvink (1993). Previous research has show 8. Solitary Wave and Wave Front as Viewed From Curvature Institute of Scientific and Technical Information of China (English) LIUShi-Kuo; FUZun-Tao; LIUShi-Da; LIANGFu-Ming; XINGuo-Jun 2004-01-01 The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s),which varies with arc length s. For solitary wave when s→±∞, then its curvature c(s) approaches zero, and whens = 0, the curvature c(s) reaches its maximum. For wave front, when s→±∞, then its curvature c(s) approaches zero,and when s = 0, the curvature c(s) is still zero, but c'(s)≠0. That is, s = 0 is a turning point. When c(s) is given,the variance at some point (x, y) in stream line with arc length s satisfies a 2-order linear variable-coeffcient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front. 9. From the Somigliana waves to the evanescent waves Directory of Open Access Journals (Sweden) Pietro Caloi 2010-02-01 Full Text Available The Rayleigh equation has real coefficients; therefore, also the case of complex conjugated roots may be explained physically. The Author proves that the Somigliana waves may be formed for Poisson ratio values until 0.30543; for gradually less rigid media, they are missing altogether and degenerate into evanescent waves. 10. Broadband wave manipulation in surface-wave photonic crystal CERN Document Server Gao, Zhen 2016-01-01 The ability to perfectly guide surface electromagnetic waves around ultra-sharp corners without back-scattering and radiation is in great demand for various photonic and plasmonic applications. This is fundamentally difficult to realize because of the dramatic momentum mismatch and wave nature of radiation at the sharp corners. Here we experimentally demonstrate that a simple photonic structure, a periodic square array of metallic cylinders standing on a metal surface, can behaves as a surface-wave photonic crystal with complete photonic band gap to overcome this bottleneck simply. A line-defect waveguide can support and guide surface waves around ultra-sharp corners without perceptible radiation and reflection, achieving almost perfect transmission efficiency in a broad frequency range. We also demonstrate an ideal T-shaped splitter to split input surface waves equally into two arms and a square radiation-suppressed plasmonic open resonator with high quality factors by simply inducing line-defects in this fu... 11. Surface Shear, Persistent Wave Groups and Rogue Waves CERN Document Server Chafin, Clifford 2014-01-01 We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevations induced by wave packets and by directly considering the necessary forces to prevent packet spreading in the deep water limit. Narrow surface shear flows are shown to exert strong localizing and stabilizing forces on wavepackets to maintain their strength and amplify their intensity even in the linear regime. Necessary criticisms of some earlier notions of stress and angular momentum of waves are included and we argue that nonlinearity enters the system in a way that makes the formation of rogue waves nonperturbative. Quantitative bounds on the surface shear flow necessary to stabilize packets of any wave amplitude are given. 12. Wave-to-wire Modelling of Wave Energy Converters DEFF Research Database (Denmark) Ferri, Francesco , but talking about renewable energy partially ravels the problem out. Wave energy is a large, mostly untapped, renewable energy resource. It has the potential to contribute significantly to the future energy mix, but the sector has not yet rolled off into the market in consequence of a number of technical...... and non-technical issues. These can be efficiently summarised in the cost of the energy produced by the various wave energy converters: If compared with other renewable energy technologies the cost of energy from the ocean waves is still significantly higher. Holding the comparison it also important...... to noticed that there is not a clear front runner in the wave energy sector, which fades effort and funding over a too broad frame. In order to assist efficient development and analysis of wave energy converters and therefore to accelerate the sector progression towards commercialisation, a generally... 13. Turbulent wind waves on a water current Directory of Open Access Journals (Sweden) M. V. Zavolgensky 2008-05-01 Full Text Available An analytical model of water waves generated by the wind over the water surface is presented. A simple modeling method of wind waves is described based on waves lengths diagram, azimuthal hodograph of waves velocities and others. Properties of the generated waves are described. The wave length and wave velocity are obtained as functions on azimuth of wave propagation and growth rate. Motionless waves dynamically trapped into the general picture of three dimensional waves are described. The gravitation force does not enter the three dimensional of turbulent wind waves. That is why these waves have turbulent and not gravitational nature. The Langmuir stripes are naturally modeled and existence of the rogue waves is theoretically proved. 14. Lidar Observations of Wave Shape Science.gov (United States) Brodie, K. L.; Raubenheimer, B.; Spore, N.; Gorrell, L.; Slocum, R. K.; Elgar, S. 2016-02-01 As waves propagate across the inner-surf zone, through a shorebreak, to the swash, their shapes can evolve rapidly, particularly if there are large changes in water depth over a wavelength. As wave shapes evolve, the time history of near-bed wave-orbital velocities also changes. Asymmetrical near-bed velocities result in preferential directions for sediment transport, and spatial variations in asymmetries can lead to morphological evolution. Thus, understanding and predicting wave shapes in the inner-surf and swash zones is important to improving sediment transport predictions. Here, rapid changes in wave shape, quantified by 3rd moments (skewness and asymmetry) of the sea-surface elevation time series, were observed on a sandy Atlantic Ocean beach near Duck, NC using terrestrial lidar scanners that measure the elevation of the water surface along a narrow cross-shore transect with high spatial [O(1 cm)] and temporal [O(0.5 s)] resolution. The terrestrial lidar scanners were mounted on a tower on the beach dune (about 8 m above the water surface) and on an 8-m tall amphibious tripod [the Coastal Research Amphibious Buggy (CRAB)]. Observations with the dune lidar are used to investigate how bulk wave shape parameters such as wave skewness and asymmetry, and the ratio of wave height to water depth (gamma) vary with beach slope, tide level, and offshore wave conditions. Observations with the lidar mounted on the CRAB are used to investigate the evolution of individual waves propagating across the surf zone and shorebreak to the swash. For example, preliminary observations from the CRAB include a wave that appeared to shoal and then "pitch" backwards immediately prior to breaking and running up the beach. Funded by the USACE Coastal Field Data Collection Program, ASD(R&E), and ONR. 15. Advanced millimeter wave chemical sensor. Energy Technology Data Exchange (ETDEWEB) Gopalsami, N. 1999-03-24 This paper discusses the development of an advanced millimeter-wave (mm-wave) chemical sensor and its applications for environmental monitoring and arms control treaty verification. The purpose of this work is to investigate the use of fingerprint-type molecular rotational signatures in the mm-wave spectrum to sense airborne chemicals. The mm-wave spectrum to sense airborne chemicals. The mm-wave sensor, operating in the frequency range of 220-300 GHz, can work under all weather conditions and in smoky and dusty environments. The basic configuration of the mm-wave sensor is a monostatic swept-frequency radar consisting of a mm-wave sweeper, a hot-electron-bolometer or Schottky barrier detector, and a trihedral reflector. The chemical plume to be detected is situated between the transmitter/detector and the reflector. Millimeter-wave absorption spectra of chemicals in the plume are determined by measuring the swept-frequency radar return signals with and without the plume in the beam path. The problem of pressure broadening, which hampered open-path spectroscopy in the past, has been mitigated in this work by designing a fast sweeping source over a broad frequency range. The heart of the system is a Russian backward-wave oscillator (BWO) tube that can be tuned over 220-350 GHz. Using the Russian BWO tube, a mm-wave radar system was built and field-tested at the DOE Nevada Test Site at a standoff distance of 60 m. The mm-wave system detected chemical plumes very well; the detection sensitivity for polar molecules like methyl chloride was down to a concentration of 12 ppm. 16. Evanescent Wave Atomic Mirror Science.gov (United States) Ghezali, S.; Taleb, A. 2008-09-01 A research project at the "Laboratoire d'électronique quantique" consists in a theoretical study of the reflection and diffraction phenomena via an atomic mirror. This poster presents the principle of an atomic mirror. Many groups in the world have constructed this type of atom optics experiments such as in Paris-Orsay-Villetaneuse (France), Stanford-Gaithersburg (USA), Munich-Heidelberg (Germany), etc. A laser beam goes into a prism with an incidence bigger than the critical incidence. It undergoes a total reflection on the plane face of the prism and then exits. The transmitted resulting wave out of the prism is evanescent and repulsive as the frequency detuning of the laser beam compared to the atomic transition δ = ωL-ω0 is positive. The cold atomic sample interacts with this evanescent wave and undergoes one or more elastic bounces by passing into backward points in its trajectory because the atoms' kinetic energy (of the order of the μeV) is less than the maximum of the dipolar potential barrier ℏΩ2/Δ where Ω is the Rabi frequency [1]. In fact, the atoms are cooled and captured in a magneto-optical trap placed at a distance of the order of the cm above the prism surface. The dipolar potential with which interact the slow atoms is obtained for a two level atom in a case of a dipolar electric transition (D2 Rubidium transition at a wavelength of 780nm delivered by a Titane-Saphir laser between a fundamental state Jf = l/2 and an excited state Je = 3/2). This potential is corrected by an attractive Van der Waals term which varies as 1/z3 in the Lennard-Jones approximation (typical atomic distance of the order of λ0/2π where λ0 is the laser wavelength) and in 1/z4 if the distance between the atom and its image in the dielectric is big in front of λ0/2π. This last case is obtained in a quantum electrodynamic calculation by taking into account an orthornormal base [2]. We'll examine the role of spontaneous emission for which the rate is inversely 17. Relativistic electron scattering by magnetosonic waves: Effects of discrete wave emission and high wave amplitudes Energy Technology Data Exchange (ETDEWEB) Artemyev, A. V., E-mail: [email protected] [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS - University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States) 2015-06-15 In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail. 18. Three-dimensional freak waves and higher-order wave-wave resonances Science.gov (United States) Badulin, S. I.; Ivonin, D. V.; Dulov, V. A. 2012-04-01 Quite often the freak wave phenomenon is associated with the mechanism of modulational (Benjamin-Feir) instability resulted from resonances of four waves with close directions and scales. This weakly nonlinear model reflects some important features of the phenomenon and is discussing in a great number of studies as initial stage of evolution of essentially nonlinear water waves. Higher-order wave-wave resonances attract incomparably less attention. More complicated mathematics and physics explain this disregard partially only. The true reason is a lack of adequate experimental background for the study of essentially three-dimensional water wave dynamics. We start our study with the classic example of New Year Wave. Two extreme events: the famous wave 26.5 meters and one of smaller 18.5 meters height (formally, not freak) of the same record, are shown to have pronounced features of essentially three-dimensional five-wave resonant interactions. The quasi-spectra approach is used for the data analysis in order to resolve adequately frequencies near the spectral peak fp ≈ 0.057Hz and, thus, to analyze possible modulations of the dominant wave component. In terms of the quasi-spectra the above two anomalous waves show co-existence of the peak harmonic and one at frequency f5w = 3/2fp that corresponds to maximum of five-wave instability of weakly nonlinear waves. No pronounced marks of usually discussed Benjamin-Feir instability are found in the record that is easy to explain: the spectral peak frequency fp corresponds to the non-dimensional depth parameter kD ≈ 0.92 (k - wavenumber, D ≈ 70 meters - depth at the Statoil platform Draupner site) that is well below the shallow water limit of the instability kD = 1.36. A unique data collection of wave records of the Marine Hydrophysical Institute in the Katsiveli platform (Black Sea) has been analyzed in view of the above findings of possible impact of the five-wave instability on freak wave occurrence. The data cover 19. Topography-induced focusing of random waves NARCIS (Netherlands) Smit, P.B.; Janssen, T.T.; Herbers, T.H.C. 2012-01-01 Refraction of narrow-band surface waves in coastal areas can result in wave-focal zones where due to interference, wave statistics vary rapidly and on similar length scales as those of individual waves. However such interference patterns, or wave coherence, are not accounted for in conventional stoc 20. Control of optical solitons by light waves. Science.gov (United States) Grigoryan, V S; Hasegawa, A; Maruta, A 1995-04-15 A new method of controlling optical solitons by means of light wave(s) in fibers is presented. By a proper choice of light wave(s), parametric four-wave mixing can control the soliton shape as well as the soliton parameters (amplitude, frequency, velocity, and position). 1. Regularity of rotational travelling water waves. Science.gov (United States) Escher, Joachim 2012-04-13 Several recent results on the regularity of streamlines beneath a rotational travelling wave, along with the wave profile itself, will be discussed. The survey includes the classical water wave problem in both finite and infinite depth, capillary waves and solitary waves as well. A common assumption in all models to be discussed is the absence of stagnation points. 2. Encounter Probability of Significant Wave Height DEFF Research Database (Denmark) Liu, Z.; Burcharth, H. F. The determination of the design wave height (often given as the significant wave height) is usually based on statistical analysis of long-term extreme wave height measurement or hindcast. The result of such extreme wave height analysis is often given as the design wave height corresponding to a c... 3. Current status of gravitational-wave observations OpenAIRE Fairhurst, Stephen; Guidi, Gianluca M.; Hello, Patrice; Whelan, John T; Woan, Graham 2009-01-01 The first generation of gravitational wave interferometric detectors has taken data at, or close to, their design sensitivity. This data has been searched for a broad range of gravitational wave signatures. An overview of gravitational wave search methods and results are presented. Searches for gravitational waves from unmodelled burst sources, compact binary coalescences, continuous wave sources and stochastic backgrounds are discussed. 4. Waves in metamaterials CERN Document Server Solymar, Laszlo 2014-01-01 Metamaterials is a young subject born in the 21st century. It is concerned with artificial materials which can have electrical and magnetic properties difficult or impossible to find in nature. The building blocks in most cases are resonant elements much smaller than the wavelength of the electromagnetic wave. The book offers a comprehensive treatment of all aspects of research in this field at a level that should appeal to final year undergraduates in physics or in electrical and electronic engineering. The mathematics is kept at a minimum; the aim is to explain the physics in simple terms and enumerate the major advances. It can be profitably read by graduate and post-graduate students in order to find out what has been done in the field outside their speciality, and by experts who may gain new insight about the inter-relationship of the physical phenomena involved. 5. Frozen waves: experimental generation. Science.gov (United States) Vieira, Tarcio A; Gesualdi, Marcos R R; Zamboni-Rached, Michel 2012-06-01 Frozen waves (FWs) are very interesting particular cases of nondiffracting beams whose envelopes are static and whose longitudinal intensity patterns can be chosen a priori. We present here for the first time (that we know of) the experimental generation of FWs. The experimental realization of these FWs was obtained using a holographic setup for the optical reconstruction of computer generated holograms (CGH), based on a 4-f Fourier filtering system and a nematic liquid crystal spatial light modulator (LC-SLM), where FW CGHs were first computationally implemented, and later electronically implemented, on the LC-SLM for optical reconstruction. The experimental results are in agreement with the corresponding theoretical analytical solutions and hold excellent prospects for implementation in scientific and technological applications. 6. Focusing of electromagnetic waves Energy Technology Data Exchange (ETDEWEB) Dhayalan, V. 1996-12-31 The focusing of electromagnetic waves inside a slab has been examined together with two special cases in which the slab is reduced to a single interface or a single medium. To that end the exact solutions for the fields inside a layered medium have been used, given in terms of the outside current source in order to obtain the solutions for the focused electric field inside a slab. Both exact and asymptotic solutions of the problem have been considered, and the validity of the latter has been discussed. The author has developed a numerical algorithm for evaluation of the diffraction integral with special emphasis on reducing the computing time. The numerical techniques in the paper can be readily applied to evaluate similar diffraction integrals occurring e.g. in microstrip antennas. 46 refs. 7. Geophysical wave tomography Science.gov (United States) Zhou, Chaoguang 2000-11-01 This study is concerned with geophysical wave tomography techniques that include advanced diffraction tomography, traveltime calculation techniques and simultaneous attenuation and velocity tomography approaches. We propose the source independent approximation, the Modified Quasi-Linear approximation and develop a fast and accurate diffraction tomography algorithm that uses this approximation. Since the Modified Quasi-Linear approximation accounts for the scattering fields within scatterers, this tomography algorithm produces better image quality than conventional Born approximation tomography algorithm does with or without the presence of multiple scatterers and can be used to reconstruct images of high contrast objects. Since iteration is not required, this algorithm is efficient. We improve the finite difference traveltime calculation algorithm proposed by Vidale (1990). The bucket theory is utilized in order to enhance the sorting efficiency, which accounts for about ten percent computing time improvement for large velocity models. Snell's law is employed to solve the causality problem analytically, which enables the modified algorithm to compute traveltimes accurately and rapidly for high velocity contrast media. We also develop two simultaneous attenuation and velocity tomography approaches, which use traveltimes and amplitude spectra of the observed data, and discuss some of their applications. One approach is processing geophysical data that come from one single survey and the other deals with the repeated survey cases. These approaches are nonlinear and therefore more accurate than linear tomography. A linear system for wave propagation and constant-Q media are assumed in order to develop the tomography algorithms. These approaches not only produce attenuation and velocity images at the same time but also can be used to infer the physical rock properties, such as the dielectric permittivity, the electric conductivity, and the porosity. A crosshole radar 8. Book review: Extreme ocean waves Science.gov (United States) Geist, Eric L. 2017-01-01 “Extreme Ocean Waves”, edited by E. Pelinovsky and C. Kharif, second edition, Springer International Publishing, 2016; ISBN: 978-3-319-21574-7, ISBN (eBook): 978-3-319-21575-4The second edition of “Extreme Ocean Waves” published by Springer is an update of a collection of 12 papers edited by Efim Pelinovsky and Christian Kharif following the April 2007 meeting of the General Assembly of the European Geosciences Union. In this edition, three new papers have been added and three more have been substantially revised. Color figures are now included, which greatly aids in reading several of the papers, and is especially helpful in visualizing graphs as in the paper on symbolic computation of nonlinear wave resonance (Tobisch et al.). A note on terminology: extreme waves in this volume broadly encompass different types of waves, including deep-water and shallow-water rogue waves (which are alternatively termed freak waves), and internal waves. One new paper on tsunamis (Viroulet et al.) is now included in the second edition of this volume. Throughout the book, the reader will find a combination of laboratory, theoretical, and statistical/empirical treatment necessary for the complete examination of this subject. In the Introduction, the editors underscore the importance of studying extreme waves, documenting a dramatic instance of damaging extreme waves that recently occurred in 2014. 9. A sand wave simulation model NARCIS (Netherlands) Nemeth, A.A.; Hulscher, S.J.M.H.; Damme, van R.M.J. 2003-01-01 Sand waves form a prominent regular pattern in the offshore seabeds of sandy shallow seas. A two dimensional vertical (2DV) flow and morphological numerical model describing the behaviour of these sand waves has been developed. The model contains the 2DV shallow water equations, with a free water su 10. Wave Overtopping at Coastal Structures DEFF Research Database (Denmark) Geeraearts, Jimmy; De Rouck, Julien; Troch, Peter; 2006-01-01 The European research project CLASH (EVK3-CT-2001-00058) investigated wave overtopping at coastal structures. More specific it was to develop a generic prediction method for wave overtopping and to solve the problem of suspected scale effects. The paper summarizes the main results concerning... 11. Surface Waves on Metamaterials Interfaces DEFF Research Database (Denmark) Takayama, Osamu; Shkondin, Evgeniy; Panah, Mohammad Esmail Aryaee 2016-01-01 We analyze surface electromagnetic waves supported at the interface between isotropic medium and effective anisotropic material that can be realized by alternating conductive and dielectrics layers. This configuration can host various types of surface waves and therefore can serve as a rich platf... 12. Probabilistic aspects of ocean waves NARCIS (Netherlands) Battjes, J.A. 1977-01-01 Background material for a special lecture on probabilistic aspects of ocean waves for a seminar in Trondheim. It describes long term statistics and short term statistics. Statistical distributions of waves, directional spectra and frequency spectra. Sea state parameters, response peaks, encounter 13. Sediment transport under breaking waves DEFF Research Database (Denmark) Christensen, Erik Damgaard; Hjelmager Jensen, Jacob; Mayer, Stefan 2000-01-01 generated at the surface where the wave breaks as well as the turbulence generated near the bed due to the wave-motion and the undertow. In general, the levels of turbulent kinetic energy are found to be higher than experiments show. This results in an over prediction of the sediment transport. Nevertheless... 14. Numerical modeling of water waves CERN Document Server Lin, Pengzhi 2008-01-01 Modelling large-scale wave fields and their interaction with coastal and offshore structures has become much more feasible over the last two decades with increases in computer speeds. Wave modelling can be viewed as an extension of wave theory, a mature and widely published field, applied to practical engineering through the use of computer tools. Information about the various wave models which have been developed is often widely scattered in the literature, and consequently this is one of the first books devoted to wave models and their applications. At the core of the book is an introduction to various types of wave models. For each model, the theoretical assumptions, the application range, and the advantages and limitations are elaborated. The combined use of different wave models from large-scale to local-scale is highlighted with a detailed discussion of the application and matching of boundary conditions. At the same time the book provides a grounding in hydrodynamics, wave theory, and numerical methods... 15. Spin waves theory and applications CERN Document Server Stancil, Daniel D 2009-01-01 Magnetic materials can support propagating waves of magnetization; since these are oscillations in the magneto static properties of the material, they are called magneto static waves (sometimes 'magnons' or 'magnetic polarons'). This book discusses magnetic properties of materials, and magnetic moments of atoms and ions 16. Regeneration of dredged sand waves NARCIS (Netherlands) Hulscher, Suzanne J.M.H.; Knaapen, Michiel; Scholl, Olaf; Scholl, O.; Trenteseaux., A.; Garlan, T. 2000-01-01 Sand waves form a wavy pattern in the offshore sandy seabed. Since their crests reduce the navigability, it is important to know their evolution. A simple model is presented to estimate the recovery of sand wave amplitudes. This model is partially based on the similarity with sea ripples and 17. Solitons in a wave tank Science.gov (United States) Olsen, M.; Smith, H.; Scott, A. C. 1984-09-01 A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations. 18. Surface Waves on Metamaterials Interfaces DEFF Research Database (Denmark) Takayama, Osamu; Shkondin, Evgeniy; Panah, Mohammad Esmail Aryaee; 2016-01-01 We analyze surface electromagnetic waves supported at the interface between isotropic medium and effective anisotropic material that can be realized by alternating conductive and dielectrics layers. This configuration can host various types of surface waves and therefore can serve as a rich platf... 19. Are rogue waves really unexpected? CERN Document Server Fedele, Francesco 2015-01-01 We present a third-order nonlinear model for the statistics of unexpected waves drawing on the work of Gemmrich & Garrett (2008). The model is verified by way of Monte Carlo simulations of Gaussian seas and comparisons to oceanic measurements. In particular, the analysis of oceanic data suggests that both skewness and kurtosis effects must be accounted for to obtain accurate predictions. As a specific application, the unexpectedness of the Andrea and WACSIS rogue wave events is examined in detail. Observations indicate that the crests of these waves have nearly the same amplitude ratio$h/H_s\\sim1.6$, where$H_s$is the significant wave height. Both waves appeared without warning and they were nearly two-times larger than the surrounding$O(10)$waves, and thus unexpected. The model developed here predicts that the two rogue waves are stochastically similar as they occur on average once every$10^{4}$waves. Further, the maximum crest height actually observed is nearly the same as the threshold$h_{10^{6}... 20. Probabilistic aspects of ocean waves NARCIS (Netherlands) Battjes, J.A. 1977-01-01 Background material for a special lecture on probabilistic aspects of ocean waves for a seminar in Trondheim. It describes long term statistics and short term statistics. Statistical distributions of waves, directional spectra and frequency spectra. Sea state parameters, response peaks, encounter pr 1. Wave Generation in Physical Models DEFF Research Database (Denmark) Andersen, Thomas Lykke; Frigaard, Peter The present book describes the most important aspects of wave generation techniques in physical models. Moreover, the book serves as technical documentation for the wave generation software AwaSys 6, cf. Aalborg University (2012). In addition to the two main authors also Tue Hald and Michael... 2. Collected papers on wave mechanics CERN Document Server Schrödinger, Erwin 1929-01-01 Quantisation as a problem of proper values ; the continuous transition from micro- to macro-mechanics ; on the relation between the quantum mechanics of Heisenberg, Born, and Jordan, and that of Schrödinger ; the Compton effect ; the energy-momentum theorem for material waves ; the exchange of energy according to wave mechanics 3. Just How Does Sound Wave? Science.gov (United States) Shipman, Bob 2006-01-01 When children first hear the term "sound wave" perhaps they might associate it with the way a hand waves or perhaps the squiggly line image on a television monitor when sound recordings are being made. Research suggests that children tend to think sound somehow travels as a discrete package, a fast-moving invisible thing, and not something that… 4. Matrix Theory of pp Waves CERN Document Server Michelson, J 2004-01-01 The Matrix Theory that has been proposed for various pp wave backgrounds is discussed. Particular emphasis is on the existence of novel nontrivial supersymmetric solutions of the Matrix Theory. These correspond to branes of various shapes (ellipsoidal, paraboloidal, and possibly hyperboloidal) that are unexpected from previous studies of branes in pp wave geometries. 5. Solar Magnetic Waves and Oscillations Science.gov (United States) Erdelyi von Fay-Siebenburgen, R. 2006-11-01 Recent solar and space satellite missions (e.g. SOHO, Trace) and high- resolution ground-based observations (e.g. Swedish Solar Telescope, Dutch Open Telescope) have opened new avenues for 21st century plasma physics. With unprecedented details a very rich and abundant structure of the solar atmosphere is unveiled. Revolutionary observations clearly confirmed the existence of MHD waves and oscillations in a wide range of solar atmospheric magnetic structures, commonly described in the form of solar flux tubes. The objectives of this review are to give an up-to-date account of the theory of MHD waves and oscillations in solar and astrophysical magnetic wave-guides. Since magnetic structuring acts as excellent wave guides, plasma waves and oscillations are able to propagate from sub-surface solar regions through the solar atmosphere deep into the interplanetary space. Observations and theoretical modeling of waves can provide excellent diagnostic tools about the state of solar plasma. Key examples of the various types of MHD waves and oscillations will be discussed both from observational and theoretical perspectives and the concept of atmospheric (coronal) and magneto-seismology will be introduced. The lecture will also contain a few short exercises in order to highlight the important points of the applications of solar MHD wave theory. 6. Solitons in a wave tank DEFF Research Database (Denmark) Olsen, M.; Smith, H.; Scott, Alwyn C. 1984-01-01 A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment... 7. Compressive passive millimeter wave imager Science.gov (United States) Gopalsami, Nachappa; Liao, Shaolin; Elmer, Thomas W; Koehl, Eugene R; Heifetz, Alexander; Raptis, Apostolos C 2015-01-27 A compressive scanning approach for millimeter wave imaging and sensing. A Hadamard mask is positioned to receive millimeter waves from an object to be imaged. A subset of the full set of Hadamard acquisitions is sampled. The subset is used to reconstruct an image representing the object. 8. Gravitational lensing by gravitational waves OpenAIRE Bisnovatyi-Kogan, G. S.; Tsupko, O. Yu. 2008-01-01 Gravitational lensing by gravitational wave is considered. We notice that although final and initial direction of photons coincide, displacement between final and initial trajectories occurs. This displacement is calculated analytically for the plane gravitational wave pulse. Estimations for observations are discussed. 9. Opdriftsbaserede modeller for Wave Star DEFF Research Database (Denmark) Kramer, Morten Formålet med dette skrift er at få en forhåndsvurdering af mulige effektforøgelser for Wave Star ved anvendelse af aktiv akkumulatordrift. Disse vurderinger baseres på simuleringsmodeller for driften af Wave Star i uregelmæssige bølger. Modellen er udarbejdet i programmeringssproget Delphi og er en... 10. Multichannel analysis of surface waves Science.gov (United States) Park, C.B.; Miller, R.D.; Xia, J. 1999-01-01 The frequency-dependent properties of Rayleigh-type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface-wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental-mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source-generated noise inhibits the reliability of shear-wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental-mode Rayleigh waves (noise) are body waves, scattered and nonsource-generated surface waves, and higher-mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear-wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace-to-trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable-frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real-time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface-wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single-measurement surveying of a broad depth range, high levels of 11. Aircraft measurements of wave cloud Directory of Open Access Journals (Sweden) Z. Cui 2012-05-01 Full Text Available In this paper, aircraft measurements are presented of liquid phase (ice-free wave clouds made at temperatures greater than −5 °C that formed over Scotland, UK. The horizontal variations of the vertical velocity across wave clouds display a distinct pattern. The maximum updraughts occur at the upshear flanks of the clouds and the strong downdraughts at the downshear flanks. The cloud droplet concentrations were a couple of hundreds per cubic centimetres, and the drops generally had a mean diameter between 15–45 μm. A small proportion of the drops were drizzle. A new definition of a mountain-wave cloud is given, based on the measurements presented here and previous studies. The results in this paper provide a case for future numerical simulation of wave cloud and the interaction between wave and clouds. 12. Study on wave rotor refrigerators Institute of Scientific and Technical Information of China (English) Yuqiang DAI; Dapeng HU; Meixia DING 2009-01-01 As a novel generation of a rotational gas wave machine, the wave rotor refrigerator (WRR) is an unsteady flow device used for refrigeration, in whose passages pressured streams directly contact and exchange energy due to the movement of pressure waves. In this paper, the working mechanism and refrigeration principle are inves-tigated based on the one-dimensional unsteady flow theory.A basic limitation on main structural parameters and operating parameters is deduced and the wave diagram of WRR to guide designing is sketched. The main influential factors are studied through an experiment. In the DUT Gas Wave Refrigeration Studying and Development Center (GWRSDC) lab, the isentropic efficiency can now reach about 65%. The results show that the WRR is a feasible and promising technology in pressured gas refrigeration cases. 13. Strong winds and waves offshore DEFF Research Database (Denmark) Larsén, Xiaoli Guo 2016-01-01 This report is prepared for Statoil, with the intention to introdu e DTU Wind Energy's ongoing resear h a tivities on o shore extreme wind and wave onditions. The purpose is to share our re ent ndings and to establish possible further ollaboration with Statoil. The fo us of this report is on the ......This report is prepared for Statoil, with the intention to introdu e DTU Wind Energy's ongoing resear h a tivities on o shore extreme wind and wave onditions. The purpose is to share our re ent ndings and to establish possible further ollaboration with Statoil. The fo us of this report...... is on the meteorologi al and o eani onditions related to storm winds and waves over the North Sea. With regard to the o shore wind energy appli ation, the parameters addressed here in lude: extreme wind and extreme waves, storm wind and waves and turbulen e issues for o shore onditions.... 14. Shallow water cnoidal wave interactions Directory of Open Access Journals (Sweden) A. R. Osborne 1994-01-01 Full Text Available The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV and Kadomtsev-Petvishvilli (KP equations, are considered. These equations are important for describing the propagation of small-but-finite amplitude waves in shallow water; the solutions to KdV are unidirectional while those of KP are directionally spread. Herein solutions are constructed from the 0-function representation of their appropriate inverse scattering transform formulations. To this end a general theorem is employed in the construction process: All solutions to the KdV and KP equations can be written as the linear superposition of cnoidal waves plus their nonlinear interactions. The approach presented here is viewed as significant because it allows the exact construction of N degree-of-freedom cnoidal wave trains under rather general conditions. 15. PMP-2: Equatorial wave dynamics Science.gov (United States) Hirota, I. 1982-01-01 After the discovery of the quasi-biennial oscillation (QBO) in the stratospheric zonal wind, there were, in the last two decades, a large number of observational and theoretical studies on the structure and behavior of the mean zonal wind and waves in the tropical stratosphere. Planetary-scale, vertically propagating equatorial waves play an important role in producing the QBO through the mechanism of wave-mean flow interaction. Concerning the dynamics of the equatorial upper stratosphere and mesosphere, however, little was known about the possible wave motions, except for tides, mainly because of the lack of adequate observations in this region. The main purpose is to provide the nature of various types of equatorial wave modes, with the aid of improved sounding techniques and sophisticated numerical modelings. 16. Aspects of unconventional density waves Science.gov (United States) Maki, Kazumi; Dóra, Balázs; Virosztek, Attila 2003-12-01 Recently many people discuss unconventional density waves (i.e. unconventional charge density waves (UCDW) and unconventional spin density waves (USDW)). Unlike in conventional density waves, the quasiparticle spectrum in these systems is gapless. Also these systems remain metallic. Indeed it appears that there are many candidates for UDW. The low temperature phase of α-(BEDT-TTF)2KHg(SCN)4, the antiferromagnetic phase in URu2Si2, the CDW in transition metal dichalcogenite NbSe2, the pseudogap phase in high Tc cuprate superconductors, the glassy phase in organic superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br. After a brief introduction on UCDW and USDW, we shall discuss some of the above systems, where we believe we have evidence for unconventional density waves. 17. Bubble Dynamics and Shock Waves CERN Document Server 2013-01-01 This volume of the Shock Wave Science and Technology Reference Library is concerned with the interplay between bubble dynamics and shock waves. It is divided into four parts containing twelve chapters written by eminent scientists. Topics discussed include shock wave emission by laser generated bubbles (W Lauterborn, A Vogel), pulsating bubbles near boundaries (DM Leppinen, QX Wang, JR Blake), interaction of shock waves with bubble clouds (CD Ohl, SW Ohl), shock propagation in polydispersed bubbly liquids by model equations (K Ando, T Colonius, CE Brennen. T Yano, T Kanagawa, M Watanabe, S Fujikawa) and by DNS (G Tryggvason, S Dabiri), shocks in cavitating flows (NA Adams, SJ Schmidt, CF Delale, GH Schnerr, S Pasinlioglu) together with applications involving encapsulated bubble dynamics in imaging (AA Doinikov, A Novell, JM Escoffre, A Bouakaz), shock wave lithotripsy (P Zhong), sterilization of ships’ ballast water (A Abe, H Mimura) and bubbly flow model of volcano eruptions ((VK Kedrinskii, K Takayama... 18. Tube-wave seismic imaging Science.gov (United States) Korneev, Valeri A [LaFayette, CA 2009-05-05 The detailed analysis of cross well seismic data for a gas reservoir in Texas revealed two newly detected seismic wave effects, recorded approximately 2000 feet above the reservoir. A tube-wave (150) is initiated in a source well (110) by a source (111), travels in the source well (110), is coupled to a geological feature (140), propagates (151) through the geological feature (140), is coupled back to a tube-wave (152) at a receiver well (120), and is and received by receiver(s) (121) in either the same (110) or a different receiving well (120). The tube-wave has been shown to be extremely sensitive to changes in reservoir characteristics. Tube-waves appear to couple most effectively to reservoirs where the well casing is perforated, allowing direct fluid contact from the interior of a well case to the reservoir. 19. Multi-Wave Mixing Processes CERN Document Server Zhang, Yanpeng 2009-01-01 "Multi-Wave Mixing Processes - From Ultrafast Polarization Beats to Electromagnetically Induced Transparency" discusses the interactions of efficient multi-wave mixing (MWM) processes enhanced by atomic coherence in multilevel atomic systems. It covers topics in five major areas: attosecond and femtosecond polarization beats of four-wave mixing (FWM) processes; heterodyne detection of FWM, six-wave mixing (SWM) and eight-wave mixing (EWM) processes; Raman and Rayleigh enhanced polarization beats; coexistence and interactions of MWM processes via electromagnetically induced transparency(EIT); multi-dressing MWM processes. The book is intended for researchers, advanced undergraduate and graduate students in Nonlinear Optics. Dr. Yanpeng Zhang is a professor at the Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University. Dr. Min Xiao is a professor of Physics at University of Arkansas, Fayetteville, U.S.A. 20. Inherently Unstable Internal Gravity Waves CERN Document Server Liang, Y 2016-01-01 Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. We show that, in fact, there are countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not obtain if a simplified boundary condition such as rigid lid or linear form is employed. Harmonic-generation resonance presented here also provides a mechanism for the transfer of the energy of the internal waves to the higher-frequency part of the spectrum where internal waves are more prone to breaking, hence losing energy to turbulence and heat and contributing to oceanic mixing. 1. The SSG Wave Energy Converter DEFF Research Database (Denmark) Vicinanza, Diego; Margheritini, Lucia; Kofoed, Jens Peter 2012-01-01 The Sea-wave Slot-cone Generator concept (SSG) is a Wave Energy Converter based on the wave overtopping principle utilizing several reservoirs placed on top of each other, in which the energy of the incoming wave will be stored as potential energy. The water captured in the reservoirs will then run...... through turbines for electricity production. The system utilizes a wide spectrum of different wave conditions by means of multiple reservoirs, located at different levels above the still water level. Thereby, it obtains a high overall efficiency and it can be suitable for shoreline and breakwater...... applications, presenting particular advantages such as: sharing structure costs, availability of grid connection and infrastructures, recirculation of water inside the harbor, as the outlet of the turbines is on the rear part of the system. Recently, plans for the SSG pilot installation were in progress... 2. Evaluation of the Wave Energy Conversion Efficiency in Various Coastal Environments Directory of Open Access Journals (Sweden) Eugen Rusu 2014-06-01 Full Text Available The main objective of the present work was to assess and compare the wave power resources in various offshore and nearshore areas. From this perspective, three different groups of coastal environments were considered: the western Iberian nearshore, islands and an enclosed environment with sea waves, respectively. Some of the most representative existent wave converters were evaluated in the analysis and a second objective was to compare their performances at the considered locations, and in this way to determine which is better suited for potential commercial exploitation. In order to estimate the electric power production expected in a certain location, the bivariate distributions of the occurrences corresponding to the sea states, defined by the significant wave height and the energy period, were constructed in each coastal area. The wave data were provided by hindcast studies performed with numerical wave models or based on measurements. The transformation efficiency of the wave energy into electricity is evaluated via the load factor and also through the capture width, defined as the ratio between the electric power estimated to be produced by each specific wave energy converters (WEC and the expected wave power corresponding to the location considered. Finally, by evaluating these two different indicators, comparisons of the performances of three WEC types (Aqua Buoy, Pelamis and Wave Dragon in the three different groups of coastal environments considered have been also carried out. The work provides valuable information related to the effectiveness of various technologies for the wave energy extraction that would operate in different coastal environments. 3. Shoreline dissipation of infragravity waves Science.gov (United States) de Bakker, A. T. M.; Tissier, M. F. S.; Ruessink, B. G. 2014-01-01 Infragravity waves (0.005-0.05 Hz) have recently been observed to dissipate a large part of their energy in the short-wave (0.05-1 Hz) surf zone, however, the underlying mechanism is not well understood. Here, we analyse two new field data sets of near-bed pressure and velocity at up to 13 cross-shore locations in ≲2.5 m depth on a ≈1:80 and a ≈1:30 sloping beach to quantify infragravity-wave dissipation close to the shoreline and to identify the underlying dissipation mechanism. A frequency-domain Complex Eigenfunction analysis demonstrated that infragravity-wave dissipation was frequency dependent. Infragravity waves with a frequency larger than ≈0.0167-0.0245 Hz were predominantly onshore progressive, indicative of strong dissipation of the incoming infragravity waves. Instead, waves with a lower frequency showed the classic picture of cross-shore standing waves with minimal dissipation. Bulk infragravity reflection coefficients at the shallowest position (water depth ≈0.7 m) were well below 1 (≈0.20), implying that considerable dissipation took place close to the shoreline. We hypothesise that for our data sets infragravity-wave breaking is the dominant dissipation mechanism close to the shoreline, because the reflection coefficient depends on a normalised bed slope, with the higher infragravity frequencies in the mild-sloping regime where breaking is known to dominate dissipation. Additional numerical modelling indicates that, close to the shoreline of a 1:80 beach, bottom friction contributes to infragravity-wave dissipation to a limited extent, but that non-linear transfer of infragravity energy back to sea-swell frequencies is unimportant. 4. Tropical cyclogenesis in a tropical wave critical layer: easterly waves Directory of Open Access Journals (Sweden) T. J. Dunkerton 2009-08-01 Full Text Available The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, is identified herein as the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The recirculating Kelvin cat's eye within the critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development is given by the intersection of the wave's critical latitude and trough axis at the center of the cat's eye, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally the associated Lagrangian motions, one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. In this co-moving frame, streamlines are approximately equivalent to particle trajectories. The closed circulation is quasi-stationary, and a dividing streamline separates air within the cat's eye from air outside. The critical layer equatorward of the easterly jet axis is important to tropical cyclogenesis because its cat's eye provides (i a region of 5. Wave "Coherency" and Implications for Wave-Particle Interactions Science.gov (United States) Tsurutani, Bruce; Singh Lakhina, Gurbax; Bhanu, Remya; Lee, Lou-Chuang 2016-07-01 Wave "coherency" was introduced in 2009 by Tsurutani et al. (JGR, doi:10.1029/2008JA013353, 2009) to describe the waves detected in the ~10 to 100 ms duration subelements which are the fundamental components of ~0.1 to 0.5 s chorus "elements". In this talk we will show examples of what we mean by coherency, quasi-coherency and incoherency for a variety of magnetospheric plasma waves. We will show how to measure coherency/quasicoherency quantitatively for electromagnetic whistler mode chorus, electromagnetic ion cyclotron (EMIC) waves, plasmaspheric hiss and linearly polarized magnetosonic waves. If plasma waves are coherent, their interactions with resonant particles will be substantially different. Specific examples will be used to show that the pitch angle scattering rates for energetic charged particles is roughly 3 orders of magnitude faster than the Kennel-Petschek diffusion (which assumes incoherent waves) rate. We feel that this mechanism is the only one that can explain ~ 0.1- 0.5 s bremsstrahlung x-ray microbursts. 6. Wave-particle interaction in the Faraday waves. Science.gov (United States) Francois, N; Xia, H; Punzmann, H; Shats, M 2015-10-01 Wave motion in disordered Faraday waves is analysed in terms of oscillons or quasi-particles. The motion of these oscillons is measured using particle tracking tools and it is compared with the motion of fluid particles on the water surface. Both the real floating particles and the oscillons, representing the collective fluid motion, show Brownian-type dispersion exhibiting ballistic and diffusive mean squared displacement at short and long times, respectively. While the floating particles motion has been previously explained in the context of two-dimensional turbulence driven by Faraday waves, no theoretical description exists for the random walk type motion of oscillons. It is found that the r.m.s velocity ⟨μ̃(osc)⟩(rms) of oscillons is directly related to the turbulent r.m.s. velocity ⟨μ̃⟩(rms) of the fluid particles in a broad range of vertical accelerations. The measured ⟨μ̃(osc)⟩(rms) accurately explains the broadening of the frequency spectra of the surface elevation observed in disordered Faraday waves. These results suggest that 2D turbulence is the driving force behind both the randomization of the oscillons motion and the resulting broadening of the wave frequency spectra. The coupling between wave motion and hydrodynamic turbulence demonstrated here offers new perspectives for predicting complex fluid transport from the knowledge of wave field spectra and vice versa. 7. Wave chaotic experiments and models for complicated wave scattering systems Science.gov (United States) Yeh, Jen-Hao Wave scattering in a complicated environment is a common challenge in many engineering fields because the complexity makes exact solutions impractical to find, and the sensitivity to detail in the short-wavelength limit makes a numerical solution relevant only to a specific realization. On the other hand, wave chaos offers a statistical approach to understand the properties of complicated wave systems through the use of random matrix theory (RMT). A bridge between the theory and practical applications is the random coupling model (RCM) which connects the universal features predicted by RMT and the specific details of a real wave scattering system. The RCM gives a complete model for many wave properties and is beneficial for many physical and engineering fields that involve complicated wave scattering systems. One major contribution of this dissertation is that I have utilized three microwave systems to thoroughly test the RCM in complicated wave systems with varied loss, including a cryogenic system with a superconducting microwave cavity for testing the extremely-low-loss case. I have also experimentally tested an extension of the RCM that includes short-orbit corrections. Another novel result is development of a complete model based on the RCM for the fading phenomenon extensively studied in the wireless communication fields. This fading model encompasses the traditional fading models as its high-loss limit case and further predicts the fading statistics in the low-loss limit. This model provides the first physical explanation for the fitting parameters used in fading models. I have also applied the RCM to additional experimental wave properties of a complicated wave system, such as the impedance matrix, the scattering matrix, the variance ratio, and the thermopower. These predictions are significant for nuclear scattering, atomic physics, quantum transport in condensed matter systems, electromagnetics, acoustics, geophysics, etc. 8. Wave directional spectrum from array measurements Digital Repository Service at National Institute of Oceanography (India) Fernandes, A.A; Sarma, Y.V.B.; Menon, H.B. Using the method of Esteva (1976, 1977), whcih assumes that at the frequency band the waves approach from just a single "mean" wave direction, wave direction has been consistently, accurately and unambiguously evaluated as a function of frequency... 9. Propagation of sound waves in ducts DEFF Research Database (Denmark) Jacobsen, Finn 2000-01-01 Plane wave propagation in ducts with rigid walls, radiation from ducts, classical four-pole theory for composite duct systems, and three-dimentional waves in wave guides of various cross-sectional shape are described.... 10. Statistical distribution of nonlinear random wave height Institute of Scientific and Technical Information of China (English) HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi 2006-01-01 A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution. 11. Licensing and Environmental Issues of Wave Energy Projects DEFF Research Database (Denmark) Neumann, Frank; Tedd, James; Prado, Miguel 2006-01-01 The major non-technical barrier for large-scale wave energy implementation is the wide range of licensing issues and potential environmental concerns, in addition to significant National/regional differences in licensing procedures and permit requirements. Whereas some pilot plants have had...... as concerning ocean space use and environmental concerns. Despite recent efforts to streamline European EIA (Environmental Impact Assessment) in general, potential project developers are far from having a clear view of present and future requirements concerning these barriers on a trans-national level...... pilot plants and exemplary presents the ongoing permitting process of the Wave Dragon in Wales. Comments on future park-scale application issues are made based on the present situation in different countries.... 12. Are "EIT Waves" Fast-Mode MHD Waves? CERN Document Server Wills-Davey, M J; Stenflo, J O 2007-01-01 We examine the nature of large-scale, coronal, propagating wave fronts (EIT waves'') and find they are incongruous with solutions using fast-mode MHD plane-wave theory. Specifically, we consider the following properties: non-dispersive single pulse manifestions, observed velocities below the local Alfven speed, and different pulses which travel at any number of constant velocities, rather than at the `predicted'' fast-mode speed. We discuss the possibility of a soliton-like explanation for these phenomena, and show how it is consistent with the above-mentioned aspects. 13. The wave buoy analogy - estimating high-frequency wave excitations DEFF Research Database (Denmark) Nielsen, Ulrik Dam 2008-01-01 The paper deals with the wave buoy analogy where a ship is considered as a wave buoy, so that measured ship responses are used as a basis to estimate wave spectra and associated sea state parameters. The study presented follows up on a previous paper, Nielsen [Nielsen UD. Response-based estimation...... processes are carried out in the present paper; however with one of the responses being the relative motion which is a type of response that is sensitive to high-frequency excitations. Based on the present study it is shown that by including the relative motion, the frequency-wise energy distribution can... 14. Tropical cyclogenesis in a tropical wave critical layer: easterly waves Directory of Open Access Journals (Sweden) T. J. Dunkerton 2008-06-01 Full Text Available The development of tropical depressions within tropical waves over the Atlantic and eastern Pacific is usually preceded by a "surface low along the wave" as if to suggest a hybrid wave-vortex structure in which flow streamlines not only undulate with the waves, but form a closed circulation in the lower troposphere surrounding the low. This structure, equatorward of the easterly jet axis, resembles the familiar critical layer of waves in shear flow, a flow configuration which arguably provides the simplest conceptual framework for tropical cyclogenesis resulting from tropical waves, their interaction with the mean flow, and with diabatic processes associated with deep moist convection. The critical layer represents a sweet spot for tropical cyclogenesis in which a proto-vortex may form and grow within its parent wave. A common location for storm development within the critical layer is given by the intersection of the wave's critical latitude and trough axis, with analyzed vorticity centroid nearby. The wave and vortex live together for a time, and initially propagate at approximately the same speed. In most cases this coupled propagation continues for a few days after a tropical depression is identified. For easterly waves, as the name suggests, the propagation is westward. It is shown that in order to visualize optimally this "marsupial paradigm" one should view the flow streamlines, or stream function, in a frame of reference translating horizontally with the phase propagation of the parent wave. This translation requires an appropriate "gauge" that renders translating streamlines and isopleths of translating stream function approximately equivalent to flow trajectories. In the translating frame, the closed circulation is stationary, and a dividing streamline effectively separates air within the critical layer from air outside. The critical layer equatorward of the easterly jet axis is important to tropical cyclogenesis because it 15. Dichromatic Langmuir waves in degenerate quantum plasma Science.gov (United States) Dubinov, A. E.; Kitayev, I. N. 2015-06-01 Langmuir waves in fully degenerate quantum plasma are considered. It is shown that, in the linear approximation, Langmuir waves are always dichromatic. The low-frequency component of the waves corresponds to classical Langmuir waves, while the high-frequency component, to free-electron quantum oscillations. The nonlinear problem on the profile of dichromatic Langmuir waves is solved. Solutions in the form of a superposition of waves and in the form of beatings of its components are obtained. 16. The gravitational-wave memory effect OpenAIRE Favata, Marc 2010-01-01 The nonlinear memory effect is a slowly-growing, non-oscillatory contribution to the gravitational-wave amplitude. It originates from gravitational waves that are sourced by the previously emitted waves. In an ideal gravitational-wave interferometer a gravitational-wave with memory causes a permanent displacement of the test masses that persists after the wave has passed. Surprisingly, the nonlinear memory affects the signal amplitude starting at leading (Newtonian-quadrupole) order. Despite ... 17. Propagation of sound waves in ducts DEFF Research Database (Denmark) Jacobsen, Finn 2000-01-01 Plane wave propagation in ducts with rigid walls, radiation from ducts, classical four-pole theory for composite duct systems, and three-dimentional waves in wave guides of various cross-sectional shape are described.......Plane wave propagation in ducts with rigid walls, radiation from ducts, classical four-pole theory for composite duct systems, and three-dimentional waves in wave guides of various cross-sectional shape are described.... 18. Ultrasonic guided wave nondestructive evaluation using generalized anisotropic interface waves Science.gov (United States) Gardner, Michael D. The motivation for this work is a goal to inspect interfaces between thick layers of materials that can be anisotropic. The specific application is a thick composite bonded to a metal substrate. The interface is inspected for disbonds between the metal and composite. The large thickness allows the problem to be modeled as a half space. The theory behind guided waves in plates is presented. This theory includes the calculation and analysis of dispersion curves and the resulting wave structure. It is noted that for high frequency-thickness values, certain modes will converge to the half-space waves, e.g. the Rayleigh wave and the Stoneley wave. Points of high energy, especially shear energy, at the interface are desirable for interfacial inspection. Therefore, the wave structure for all modes and frequencies is searched for ideal inspection points. Interface waves are inherently good modes to use for interface inspection. Results from the dispersion curves and wave structures are verified in the finite element model software package called Abaqus. It is confirmed that the group speeds and wave structures of the modes match the predicted values. A theoretical development of interface waves is given wherein Rayleigh, Stoneley, and generalized interface waves are discussed. This is applied to both isotropic and anisotropic materials. It is shown that the Stoneley wave only exists for a certain range of material parameters. Because the Stoneley wave is the interface wave between two solid half spaces, it might appear that only certain pairs of solids would allow for inspection via interface wave. However, it is shown that for perturbations of the Stoneley-wave-valid material properties, interface waves which leak energy away from the interface can still propagate. They can also be used for inspection. Certain choices of materials will leak less energy and will therefore allow for longer inspection distances. The solutions to the isotropic leaky wave problem exist on 19. Compression Waves and Phase Plots: Simulations CERN Document Server Orlikowski, Daniel 2011-01-01 Compression wave analysis started nearly 50 years ago with Fowles.[1] Coperthwaite and Williams [2] gave a method that helps identify simple and steady waves. We have been developing a method that gives describes the non-isentropic character of compression waves, in general.[3] One result of that work is a simple analysis tool. Our method helps clearly identify when a compression wave is a simple wave, a steady wave (shock), and when the compression wave is in transition. This affects the analysis of compression wave experiments and the resulting extraction of the high-pressure equation of state. 20. On the atmospheric internal ship waves Institute of Scientific and Technical Information of China (English) 桑建国 1997-01-01 The analytical solutions of the atmospheric internal ship waves induced by three-dimensional terrain are obtained by solving the atmospheric wave equation. The solutions show that the waves consist of the untrapped and trapped parts. The patterns of the diverging wave and transverse wave in the untrapped parts are mainly determined by the shape and orientation of the terrain. This kind of wave may transport the wave energy to the upper atmosphere. The patterns of trapped lee waves are decided by the atmospheric conditions such as stratification, mean wind speeds and wind shear. 1. Ion cyclotron waves at Titan Science.gov (United States) Russell, C. T.; Wei, H. Y.; Cowee, M. M.; Neubauer, F. M.; Dougherty, M. K. 2016-03-01 During the interaction of Titan's thick atmosphere with the ambient plasma, it was expected that ion cyclotron waves would be generated by the free energy of the highly anisotropic velocity distribution of the freshly ionized atmospheric particles created in the interaction. However, ion cyclotron waves are rarely observed near Titan, due to the long growth times of waves associated with the major ion species from Titan's ionosphere, such as CH4+ and N2+. In the over 100 Titan flybys obtained by Cassini to date, there are only two wave events, for just a few minutes during T63 flyby and for tens of minutes during T98 flyby. These waves occur near the gyrofrequencies of proton and singly ionized molecular hydrogen. They are left-handed, elliptically polarized, and propagate nearly parallel to the field lines. Hybrid simulations are performed to understand the wave growth under various conditions in the Titan environment. The simulations using the plasma and field conditions during T63 show that pickup protons with densities ranging from 0.01 cm-3 to 0.02 cm-3 and singly ionized molecular hydrogens with densities ranging from 0.015 cm-3 to 0.25 cm-3 can drive ion cyclotron waves with amplitudes of ~0.02 nT and of ~0.04 nT within appropriate growth times at Titan, respectively. Since the T98 waves were seen farther upstream than the T63 waves, it is possible that the instability was stronger and grew faster on T98 than T63. 2. Submillimeter Wave Antenna With Slow Wave Feed Line DEFF Research Database (Denmark) Zhurbenko, Vitaliy; Krozer, Viktor; Kotiranta, Mikko 2009-01-01 of the electromagnetic spectrum, and to create innovative imaging and sensing techniques that hold enormous potential in biomedical, metrological and security applications. Considering that realization of submillimeter wave components and antennas is still heavily constrained by problems arising from technological... 3. A Numerical Wave Tank for Nonlinear Waves with Passive Absorption Institute of Scientific and Technical Information of China (English) 周宗仁; 尹彰; 石瑞祥 2001-01-01 A numerical wave tank with passive absorption for irregular waves is considered in this paper. Waves with spectralshapes corresponding to that of the Mitsuyasu-Bretschneider type are used as the initial condition at one end of theflume. An absorbing boundary is imposed at the other end of the wave flume to minimize reflection. By use of aLagrangian description for the surface elevation, and finite difference for approximation of the time derivative, the problem is then solved by the boundary element method. The effects of the absorbing boundary are investigated by varyingthe values of the absorption coefficient μ, and studying the time histories of the surface elevations "recorded" on pre-se-lected locations. 4. Conversion of Internal Gravity Waves into Magnetic Waves CERN Document Server Lecoanet, Daniel; Fuller, Jim; Cantiello, Matteo; Burns, Keaton J 2016-01-01 Asteroseismology probes the interiors of stars by studying oscillation modes at a star's surface. Although pulsation spectra are well understood for solar-like oscillators, a substantial fraction of red giant stars observed by Kepler exhibit abnormally low-amplitude dipole oscillation modes. Fuller et al. (2015) suggests this effect is produced by strong core magnetic fields that scatter dipole internal gravity waves (IGWs) into higher multipole IGWs or magnetic waves. In this paper, we study the interaction of IGWs with a magnetic field to test this mechanism. We consider two background stellar structures: one with a uniform magnetic field, and another with a magnetic field that varies both horizontally and vertically. We derive analytic solutions to the wave propagation problem and validate them with numerical simulations. In both cases, we find perfect conversion from IGWs into magnetic waves when the IGWs propagate into a region exceeding a critical magnetic field strength. Downward propagating IGWs canno... 5. Onset behavior of standing wave thermoacoustic pressure wave generator Science.gov (United States) Mehta, Shreya; Desai, Keyur; Naik, Hemant Bhimbhai; Atrey, Milind 2012-06-01 A standing wave type thermoacoustic pressure wave generator for 300 Hz operating frequency is designed and developed for helium as a working fluid. The device is designed as a half wave length resonator. A parallel plate type SS 304 stack is designed and fabricated. An electric heater is used for heat supply to the hot end heat exchanger while a water cooled heat exchanger is used to maintain the other end of the stack near ambient temperature. An acoustic amplifier is used to amplify the pressure ratio generated. Experiments are conducted to study the onset behavior of pressure wave generator in terms of temperature range. Observations are recorded using piezoelectric pressure transducer. The results are obtained with different charging pressure and heat inputs. A pressure ratio of around 1.1 to 1.15 has been obtained using Nitrogen as a working fluid. The onset of thermoacoustic oscillations are studied for different filling pressure and for a range of hot end temperature. 6. Surface acoustic wave microfluidics. Science.gov (United States) Ding, Xiaoyun; Li, Peng; Lin, Sz-Chin Steven; Stratton, Zackary S; Nama, Nitesh; Guo, Feng; Slotcavage, Daniel; Mao, Xiaole; Shi, Jinjie; Costanzo, Francesco; Huang, Tony Jun 2013-09-21 The recent introduction of surface acoustic wave (SAW) technology onto lab-on-a-chip platforms has opened a new frontier in microfluidics. The advantages provided by such SAW microfluidics are numerous: simple fabrication, high biocompatibility, fast fluid actuation, versatility, compact and inexpensive devices and accessories, contact-free particle manipulation, and compatibility with other microfluidic components. We believe that these advantages enable SAW microfluidics to play a significant role in a variety of applications in biology, chemistry, engineering and medicine. In this review article, we discuss the theory underpinning SAWs and their interactions with particles and the contacting fluids in which they are suspended. We then review the SAW-enabled microfluidic devices demonstrated to date, starting with devices that accomplish fluid mixing and transport through the use of travelling SAW; we follow that by reviewing the more recent innovations achieved with standing SAW that enable such actions as particle/cell focusing, sorting and patterning. Finally, we look forward and appraise where the discipline of SAW microfluidics could go next. 7. Wave propagation in elastic solids CERN Document Server Achenbach, Jan 1984-01-01 The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treat 8. Wave turbulence in magnetized plasmas Directory of Open Access Journals (Sweden) S. Galtier 2009-02-01 Full Text Available The paper reviews the recent progress on wave turbulence for magnetized plasmas (MHD, Hall MHD and electron MHD in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic turbulence which usually provides the best theoretical framework to investigate space and laboratory plasmas. The solar wind and the coronal heating problems are presented as two examples of application of anisotropic wave turbulence. The most important results of wave turbulence are reported and discussed in the context of natural and simulated magnetized plasmas. Important issues and possible spurious interpretations are also discussed. 9. Interference of diffusive light waves. Science.gov (United States) Schmitt, J M; Knüttel, A; Knutson, J R 1992-10-01 We examine interference effects resulting from the superposition of photon-density waves produced by coherently modulated light incident upon a turbid medium. Photon-diffusion theory is used to derive expressions for the ac magnitude and phase of the aggregate diffusive wave produced in full- and half-space volumes by two sources. Using a frequency-domain spectrometer operating at 410 MHz, we verify interference patterns predicted by the model in scattering samples having optical properties similar to those of skin tissue. Potential imaging applications of interfering diffusive waves are discussed in the context of the theoretical and experimental results. 10. Tracking Target and Spiral Waves DEFF Research Database (Denmark) Jensen, Flemming G.; Sporring, Jon; Nielsen, Mads 2002-01-01 A new algorithm for analyzing the evolution of patterns of spiral and target waves in large aspect ratio chemical systems is introduced. The algorithm does not depend on finding the spiral tip but locates the center of the pattern by a new concept, called the spiral focus, which is defined...... by the evolutes of the actual spiral or target wave. With the use of Gaussian smoothing, a robust method is developed that permits the identification of targets and spirals foci independently of the wave profile. Examples of an analysis of long image sequences from experiments with the Belousov... 11. Millimeter Wave Alternate Route Study. Science.gov (United States) 1981-04-01 A0-AI02 303 HARRIS CORP MELBOURNE FL GOVERNMENT COMMUNICATION ST--ETC FIG 17/2.1 MILLIMETER WAVE ALENT ROUTE STUDT.(U) APR W C ADAMS J J PAN, W C...481-487. 4-7 abm ADAOO0 303 HARRIS CORP MELBOURNE FL GOVERNMENT COMMUNICATION S -ETC F/G 17/2.1 MILLIMETER WAVE ALTERNATE ROUTE STUDY.(U) APR 81 W C...7-21L’j r AD-A102 303 HARRIS CORP MELBOURNE FL GOVERNMENT COMMUNICATION ST--ETC F/A 17/2.1 MILLIMETER WAVE ALTERNATE ROUTE STUDY(U) APR 81 W C ADAMS 12. Tracking Target and Spiral Waves DEFF Research Database (Denmark) Jensen, Flemming G.; Sporring, Jon; Nielsen, Mads; 2002-01-01 A new algorithm for analyzing the evolution of patterns of spiral and target waves in large aspect ratio chemical systems is introduced. The algorithm does not depend on finding the spiral tip but locates the center of the pattern by a new concept, called the spiral focus, which is defined...... by the evolutes of the actual spiral or target wave. With the use of Gaussian smoothing, a robust method is developed that permits the identification of targets and spirals foci independently of the wave profile. Examples of an analysis of long image sequences from experiments with the Belousov... 13. Popsicle-Stick Cobra Wave Science.gov (United States) Boucher, Jean-Philippe; Clanet, Christophe; Quéré, David; Chevy, Frédéric 2017-08-01 The cobra wave is a popular physical phenomenon arising from the explosion of a metastable grillage made of popsicle sticks. The sticks are expelled from the mesh by releasing the elastic energy stored during the weaving of the structure. Here we analyze both experimentally and theoretically the propagation of the wave front depending on the properties of the sticks and the pattern of the mesh. We show that its velocity and its shape are directly related to the recoil imparted to the structure by the expelled sticks. Finally, we show that the cobra wave can only exist for a narrow range of parameters constrained by gravity and rupture of the sticks. 14. Holographic d-wave superconductors CERN Document Server Kim, Keun-Young 2013-01-01 We construct top down models for holographic d-wave superfluids in which the order parameter is a charged spin two field in the bulk. Close to the transition temperature the condensed phase can be captured by a charged spin two field in an R-charged black hole background (downstairs picture) or equivalently by specific graviton perturbations of a spinning black brane (upstairs picture). We analyse the necessary conditions on the mass and the charge of the spin two field for a condensed phase to exist and we discuss the competition of the d-wave phase with other phases such as s-wave superfluids. 15. INTERFERENCE OF COUNTERPROPAGATING SHOCK WAVES Directory of Open Access Journals (Sweden) P. V. Bulat 2015-03-01 Full Text Available The subject of study. We examined the interaction of counterpropagating shock waves. The necessity of counterpropagating shock waves studying occurs at designing of high Mach number modern internal compression air intakes, Ramjets with subsonic and supersonic combustion, in asymmetrical supersonic nozzles and in some other cases. In a sense, this problem is a generalization of the case of an oblique shock reflection from the wall or from the plane of symmetry. With the renewed vigor, the interest to this problem emerged at the end of the 90s. This was due to the start of the programs for flight study at hypersonic speeds. The first experiments performed with air intakes, which realized the interaction of counterpropagating shock waves have shown that the change in flow velocity is accompanied by abrupt alteration of shock-wave structure, the occurrence of nonstationary and oscillatory phenomena. With an increase of flow velocity these phenomena undesirable for aircraft structure became more marked. The reason is that there are two fundamentally different modes of interaction of counterpropagating shock waves: a four-wave regular and a five-wave irregular. The transition from one mode to another can be nonstationary abrupt or gradual, it can also be accompanied by hysteresis. Main results. Criteria for the transition from regular reflection of counterpropagating shock waves to irregular are described: the criterion of von Neumann and the stationary Mach configuration criterion. We described areas in which the transition from one reflection type to another is possible only in abrupt way, as well as areas of possible gradual transition. Intensity dependences of the reflected shock waves from the intensity of interacting counterpropagating shocks were given. Qualitative pictures of shock-wave structures arising from the interaction of counterpropagating shock waves were shown. Calculation results of the intensity of outgoing gas 16. Charge density waves in solids CERN Document Server Gor'kov, LP 2012-01-01 The latest addition to this series covers a field which is commonly referred to as charge density wave dynamics.The most thoroughly investigated materials are inorganic linear chain compounds with highly anisotropic electronic properties. The volume opens with an examination of their structural properties and the essential features which allow charge density waves to develop.The behaviour of the charge density waves, where interesting phenomena are observed, is treated both from a theoretical and an experimental standpoint. The role of impurities in statics and dynamics is considered and an 17. Wave Physics Oscillations - Solitons - Chaos CERN Document Server Nettel, Stephen 2009-01-01 This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior. 18. The physical simulation of wave groups and their variations in a wave flume Institute of Scientific and Technical Information of China (English) LIU Si; ZHANG Yongliang; LIU Shuxue; LI Jinxuan; XIA Zhisheng 2013-01-01 The physical simulation method of wave groups in a wave flume is proposed and verified by the exper-iments. The experimental results demonstrate that random waves with desired wave groupiness, which simultaneously includes the wave group height and length, can be generated satisfactorily at the specified position in a wave flume using the proposed method. Furthermore, the transformation properties of the wave groupiness along the flat-bottomed wave flume are investigated based on the physically simulated waves. Associated proposals with the physical simulation of wave groups are given. 19. Plane-wave scattering from half-wave dipole arrays DEFF Research Database (Denmark) Jensen, Niels E. 1970-01-01 A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays.......A matrix equation for determination of plane-wave scattering from arrays of thin short-circuited dipoles of lengths about half a wavelength is derived. Numerical and experimental results are presented for linear, circular, and concentric circular arrays.... 20. Breaking Wave Characteristics and Breaking Wave Forces on Slender Cylinders OpenAIRE Chella, Mayilvahanan Alagan 2016-01-01 Offshore wind farms have become an increasingly important source of clean and renewable energy. Most recent offshore wind farms are deployed close to the coast in shallow waters. One of the major factors influencing the initial investment of this technology is the design of the substructure and foundation. The physical processes associated with the non-linear shallow water hydrodynamics are rather complex since the wave motion is strongly influenced by the seabed. Breaking wave...	{"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": 0.8586525917053223, "perplexity": 2668.870537180769}, "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-2018-09/segments/1518891812756.57/warc/CC-MAIN-20180219151705-20180219171705-00658.warc.gz"}
http://clay6.com/qa/575/let-x-represent-the-difference-between-the-number-of-heads-and-the-number-o	Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X? $\begin{array}{1 1}1,2,4 \\ 0,3,6 \\ 0,2,4,6 \\ 1,3,5 \end{array}$ 1 Answer If a coin is tossed 6 times, the number of heads (or tails) can assume one of the following values: {0, 1, 2, 3, 4, 5, 6}. In fact the number of heads + number of tails must be = 6. If the number of heads = {0,1,2,3,4,5,6}, then the corresponding # of tails = {6-0, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6} = {6,5,4,3,2,1,0}. The (modulus) difference between the values in the two set of events X = {6-0, 5-1, 4-2, 3-3, 4-2, 5-1, 6-0} = {6,4,2,0,2,4,6}. Therefore the possible values of X are 0, 2, 4 and 6. answered Jun 19, 2013 1 answer 1 answer 1 answer 1 answer 1 answer 1 answer 1 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": 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": 0.8475051522254944, "perplexity": 423.6412278929235}, "config": {"markdown_headings": false, "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-2017-51/segments/1512948609934.85/warc/CC-MAIN-20171218063927-20171218085927-00655.warc.gz"}
https://stats.stackexchange.com/questions/358732/residualizing-dependent-variable-and-two-step-linear-regression	# Residualizing dependent variable and two step linear regression Assume we have a DGP of the form $y = \beta_0 + \beta_1 * x_1 + \beta_2 * x_2 + \beta_3 * x_3 + \epsilon$ where $\epsilon$ is a standard i.i.d. error term. Does residualizing $y$ using a linear regression including only an intercept, $x_1$ and $x_2$ and regressing the resulting residuals on $x_3$ give us the same estimate for the coefficient of $x_3$ as in the full specification? More formally, if you estimate the model in a two step procedure of the form $y = \bar{\beta_0} + \bar{\beta_1} * x_1 + \bar{\beta_2} * x_2 + \eta$ $\hat{\eta} = \bar{\beta_3} * x_3 + \xi$ where $\eta$ and $\xi$ are error terms and $\hat{\eta}$ are the estimated residuals from the first regression, is it proven that $\bar{\beta_3}$ and $\beta_3$ will be the same? If I simulate a model in R, it seems to work flawlessly. However, I have a problem when trying to replicate the two step procedure with a real dataset. Now I'm not sure whether I made a coding error or whether this two step procedure is wrong. Simulation Code x1 <- rnorm(1000) x2 <- rnorm(1000) x3 <- rnorm(1000) y <- 4 + 3x1 - 2x2 + 22x3 + rnorm(1000) res <- resid(lm(y~x1+x2)) summary(lm(res~x3-1)) It general these regressions are not the same, but since you have simulated independence it works out. Consider the full regression \begin{align} Y = \alpha + X_1\beta_1 + X_2\beta_2 + X_3\beta_3 +\epsilon \end{align} Let me define a $n\times 3$ matrix $Z = [1,X_1,X_2]$, a column of ones then the values of $X_1$ and $X_3$. Let $M_z$ be the residual making projection matrix. In other words this matrix when applied to a variable is the same as regression that variable on a column of ones, $X_1$ and $X_2$. $$\hat{\beta_3} = \frac{X_3^TM_zY}{X_3^TM_zX_3}$$ The above formula follows from the application of the FWL theorem. You can derive the result equally from minimizing the sum of squared residuals, but the matrix notation and FWL theorem make things much cleaner and in this case give us insight into the question you asked. Recall that in simple regression, the general formula for the OLS estimate is $\hat{\beta} = \frac{X^TY}{X^TX}$. You can show for yourself using this formula that the $\beta_3$ that we derived above is the same as the following simple regression: \begin{align} M_zY = M_zX_3\beta_3 + \epsilon \end{align*} (Note: $(M_z)^TM_z = M_z$ by properties of orthogonal projection matrices. Second note, I wrote $\epsilon$ again because these residuals are numerically the same by FWL. In other words this is the exact same regression). So to answer the question, it would be same as residualizes Y by regression in a constant, $X_1$ and $X_2$ and then regressing these residuals on the residuals of $X_3$ regressed on a constant, $X_1$ and $X_2$. In you simulation you have all your $Xs$ as independent standard normal variables. In expectation when you regress $X_3$ on the others, the result is the same so the residualizing of $X_3$ doesn't matter. In the real data, my guess is that $X_3$ is not mean 0 and has some real relationship with the other two variables so it will not work.	{"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9307608604431152, "perplexity": 373.8042437206033}, "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-2019-26/segments/1560627997533.62/warc/CC-MAIN-20190616022644-20190616044644-00388.warc.gz"}
https://badisydri.blogspot.com/2021/09/	## LATEX ### Matrix models of noncommutative geometry and string theory Feynman path integrals and phase transitions in quantum field theory. The Ising model and commutative scalar phi-four theory. String theory in 2 dimensions as discretized surfaces and random matrices. The large N saddle point and orthogonal polynomial methods. The $\theta=0$ and $\theta=\infty$ limits of noncommutative field theory. The multitrace expansion of noncommutative scalar field theory. Monte Carlo algorithms for matrix models. The phase structure of noncommutative phi-four. The IKKT matrix model and non-perturbative superstring theory. Yang-Mills matrix models of noncommutative gauge theory. BFSS matrix quantum mechanics, M-(atrix) theory and the gauge/gravity duality. Yang-Mills matrix quantum mechanical models. Large $d$ expansion of Yang-Mills quantum mechanics. Emergent geometry and noncommutative gauge theory in Yang-Mills matrix models. AdS/CFT correspondence in two dimensions and noncommutative geometry. Wilson renormalization group equations for matrix and noncommutative models. Noncommutative quantum black holes. Emergent gravity and quantized symplectic geometry. Matrix cosmology and emergent time in IKKT and BFSS matrix models. ### Quantum Gravity: Noncommutative Geometry, The Gauge/Gravity Correspondence And Matrix Models Noncommutative geometry (and its matrix models) presents a distinct solution to the problem of quantum gravity whereas the gauge/gravity correspondence is currently the most successful proposal for quantum gravity. The two approaches intersect within the quantum mechanics of the BFSS (or M-(atrix)) theory and also within the IKKT matrix model which should be viewed as providing the starting unifying framework. The BFSS-type Yang-Mills quantum mechanics and the IKKT-type Yang-Mills matrix models provide a non-perturbative formulation of superstring theory and its underlying eleven-dimensional M-theory. But they also provide a quantum gravitational formulation (gravitational Feynman path integral) of Connes' noncommutative geometry (classical phase space). In other words, we should think of noncommutative geometry as a "first quantization of geometry" (classical gravity) and think of the corresponding matrix models as a "second quantization" of geometry " (quantum gravity). Poisson manifolds play therefore the fundamental role of "curved spacetime", the Darboux theorem plays the role of the "equaivalence principle" while Moyal-Weyl spaces are what defines our "flat spacetime". The nature of quantum geometry can also be probed by means of multitrace matrix models where both the renormalization group equation, the large N saddle point analysis and the Monte Carlo method come together in a symphony of mathematical and computational methods applied to the same theoretical problem (which is quite rare). The multitrace matrix models is in fact an alternative to Yang-Mills matrix models which allow for emergent geometry (quantum geometry), emergent gravity (quantum gravity) and emergent time (quantum cosmology). Another important gauge/gravity duality (besides the BFSS-type Yang-Mills quantum mechanics) is the AdS/CFT correspondence. The case of two dimensions is the most mysterious and is the most important for quantum black holes as well as it is the case most closely related to noncommutative geometry which is very intriguing indeed. Question 1: Towards "computational physics of string theory"! Answer 1: Preliminary results are reported in https://arxiv.org/abs/2007.04488. Question 2: What is the relation between multitrace matrix models and quantum geometry? Answer 2: The discussion of the fixed points of a cubic multitrace matrix model (which is important to a very important case of emergent noncommutative geometry in two dimensions, i.e. the fuzzy sphere, the noncommutative torus and the Moyal-Weyl plane) is discussed in https://arxiv.org/abs/2008.09564. Question 3: Can we reformulate a noncommutative theory of the AdS/CFT correspondence and black hole evaporation problem? ### Symmetric Spaces We start off with a brief discussion of the differential geometry of maximally symmetric spaces in two dimensions such as $\mathbb{S}^2$, ${\rm dS}^2$, $\mathbb{H}^2$ and ${\rm AdS}^2$ which play a prominent role in the near-horizon geometry of black holes, in Euclidean quantum field theory, in noncommutative geometry and in the ${\rm AdS}^{d+1}/{\rm CFT}_d$ correspondence. First we note that maximally symmetric spaces are essential ingredient in quantum gravity theories and cosmological models. These homogeneous and isotropic spaces enjoy the largest possible amount of spactime symmetries (isometries) and in Lorentzian signature they are exhausted with the three maximally symmetric spaces \cite{Bengtsson}: The de Sitter spacetime ${\rm dS}^d$ (positive scalar curvature, repulsive cosmological constant, topology $\mathbb{S}^{d-1}\times \mathbb{R}$) which is relevant to cosmology. The de Sitter spacetime ${\rm dS}^d$ as embedded in $\mathbb{M}^{1,d}$ is given by the ambiant metric and the quadric form \begin{eqnarray} &&ds^2=-dX_1^2+dX_2^2+...+dX_{d+1}^2\nonumber\\ &&-X_1^2+X_2^2+...+X_{d+1}^2=R^2. \end{eqnarray} Minkowski spacetime $\mathbb{M}^d$ (zero scalar curvature, zero cosmological constant, topology $\mathbb{R}^d$) which can be viewed as a zero cosmological constant limit of de Sitter spacetime $\mathbb{dS}^d$. The anti-de Sitter spacetime ${\rm AdS}^d$ (negative scalar curvature, attractive cosmological constant, topology $\mathbb{R}^{d-1}\times \mathbb{S}^1$) which is relevant to quantum gravity. The anti-de Sitter spacetime ${\rm AdS}^d$ as embedded in $\mathbb{M}^{2,d-1}$ is given by the ambiant metric and the quadric form \begin{eqnarray} &&ds^2=-dX_1^2-dX_2^2+dX_3^2+...+dX_{d+1}^2\nonumber\\ &&-X_1^2-X_2^2+X_3^2+...+X_{d+1}^2=-R^2. \end{eqnarray} However, Wick rotation to Euclidean signature remains crucial to both quantum field theory and noncommutative geometry where quantization of fields and geometries makes strict sense only in Euclidean setting. In Euclidean signature, the maximally symmetric spaces are then given by the three spaces \cite{Bengtsson}: The sphere $\mathbb{S}^d$ (positive curvature). The sphere $\mathbb{S}^d$ as embedded in $\mathbb{R}^{d+1}$ is given by the ambiant metric and the quadric form \begin{eqnarray} &&ds^2=dX_1^2+...+dX_{d+1}^2\nonumber\\ &&X_1^2+...+X_{d+1}^2=R^2. \end{eqnarray} The Killing vectors fields which leave both the ambiant metric and the quadric form invariant are \begin{eqnarray} J_{\alpha\beta}=X_{\alpha}\partial_{\beta}-X_{\beta}\partial_{\alpha}.\label{isometry} \end{eqnarray} These $d(d+1)/2$ isometries generate the group of rotations $SO(d+1)$. This is to be contrasted with the isometry group of de Sitter spacetime is $SO(1,d)$. Euclidean space $\mathbb{R}^d$ (zero curvature). The pseudo-sphere $\mathbb{H}^d$ (negative curvature). The pseudo-sphere (Hyperboloic space) $\mathbb{H}^d$ as embedded in $\mathbb{M}^{1,d}$ is given by the ambiant metric and the quadric form \begin{eqnarray} &&ds^2=-dX_1^2+dX_2^2+...+dX_{d+1}^2\nonumber\\ &&-X_1^2+X_2^2+...+X_{d+1}^2=-R^2. \end{eqnarray} The Hyperboloic space $\mathbb{H}^d$ is defined as the upper sheet of the two-sheeted hyperboloid $-X_1^2+X_2^2...+X_{d+1}^2=-R^2$. The Killing vectors fields which leave both the ambiant metric and the quadric form invariant are still given by as before but the underlying symmetry group is now given by $SO(1,d)$. This is to be contrasted with the isometry group of anti-de Sitter spacetime which is given by $SO(2,d-1)$. It is intriguing to note that in two dimensions the spaces $\mathbb{S}^2$, ${\rm dS}^2$, $\mathbb{H}^2$ and ${\rm AdS}^2$ are simply related. For example, we can go from ${\rm AdS}^2$ (closed timelike curves with isometry group $SO(2,1)$) to ${\rm dS}^2$ (closed spacelike curves with isometry group $SO(1,2)$) and vice versa by switching the meaning of timelike and spacelike. While both ${\rm dS}^2$ and $\mathbb{H}^2$ share precisely the same isometry group $SO(1,2)$. And we can go from ${\rm dS}^2$ to $\mathbb{S}^2$ by an ordinary Wick rotation. We can also go from ${\rm AdS}^2$ to $\mathbb{H}^2$ by a Wick rotation. Representation theory of the Lorentz groups $SO(1,2)$ and $SO(2,1)$ can be found for example in \cite{barg,bns}. See also \cite{Mukunda:1974gb,Girelli:2015ija,Basu:1981ju}. In this article we will focus on the case of two dimensions with Euclidean signature where the positive curvature space is given by a sphere $\mathbb{S}^2$ with isometry group $SO(3)$ and the negative curvature space is given by a pseudo-sphere $\mathbb{H}^2$ with isometry group $SO(1,2)$. We will be mostly interested in the case of the pseudo-sphere $\mathbb{H}^2$ which we will simply denote by ${\rm AdS}^2$. The quantization of these two spaces yields the fuzzy sphere $\mathbb{S}^2_N$ \cite{Hoppe,Madore:1991bw} and the noncommutative pseudo-sphere ${\rm AdS}^2_{\theta}$ \cite{Ho:2000fy,Ho:2000br,Jurman:2013ota,Pinzul:2017wch} respectively which enjoy the same isometry groups $SO(3)$ and $SO(1,2)$ as their commutative counterparts. The fuzzy sphere is unstable and suffers collapse in a phase transition to Yang-Mills matrix models (topology change or geometric transition) whereas the noncommutative pseudo-sphere can sustain black hole configurations (by including a dilaton field) and also suffers collapse in the form of the information loss process (quantum gravity transition). In fact, the product space $\mathbb{S}^2\times {\rm AdS}^2$ is the near-horizon geometry of extremal black holes in general relativity and string theory, e.g. the four-dimensional Reissner-Nordstrom black hole. It is then observed that the information loss problem in four dimensions on $\mathbb{S}^2_N\times {\rm AdS}^2_{\theta}$ reduces to the information loss problem in two dimensions on noncommutative ${\rm AdS}^2_{\theta}$. As we have said we will be mostly interested here in the case of the pseudo-sphere $\mathbb{H}^2$ or the Euclidean ${\rm AdS}^2$. The goal naturally is to construct a consistent ${\rm AdS}^2$/${\rm CFT}_1$ correspondence. ### Author biography Badis Ydri —currently a professor of theoretical particle physics, teaching at the Department of Physics, Badji-Mokhtar Annaba University, Algeria—received his PhD from Syracuse University, New York, USA in 2001 and his Habilitation from Annaba University, Annaba, Algeria in 2011. His doctoral work, titled ‘Fuzzy Physics’, was supervised by Professor A P Balachandran. Professor Ydri is an Adjunct Professor at the Dublin Institute for Advanced Studies, Dublin, Ireland, and a research associate (regular ICTP associate) at the Abdus Salam Center for Theoretical Physics, Trieste, Italy. His post-doctoral experience comprises a Marie Curie fellowship at Humboldt University Berlin, Germany, and a Hamilton fellowship at the Dublin Institute for His current research directions include: noncommutative geometry; the gauge/gravity duality; computational physics of string theory; renormalization group and Monte Carlo methods in matrix models and noncommutative field theories; emergent geometry, gravity and cosmology from matrix models; and foundations of quantum mechanics. Other related interests include string theory; quantum information; causal dynamical triangulation; Horava–Lifshitz gravity; supersymmetric and noncommutative standard models; and supersymmetric gauge theory in four dimensions. He has recently published six books. His other intellectual interests include philosophy of physics and existential philosophy. ### The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry Part I: A QM/NCG Correspondence https://arxiv.org/abs/2108.13982 Part II: Noncommutative Quantum Black holes https://arxiv.org/abs/2109.00380 Part III: Phase Structure of Noncommutative AdS^2_θ x S^2_N https://arxiv.org/abs/2109.01010	{"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": 0.8073905110359192, "perplexity": 898.6455906226129}, "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-2023-14/segments/1679296949701.56/warc/CC-MAIN-20230401063607-20230401093607-00703.warc.gz"}
http://www.nolimitszone.com/gamma-ray-bursts-are-the-most-deadly-things-in-the-universe	Every few seconds, a supernova emits jets of deadly gamma rays somewhere in the universe. If one of these gamma ray bursts should happen sufficiently close to the solar system, all life would perish. Gamma-ray bursts (GRBs) are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant galaxies. They are the brightest electromagnetic events known to occur in the universe. Bursts can last from ten milliseconds to several minutes. The initial burst is usually followed by a longer-lived “afterglow” emitted at longer wavelengths (X-ray, ultraviolet, optical, infrared, microwave and radio). Most observed GRBs are believed to consist of a narrow beam of intense radiation released during a supernova or hypernova as a rapidly rotating, high-mass star collapses to form a neutron star, quark star, or black hole. A subclass of GRBs (the “short” bursts) appear to originate from a different process – this may be due to the merger of binary neutron stars. The cause of the precursor burst observed in some of these short events may be due to the development of a resonance between the crust and core of such stars as a result of the massive tidal forces experienced in the seconds leading up to their collision, causing the entire crust of the star to shatter. The sources of most GRBs are billions of light years away from Earth, implying that the explosions are both extremely energetic (a typical burst releases as much energy in a few seconds as the Sun will in its entire 10-billion-year lifetime) and extremely rare (a few per galaxy per million years). All observed GRBs have originated from outside the Milky Way galaxy, although a related class of phenomena, soft gamma repeater flares, are associated with magnetars within the Milky Way. It has been hypothesized that a gamma-ray burst in the Milky Way, pointing directly towards the Earth, could cause a mass extinction event. GRBs were first detected in 1967 by the Vela satellites, a series of satellites designed to detect covert nuclear weapons tests. Hundreds of theoretical models were proposed to explain these bursts in the years following their discovery, such as collisions between comets and neutron stars. Little information was available to verify these models until the 1997 detection of the first X-ray and optical afterglows and direct measurement of their redshifts using optical spectroscopy, and thus their distances and energy outputs. These discoveries, and subsequent studies of the galaxies and supernovae associated with the bursts, clarified the distance and luminosity of GRBs. These facts definitively placed them in distant galaxies and also connected long GRBs with the explosion of massive stars, the only possible source for the energy outputs observed. On November 21, 2013, NASA released detailed data about one of the strongest gamma-ray burst, designated GRB 130427A, that was observed on April 27, 2013 https://youtu.be/7HIokbQMHB8 SHARE	{"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": 0.8962088227272034, "perplexity": 1076.5531711230647}, "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-2017-51/segments/1512948523222.39/warc/CC-MAIN-20171213123757-20171213143757-00458.warc.gz"}
http://math.stackexchange.com/questions/891674/fixed-point-for-a-continuous-function-on-a-compact-set	# Fixed point for a continuous function on a compact set? If $f:X \rightarrow X$ is continuous and X is compact, will $f$ have a fixed point? We know that a contraction will have a fixed point but I have not come across an example of a continuous function on a compact set that does not have a fixed point (admittedly I have not worked with functions outside $\mathbb{R}^k$ where Brouwer's fixed point theorem applies). Is there an example of a continuous function on a compact set such that the function does not have a fixed point? - Take $X$ to be the unit circle (not disk) and $f$ a non-trivial rotation. For an example in the real line, take $X=[-2,-1] \cup [1,2]$ and $f(x)=-x$. What fails in both cases is that $X$ is not convex. - Let $X=\{-1,1\}$ and let $f(x)=-x$. - Take the unit circle in $\mathbb{R}^2$ and the map f, as f(x) going to its diametrically opposite point. This map is continuous but has no fixed point. - Each finite set $X$ is compact. Using the discrete topology on $X$ each map is continuous. So each permutation without a fixpoint will do the job. For $\|X\|>1$ we always have permutations without a fixpoint. By the way: The discrete topology is just the induced topology if you consider finite subsets of $\mathbb{R}^n$. -	{"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": 0.9729316234588623, "perplexity": 106.35951788932692}, "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-2014-49/segments/1416931010938.65/warc/CC-MAIN-20141125155650-00203-ip-10-235-23-156.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/simple-harmonic-motion-of-a-machine-part-problem.276553/	# Simple Harmonic Motion of a machine part problem 1. Dec 2, 2008 ### veronicak5678 1. The problem statement, all variables and given/known data A machine part is undergoing SHM with a frequency of 5 Hz and an amplitude of 1.8 cm. How long does it take the part to go from x=0 to x=-1.80 cm ? 2. Relevant equations x = Acos (ωt + φ) 3. The attempt at a solution 1.80 cm = 1.80 cm * cos (ωt + φ) ω = 2πf = 2π* 5hz cos (ωt + φ) = 1 ωt + φ = 2π What would φ be? 2. Dec 2, 2008 ### naresh The phase φ in simple harmonic motion is basically your choice of time origin, i.e. it tells you what the displacement and velocities are at t = 0. For example, at t=0, if you started the motion at x = -A, you would get φ = π. If your initial condition was x = 0, you have φ = +/- π/2. (Whether it is plus or minus depends on which direction you are moving at t = 0). And so on. Back to this problem, choose an initial condition of your liking (it does not matter what you choose, you can always choose an arbitrary time origin). Then you can work out what φ is. Hint: There is an easier way to do this problem, by symmetry considerations. 3. Dec 2, 2008 ### veronicak5678 Unfortunately, I don't know what you mean by symmetry conditions. However, I think I understand what you said. I came up with an answer of .05 seconds. Last edited: Dec 2, 2008 4. Dec 2, 2008 ### LowlyPion Isn't the question really how long does it take for a sinusoidal to go from the zero crossing to maximum negative amplitude? What part of a cycle is that? How long would that be then?	{"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": 0.9306684732437134, "perplexity": 721.895285027344}, "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-2016-50/segments/1480698541517.94/warc/CC-MAIN-20161202170901-00394-ip-10-31-129-80.ec2.internal.warc.gz"}
https://stacks.math.columbia.edu/tag/06RB	## 100.29 Stratification by gerbes The goal of this section is to show that many algebraic stacks $\mathcal{X}$ have a “stratification” by locally closed substacks $\mathcal{X}_ i \subset \mathcal{X}$ such that each $\mathcal{X}_ i$ is a gerbe. This shows that in some sense gerbes are the building blocks out of which any algebraic stack is constructed. Note that by stratification we only mean that $\|\mathcal{X}\| = \bigcup \nolimits _ i \|\mathcal{X}_ i\|$ is a stratification of the topological space associated to $\mathcal{X}$ and nothing more (in this section). Hence it is harmless to replace $\mathcal{X}$ by its reduction (see Properties of Stacks, Section 99.10) in order to study this stratification. The following proposition tells us there is (almost always) a dense open substack of the reduction of $\mathcal{X}$ Proposition 100.29.1. Let $\mathcal{X}$ be a reduced algebraic stack such that $\mathcal{I}_\mathcal {X} \to \mathcal{X}$ is quasi-compact. Then there exists a dense open substack $\mathcal{U} \subset \mathcal{X}$ which is a gerbe. Proof. According to Proposition 100.28.9 it is enough to find a dense open substack $\mathcal{U}$ such that $\mathcal{I}_\mathcal {U} \to \mathcal{U}$ is flat and locally of finite presentation. Note that $\mathcal{I}_\mathcal {U} = \mathcal{I}_\mathcal {X} \times _\mathcal {X} \mathcal{U}$, see Lemma 100.5.5. Choose a presentation $\mathcal{X} = [U/R]$. Let $G \to U$ be the stabilizer group algebraic space of the groupoid $R$. By Lemma 100.5.7 we see that $G \to U$ is the base change of $\mathcal{I}_\mathcal {X} \to \mathcal{X}$ hence quasi-compact (by assumption) and locally of finite type (by Lemma 100.5.1). Let $W \subset U$ be the largest open (possibly empty) subscheme such that the restriction $G_ W \to W$ is flat and locally of finite presentation (we omit the proof that $W$ exists; hint: use that the properties are local). By Morphisms of Spaces, Proposition 66.32.1 we see that $W \subset U$ is dense. Note that $W \subset U$ is $R$-invariant by More on Groupoids in Spaces, Lemma 78.6.2. Hence $W$ corresponds to an open substack $\mathcal{U} \subset \mathcal{X}$ by Properties of Stacks, Lemma 99.9.11. Since $\|U\| \to \|\mathcal{X}\|$ is open and $\|W\| \subset \|U\|$ is dense we conclude that $\mathcal{U}$ is dense in $\mathcal{X}$. Finally, the morphism $\mathcal{I}_\mathcal {U} \to \mathcal{U}$ is flat and locally of finite presentation because the base change by the surjective smooth morphism $W \to \mathcal{U}$ is the morphism $G_ W \to W$ which is flat and locally of finite presentation by construction. See Lemmas 100.25.4 and 100.27.11. $\square$ The above proposition immediately implies that any point has a residual gerbe on an algebraic stack with quasi-compact inertia, as we will show in Lemma 100.31.1. It turns out that there doesn't always exist a finite stratification by gerbes. Here is an example. Example 100.29.2. Let $k$ be a field. Take $U = \mathop{\mathrm{Spec}}(k[x_0, x_1, x_2, \ldots ])$ and let $\mathbf{G}_ m$ act by $t(x_0, x_1, x_2, \ldots ) = (tx_0, t^ p x_1, t^{p^2} x_2, \ldots )$ where $p$ is a prime number. Let $\mathcal{X} = [U/\mathbf{G}_ m]$. This is an algebraic stack. There is a stratification of $\mathcal{X}$ by strata 1. $\mathcal{X}_0$ is where $x_0$ is not zero, 2. $\mathcal{X}_1$ is where $x_0$ is zero but $x_1$ is not zero, 3. $\mathcal{X}_2$ is where $x_0, x_1$ are zero, but $x_2$ is not zero, 4. and so on, and 5. $\mathcal{X}_{\infty }$ is where all the $x_ i$ are zero. Each stratum is a gerbe over a scheme with group $\mu _{p^ i}$ for $\mathcal{X}_ i$ and $\mathbf{G}_ m$ for $\mathcal{X}_{\infty }$. The strata are reduced locally closed substacks. There is no coarser stratification with the same properties. Nonetheless, using transfinite induction we can use Proposition 100.29.1 find possibly infinite stratifications by gerbes...! Lemma 100.29.3. Let $\mathcal{X}$ be an algebraic stack such that $\mathcal{I}_\mathcal {X} \to \mathcal{X}$ is quasi-compact. Then there exists a well-ordered index set $I$ and for every $i \in I$ a reduced locally closed substack $\mathcal{U}_ i \subset \mathcal{X}$ such that 1. each $\mathcal{U}_ i$ is a gerbe, 2. we have $\|\mathcal{X}\| = \bigcup _{i \in I} \|\mathcal{U}_ i\|$, 3. $T_ i = \|\mathcal{X}\| \setminus \bigcup _{i' < i} \|\mathcal{U}_{i'}\|$ is closed in $\|\mathcal{X}\|$ for all $i \in I$, and 4. $\|\mathcal{U}_ i\|$ is open in $T_ i$. We can moreover arrange it so that either (a) $\|\mathcal{U}_ i\| \subset T_ i$ is dense, or (b) $\mathcal{U}_ i$ is quasi-compact. In case (a), if we choose $\mathcal{U}_ i$ as large as possible (see proof for details), then the stratification is canonical. Proof. Let $T \subset \|\mathcal{X}\|$ be a nonempty closed subset. We are going to find (resp. choose) for every such $T$ a reduced locally closed substack $\mathcal{U}(T) \subset \mathcal{X}$ with $\|\mathcal{U}(T)\| \subset T$ open dense (resp. nonempty quasi-compact). Namely, by Properties of Stacks, Lemma 99.10.1 there exists a unique reduced closed substack $\mathcal{X}' \subset \mathcal{X}$ such that $T = \|\mathcal{X}'\|$. Note that $\mathcal{I}_{\mathcal{X}'} = \mathcal{I}_\mathcal {X} \times _\mathcal {X} \mathcal{X}'$ by Lemma 100.5.6. Hence $\mathcal{I}_{\mathcal{X}'} \to \mathcal{X}'$ is quasi-compact as a base change, see Lemma 100.7.3. Therefore Proposition 100.29.1 implies there exists a dense maximal (see proof proposition) open substack $\mathcal{U} \subset \mathcal{X}'$ which is a gerbe. In case (a) we set $\mathcal{U}(T) = \mathcal{U}$ (this is canonical) and in case (b) we simply choose a nonempty quasi-compact open $\mathcal{U}(T) \subset \mathcal{U}$, see Properties of Stacks, Lemma 99.4.9 (we can do this for all $T$ simultaneously by the axiom of choice). Using transfinite recursion we construct for every ordinal $\alpha$ a closed subset $T_\alpha \subset \|\mathcal{X}\|$. For $\alpha = 0$ we set $T_0 = \|\mathcal{X}\|$. Given $T_\alpha$ set $T_{\alpha + 1} = T_\alpha \setminus \|\mathcal{U}(T_\alpha )\|.$ If $\beta$ is a limit ordinal we set $T_\beta = \bigcap \nolimits _{\alpha < \beta } T_\alpha .$ We claim that $T_\alpha = \emptyset$ for all $\alpha$ large enough. Namely, assume that $T_\alpha \not= \emptyset$ for all $\alpha$. Then we obtain an injective map from the class of ordinals into the set of subsets of $\|\mathcal{X}\|$ which is a contradiction. The claim implies the lemma. Namely, let $I = \{ \alpha \mid \mathcal{U}_\alpha \not= \emptyset \} .$ This is a well-ordered set by the claim. For $i = \alpha \in I$ we set $\mathcal{U}_ i = \mathcal{U}_\alpha$. So $\mathcal{U}_ i$ is a reduced locally closed substack and a gerbe, i.e., (1) holds. By construction $T_ i = T\alpha$ if $i = \alpha \in I$, hence (3) holds. Also, (4) and (a) or (b) hold by our choice of $\mathcal{U}(T)$ as well. Finally, to see (2) let $x \in \|\mathcal{X}\|$. There exists a smallest ordinal $\beta$ with $x \not\in T_\beta$ (because the ordinals are well-ordered). In this case $\beta$ has to be a successor ordinal by the definition of $T_\beta$ for limit ordinals. Hence $\beta = \alpha + 1$ and $x \in \|\mathcal{U}(T_\alpha )\|$ and we win. $\square$ Remark 100.29.4. We can wonder about the order type of the canonical stratifications which occur as output of the stratifications of type (a) constructed in Lemma 100.29.3. A natural guess is that the well-ordered set $I$ has cardinality at most $\aleph _0$. We have no idea if this is true or false. If you do please email [email protected]. In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	{"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": 2, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9895007014274597, "perplexity": 187.37498104545313}, "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-2023-06/segments/1674764499967.46/warc/CC-MAIN-20230202070522-20230202100522-00845.warc.gz"}
http://aas.org/archives/BAAS/v30n4/aas193/478.htm	AAS Meeting #193 - Austin, Texas, January 1999 Session 99. Stellar Atmospheric Activity and Luminous Blue Variables Display, Saturday, January 9, 1999, 9:20am-4:00pm, Exhibit Hall 1 ## [99.03] Activity in Old Dwarf and Subgiant Stars C.L. Slesnick (New York University \& SAO), R.A. Donahue, S.L. Baliunas (Harvard-Smithsonian \& MWO) Chromospheric Ca \sc ii \rm H and K fluxes of ~150 F and G stars on or near the main sequence were analyzed to determine whether previously established relationships between stellar magnetic activity and rotation (age) hold for those stars that have begun to evolve off the Main Sequence. Each star's time series (up to 33 years) was analyzed year by year to detect variability which could be attributed to rotation. In several cases, more than one locus of periods was measured for a star. These periods were compared to the estimated rotation periods from a relationship derived by Noyes et al. (1984) using a star's B-V color and the mean emission flux level of the chromospheric Ca \sc ii \rm H and K lines. In general, the periods observed correspond to the predicted rotation period. Those which did not were analyzed in further detail in order to posit a cause for their values. Rotational velocities inferred from the observed periods and the calculated radius of each star were compared to v \sin i values collected from the Stellar Rotational Velocity Catalog (Bernacca & Perinotto 1970, 1971, 1973). In several cases the observed periods are inconsistent with rotation; however, a few stars which have begun to evolve off the Main Sequence may show characteristically longer periods than expected, suggesting that they have either begun to lose angular momentum or are conserving it by slowing their velocity as they expand.	{"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": 0.9578612446784973, "perplexity": 2959.2780912961284}, "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/1427131294307.1/warc/CC-MAIN-20150323172134-00030-ip-10-168-14-71.ec2.internal.warc.gz"}
https://astarmathsandphysics.com/a-level-maths-notes/fp2/4025-factorising-the-equation-for-roots-of-unity.html	## Factorising the Equation for Roots of Unity The cube roots of unity are the roots of $\omega^3 =1 \rightarrow \omega^3 -1=0$ . There are three cube roots of unity. The sixth roots of unity are the roots of $\omega^6-1=0$ . There are six xis th roots of unity. All the cube roots of unity are sixth roots of unity. This means that a factor of $\omega^6-1=0$ is $\omega^3 -1$ . In fact, $\omega^6-1=(\omega^3+1)(\omega^3-1)$ . The ninth roots of unity are the roots of nbsp; $\omega^99-1=0$ . There are nine ninth roots of unity. All the cube roots of unity are ninth roots of unity. This means that a factor of $\omega^9-1=0$ is $\omega^3 -1$ . In fact, $\omega^9-1=(\omega^6 +\omega^3+1)(\omega^3-1)$ . In fact, the $3nth$ roots of unity are the roots of the equation $\omega^{3n} -1=0$ All the cube roots of unity are $3nth$ roots of unity, so as before $\omega^3 -1$ should be a factor of $\omega^{3n} -1=0$ . In fact, $\omega^{3n} -1=(\omega^{3n-3} + \omega^{3n-6} + ...+ \omega^3 + 1)( \omega^3 -1)$ In fact, if If there are m roots of unity, the solutions of the equation $\omega^{n} -1=0$ and $m$ is any divisor of $n$ then \begin{aligned} \omega^{n} -1 &= (\omega^{n-m} + \omega^{n-2m} + ...+ \omega^m + 1)( \omega^m -1) \\ &= (\omega^{n-m} + \omega^{n-2m} + ...+ \omega^m + 1)( \omega^{m-1} + \omega^{m-2} + \omega^{m-3} + ...+ \omega + +1)(\omega-1) \end{aligned}	{"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9977111220359802, "perplexity": 1259.323041450229}, "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/1637964363437.15/warc/CC-MAIN-20211208022710-20211208052710-00087.warc.gz"}
http://www.science21c.org/moodle/mod/glossary/view.php?id=2&mode=&hook=ALL&sortkey=&sortorder=&fullsearch=0&page=5	## IB Physics Glossary Search full text Browse the glossary using this index Special \| A \| B \| C \| D \| E \| F \| G \| H \| I \| J \| K \| L \| M \| N \| O \| P \| Q \| R \| S \| T \| U \| V \| W \| X \| Y \| Z \| ALL Page: (Previous) 1 2 3 4 5 6 7 8 9 10 ... 23 (Next) ALL ### D #### Dose equivalent H, indicates the effective absorbed dose based on the type of ionization radiation being used. $$H = Q D$$, where is the quality factor of the ionization. The units for H is also Jkg-1 (Gy) but we use the Sievert (Sv) to distinguish it from absorbed dose. Keyword(s): I3 ### E #### Eclipsing binary stars are identified by a periodic dip in their combined brightness-time curve. Keyword(s): E2 #### Effective half-life the time taken for the activity of a medical radioactive isotope to reduce by half, taking into account both physical and biological removal of activity from the body such that $$\frac{1}{T_E} = \frac{1}{T_P} + \frac{1}{T_B}$$ or $$T_E = \frac{T_P \times T_B} {T_P + T_B}$$ where TE is the effective half-life, TP is the physical half-life and TB is the biological half-life. $$\lambda_E = \lambda_P + \lambda_B$$. Keyword(s): I3 #### Efficiency is the ratio of useful power of a system to the input power or the ratio of useful energy transformed to the total energy input. (d) Approximate overall energy efficiencies for different types of power station are Coal: 35%, Gas: 45% & Oil: 38%. Keyword(s): 2.3, 8.1 #### Elastic collisions occur when the total kinetic energy of a system remains constant. Keyword(s): 2.3 #### Electric current is defined in terms of force per unit length between two parallel current-carrying conductors. (d) The electric current flowing in a circuit is the rate of flow of charge, $$I = \frac{\Delta q}{\Delta t}$$. Keyword(s): 5.1 #### Electric field strength is the force per unit charge exerted on a positive test charge placed in the field. $$E = \frac{F}{q}=\frac{k\frac{Qq}{r^2}}{q}=k \frac{Q}{r^2}$$. Its unit is NC-1. It is a vector quantity and is always directed from the positive charge (+) to the negative charge (-) and points tangentially ($$\perp$$) to the surface of the charge. Note: 1. An attractive force 2. A repulsive force (no field lines at centre) 3. Positive point charge to ground 4. Parallel plates (no edge effects) with constant electric field For charges of unequal magnitude, the field lines are shifted towards the lower magnitude charge. The field line pattern is pear-shaped with the "apex" closer to the lower magnitude charge. The field around a charged conductor At equilibrium, the charge and electric field follow these guidelines: • the excess charge lies only at the surface of the conductor • the electric field is zero within the solid part of the conductor • the electric field at the surface of the conductor is perpendicular to the surface • charge accumulates, and the field is strongest, on pointy parts of the conductor [source, http://physics.bu.edu/~duffy/py106/Electricfield.html] For a sphere of radius R the electric field varies with distance r from centre of sphere as shown below. #### Electric Potential Difference is the work done per unit charge in moving a small positive charge between two points. (d) Keyword(s): 5.1 #### Electrical circuit symbols Keyword(s): 5.2 #### Electrical power can be expressed in three ways $$P = V I$$ $$P = I^2 R$$ - used for power dissiapation due to heating in the transmission of electricity. $$P = \frac{V^2}{R}$$. Keyword(s): 5.1 Page: (Previous) 1 2 3 4 5 6 7 8 9 10 ... 23 (Next) ALL	{"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": 0.9454683065414429, "perplexity": 753.0324326174707}, "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/1593655891640.22/warc/CC-MAIN-20200707013816-20200707043816-00013.warc.gz"}
https://plainmath.net/80749/prove-munderover-x	# Prove <munderover> ∑<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> k = Prove $\sum _{k=0}^{n}\frac{\left(2k\right)!\left(2n-2k\right)!}{{2}^{2n}\left(2k+1\right)\left[k!\left(n-k\right)!{\right]}^{2}}=\frac{\left[{2}^{n}n!{\right]}^{2}}{\left(2n+1\right)!}$ using mathematical induction Since I already know the way using combinatorial proof, I am trying to prove it by mathematical induction but it is not easy to show. I derived that ${S}_{n}=\frac{2n}{2n+1}{S}_{n-1}$ from RHS, but how can I proceed from this? I mean, how can I organize the LHS? I cannot organize LHS properly because of different . You can still ask an expert for help ## Want to know more about Discrete math? • Questions are typically answered in as fast as 30 minutes Solve your problem for the price of one coffee • Math expert for every subject • Pay only if we can solve it Maggie Bowman Step 1 First of all notice that: $\left(2n+1\right)!=1\cdot 2\cdot 3\cdot 4\cdot \dots \cdot 2n\cdot \left(2n+1\right)=\left[1\cdot 3\cdot 5\cdot \dots \cdot \left(2n+1\right)\right]\cdot {2}^{n}\left[1\cdot 2\cdot \dots \cdot n\right]=\left(2n+1\right)!!\cdot {2}^{n}\cdot n!$ Step 2 Based on the first hint, you want to prove that: ${S}_{n}=\frac{\left[{2}^{n}n!{\right]}^{2}}{\left(2n+1\right)!}=\frac{{2}^{n}n!}{\left(2n+1\right)!!}$ Step 3 What does the second hint and the rule: ${S}_{n}=\frac{2n}{2n+1}{S}_{n-1}$ have in common?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 36, "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": 0.9026344418525696, "perplexity": 1000.5587201864931}, "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-2022-49/segments/1669446710972.37/warc/CC-MAIN-20221204104311-20221204134311-00676.warc.gz"}
http://worldwidescience.org/topicpages/0-9/29s+excited+states.html	#### Sample records for 29s excited states 1. Excited states Lim, Edward C 1974-01-01 Excited States, Volume I reviews radiationless transitions, phosphorescence microwave double resonance through optical spectra in molecular solids, dipole moments in excited states, luminescence of polar molecules, and the problem of interstate interaction in aromatic carbonyl compounds. The book discusses the molecular electronic radiationless transitions; the double resonance techniques and the relaxation mechanisms involving the lowest triplet state of aromatic compounds; as well as the optical spectra and relaxation in molecular solids. The text also describes dipole moments and polarizab 2. Excited states v.6 Lim, Edward C 2013-01-01 Excited States, Volume 6 is a collection of papers that discusses the excited states of molecules. The first paper discusses the linear polyene electronic structure and potential surfaces, considering both the theoretical and experimental approaches in such electronic states. This paper also reviews the theory of electronic structure and cites some experimental techniques on polyene excitations, polyene spectroscopic phenomenology, and those involving higher states of polyenes and their triplet states. Examples of these experimental studies of excited states involve the high-resolution one-pho 3. Excited states 2 Lim, Edward C 2013-01-01 Excited States, Volume 2 is a collection of papers that deals with molecules in the excited states. The book describes the geometries of molecules in the excited electronic states. One paper describes the geometries of a diatomic molecule and of polyatomic molecules; it also discusses the determination of the many excited state geometries of molecules with two, three, or four atoms by techniques similar to diatomic spectroscopy. Another paper introduces an ordered theory related to excitons in pure and mixed molecular crystals. This paper also presents some experimental data such as those invo 4. Excited states 4 Lim, Edward C 2013-01-01 Excited States, Volume 4 is a collection of papers that deals with the excited states of molecular activity. One paper investigates the resonance Raman spectroscopy as the key to vibrational-electronic coupling. This paper reviews the basic theory of Raman scattering; it also explains the derivation of the Raman spectra, excitation profiles, and depolarization ratios for simple resonance systems. Another paper reviews the magnetic properties of triplet states, including the zero-field resonance techniques, the high-field experiments, and the spin Hamiltonian. This paper focuses on the magnetic 5. Excited Charm States Characteristics of mass spectra and decays of orbitally excited charm mesons and baryons, expected on the basis of quark models and Heavy Quark Symmetry, are briefly described. The difficulties associated with measurements on these excited states are discussed. The accuracy and reliability of currently available experimental information is examined. The reasons, for the widely accepted spin-parity assignments to the observed excited mesons and baryons, are stated. Finally, the experimental data, with the accepted spin-parity assignments, is compared with expectations based on quark models and Heavy Quark Symmetry 6. β-delayed proton decay of 29S The 28Si(3He,2n) reaction at 32 MeV has been used to produce 29S; delayed protons have been observed following the positron decay of 29S to proton unbound levels in 29P. The half-life of 29S was measured to be 187 +- 6 ms which, combined with previous results, gives a weighted average value of 188.0 +- 4.3 ms. Precise level energies have confirmed several recently observed states in 29P from 4.0 to 9.5 MeV in excitation energy. From the intensities of these proton groups and assuming isospin purity for the lowest T = 3/2 level in 29P, absolute log ft values for each transition were determined. The measured excitation energies and β decay transition rates to levels in 29P are compared to recent shell-model calculations 7. Excited States in 207Rn 罗万居; 郭应祥; 周小红; 张玉虎; 雷相国; 刘忠; 郑勇; 柳敏良; 何建军; 竺礼华; 温书贤 2003-01-01 Excited states in 207Rn are investigated via the 196Pt(16O,Sn)207Rn reaction at beam energies from 85 to 95 MeV using techniques of in-beam γ-ray spectroscopy. Measurements ofγ-ray excitation function, x - γ and γ - γ- t coincidences are performed with ten BGO(AC)HPGe detectors. Based on these measurements, a level scheme of207Rn, including 17 γ-rays and 18 levels, is established. Spins for most of the levels are proposed according to the measured DCO ratios. The level structure is compared with a weak-coupling calculation using the interaction energies extracted from neighbouring nuclei. 8. Excited state Intramolecular Proton Transfer in Anthralin Møller, Søren; Andersen, Kristine B.; Spanget-Larsen, Jens; 1998-01-01 Quantum chemical calculations performed on anthralin (1,8-dihydroxy-9(10H)-anthracenone) predict the possibility of an excited-state intramolecular proton transfer process. Fluorescence excitation and emission spectra of the compound dissolved in n-hexane at ambient temperature results in an......, associated with an excited-state intramolecular proton transfer process.... 9. Excited states in Pd99 Sihotra, S.; Naik, Z.; Kumar, S.; Singh, K.; Goswamy, J.; Singh, N.; Kumar, R.; Singh, R. P.; Muralithar, S.; Bhowmik, R. K.; Palit, R.; Mehta, D. 2011-02-01 Excited states in the Pd99 nucleus populated in the As75(Si28, p3n) fusion-evaporation reaction at Elab=120 MeV have been investigated through in-beam γ-ray spectroscopic techniques using an array of Compton-suppressed clover detectors. The level scheme is established up to excitation energy ~11.5 MeV and spin ~25ℏ with the addition of about 60 new transitions. The level structures observed in Pd99 have been interpreted in the framework of a microscopic theory based on the deformed Hartree-Fock and angular momentum projection techniques. Band structures at lower spins are based on the low-Ω νg7/2 and νd5/2 orbitals, and those at higher spins are reproduced for the π(g9/2)5⊗π(g7/2)⊗ν(g7/2)2⊗ν(h11/2)2⊗ν(g9/2)-1 and π(g9/2)6⊗ν(g9/2)10⊗ν(g7/2)2⊗ν(h11/2) configurations. The octupole correlations in Pd99 have been inferred from new interband E1 transitions linking the ΔI=1 states of the bands based on the νh11/2 and νd5/2 orbitals (Δl=3, Δj=3, and Δπ=-1) with the deduced B(E1) values ~10-6 W.u. 10. The mechanisms of Excited states in enzymes Petersen, Frederic Nicolas Rønne; Bohr, Henrik 2010-01-01 Enzyme catalysis is studied on the basis of excited state processes, which are of electronic, vibrational and thermal nature. The ways of achieving the excited state, such as photo-absorption and ligand binding, are discussed and exemplified by various cases of enzymes.......Enzyme catalysis is studied on the basis of excited state processes, which are of electronic, vibrational and thermal nature. The ways of achieving the excited state, such as photo-absorption and ligand binding, are discussed and exemplified by various cases of enzymes.... 11. Excited states rotational effects on the behavior of excited molecules Lim, Edward C 2013-01-01 Excited States, Volume 7 is a collection of papers that discusses the excited states of molecules. The first paper reviews the rotational involvement in intra-molecular in vibrational redistribution. This paper analyzes the vibrational Hamiltonian as to its efficacy in detecting the manifestations of intra-molecular state-mixing in time-resolved and time-averaged spectroscopic measurements. The next paper examines the temporal behavior of intra-molecular vibration-rotation energy transfer (IVRET) and the effects of IVRET on collision, reaction, and the decomposition processes. This paper also 12. Excited states of {sup 15}C Cappuzzello, F.; Orrigo, S.E.A.; Cunsolo, A.; Allia, M.C.; Lazzaro, A.; Nociforo, C.; Winfield, J.S. [Istituto Nazionale di Fisica Nucleare, Lab. Nazionali del Sud, Catania (Italy); Lazzaro, A. [Catania Univ., Dipt. Fisica (Italy); Lenske, H. [Giessen Univ. (Germany). Inst. fuer Theoretische Physik; Beaumel, D.; Fortier, S. [Institut de Physique Nucleaire, (IN2P3/CNRS) 91 - Orsay (France); Foti, A. [Istituto Nazionale di Fisica Nucleare, Catania (Italy) 2004-03-01 The N{sup 15}(Li{sup 7},Be{sup 7})C{sup 15} reaction at 55 MeV incident energy was studied at forward angles in order to explore the C{sup 15} excitation energy spectrum. The C{sup 15} ground state and the states at E{sub x} = 0.77, 6.77, 7.30, 8.50 MeV excitation energies were populated. The energy resolution ({approx} 250 keV) allowed the identification of these transitions each for Be{sup 7} ground and first-excited state at E{sub x} = 0.429 MeV. Quasi-particle random phase approximation (QRPA) calculations reproduce the C{sup 15} level structure below 1.5 MeV excitation energy. The strength observed at higher excitation energies probably arises from core-excited components of C{sup 15}. (authors) 13. Excited-state dynamics of astaxanthin aggregates Fuciman, M.; Durchan, Milan; Šlouf, V.; Kesan, G.; Polívka, Tomáš 2013-01-01 Roč. 568, č. 1 (2013), s. 21-25. ISSN 0009-2614 Institutional support: RVO:60077344 Keywords : astaxanthin * aggregates * excited states Subject RIV: BO - Biophysics Impact factor: 1.991, year: 2013 14. Excited state g factors in Te125 Chamoli, S. K.; Stuchbery, A. E.; East, M. C. 2009-11-01 The transient-field technique has been used to measure, with considerably improved precision, the g factors of the 3/2+ and 5/2+ states in Te125 at 444 and 463 keV, respectively, relative to the g factor of the first excited state in Te126. Together with shell model and weak-coupling core-excitation model calculations, the g-factor measurements provide insight into the orbital occupation of the odd neutron for the low-excitation states in Te125. A new 9/2+ level at 1029 keV, together with a firm 7/2+ spin assignment for the level at 1018 keV, identifies candidate states for the coupling of the s1/2 neutron to the 4+ core excitation. 15. Excited-state properties of hydrophilic carotenoids Fuciman, M.; Chábera, P.; Naqvi, K.R.; Melo, T.B.; Sliwka, H.R.; Partali, V.; Lockwood, S.; Jackson, H.L.; Polívka, Tomáš - : -, 2009. s. 408. ISBN N. [International Conference on Photochemistry /24./. 19.07.2009-24.07.2009, Toledo] Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoids * excited-state dynamics * femtosecond spectroscopy Subject RIV: BO - Biophysics 16. Excitation Halo States of 12B 林承键; 刘祖华; 张焕乔; 吴岳伟; 杨峰; 阮明 2001-01-01 Angular distributions for the 11 B(d,p)12 B transfer reactions have been measured at E1ab = 11.8 Me V. The asymp-totic normalization coefficients (ANC) of the ground state, the second and third excitation states for 12B ( 11 B+n) are extracted from the differential cross sections at three forward angles. With these ANCs, the root-mean-square radii are calculated for these three states. The results show that the second and third excitation states of 12B are neutron halo states. 17. Rearrangements in ground and excited states de Mayo, Paul 2013-01-01 Rearrangements in Ground and Excited States, Volume 3 presents essays on the chemical generation of excited states; the cis-trans isomerization of olefins; and the photochemical rearrangements in trienes. The book also includes essays on the zimmerman rearrangements; the photochemical rearrangements of enones; the photochemical rearrangements of conjugated cyclic dienones; and the rearrangements of the benzene ring. Essays on the photo rearrangements via biradicals of simple carbonyl compounds; the photochemical rearrangements involving three-membered rings or five-membered ring heterocycles; 18. Excited states of 129Xe Here investigation of the observed yrast and excited bands in 129Xe populated by the heavy-ion fusion reaction 124Sn(11B, p5n)129Xe has been presented. An isotopically enriched (99.9%) self-supporting 124Sn target of thickness 2.2 mg/cm2 was utilized. The experiment was performed at the Linac accelerator facility at the Tata Institute of Fundamental Research (TIFR), Mumbai, India. The experimental set-up, called the Indian National Gamma Array (INGA), consisted of 21 Compton suppressed clover HPGe detectors. Two of these detectors were placed at 23°, three at 40°, three at 65°, four at 90°, three at 140°, three at 115° and three at 157° with respect to the beam direction. The triple gamma coincidence data were collected in the event-by-event mode 19. Photoionization of excited molecular states using multiphoton excitation techniques Photoelectron spectra are reported for three photon resonant, four photon ionization of H2 via the B 1Σ/sub u/+, v = 7 (J = 2,4) and C 1π/sub u'/, v = 0-4 (J = 1) levels and of N2 via the o31π/sub u'/, v = 1,2, b 1π/sub u'/, v = 3-5, and c 1π/sub u'/, v = 0 levels. The results reflect both the spectroscopy and the dynamics of photoionization of excited molecular states and are discussed in terms of the selection rules for photoionization and the relative probabilities of photoionization from Rydberg and valence states. In some cases, in accordance with the Franck-Condon principle, the results demonstrate that resonant multiphoton ionization through Rydberg states may be a powerful technique for the production of electronic, vibrational, and rotational state selected ions. However, in other cases, systematic departures from Franck-Condon factors are observed, which reflect the more subtle dynamics of excited state photoionization. 23 references, 6 figures, 2 tables 20. Photoionization of excited molecular states using multiphoton excitation techniques Dehmer, Patricia M. [Argonne National Laboratory (ANL), Argonne, IL (United States); Pratt, Stephen T. [Argonne National Laboratory (ANL), Argonne, IL (United States); Dehmer, Joseph L. [Argonne National Laboratory (ANL), Argonne, IL (United States) 1984-01-01 Photoelectron spectra are reported for three photon resonant, four photon ionization of H₂ via the B ¹Σu⁺, v = 7 (J = 2,4) and C ¹Πu v = 0-4 (J = 1) levels and of N₂ via the o₃ ¹Πu, v = 1,2, b ¹Πu, v = 3-5, and c ¹Πu, v = 0 levels. The results reflect both the spectroscopy and the dynamics of photoionization of excited molecular states and are discussed in terms of the selection rules for photoionization and the relative probabilities of photoionization from Rydberg and valence states. In some cases, in accordance with the Franck-Condon principle, the results demonstrate that resonant multiphoton ionization through Rydberg states may be a powerful technique for the production of electronic, vibrational, and rotational state selected ions. However, in other cases, systematic departures from Franck-Condon factors are observed, which reflect the more subtle dynamics of excited state photoionization. 1. Electron excitation from ground state to first excited state: Bohmian mechanics method Yang, Song; Shuang, Zhao; Fu-Ming, Guo; Yu-Jun, Yang; Su-Yu, Li 2016-03-01 The excitation process of electrons from the ground state to the first excited state via the resonant laser pulse is investigated by the Bohmian mechanics method. It is found that the Bohmian particles far away from the nucleus are easier to be excited and are excited firstly, while the Bohmian particles in the ground state is subject to a strong quantum force at a certain moment, being excited to the first excited state instantaneously. A detailed analysis for one of the trajectories is made, and finally we present the space and energy distribution of 2000 Bohmian particles at several typical instants and analyze their dynamical process at these moments. Project supported by the Doctoral Research Start-up Funding of Northeast Dianli University, China (Grant No. BSJXM-201332), the National Natural Science Foundation of China (Grant Nos. 11547114, 11534004, 11474129, 11274141, 11447192, and 11304116), and the Graduate Innovation Fund of Jilin University, China (Grant No. 2015091). 2. Application of the coherent state formalism to multiply excited states A general expression is obtained for the matrix element of an m-body operator between coherent states constructed from multiple orthogonal coherent boson species. This allows the coherent state formalism to be applied to states possessing an arbitrarily large number of intrinsic excitation quanta. For illustration, the formalism is applied to the two-dimensional vibron model (U(3) model), to calculate the energies of all excited states in the large-N limit 3. Nodal Variational Principle for Excited States Zahariev, Federico; Levy, Mel 2016-01-01 It is proven that the exact excited-state wavefunction and energy may be obtained by minimizing the energy expectation value of a trial wave function that is constrained only to have the correct nodes of the state of interest. This excited-state nodal minimum principle has the advantage that it requires neither minimization with the con- straint of wavefunction orthogonality to all lower eigenstates nor the antisymmetry of the trial wavefunctions. It is also found that the minimization over the entire space can be partitioned into several in- terconnected minimizations within the individual nodal regions, and the exact excited-state energy may be obtained by a minimization in just one or several of these nodal regions. For the proofs of the the- orem, it is observed that the many-electron eigenfunction, restricted to a nodal region, is equivalent to a ground state wavefunction of one electron in a higher dimensional space; and an explicit excited-state energy variational expression is obtained by generalizing... 4. Computing Correct Truncated Excited State Wavefunctions Bacalis, N C; Zang, J; Karaoulanis, D 2016-01-01 We demonstrate that, if a truncated expansion of a wave function is small, then the standard excited states computational method, of optimizing one root of a secular equation, may lead to an incorrect wave function - despite the correct energy according to the theorem of Hylleraas, Undheim and McDonald - whereas our proposed method [J. Comput. Meth. Sci. Eng. 8, 277 (2008)] (independent of orthogonality to lower lying approximants) leads to correct reliable small truncated wave functions. The demonstration is done in He excited states, using truncated series expansions in Hylleraas coordinates, as well as standard configuration-interaction truncated expansions. 5. Impact of ground- and excited-state aromaticity on cyclopentadiene and silole excitation energies and excited-state polarities. Jorner, Kjell; Emanuelsson, Rikard; Dahlstrand, Christian; Tong, Hui; Denisova, Aleksandra V; Ottosson, Henrik 2014-07-21 A new qualitative model for estimating the properties of substituted cyclopentadienes and siloles in their lowest ππ* excited states is introduced and confirmed through quantum chemical calculations, and then applied to explain earlier reported experimental excitation energies. According to our model, which is based on excited-state aromaticity and antiaromaticity, siloles and cyclopentadienes are cross-hyperconjugated "aromatic chameleons" that adapt their electronic structures to conform to the various aromaticity rules in different electronic states (Hückel's rule in the π(2) electronic ground state (S0) and Baird's rule in the lowest ππ* excited singlet and triplet states (S1 and T1)). By using pen-and-paper arguments, one can explain polarity changes upon excitation of substituted cyclopentadienes and siloles, and one can tune their lowest excitation energies by combined considerations of ground- and excited-state aromaticity/antiaromaticity effects. Finally, the "aromatic chameleon" model can be extended to other monocyclic compound classes of potential use in organic electronics, thereby providing a unified view of the S0, T1, and S1 states of a range of different cyclic cross-π-conjugated and cross-hyperconjugated compound classes. PMID:25043523 6. Excited state properties of aryl carotenoids Fuciman, M.; Chábera, P.; Župčanová, Anita; Hříbek, P.; Arellano, J.B.; Vácha, František; Pšenčík, J.; Polívka, Tomáš 2010-01-01 Roč. 12, č. 13 (2010), s. 3112-3120. ISSN 1463-9076 R&D Projects: GA AV ČR IAA608170604 Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoids * excited-states * femtosecond spectroscopy Subject RIV: BO - Biophysics Impact factor: 3.454, year: 2010 7. Excited-state properties of hydrophilic carotenoids Chábera, P.; Naqvi, K.R.; Melo, T.B.; Sliwka, H.R.; Partali, V.; Lockwood, S.; Nodolski, G.; Polívka, Tomáš Nové Hrady : Academic and University Center, 2008. s. 40. [ESF Workshop on Novel Methods in Exploring Carotenoid Excited State Dynamics. 21.09.2008-25.09.2008, Nové Hrady] Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoids * biophysics Subject RIV: BO - Biophysics 8. Femtosecond spectroscopy of reacting excited states Thanks to recent advance of ultra short pulse lasers, we are now able to observe ultra fast phenomena taking place in a time scale as short as 10 fs. This time scale is the time scale of the nuclear motion of molecules, and the observation of coherent nuclear wavepacket motion is a central issue of femtosecond spectroscopy. One of the dreams of chemists is to see chemical reactions, i.e., the change of chemical bonds, in real time. In a sense, observation of the wavepacket motion of reacting molecules is realization of this dream. However, the significance of the coherent nuclear motion in chemical reactions is still unclear for polyatomic molecules where the reaction coordinate does not simply correspond to the change of a particular chemical bond. To discuss the relation between the initial coherent wavepacket motion and the reaction coordinate, we studied several fundamental photochemical reactions in solution, i.e., photoisomerization of cis-stilbene, photodissociation of diphenylcyclopropenone and excited-state intramolecular proton transfer of 10-hydorxybenzoquinoline, using two-color pump-probe spectroscopy with time resolution of 30-70 fs. The photoisomerization of cis-stilbene proceeds in the S1 state in a time scale of ∼1 ps. Time-resolved absorption of cis-stilbene in cyclohexane (pump 315 nm; probe 660 nm) clearly showed an oscillatory feature, which was attributed to the ∼220 cm-1 wavepacket motion in the S1 state. The dephasing time of the wavepacket motion was 0.21±0.04 ps, which was much shorter than the isomerization time of S1 cis-stilbene (1.25 ps). This indicates that a fast dephasing of the vibrational coherence takes place before isomerization. The result of the experiments on the solvent dependence demonstrated that the dephasing rate and isomerization rate do not correlate with each other, indicating that the observed wavepacket motion is not directly coupled with the isomerization coordinate. Photoexcitation to the S2 state of 9. Extension of LCAO to excited states Koval, Peter; Foerster, Dietrich 2009-01-01 We extend the LCAO (Linear Combination of Atomic Orbitals) method to excited states by constructing a particularly simple basis in the space of orbital products. The residual error of our procedure vanishes exponentially with the number of products and our procedure avoids auxiliary sets of fitting functions and their intrinsic ambiguities. As an application of our technique, we compute the Kohn--Sham density response function $\\chi_{0}$ for a molecule consisting of $N$ atoms in $O(N^{2}N_{\\o... 10. Rearrangements in ground and excited states de Mayo, Paul 2013-01-01 Rearrangements in Ground and Excited States, Volume 2 covers essays on the theoretical approach of rearrangements; the rearrangements involving boron; and the molecular rearrangements of organosilicon compounds. The book also includes essays on the polytopal rearrangement at phosphorus; the rearrangement in coordination complexes; and the reversible thermal intramolecular rearrangements of metal carbonyls. Chemists and people involved in the study of rearrangements will find the book invaluable. 11. Excited States in Solution through Polarizable Embedding Olsen, Jógvan Magnus; Aidas, Kestutis; Kongsted, Jacob 2010-01-01 We present theory and implementation of an advanced quantum mechanics/molecular mechanics (QM/MM) approach using a fully self-consistent polarizable embedding (PE) scheme. It is a polarizable layered model designed for effective yet accurate inclusion of an anisotropic medium in a quantum mechani......, nanoparticles and solute−solvent systems. Here, we present numerical examples of solvent shifts and excited-state properties related to a set of organic molecules in aqueous solution.... 12. Identification of excited states in conjugated polymers Hartwell, L J 2003-01-01 This thesis reports quasi steady state photoinduced absorption measurements from three conjugated polymers: polypyridine (PPy), polyfluorene (PFO) and the emeraldine base (EB) form of polyaniline. The aim of these experiments was to determine the nature of the photoexcited states existing in these materials in the millisecond time domain, as this has important consequences for the operation of real devices manufactured using these materials. The results from the photoinduced absorption experiments are closely compared with published results from pulse radiolysis experiments. In all cases there is very good correspondence between the two data sets, which has enabled the photoexcited states to be assigned with a high degree of confidence. Quasi steady-state photoinduced absorption involves the measurement of the change in absorption of a material in response to optical excitation with a laser beam. The changes in absorption are small, so a instrument was developed and optimised for each different sample. Lock-i... 13. Holographic Construction of Excited CFT States Christodoulou, Ariana 2016-01-01 We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensional CFTs, either on$R \\times S^1$or on$R^{1,1}$. We compute the 1-point function both in the CFT and in the bulk, finding exact agreement. We comment on the relation with other reconstruction approaches. 14. Ultrafast excited-state dynamics of isocytosine. Szabla, Rafał; Góra, Robert W; Šponer, Jiří 2016-07-27 The alternative nucleobase isocytosine has long been considered as a plausible component of hypothetical primordial informational polymers. To examine this hypothesis we investigated the excited-state dynamics of the two most abundant forms of isocytosine in the gas phase (keto and enol). Our surface-hopping nonadiabatic molecular dynamics simulations employing the algebraic diagrammatic construction to the second order [ADC(2)] method for the electronic structure calculations suggest that both tautomers undergo efficient radiationless deactivation to the electronic ground state with time constants which amount to τketo = 182 fs and τenol = 533 fs. The dominant photorelaxation pathways correspond to ring-puckering (ππ* surface) and C[double bond, length as m-dash]O stretching/N-H tilting (nπ* surface) for the enol and keto forms respectively. Based on these findings, we infer that isocytosine is a relatively photostable compound in the gas phase and in these terms resembles biologically relevant nucleobases. The estimated S1 [radiolysis arrow - arrow with voltage kink] T1 intersystem crossing rate constant of 8.02 × 10(10) s(-1) suggests that triplet states might also play an important role in the overall excited-state dynamics of the keto tautomer. The reliability of ADC(2)-based surface-hopping molecular dynamics simulations was tested against multireference quantum-chemical calculations and the potential limitations of the employed ADC(2) approach are briefly discussed. PMID:27346684 15. Dynamic hyperpolarizabilities of excited states of hydrogen On the basis of the generalized Sturm expansion of the radial part of the Coulomb Green function, a computational method is proposed and numerical results are presented for the dynamic hyperpolarizability γ and the corrections E(4) (quadratic in the light intensity) to the quasi-energy of the ground and excited states of hydrogen with principal quantum numbers n ≤ 5 in a monochromatic light field. In this approach, the problem is reduced to the summation of well-convergent double series of the hypergeometric kind, which ensures reliable numerical results both for states with a large n, and in a wide range of field frequencies ω, including the above-threshold frequency range of (ℎ/2π)ω >> vertical bar En vertical bar (vertical bar En vertical bar is the ionization potential of the state \|nlm> under investigation). We consider the frequency dependence of γ and E(4), their differences for the cases of linear and circular polarizations of the field, and the relation between their real and imaginary parts, which determine the laser field-induced corrections to the position and width of energy levels. For n = 5, the significant role of mixing the vertical bar nlm> states with different values of l by a laser field in the region of resonances on intermediate bound states is demonstrated. The linear (in intensity) corrections to the photoionization cross section for excited states are analyzed and the threshold intensity corresponding to the onset of atomic level stabilization is estimated for a number of states with n = 3 and n = 5 16. Excited state dynamics of DNA bases Kleinermanns, K.; Nachtigallová, Dana; de Vries, M. S. 2013-01-01 Roč. 32, č. 2 (2013), s. 308-342. ISSN 0144-235X R&D Projects: GA ČR GAP208/12/1318 Grant ostatní: National Science Foundation(US) CHE-0911564; NASA(US) NNX12AG77G; Deutsche Forschungsgemeinschaft(DE) SFB 663; Deutsche Forschungsgemeinschaft(DE) KI 531-29 Institutional support: RVO:61388963 Keywords : DNA bases * nucleobases * excited state * dynamics * computations * gas phase * conical intersections Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 4.920, year: 2013 17. Excited states of muonium in atomic hydrogen V S Kulhar 2006-06-01 Muonium formation in excited states in muon-hydrogen charge-exchange collision is investigated using a method developed in a previous paper. Differential cross-section results are found to resemble positronium formation cross-section results of positron-hydrogen charge-exchange problem. Forward differential and integrated cross-sections are computed for muon energy of 2 keV and higher. Total muonium formation cross-sections are computed using Jackson and Schiff scaling rules. Muonium formation cross-section results obtained from proton-hydrogen charge-exchange cross-section results, using velocity scaling are compared with the results of the present calculation. 18. Excited state halos in 10Be The structure of certain bound excited states in 10Be have been shown to have exotic features because of their weak binding and cluster-like configurations. In this article, we investigate E1 and E2 transitions between these states and compare the findings with recent experimental results. We compare the predictions of two types of structure calculations: a microscopic multicluster model and an ab initio no-core shell model. Both predict very similar transition strengths. By considering the relative contributions from the various matrix elements contributing to the transitions arising from the coupling of different 9Bexn configurations in the wave functions making up the states, we conclude that the very weak B(E1;2-→21+) can only be understood if the 2- state (with a separation energy of its predominantly 1s1/2 neutron of just 0.548 MeV) is a clear halo state. Other nearby states, such as the 22+, do not exhibit a clear halo signature because of the less than clean decoupling into the well-defined 9Be core plus halo neutron 19. Excited-state relaxation of some aminoquinolines B. M. Uzhinov 2006-04-01 Full Text Available The absorption and fluorescence spectra, fluorescence quantum yields and lifetimes, and fluorescence rate constants (kf of 2-amino-3-(2Ã¢Â€Â²-benzoxazolylquinoline (I, 2-amino-3-(2Ã¢Â€Â²-benzothiazolylquinoline (II, 2-amino-3-(2Ã¢Â€Â²-methoxybenzothiazolyl-quinoline (III, 2-amino-3-(2Ã¢Â€Â²-benzothiazolylbenzoquinoline (IV at different temperatures have been measured. The shortwavelength shift of fluorescence spectra of compounds studied (23Ã¢Â€Â“49 nm in ethanol as the temperature decreases (the solvent viscosity increases points out that the excited-state relaxation process takes place. The rate of this process depends essentially on the solvent viscosity, but not the solvent polarity. The essential increasing of fluorescence rate constant kf (up to about 7 times as the solvent viscosity increases proves the existence of excited-state structural relaxation consisting in the mutual internal rotation of molecular fragments of aminoquinolines studied, followed by the solvent orientational relaxation. 20. Lifetimes of excited states in 164Hf Lifetimes of excited states in 164Hf were measured using the Doppler-shift recoil-distance method. Gamma-gamma coincidences at eleven target-stopper distances were measured using the twelve Compton-suppressed Ge-detectors of the OSIRIS spectrometer. From the coincidence spectra the intensities of the Doppler-shifted and unshifted γ-lines were determined. The quadrupole moments Qt of transitions within the rotational bands derived from the lifetimes are constant within the experimental uncertainties up to the 18+ state. The Qt value for the transition between the ground- and the neutron i213/2 band (s-band) which is strongly reduced compared to the values of the in-band transitions is used to deduce a band interaction energy of 34 keV≤V≤57 keV. (orig.) 1. Lifetimes of 167Yb excited states Lifetimes of 167Yb excited states arising at the decay of 167Lu → 167Yb monoisotope have been determined using eγ and γγ delayed coincidence methods. The time spectrometers mounted on the base of a magnetic lens β-spectrometer and a scintillation detector, a scintillation and a Ge(Li) detectors, a scintillation and Si(Li)-detectors are used. 167Yb level fifetimes are measured with energies of 29 keV (Tsub(1/2)=13.5(7) ns), 78 keV (Tsub(1/2=0.84(4) ns), 178 keV (Tsub(1/2)167Yb investigated levels are analysed. On the basis of intrarotational transitions internal quadrupole momenta of 5/2-/523/, 3/2-/512/ and 1/2-/521/ bands have been determined 2. Excited state quantum phase transitions in many-body systems Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions 3. Representation of electronic excited states by conditional wavefunction Koichiro, Yamaguchi; Yoshiaki, Ito; Takeshi, Mukoyama 2000-03-01 Hartree-Fock scheme is an ordinary method to calculate the zeroth order approximation for non-relativistic electronic excited states of atoms and molecules. The accuracy of zeroth order hamiltonian affects the efficiency of higher order estimation of the Hamiltonian and the Green's function. To improve the preciseness of zeroth order Hamiltonian, we try to include the relaxation of electronic excited states into zeroth order approximation by using conditional wavefunction representation instead of Hartree-Fock method. Our method is illustrated by the calculation of electronic double-excited states of Helium and single-excited states of Neon. Further extention of our formulation for multiple-exfcited states are also discussed. 4. Computing electronic structures: A new multiconfiguration approach for excited states We present a new method for the computation of electronic excited states of molecular systems. This method is based upon a recent theoretical definition of multiconfiguration excited states [due to one of us, see M. Lewin, Solutions of the multiconfiguration equations in quantum chemistry, Arch. Rat. Mech. Anal. 171 (2004) 83-114]. Our algorithm, dedicated to the computation of the first excited state, always converges to a stationary state of the multiconfiguration model, which can be interpreted as an approximate excited state of the molecule. The definition of this approximate excited state is variational. An interesting feature is that it satisfies a non-linear Hylleraas-Undheim-MacDonald type principle: the energy of the approximate excited state is an upper bound to the true excited state energy of the N-body Hamiltonian. To compute the first excited state, one has to deform paths on a manifold, like this is usually done in the search for transition states between reactants and products on potential energy surfaces. We propose here a general method for the deformation of paths which could also be useful in other settings. We also compare our method to other approaches used in Quantum Chemistry and give some explanation of the unsatisfactory behaviours which are sometimes observed when using the latter. Numerical results for the special case of two-electron systems are provided: we compute the first singlet excited state potential energy surface of the H 2 molecule 5. Excited states in DNA strands investigated by ultrafast laser spectroscopy. Chen, Jinquan; Zhang, Yuyuan; Kohler, Bern 2015-01-01 Ultrafast laser experiments on carefully selected DNA model compounds probe the effects of base stacking, base pairing, and structural disorder on excited electronic states formed by UV absorption in single and double DNA strands. Direct π-orbital overlap between two stacked bases in a dinucleotide or in a longer single strand creates new excited states that decay orders of magnitude more slowly than the generally subpicosecond excited states of monomeric bases. Half or more of all excited states in single strands decay in this manner. Ultrafast mid-IR transient absorption experiments reveal that the long-lived excited states in a number of model compounds are charge transfer states formed by interbase electron transfer, which subsequently decay by charge recombination. The lifetimes of the charge transfer states are surprisingly independent of how the stacked bases are oriented, but disruption of π-stacking, either by elevating temperature or by adding a denaturing co-solvent, completely eliminates this decay channel. Time-resolved emission measurements support the conclusion that these states are populated very rapidly from initial excitons. These experiments also reveal the existence of populations of emissive excited states that decay on the nanosecond time scale. The quantum yield of these states is very small for UVB/UVC excitation, but increases at UVA wavelengths. In double strands, hydrogen bonding between bases perturbs, but does not quench, the long-lived excited states. Kinetic isotope effects on the excited-state dynamics suggest that intrastrand electron transfer may couple to interstrand proton transfer. By revealing how structure and non-covalent interactions affect excited-state dynamics, on-going experimental and theoretical studies of excited states in DNA strands can advance understanding of fundamental photophysics in other nanoscale systems. PMID:25326834 6. Initial state dependence of convoy electrons emitted from the excited ions by resonant coherent excitation Azuma, T.; Nakano, Y.; Metoki, K.; Hatakeyama, A.; Nakai, Y.; Komaki, K.; Yamazaki, Y.; Takada, E.; Murakami, T. 2009-11-01 Convoy electrons emitted from 416 MeV/u heliumlike Ar16+ ions excited by three-dimensional resonant coherent excitation (3D-RCE) have been explored. The 1s electron in the ground state was excited to the 2p state by a periodic crystal field during the passage through a Si crystal and released into the continuum by collisions with target atoms to form a cusp-shaped peak in the energy distribution, referred to as convoy electron. Under the resonance condition, we found not only enhancement of the convoy electron yield but also significant narrowing in the energy distribution, reflecting the initial bound state momentum distribution of the excited ions. This suggests that RCE is well-suited to study fast ion collisions involving the specific excited state. 7. Exact ensemble density-functional theory for excited states Yang, Zeng-hui; Pribram-Jones, Aurora; Burke, Kieron; Needs, Richard J; Ullrich, Carsten A 2014-01-01 We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) of excited states from the ground and excited states of helium. The exchange-correlation potential is compared with current approximations, which miss prominent features. The ensemble derivative discontinuity is tested, and the virial theorem is proven and illustrated. 8. Charge-displacement analysis for excited states Ronca, Enrico, E-mail: [email protected]; Tarantelli, Francesco, E-mail: [email protected] [Istituto CNR di Scienze e Tecnologie Molecolari, via Elce di Sotto 8, I-06123 Perugia (Italy); Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, via Elce di Sotto 8, I-06123 Perugia (Italy); Pastore, Mariachiara, E-mail: [email protected]; Belpassi, Leonardo; De Angelis, Filippo [Istituto CNR di Scienze e Tecnologie Molecolari, via Elce di Sotto 8, I-06123 Perugia (Italy); Angeli, Celestino; Cimiraglia, Renzo [Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Ferrara, via Borsari 46, I-44100 Ferrara (Italy) 2014-02-07 We extend the Charge-Displacement (CD) analysis, already successfully employed to describe the nature of intermolecular interactions [L. Belpassi et al., J. Am. Chem. Soc. 132, 13046 (2010)] and various types of controversial chemical bonds [L. Belpassi et al., J. Am. Chem. Soc. 130, 1048 (2008); N. Salvi et al., Chem. Eur. J. 16, 7231 (2010)], to study the charge fluxes accompanying electron excitations, and in particular the all-important charge-transfer (CT) phenomena. We demonstrate the usefulness of the new approach through applications to exemplary excitations in a series of molecules, encompassing various typical situations from valence, to Rydberg, to CT excitations. The CD functions defined along various spatial directions provide a detailed and insightful quantitative picture of the electron displacements taking place. 9. Bogoliubov Excited States and the Lyth Bound Aravind, Aditya; Paban, Sonia 2014-01-01 We show that Bogoliubov excited scalar and tensor modes do not alleviate Planckian evolution during inflation if one assumes that$r$and the Bogoliubov coefficients are approximately scale invariant. We constrain the excitation parameter for the scalar fluctuations,$\\beta$, and tensor perturbations,$\\tilde{\\beta}$, by requiring that there be at least three decades of scale invariance in the scalar and tensor power spectrum. For the scalar fluctuations this is motivated by the observed nearly scale invariant scalar power spectrum. For the tensor fluctuations this assumption may be shown to be valid or invalid by future experiments. 10. Inelastic scattering of 9Li and excitation mechanism of its first excited state The first measurement of inelastic scattering of 9Li from deuterons at the ISAC facility is reported. The measured angular distribution for the first excited state confirms the nature of excitation to be an E2 transition. The quadrupole deformation parameter is extracted from an analysis of the angular distribution 11. Density functional theory generalized to degenerate excited states In this paper it is shown that the density functional theory can be generalized to systems with degenerate excited states. There is a one-to-one map between the subspace, spanned by the ground state and any one of the first degenerate excited states, and the sum of their densities. But only a one way correspondence exists between external potential and subspace, as well as between external potential and the sum of densities. The extension of the Hohenberg-Kohn-Sham theory for degenerate excited states has also been developed. (author) 12. Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme Theophilou, Iris; Thanos, S 2014-01-01 Photoinduced charge transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for accurate and computationally inexpensive treatment of charge transfer excitations is a topic that attracts nowadays a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations (M. Tassi, I. Theophilou and S. Thanos, Int. J. Quantum Chem., {113}, 690 (2013), M. Tassi, I. Theophilou and S. Thanos, J. Chem. Phys. {138}, 124107 (2013)) to allow for the description of intermolecular charge transfer excitations. For the description of an excitation where an electron is transferred from a donor system to an acceptor one, it is necessary to keep the excited state orthogonal to the ground sate in order to avoid variational collapse. These conditions are achieved by decomposing the subspace spanned by the Hartree-Fock (HF) ground state orbitals to four subspaces: The subspace spanned ... 13. 18Ne Excited States Two-Proton Decay de Napoli, M.; Rapisarda, E.; Raciti, G.; Cardella, G.; Amorini, F.; Giacoppo, F.; Sfienti, C. 2008-04-01 Two-proton radioactivity studies have been performed on excited states of 18Ne produced by 20Ne fragmentation at the FRS of the Laboratori Nazionali del Sud and excited via Coulomb excitation on a 209Pb target. The 18Ne levels decay has been studied by complete kinematical reconstruction. In spite of the low statistic, the energy and angular correlations of the emitted proton pairs indicate the presence of 2He emission toghether with the democratic decay. 14. Photoionization of excited states of neon-like Mg III Narendra Singh; Man Mohan 2002-04-01 The close coupling -matrix method is used to calculate cross-sections for photoionization of Mg III from its ﬁrst three excited states. Conﬁguration interaction wave functions are used to represent two target states of Mg III retained in the -matrix expansion. The positions and effective quantum numbers for the Rydberg series converging to the excited state 2226 \\ 2 of the residual ion, are predicted. 15. Quantum entanglement of localized excited states at finite temperature Caputa, Pawel; Simón, Joan; Štikonas, Andrius(School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King’s Buildings, Edinburgh, EH9 3FD, U.K.); Takayanagi, Tadashi 2015-01-01 In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature.We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional ... 16. Energy levels of Sm2+ excited state The energy levels of excited configurations 4f5u'l' of Sm2+ calculated in detail by using unitary group approach are covered. The energy expressions with slater integral as parameters are given and the spin-orbit coupling is considered according to the Russell-Saunders approximation. The coupling parameters λ of the main energy levels are also calculated in the paper 17. Excited state systematics in extracting nucleon electromagnetic form factors Capitani, Stefano; von Hippel, Georg; Jäger, Benjamin; Knippschild, Bastian; Meyer, Harvey B; Rae, Thomas D; Wittig, Hartmut 2012-01-01 We present updated preliminary results for the nucleon electromagnetic form factors for non-perturbatively$\\mathcal{O}(a)$improved Wilson fermions in$N_f=2$QCD measured on the CLS ensembles. The use of the summed operator insertion method allows us to suppress the influence of excited states in our measurements. A study of the effect that excited state contaminations have on the$Q^2$dependence of the extracted nucleon form factors may then be made through comparisons of the summation method to standard plateau fits, as well as to excited state fits. 18. Coherent excitation of a single atom to a Rydberg state Miroshnychenko, Yevhen; Gaëtan, Alpha; Evellin, Charles; 2010-01-01 We present the coherent excitation of a single Rubidium atom to the Rydberg state 58d3/2 using a two-photon transition. The experimental setup is described in detail, as are experimental techniques and procedures. The coherence of the excitation is revealed by observing Rabi oscillations between... 19. Anisotropy of electronic states excited in ion-atom collisions The author reports coincidence measurements made on the He+ + Ne and He+ + He systems. The complex population amplitudes for the magnetic sublevels of the investigated excited states, Ne(2p43s2)1D and He(2p2)1D, were completely determined and possible excitation mechanisms are described. (Auth.) 20. Superposition of Fragment Excitations for Excited States of Large Clusters with Application to Helium Clusters. Closser, Kristina D; Ge, Qinghui; Mao, Yuezhi; Shao, Yihan; Head-Gordon, Martin 2015-12-01 We develop a local excited-state method, based on the configuration interaction singles (CIS) wave function, for large atomic and molecular clusters. This method exploits the properties of absolutely localized molecular orbitals (ALMOs), which strictly limits the total number of excitations, and results in formal scaling with the third power of the system size for computing the full spectrum of ALMO-CIS excited states. The derivation of the equations and design of the algorithm are discussed in detail, with particular emphasis on the computational scaling. Clusters containing ∼500 atoms were used in evaluating the scaling, which agrees with the theoretical predictions, and the accuracy of the method is evaluated with respect to standard CIS. A pioneering application to the size dependence of the helium cluster spectrum is also presented for clusters of 25-231 atoms, the largest of which results in the computation of 2310 excited states per sampled cluster geometry. PMID:26609558 1. Vibronic coupling in the excited-states of carotenoids. Miki, Takeshi; Buckup, Tiago; Krause, Marie S; Southall, June; Cogdell, Richard J; Motzkus, Marcus 2016-04-20 The ultrafast femtochemistry of carotenoids is governed by the interaction between electronic excited states, which has been explained by the relaxation dynamics within a few hundred femtoseconds from the lowest optically allowed excited state S2 to the optically dark state S1. Extending this picture, some additional dark states (3A and 1B) and their interaction with the S2 state have also been suggested to play a major role in the ultrafast deactivation of carotenoids and their properties. Here, we investigate the interaction between such dark and bright electronic excited states of open chain carotenoids, particularly its dependence on the number of conjugated double bonds (N). We focus on the ultrafast wave packet motion on the excited potential surface, which is modified by the interaction between bright and dark electronic states. Such a coupling between electronic states leads to a shift of the vibrational frequency during the excited-state evolution. In this regard, pump-degenerate four-wave mixing (pump-DFWM) is applied to a series of carotenoids with different numbers of conjugated double bonds N = 9, 10, 11 and 13 (neurosporene, spheroidene, lycopene and spirilloxanthin, respectively). Moreover, we demonstrate in a closed-chain carotenoid (lutein) that the coupling strength and therefore the vibrational shift can be tailored by changing the energy degeneracy between the 1B and 1B states via solvent interaction. PMID:27055720 2. Quantification of Entanglement Entropies for Doubly Excited States in Helium In this work, we study the quantum entanglement for doubly excited resonance states in helium by using highly correlated Hylleraas type functions to represent such states of the two-electron system. The doubly-excited resonance states are determined by calculation of density of resonance states under the framework of the stabilization method. The spatial (electron–electron orbital) entanglement measures for the low-lying doubly excited 2s2, 2s3s, and 2p21 Se states are carried out. Once a resonance state wave function is obtained, the linear entropy and von Neumann entropy for such a state are quantified using the Schmidt-Slater decomposition method. To check the consistence, linear entropy is also determined by solving analytically the needed four-electron (12-dimensional) integrals. (author) 3. Ultrafast Excited-State Dynamics in Biological Environments Fürstenberg, Alexandre; Vauthey, Eric 2007-01-01 We discuss and illustrate by several examples how the ultrafast excited-state dynamics of a chromophore can be altered when changing its environment from a homogenous solution to a biological molecule such as proteins or nucleic acids. 4. Optimal control of peridinin excited-state dynamics Chábera, P.; Dietzek, B.; Yartsev, A.; Polívka, Tomáš Nové Hrady: Academic and University Center, 2008. s. 15. [ESF Workshop on Novel Methods in Exploring Carotenoid Excited State Dynamics. 21.09.2008-25.09.2008, Nové Hrady] Keywords : peridinin * biophysics Subject RIV: BO - Biophysics 5. Boson analysis of the excited O+ state in Ge isotopes Motivated by attemp to explain the strong variation in energy of the excited O+ state in even Ge isotopes in terms of a simple collective configuration, a boson mapping is introduced for proton, neutron and proton-neutron pairing 6. The examination of berberine excited state by laser flash photolysis Cheng, Lingli; Wang, Mei; Zhao, Ping; Zhu, Hui; Zhu, Rongrong; Sun, Xiaoyu; Yao, Side; Wang, Shilong 2009-07-01 The property of the excited triplet state of berberine (BBR) was investigated by using time-resolved laser flash photolysis of 355 nm in acetonitrile. The transient absorption spectra of the excited triplet BBR were obtained in acetonitrile, which have an absorption maximum at 420 nm. And the ratio of excitation to ionization of BBR in acetonitrile solvent was calculated. The self-decay and self-quenching rate constants, and the absorption coefficient of 3BBR* were investigated and the excited state quantum yield was determined. Furthermore utilizing the benzophenone (BEN) as a triplet sensitizer, and the β-carotene (Car) as an excited energy transfer acceptor, the assignment of 3BBR* was further confirmed and the related energy transfer rate constants were also determined. 7. Controlling Chimera States - The influence of excitable units Isele, Thomas; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp 2015-01-01 We explore the influence of a block of excitable units on the existence and behavior of chimera states in a nonlocally coupled ring-network of FitzHugh-Nagumo elements. The FitzHugh-Nagumo system, a paradigmatic model in many fields from neuroscience to chemical pattern formation and nonlinear electronics, exhibits oscillatory or excitable behavior depending on the values of its parameters. Until now, chimera states have been studied in networks of coupled oscillatory FitzHugh-Nagumo elements... 8. Investigation into chromophore excited-state coupling in allophycocyanin Zheng, Xiguang; Zhao, Fuli; Wang, He Z.; Gao, Zhaolan; Yu, Zhenxin; Zhu, Jinchang; Xia, Andong; Jiang, Lijin 1994-08-01 Both theoretical and experimental studies are presented on chromophore excited-state coupling in linker-free allophycocyanin (APC), one of the antenna phycobiliproteins in algal photosynthesis. A three-site-coupling model has been introduced to describe the exciton interaction mechanism amoung the excited (beta) chromophore in APC, and the exciton energy splitting is estimated. Picosecond polarized fluorescence experiments both on monomeric and trimeric APC isolated from alga Spirulina platensis have been performed. The experimental results show that APC monomer and trimer exhibit remarkedly different spectropic characteristics, and satisfy the suggestion of strong excited- state coupling among chromophores in APC. 9. Photoacoustic imaging of the excited state lifetime of fluorophores Märk, Julia; Schmitt, Franz-Josef; Laufer, Jan 2016-05-01 Photoacoustic (PA) imaging using pump-probe excitation has been shown to allow the detection and visualization of fluorescent contrast agents. The technique relies upon inducing stimulated emission using pump and probe pulses at excitation wavelengths that correspond to the absorption and fluorescence spectra. By changing the time delay between the pulses, the excited state lifetime of the fluorophore is modulated to vary the amount of thermalized energy, and hence PA signal amplitude, to provide fluorophore-specific PA contrast. In this study, this approach was extended to the detection of differences in the excited state lifetime of fluorophores. PA waveforms were measured in solutions of a near-infrared fluorophore using simultaneous and time-delayed pump-probe excitation. The lifetime of the fluorophore solutions was varied by using different solvents and quencher concentrations. By calculating difference signals and by plotting their amplitude as a function of pump-probe time delay, a correlation with the excited state lifetime of the fluorophore was observed. The results agreed with the output of a forward model of the PA signal generation in fluorophores. The application of this method to tomographic PA imaging of differences in the excited state lifetime was demonstrated in tissue phantom experiments. 10. Metastable states of highly excited heavy ions Pegg, D. J.; Griffin, P. M.; Sellin, I. A.; Smith, W. W.; Donnally, B. 1973-01-01 Description of the method used and results obtained in an experimental study of the metastable states of highly stripped heavy ions, aimed at determining the lifetimes of such states by the rates of autoionization and radiation. The significance and limitations of the results presented are discussed. 11. Excited-state Halo of 14C 2002-01-01 Neutron capture processes on carbon isotope play an important role in astrophysics ranging fromnucleosynthesis in the stellar helium and carbon burning stages to possibly inhomogeneous big bangmodels. The capture rate in astrophysical environments strongly depends on the structure of these carbonnuclei. For example, the first 1/2+ state in 13C is a neutron halo state, and these results in an enormous 12. Microwave spectroscopy of furfural in vibrationally excited states Motiyenko, R. A.; Alekseev, E. A.; Dyubko, S. F. 2007-07-01 The results of microwave spectrum investigation of the excited vibrational states of furfural in the frequency range between 49 and 149 GHz are reported. In total 15 excited vibrational states (9 for trans-furfural and 6 for cis-furfural) were assigned and analyzed. Six of the 15 investigated states were assigned for the first time. Accurate values of rigid rotor and quartic centrifugal distortion constants of asymmetric top Hamiltonian have been determined for 13 excited states. Also for some states several sextic and octic level constants were needed in order to fit the data within experimental accuracy. The vt = 3 and vs = 1, va = 1 states of trans-furfural were found to be strongly perturbed and only rotational transitions with low Ka values can be reliably identified in this study. 13. Neutral Excitations in the Gaffnian state Kang, Byungmin; Moore, Joel E. The Fractional Quantum Hall Effect (FQHE) is one of the most well-studied systems having topological order. Starting with the pioneering work by Laughlin, the model wave function approach has been shown to provide essential information for understanding topological order in gapped incompressible states. We study a model wave function called the Gaffnian state which is believed to represent a gapless, strongly correlated state that is very different from conventional metals. To understand this exotic gapless state better, we provide a representation in which the pairing structure of the Gaffnian state becomes more explicit. We employ the single-mode approximation of the Girvin-MacDonald-Platzman (GMP) mode, which is a neutral collective exitation mode, in order to have a physical picture of the gaplessness of the Gaffnian state. In particular, we discuss how to extract systematically the relevant physics in the long-distance, large electron number limit of the FQH states using a numerical calculation with relatively few electrons. 14. The excited state antiaromatic benzene ring: a molecular Mr Hyde? Papadakis, Raffaello; Ottosson, Henrik 2015-09-21 The antiaromatic character of benzene in its first ππ* excited triplet state (T1) was deduced more than four decades ago by Baird using perturbation molecular orbital (PMO) theory [J. Am. Chem. Soc. 1972, 94, 4941], and since then it has been confirmed through a range of high-level quantum chemical calculations. With focus on benzene we now first review theoretical and computational studies that examine and confirm Baird's rule on reversal in the electron count for aromaticity and antiaromaticity of annulenes in their lowest triplet states as compared to Hückel's rule for the ground state (S0). We also note that the rule according to quantum chemical calculations can be extended to the lowest singlet excited state (S1) of benzene. Importantly, Baird, as well as Aihara [Bull. Chem. Soc. Jpn. 1978, 51, 1788], early put forth that the destabilization and excited state antiaromaticity of the benzene ring should be reflected in its photochemical reactivity, yet, today these conclusions are often overlooked. Thus, in the second part of the article we review photochemical reactions of a series of benzene derivatives that to various extents should stem from the excited state antiaromatic character of the benzene ring. We argue that benzene can be viewed as a molecular "Dr Jekyll and Mr Hyde" with its largely unknown excited state antiaromaticity representing its "Mr Hyde" character. The recognition of the "Jekyll and Hyde" split personality feature of the benzene ring can likely be useful in a range of different areas. PMID:25960203 15. Controlling chimera states: The influence of excitable units Isele, Thomas; Hizanidis, Johanne; Provata, Astero; Hövel, Philipp 2016-02-01 We explore the influence of a block of excitable units on the existence and behavior of chimera states in a nonlocally coupled ring-network of FitzHugh-Nagumo elements. The FitzHugh-Nagumo system, a paradigmatic model in many fields from neuroscience to chemical pattern formation and nonlinear electronics, exhibits oscillatory or excitable behavior depending on the values of its parameters. Until now, chimera states have been studied in networks of coupled oscillatory FitzHugh-Nagumo elements. In the present work, we find that introducing a block of excitable units into the network may lead to several interesting effects. It allows for controlling the position of a chimera state as well as for generating a chimera state directly from the synchronous state. 16. Shape vibration and quasiparticle excitations in the lowest 0+ excited state in erbium isotopes Chen, Fang-Qi; Egido, J. Luis 2016-06-01 The ground and first excited 0+ states of the -172Er156 isotopes are analyzed in the framework of the generator coordinate method. The shape parameter β is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E 2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0+ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between, both degrees of freedom are necessary. 17. Shape vibrations and quasiparticle excitations in the lowest 0+ excited state of the Erbium isotopes Chen, Fang-Qi 2016-01-01 The ground and first excited 0+ states of the {156-172}Er isotopes are analyzed in the framework of the generator coordinate method. The shape parameter beta is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0+ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between both degrees of freedom are necessary . 18. Cluster structure in highly-excited states of light nuclei The cluster structure in the highly-excited states of light nuclei are investigated using the multi-cluster model. For this purpose, we propose a developed treatment method of the multi-cluster model. The method consists of two parts: One is a systematic construction method of the multi-cluster Pauli-allowed states. Another is a truncation method of the large model space of the multi-cluster system. We show that we can easily solve the equation of the orthogonality condition model (OCM) for complex multi-cluster systems by the use of the method. We apply the multi-cluster models 3α, 4α, 12C + 2α and 16O + 2α to 12C, 16O, 20Ne and 24Mg, respectively. As shown in the Ikeda diagram, these models open a very interesting problem not only of the cluster structure in the highly-excited states of those nuclei but also of the structure change between different cluster structures. We show a typical example of the 16O + 2α model for 24Mg ; 1) many excited states with the 20Ne-α cluster structure are obtained at excitation energies above 10 MeV, 2) the 16O-8Be cluster states are obtained at the energy region higher than 20 MeV, and 3) the very interesting states with the α-16O-α linear-chain-like structure are predicted at about 20 MeV excitation energy. (author) 19. Doubly excited 3P(e) resonant states in Ps(-) Ho, Y. K.; Bhatia, A. K. 1992-01-01 Doubly excited 3P(e) resonant states in Ps(-) are calculated using a method of complex-coordinate rotation. Resonance parameters (both resonance positions and widths) for doubly excited states associated with the n = 2, 3, 4, 5, and 6 thresholds of positronium atoms are evaluated using elaborate Hylleraas-type functions. In addition to ten Feshbach-type resonances lying below various Ps thresholds, three shape resonances were identified, one each lying above the n = 2, 4, and 6 Ps thresholds. It is further noted that the energy levels for the present 3P(e) states are nearly degenerate with respect to the previously calculated 1P(0) states. Such a symmetric character suggests that the highly and doubly excited Ps(-), similar to its counterpart in H(-), would exhibit rovibrational behaviors analogous to those of XYX triatomic molecules. 20. Neutron halos in the excited states for N=127 isotones SUN Qin; GUO Jian-You 2009-01-01 Properties of the ground states and the excited states of N=127 isotones are investigated by using the nonlinear relativistic mean field theory with the interactions PK1. By analyzing the rms of proton and neutron, the single particle energies of valence nucleon and the density distributions of neutron, proton and the last neutron, it can be found that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 209Pb. It is also predicted that there exists a neutron halo in the excited states of 3d5/2, 4s1/2 and 3d3/2 in 207Hg, 208Tl, 210Bi and 211Po. 1. Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme Theophilou, Iris, E-mail: [email protected] [Peter Grunberg Institut (PGI) Forschungszentrum Jülich, D-52425 Jülich (Germany); Tassi, M.; Thanos, S. [Institute for Advanced Materials, Physicochemical Processes, Nanotechnology and Microsystems, ‘Demokritos’ National Center for Scientific Research, 15310 Athens (Greece) 2014-04-28 Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations. 2. Excited states and transition metal compounds with quantum Monte Carlo Bande, Annika 2007-01-01 To the most challenging electron structure calculations belong weak interactions, excited state calculations, transition metals and properties. In this work the performance of variational (VMC) and fixed-node diffusion quantum Monte Carlo (FN-DMC) is tested for challenging electron structure problems using the quantum Monte Carlo amolqc code by Lüchow et al. The transition metal compounds under consideration are vanadium oxides. Here excitation, ionization, oxygen atom and molecule abstractio... 3. Excited State Spectra and Dynamics of Phenyl-Substituted Butadienes Wallace-Williams, Stacie E.; Schwartz, Benjamin J.; Møller, Søren; 1994-01-01 A combination of steady-state and dynamic spectral measurements are used to provide new insights into the nature of the excited-state processes of all-trans-1,4-diphenyl-1,3-butadiene and several analogs: 1,4-diphenyl- 1,3-cyclopentadiene, 1,1,4,4-tetraphenylbutadiene, 1,2,3,4-tetraphenyl-1... 4. Electronic excited states and relaxation dynamics in polymer heterojunction systems Ramon, John Glenn Santos The potential for using conducting polymers as the active material in optoelectronic devices has come to fruition in the past few years. Understanding the fundamental photophysics behind their operations points to the significant role played by the polymer interface in their performance. Current device architectures involve the use of bulk heterojunctions which intimately blend the donor and acceptor polymers to significantly increase not only their interfacial surface area but also the probability of exciton formation within the vicinity of the interface. In this dissertation, we detail the role played by the interface on the behavior and performance of bulk heterojunction systems. First, we explore the relation between the exciton binding energy to the band offset in determining device characteristics. As a general rule, when the exciton binding energy is greater than the band offset, the exciton remains the lowest energy excited state leading to efficient light-emitting properties. On the other hand, if the offset is greater than the binding energy, charge separation becomes favorable leading to better photovoltaic behavior. Here, we use a Wannier function, configuration interaction based approach to examine the essential excited states and predict the vibronic absorption and emission spectra of the PPV/BBL, TFB/F8BT and PFB/F8BT heterojunctions. Our results underscore the role of vibrational relaxation in the formation of charge-transfer states following photoexcitation. In addition, we look at the relaxation dynamics that occur upon photoexcitation. For this, we adopt the Marcus-Hush semiclassical method to account for lattice reorganization in the calculation of the interconversion rates in TFB/F8BT and PFB/F8BT. We find that, while a tightly bound charge-transfer state (exciplex) remains the lowest excited state, a regeneration pathway to the optically active lowest excitonic state in TFB/F8BT is possible via thermal repopulation from the exciplex. Finally 5. Excited-state dynamics of astaxanthin aggregates Fuciman, Marcel; Durchan, Milan; Šlouf, Václav; Keşan, Gürkan; Polívka, Tomáš 2013-05-01 Astaxanthin forms three types of aggregates in hydrated dimethyl sulfoxide (DMSO). In DMSO/water ratio of 1:1, a red-shifted J-aggregate with maximum at 570 nm is generated, while a ratio of 1:9 produces blue-shifted H-aggregates with peaks at 386 nm (H1) and 460 nm (H2). Monomeric astaxanthin in DMSO has an S1 lifetime of 5.3 ps, but a long-lived (33 ps) S∗ signal was also identified. Aggregation changes the S1 lifetimes to 17 ps (H1), 30 ps (H2), and 14 ps (J). Triplet state of astaxanthin, most likely generated via singlet homofission, was observed in H1 and H2 aggregates. 6. Quantum entanglement of localized excited states at finite temperature Caputa, Pawel; Simón, Joan; Štikonas, Andrius; Takayanagi, Tadashi 2015-01-01 In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results. 7. Quantum Entanglement of Localized Excited States at Finite Temperature Caputa, Pawel; Stikonas, Andrius; Takayanagi, Tadashi 2014-01-01 In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results. 8. State-Selective Excitation of Quantum Systems via Geometrical Optimization. Chang, Bo Y; Shin, Seokmin; Sola, Ignacio R 2015-09-01 We lay out the foundations of a general method of quantum control via geometrical optimization. We apply the method to state-selective population transfer using ultrashort transform-limited pulses between manifolds of levels that may represent, e.g., state-selective transitions in molecules. Assuming that certain states can be prepared, we develop three implementations: (i) preoptimization, which implies engineering the initial state within the ground manifold or electronic state before the pulse is applied; (ii) postoptimization, which implies engineering the final state within the excited manifold or target electronic state, after the pulse; and (iii) double-time optimization, which uses both types of time-ordered manipulations. We apply the schemes to two important dynamical problems: To prepare arbitrary vibrational superposition states on the target electronic state and to select weakly coupled vibrational states. Whereas full population inversion between the electronic states only requires control at initial time in all of the ground vibrational levels, only very specific superposition states can be prepared with high fidelity by either pre- or postoptimization mechanisms. Full state-selective population inversion requires manipulating the vibrational coherences in the ground electronic state before the optical pulse is applied and in the excited electronic state afterward, but not during all times. PMID:26575896 9. Accurate Excited State Geometries within Reduced Subspace TDDFT/TDA. Robinson, David 2014-12-01 A method for the calculation of TDDFT/TDA excited state geometries within a reduced subspace of Kohn-Sham orbitals has been implemented and tested. Accurate geometries are found for all of the fluorophore-like molecules tested, with at most all valence occupied orbitals and half of the virtual orbitals included but for some molecules even fewer orbitals. Efficiency gains of between 15 and 30% are found for essentially the same level of accuracy as a standard TDDFT/TDA excited state geometry optimization calculation. PMID:26583218 10. Coupled cluster calculations of ground and excited states of nuclei The standard and renormalized coupled cluster methods with singles, doubles, and noniterative triples and their generalizations to excited states, based on the equation of motion coupled cluster approach, are applied to the He4 and O16 nuclei. A comparison of coupled cluster results with the results of the exact diagonalization of the Hamiltonian in the same model space shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei. The bulk of the correlation effects is obtained at the coupled cluster singles and doubles level. Triples, treated noniteratively, provide the virtually exact description 11. First-principles Calculation of Excited State Spectra in QCD Jozef Dudek,Robert Edwards,Michael Peardon,David Richards,Christopher Thomas 2011-05-01 Recent progress at understanding the excited state spectra of mesons and baryons is described. I begin by outlining the application of the variational method to compute the spectrum of QCD, and then present results for the excited meson spectrum, with continuum quantum numbers of the states clearly delineated. I emphasise the need to extend the calculation to encompass multi-hadron contributions, and describe a recent calculation of the I=2 pion-pion energy-dependent phase shifts as a precursor to the study of channels with resonant behavior. I conclude with recent results for the low lying baryon spectrum, and the prospects for future calculations. 12. Kinetic studies following state-selective laser excitation The objective of this contract is the study of state-to-state, electronic energy transfer reactions following two-photon laser excitation. We have chosen to study reactions of Xe 5p5np because of their relevance to the XeCl excimer laser. We are studying deactivation reactions in collisions with heavy atoms such as Ar, Kr, and Xe and reactive collisions with chlorides. The reactants are excited by multiphoton laser absorption. Product channels are observed by their fluorescence, or by laser induced fluorescence using a second color laser. 36 refs., 16 figs., 5 tabs 13. Equations of state for self-excited MHD generator studies We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range 14. Equations of state for self-excited MHD generator studies Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K. 1980-02-26 We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range. 15. Vibrational relaxation pathways in the electronic excited state of carotenoid The intra- and inter-molecular vibrational relaxation in the electronic excited state (1Bu+) of spheroidene derivative (the number of conjugated double bonds, n=8) has been investigated at room temperature by means of femtosecond time-resolved fluorescence spectroscopy based on an optical-Kerr-gate technique. Depending on the photo-excitation either to the 1Bu+(v=1) or 1Bu+(v=2) vibronic level, remarkable differences were observed in hot luminescence spectra related to the vibrational relaxation process of high- and low-frequency modes. Under the excitation to the 1Bu+(v=2) state hot luminescence from the 1Bu+(v=1) state was observed as a dominant feature of the time-resolved spectra while the dynamic Stokes shift originating from the low-frequency-modes dynamics was clearly observed under the excitation to the 1Bu+(v=1). These observations of the excitation energy dependence of time-resolved fluorescence spectra were discussed by analyzing the Franck-Condon factors of transitions from v=0,1, and 2 levels of high-frequency modes 16. Attosecond dynamics of electron correlation in doubly excited atomic states We have solved the time-dependent Schroedinger equation describing the simultaneous interaction of the He 1s2s 1S state with two laser-generated pulses of trapezoidal or Gaussian shape, of duration 86 fs and of frequencies ω1=1.453 au and ω2=1.781 au. The system is excited to the energy region of two strongly correlated doubly excited states, chosen for this study according to specific criteria. It is demonstrated quantitatively that, provided one focuses on the dynamics occurring within the attosecond timescale, the corresponding orbital configurations, 2s2p and 2p3d 1P0, exist as nonstationary states, with occupation probabilities that are oscillating as the states decay exponentially into the 1sεp continuum, during and after the laser-atom interaction. It follows that it is feasible to probe by attosecond pulses the motion of configurations of electrons as they correlate via the total Hamiltonian. For the particular system studied here, the probe pulses could register the oscillating doubly excited configurations by de-exciting to the He 1s3d 1D state, which emits at 6680 A. (author). Letter-to-the-editor 17. Excited State Structural Dynamics of Carotenoids and Charge Transfer Systems This dissertation describes the development and implementation of a visible/near infrared pump/mid-infrared probe apparatus. Chapter 1 describes the background and motivation of investigating optically induced structural dynamics, paying specific attention to solvation and the excitation selection rules of highly symmetric molecules such as carotenoids. Chapter 2 describes the development and construction of the experimental apparatus used throughout the remainder of this dissertation. Chapter 3 will discuss the investigation of DCM, a laser dye with a fluorescence signal resulting from a charge transfer state. By studying the dynamics of DCM and of its methyl deuterated isotopomer (an otherwise identical molecule), we are able to investigate the origins of the charge transfer state and provide evidence that it is of the controversial twisted intramolecular (TICT) type. Chapter 4 introduces the use of two-photon excitation to the S1 state, combined with one-photon excitation to the S2 state of the carotenoid beta-apo-8'-carotenal. These 2 investigations show evidence for the formation of solitons, previously unobserved in molecular systems and found only in conducting polymers Chapter 5 presents an investigation of the excited state dynamics of peridinin, the carotenoid responsible for the light harvesting of dinoflagellates. This investigation allows for a more detailed understanding of the importance of structural dynamics of carotenoids in light harvesting 18. Wave packet dynamics in molecular excited electronic states We theoretically explore the use of UV pump – UV probe schemes to resolve in time the dynamics of nuclear wave packets in excited electronic states of the hydrogen molecule. The pump pulse ignites the dynamics in singly excited states, that will be probed after a given time delay by a second identical pulse that will ionize the molecule. The field-free molecular dynamics is first explored by analyizing the autocorrelation function for the pumped wave packet and the excitation probabilities. We investigate both energy and angle differential ionization probabilities and demonstrate that the asymmetry induced in the electron angular distributions gives a direct map of the time evolution of the pumped wave packet 19. Excited charmonium states from Bethe-Salpeter equation Sauli, Vladimir 2011-01-01 We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale$\\mu\\simeq 350MeV$. Using free charm quark propagators we observe that$J/\\Psi$is the only charmonium left bellow naive quark-antiquark threshold$2m_c$, while the all excited states are situated above this threshold. Within the numerical method we overcome obstacles related with threshold singularity and discuss the consequences of the use of free propagators for calculation of excited states above the threshold. 20. Size dependent deactivation of the excited state of DHICA Gauden, Magdalena; Pezzella, Alessandro; Panzella, Lucia; 2008-01-01 Melanin is a natural pigment mainly responsible for the protection of skin and eyes from UV damage. 5,6- dihydroxyindole- 2 carboxylic acid (DHICA) is a key melanin building block. We have investigated the excited state dynamics of DHICA as well as its derivatives and oligomeric units using... 1. Optimal control of peridinin excited-state dynamics Dietzek, B.; Chábera, P.; Hanf, R.; Tschierlei, S.; Popp, J.; Pascher, T.; Yartsev, A.; Polívka, Tomáš 2010-01-01 Roč. 373, 1-2 (2010), s. 129-136. ISSN 0301-0104 Institutional research plan: CEZ:AV0Z50510513 Keywords : peridin * excited-state dynamics * coherent control Subject RIV: BO - Biophysics Impact factor: 2.017, year: 2010 2. Dark excited states of carotenoids: Consensus and controversy Polívka, Tomáš; Sundström, V. 2009-01-01 Roč. 477, 1-3 (2009), s. 1-11. ISSN 0009-2614 Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoids * excited states * relaxation pathways * femtosecond spectroscopy Subject RIV: BO - Biophysics Impact factor: 2.291, year: 2009 3. Calculation of neutral beam deposition accounting for excited states Gianakon, T.A. 1992-09-01 Large-scale neutral-beam auxillary heating of plasmas has led to new plasma operational regimes which are often dominated by fast ions injected via the absorption of an energetic beam of hydrogen neutrals. An accurate simulation of the slowing down and transport of these fast ions requires an intimate knowledge of the hydrogenic neutral deposition on each flux surface of the plasma. As a refinement to the present generation of transport codes, which base their beam deposition on ground-state reaction rates, a new set of routines, based on the excited states of hydrogen, is presented as mechanism for computing the attenuation and deposition of a beam of energetic neutrals. Additionally, the numerical formulations for the underlying atomic physics for hydrogen impacting on the constiuent plasma species is developed and compiled as a numerical database. Sample results based on this excited state model are compared with the ground-state model for simple plasma configurations. 4. Calculation of neutral beam deposition accounting for excited states Large-scale neutral-beam auxillary heating of plasmas has led to new plasma operational regimes which are often dominated by fast ions injected via the absorption of an energetic beam of hydrogen neutrals. An accurate simulation of the slowing down and transport of these fast ions requires an intimate knowledge of the hydrogenic neutral deposition on each flux surface of the plasma. As a refinement to the present generation of transport codes, which base their beam deposition on ground-state reaction rates, a new set of routines, based on the excited states of hydrogen, is presented as mechanism for computing the attenuation and deposition of a beam of energetic neutrals. Additionally, the numerical formulations for the underlying atomic physics for hydrogen impacting on the constiuent plasma species is developed and compiled as a numerical database. Sample results based on this excited state model are compared with the ground-state model for simple plasma configurations 5. Direct excitation of butterfly states in Rydberg molecules Lippe, Carsten; Niederpruem, Thomas; Thomas, Oliver; Eichert, Tanita; Ott, Herwig 2016-05-01 Since their first theoretical prediction Rydberg molecules have become an increasing field of research. These exotic states originate from the binding of a ground state atom in the electronic wave function of a highly-excited Rydberg atom mediated by a Fermi contact type interaction. A special class of long-range molecular states, the butterfly states, were first proposed by Greene et al.. These states arise from a shape resonance in the p-wave scattering channel of a ground state atom and a Rydberg electron and are characterized by an electron wavefunction whose density distribution resembles the shape of a butterfly. We report on the direct observation of deeply bound butterfly states of Rydberg molecules of 87 Rb. The butterfly states are studied by high resolution spectroscopy of UV-excited Rydberg molecules. We find states bound up to - 50 GHz from the 25 P1/2 , F = 1 state, corresponding to binding lengths of 50a0 to 500a0 and with permanent electric dipole moments of up to 500 Debye. This distinguishes the observed butterfly states from the previously observed long range Rydberg molecules in rubidium. 6. Optimized resonating valence bond state in square lattice: correlations & excitations Z Nourbakhsh 2009-09-01 Full Text Available We consider RVB state as a variational estimate for the ground state of Heisenberg antiferromagnet in square lattice. We present numerical calculation of energy, spin-spin correlation function and spin excitation spectrum. We show, that the quantum flactuations reduce of magnetization respect to Neel order. Our results are in good agreement with other methods such as spin-wave calculation and series expansions. 7. Excited States of the Diatomic Molecule CrHe Pototschnig, Johann V.; Ratschek, Martin; Hauser, Andreas W.; Ernst, Wolfgang E. 2013-06-01 Chromium (Cr) atoms embedded in superfluid helium nanodroplets (He_N) have been investigated by laser induced fluorescence, beam depletion and resonant two-photon ionization spectroscopy in current experiments at our institute. Cr is found to reside inside the He_N in the a^7S ground state. Two electronically excited states, z^7P and y^7P, are involved in a photoinduced ejection process which allowed us to study Fano resonances in the photoionisation spectra The need for a better understanding of the experimental observations triggered a theoretical approach towards the computation of electronically excited states via high-level methods of computational chemistry. Two well-established, wave function-based methods, CASSCF and MRCI, are combined to calculate the potential energy curves for the three states involved. The character of the two excited states z^7P and y^7P turns out to be significantly different. Theory predicts the ejection of the Cr atom in the case of an y^7P excitation as was observed experimentally. The quasi-inert helium environment is expected to weaken spin selection rules, allowing a coupling between different spin states especially during the ejection process. We therefore extend our theoretical analysis to the lowest state in the triplet- and quintet- manifold. Most of these alternative states show very weak bonding of only a few wn. A. Kautsch, M. Hasewend, M. Koch and W. E. Ernst, Phys. Rev. A 86, 033428 (2012). A. Kautsch, M. Koch and W. E. Ernst, J. Phys. Chem. A, accepted, doi:10.1021/jp312336m}. 8. Coupling of single-particle states to collective excitations We discuss the effects of colletive vibrations of the closed shell core on the fragmentation of single-particle states in the neighbouring odd nuclei. A scheme for calculating microscopically these effects is presented. Starting from a Skyrme-type effective interaction, one can obtain the Hartree-Fock spectrum, the core excited states and giant resonances and then the energy-dependent mass operator which determines the fragmentation. Results for the 207Pb are discussed and compared with the data 9. Photodissociation of N2O: excitation of 1A" states. Schinke, Reinhard; Schmidt, Johan A 2012-11-26 We investigate the contributions of the lowest two (1)A" states in the UV photodissociation of N(2)O employing three-dimensional potential energy surfaces and transition dipole moment functions. Because the transition dipole moments are much smaller than for the 2 (1)A' state, we conclude that excitation of the (1)A" states has a marginal effect. The dense vibrational spectrum of the quasi-bound 2(1)A" state possibly explains some of the tiny, noise-like structures of the measured absorption spectrum. PMID:22536943 10. Temperature measurements from relative populations of excited states with INDRA For the first time, INDRA has been used to analyse resonances observed in correlation functions, giving thus the possibility to probe the caloric curve (correlation between the excitation energy and the temperature). First results obtained for the reaction 1836Ar+2858Ni at 95 MeV/nucleon are presented where the projectile-like apparent temperature has been evaluated. Moreover, the measured populations of excited states are compared with the predictions of a statistical model which includes an original hypothesis of excluded volume for species at the freeze-out. (author) 11. Solid-State Excitation Laser for Laser-Ultrasonics Schnars, U.; Platz, W.; Mahnke, P.; A. Fix; Frede, M; Neumann, J.; Peuser, P. 2010-01-01 The inspection speed of laser-ultrasonics compared with conventional ultrasonic testing is limited by the pulse repetition rate of the excitation laser. The maximum pulse repetition rate reported up to now for CO2-lasers, which are presently used for nearly all systems, is in the range of 400 Hz. In this paper a new approach based on a diode-pumped solid-state laser is discussed, which is currently being developed. This new excitation laser is designed for a repetition rate of 1 kHz and will ... 12. Sub-50 fs excited state dynamics of 6-chloroguanine upon deep ultraviolet excitation. Mondal, Sayan; Puranik, Mrinalini 2016-05-18 The photophysical properties of natural nucleobases and their respective nucleotides are ascribed to the sub-picosecond lifetime of their first singlet states in the UV-B region (260-350 nm). Electronic transitions of the ππ* type, which are stronger than those in the UV-B region, lie at the red edge of the UV-C range (100-260 nm) in all isolated nucleobases. The lowest energetic excited states in the UV-B region of nucleobases have been investigated using a plethora of experimental and theoretical methods in gas and solution phases. The sub-picosecond lifetime of these molecules is not a general attribute of all nucleobases but specific to the five primary nucleobases and a few xanthine and methylated derivatives. To determine the overall UV photostability, we aim to understand the effect of more energetic photons lying in the UV-C region on nucleobases. To determine the UV-C initiated photophysics of a nucleobase system, we chose a halogen substituted purine, 6-chloroguanine (6-ClG), that we had investigated previously using resonance Raman spectroscopy. We have performed quantitative measurements of the resonance Raman cross-section across the Bb absorption band (210-230 nm) and constructed the Raman excitation profiles. We modeled the excitation profiles using Lee and Heller's time-dependent theory of resonance Raman intensities to extract the initial excited state dynamics of 6-ClG within 30-50 fs after photoexcitation. We found that imidazole and pyrimidine rings of 6-ClG undergo expansion and contraction, respectively, following photoexcitation to the Bb state. The amount of distortions of the excited state structure from that of the ground state structure is reflected by the total internal reorganization energy that is determined at 112 cm(-1). The contribution of the inertial component of the solvent response towards the total reorganization energy was obtained at 1220 cm(-1). In addition, our simulation also yields an instantaneous response of the first 13. MULTIPLY CHARGED IONS COLLISIONS WITH ATOMS INTO EXCITED STATES PanGuangyan 1990-01-01 The emission spectra in collisions between Ions and Atoms have been measured by an Optical Multichannel Analysis System (OMA).The experimental results demonstrate that there are two channels of excitation in collision between single charged ions and atoms and three channels of excitation in collision between double charged ions and atoms.Emission cross cestions and excitation cross sections have been obtained.K.Kadota et al and R.Shingal et al suggested that,under the appropriate conditions,the H42+-Li and He2++Na collision systems can be used efficiently to produce a laser of Lyman-α(30,4nm) and Lyman-β(25.6nm)lines via cascade to He+(2P)state. 14. Super-atom molecular orbital excited states of fullerenes. Johansson, J Olof; Bohl, Elvira; Campbell, Eleanor E B 2016-09-13 Super-atom molecular orbitals are orbitals that form diffuse hydrogenic excited electronic states of fullerenes with their electron density centred at the centre of the hollow carbon cage and a significant electron density inside the cage. This is a consequence of the high symmetry and hollow structure of the molecules and distinguishes them from typical low-lying molecular Rydberg states. This review summarizes the current experimental and theoretical studies related to these exotic excited electronic states with emphasis on femtosecond photoelectron spectroscopy experiments on gas-phase fullerenes.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'. PMID:27501970 15. Clustered chimera states in systems of type-I excitability The chimera state is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras have been found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative of neural excitability type I. We obtain chimera states with multiple coherent regions (clustered chimeras/multi-chimeras) depending on the distance from the excitability threshold, the range of nonlocal coupling and the coupling strength. A detailed stability diagram for these chimera states and other interesting coexisting patterns (like traveling waves) is presented. (paper) 16. Controlling excited-state contamination in nucleon matrix elements Yoon, Boram; Gupta, Rajan; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank; Nucleon Matrix Elements NME Collaboration 2016-06-01 We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2 +1 -flavor ensemble with lattices of size 323×64 generated using the rational hybrid Monte Carlo algorithm at a =0.081 fm and with Mπ=312 MeV . The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a 2-state fit to data at multiple values of the source-sink separation tsep. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of tsep needed to demonstrate convergence of the isovector charges of the nucleon to the tsep→∞ estimates is presented. 17. Excited state dynamics of the astaxanthin radical cation Amarie, Sergiu; Förster, Ute; Gildenhoff, Nina; Dreuw, Andreas; Wachtveitl, Josef 2010-07-01 Femtosecond transient absorption spectroscopy in the visible and NIR and ultrafast fluorescence spectroscopy were used to examine the excited state dynamics of astaxanthin and its radical cation. For neutral astaxanthin, two kinetic components corresponding to time constants of 130 fs (decay of the S 2 excited state) and 5.2 ps (nonradiative decay of the S 1 excited state) were sufficient to describe the data. The dynamics of the radical cation proved to be more complex. The main absorption band was shifted to 880 nm (D 0 → D 3 transition), showing a weak additional band at 1320 nm (D 0 → D 1 transition). We found, that D 3 decays to the lower-lying D 2 within 100 fs, followed by a decay to D 1 with a time constant of 0.9 ps. The D 1 state itself exhibited a dual behavior, the majority of the population is transferred to the ground state in 4.9 ps, while a small population decays on a longer timescale of 40 ps. Both transitions from D 1 were found to be fluorescent. 18. Controlling Excited-State Contamination in Nucleon Matrix Elements Yoon, Boram; Bhattacharya, Tanmoy; Engelhardt, Michael; Green, Jeremy; Joó, Bálint; Lin, Huey-Wen; Negele, John; Orginos, Kostas; Pochinsky, Andrew; Richards, David; Syritsyn, Sergey; Winter, Frank 2016-01-01 We present a detailed analysis of methods to reduce statistical errors and excited-state contamination in the calculation of matrix elements of quark bilinear operators in nucleon states. All the calculations were done on a 2+1 flavor ensemble with lattices of size$32^3 \\times 64$generated using the rational hybrid Monte Carlo algorithm at$a=0.081$~fm and with$M_\\pi=312$~MeV. The statistical precision of the data is improved using the all-mode-averaging method. We compare two methods for reducing excited-state contamination: a variational analysis and a two-state fit to data at multiple values of the source-sink separation$t_{\\rm sep}$. We show that both methods can be tuned to significantly reduce excited-state contamination and discuss their relative advantages and cost-effectiveness. A detailed analysis of the size of source smearing used in the calculation of quark propagators and the range of values of$t_{\\rm sep}$needed to demonstrate convergence of the isovector charges of the nucleon to the$t_... 19. Strong-Field Photoionization as Excited-State Tunneling. Serebryannikov, E E; Zheltikov, A M 2016-03-25 We show that, in an intense laser field, ultrafast photoionization can occur through quantum pathways that cannot be categorized as multiphoton ionization or ground-state tunneling. In this regime, the subcycle electron-wave-packet dynamics leading to photoionization occurs via electron excited states, from where the electrons tunnel to the continuum within a tiny fraction of the field cycle. For high field intensities, this ionization pathway is shown to drastically enhance the dynamic leakage of the electron wave packet into the continuum, opening an ionization channel that dominates over ground-state electron tunneling. PMID:27058079 20. First observation of excited states in {sup 182}Pb. Jenkins, D. G.; Muikku, M.; Greenlees, P. T.; Hauschild, K.; Helarjutta, K.; Jones, P. M.; Julin, R.; Juutinen, S.; Kankaanpaa, H.; Kelsall, N. S.; Kettunen, H.; Kuusiniemi, P.; Leino, M.; Moore, C. J.; Nieminen, P.; O' Leary, C. D.; Page, R. D.; Rakhila, P.; Reviol, W.; Taylor, M. J.; Uusitalo, J.; Wadsworth, R.; Physics; Univ. of York; Univ. of Jyvaskyla; CEA Saclay; Univ. of Liverpool; Univ. of Tennessee 2000-01-01 Excited states in the light lead nucleus, {sup 182}Pb, have been observed for the first time, by means of the recoil-decay tagging technique. A rotational band has been observed which has features in common with bands attributed to a prolate configuration in the heavier neutron deficient lead nuclei, {sup 184-188}Pb. A variable moment of inertia fit to the states in this band suggests that the prolate minimum has risen significantly in energy compared to the next even lead nucleus, {sup 184}Pb. This constitutes firm evidence for the minimization of this configuration with respect to the spherical ground state around N=103. 1. Ultrafast excited state dynamics in 9,9'-bifluorenylidene. Conyard, Jamie; Heisler, Ismael A; Browne, Wesley R; Feringa, Ben L; Amirjalayer, Saeed; Buma, Wybren Jan; Woutersen, Sander; Meech, Stephen R 2014-08-01 9,9'-Bifluorenylidene has been proposed as an alternative and flexible electron acceptor in organic photovoltaic cells. Here we characterize its excited state properties and photokinetics, combining ultrafast fluorescence and transient IR measurements with quantum chemical calculations. The fluorescence decay is ultrafast (sub-100 fs) and remarkably independent of viscosity. This suggests that large scale structure change is not the primary relaxation mode. The ultrafast decay populates a dark state characterized by distinct vibrational and electronic spectra. This state decays with a 6 ps time constant to a hot ground state that ultimately populates the initial state with a 20 ps time constant; these times are also insensitive to solvent viscosity. No metastable intermediate structures are resolved in the photocycle after population of the dark state. The implications of these results for the operation of 9,9'-bifluorenylidene as an electron acceptor and as a potential molecular switch are discussed. PMID:25025227 2. Negative-parity nucleon excited state in nuclear matter Ohtani, Keisuke; Oka, Makoto 2016-01-01 Spectral functions of the nucleon and its negative parity excited state in nuclear matter are studied using QCD sum rules and the maximum entropy method (MEM). It is found that in-medium modifications of the spectral functions are attributed mainly to density dependencies of the $\\langle \\bar{q}q \\rangle$ and $\\langle q^{\\dagger}q \\rangle$ condensates. The MEM reproduces the lowest-energy peaks of both the positive and negative parity nucleon states at finite density up to $\\rho \\sim \\rho_N$ (normal nuclear matter density). As the density grows, the residue of the nucleon ground state decreases gradually while the residue of the lowest negative parity excited state increases slightly. On the other hand, the positions of the peaks, which correspond to the total energies of these states, are almost density independent for both parity states. The density dependencies of the effective masses and vector self-energies are also extracted by assuming the mean-field green functions for the peak states. We find that,... 3. Physical Properties, Exciton Analysis, and Visualization of Core-Excited States: An Intermediate State Representation Approach. Wenzel, Jan; Dreuw, Andreas 2016-03-01 The theoretical simulation of X-ray absorption spectra is in general a challenging task. However, for small and medium-sized organic molecules, the algebraic diagrammatic construction scheme (ADC) for the polarization operator in combination with the core-valence separation approximation (CVS) has proven to yield core-excitation energies and transition moments with almost quantitative accuracy allowing for reliable construction of X-ray absorption spectra. Still, to understand core-excitation processes in detail, it is not sufficient to only compute energies, but also properties like static dipole moments and state densities are important as they provide deeper insight into the nature of core-excited states. Here, we present for the first time an implementation of the intermediate state representation (ISR) approach in combination with the CVS approximation (CVS-ISR), which gives, in combination with the CVS-ADC method, direct access to core-excited state properties. The performance of the CVS-ADC/CVS-ISR approach is demonstrated by means of small- and medium-sized organic molecules. Besides the calculation of core-excited state dipole moments, advanced analyses of core-excited state densities are performed using descriptors like exciton sizes and distances. Plotting electron and hole densities helps to determine the character of the state, and in particular, the investigation of detachment/attachment densities provides information about orbital relaxation effects that are crucial for understanding core excitations. PMID:26845396 4. Excited states in large molecular systems through polarizable embedding. List, Nanna Holmgaard; Olsen, Jógvan Magnus Haugaard; Kongsted, Jacob 2016-07-27 In this perspective, we provide an overview of recent work within the polarizable embedding scheme to describe properties of molecules in realistic environments of increasing complexity. After an outline of the theoretical basis for the polarizable embedding model, we discuss the importance of using an accurate embedding potential, and how this may be used to significantly reduce the size of the part of the system treated using quantum mechanics without compromising the accuracy of the final results. Furthermore, we discuss the calculation of local electronic excited states based on response theory. We finally discuss aspects related to two recent extensions of the model (i) effective external field and (ii) polarizable density embedding emphasizing their importance for efficient yet accurate description of excited-state properties in complex environments. PMID:27416749 5. On the nature of highly vibrationally excited states of thiophosgene Srihari Keshavamurthy 2012-01-01 In this work an analysis of the highly vibrationally excited states of thiophosgene (SCCl2) is made in order to gain insights into some of the experimental observations and spectral features. The states analysed here lie in a spectrally complex region where strong mode mixings are expected due to the overlap of several strong anharmonic Fermi resonances. Two recent techniques, a semiclassical angle space representation of the eigenstates and the parametric variation of the eigenvalues (level-velocities) are used to identify eigenstate sequences exhibiting common localization characteristics. Preliminary results on the influence of highly excited out-of-plane bending modes on the nature of the eigenstates suggest a possible bifurcation in the system. 6. The effects of doubly excited states on ionization balance 2006-01-01 The effects of highly doubly excited states on ionization balance are investigated. In the calculation, A Collisional-Radiative model in Detailed-Configuration-Accounting (DCA) is applied to population calculations for NLTE plasmas. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree-Fock-Slater self-consistent-field method is used to calculate the electron wave functions. The mean ionization stage of high-Z plasma Lu is presented. The comparison shows that the mean ionization stage increases more than 3 stages when doubly excited states 5l6l' and 5l5l' are not included in the population calculations. 7. Time evolution of vibration-induced excited state decay Menšík, Miroslav; Nešpůrek, Stanislav 2002-01-01 Roč. 52, č. 8 (2002), s. 945-962. ISSN 0011-4626 R&D Projects: GA AV ČR IAB1050903; GA AV ČR IAA1050901 Institutional research plan: CEZ:AV0Z4050913 Keywords : excited state decay * exciton-phonon interaction Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 0.311, year: 2002 8. Algorithm for Computing Excited States in Quantum Theory Luo, X. Q.; Jirari, H.; Kroger, H; Moriarty, K. 2001-01-01 Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in the conventional approach, it is extremely difficult to compute the excited states. Here we present a different algorithm: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach. As a new example, application to the Klein-Gordon field theory is shown. 9. Clustered Chimera States in Systems of Type-I Excitability Vüllings, Andrea; Hizanidis, Johanne; Omelchenko, Iryna; Hövel, Philipp 2014-01-01 Chimera is a fascinating phenomenon of coexisting synchronized and desynchronized behaviour that was discovered in networks of nonlocally coupled identical phase oscillators over ten years ago. Since then, chimeras were found in numerous theoretical and experimental studies and more recently in models of neuronal dynamics as well. In this work, we consider a generic model for a saddle-node bifurcation on a limit cycle representative for neural excitability type I. We obtain chimera states wit... 10. Minimal-excitation states for electron quantum optics using levitons Dubois, J.; Jullien, T.; Portier, F.; Roche, P.; Cavanna, A.; Jin, Y.; Wegscheider, W.; Roulleau, P.; Glattli, D. C. 2013-10-01 The on-demand generation of pure quantum excitations is important for the operation of quantum systems, but it is particularly difficult for a system of fermions. This is because any perturbation affects all states below the Fermi energy, resulting in a complex superposition of particle and hole excitations. However, it was predicted nearly 20 years ago that a Lorentzian time-dependent potential with quantized flux generates a minimal excitation with only one particle and no hole. Here we report that such quasiparticles (hereafter termed levitons) can be generated on demand in a conductor by applying voltage pulses to a contact. Partitioning the excitations with an electronic beam splitter generates a current noise that we use to measure their number. Minimal-excitation states are observed for Lorentzian pulses, whereas for other pulse shapes there are significant contributions from holes. Further identification of levitons is provided in the energy domain with shot-noise spectroscopy, and in the time domain with electronic Hong-Ou-Mandel noise correlations. The latter, obtained by colliding synchronized levitons on a beam splitter, exemplifies the potential use of levitons for quantum information: using linear electron quantum optics in ballistic conductors, it is possible to imagine flying-qubit operation in which the Fermi statistics are exploited to entangle synchronized electrons emitted by distinct sources. Compared with electron sources based on quantum dots, the generation of levitons does not require delicate nanolithography, considerably simplifying the circuitry for scalability. Levitons are not limited to carrying a single charge, and so in a broader context n-particle levitons could find application in the study of full electron counting statistics. But they can also carry a fraction of charge if they are implemented in Luttinger liquids or in fractional quantum Hall edge channels; this allows the study of Abelian and non-Abelian quasiparticles in the 11. Doubly excited triplet states of highly stripped ions Transition energies, Coulomb repulsions and effective quantum numbers have been calculated for the doubly excited Nsnp: 3P0 (for N=2, n=N,..,5); Nsnd: 3De (for N=2, n=N+1,..,5) and Npnd: 3F0 (for N=2, n=N+1,..,5) states for the highly stripped ions Na9+,Mg10+,Al11+,Si12+,P13+ and S14+. Time-dependent perturbation theory has been applied to calculate such transitions properties. A time-dependent harmonic perturbation causes simultaneous excitation of both the electrons with a change of spin state. The doubly excited energy levels and the analytic representation of their wave functions are obtained by identifying the poles of an appropriately constructed linearized variational functional with respect to driving frequency. Most of the results are new. The transition energies and effective quantum numbers of 2s2p: 3P0 states of all the ions agree well with the only available experimental data. (orig.) 12. Spin radical enhanced magnetocapacitance effect in intermolecular excited states. Zang, Huidong; Wang, Jianguo; Li, Mingxing; He, Lei; Liu, Zitong; Zhang, Deqing; Hu, Bin 2013-11-14 This article reports the magnetocapacitance effect (MFC) based on both pristine polymer MEH-PPV and its composite system doped with spin radicals (6R-BDTSCSB). We observed that a photoexcitation leads to a significant positive MFC in the pristine MEH-PPV. Moreover, we found that a low doping of spin radicals in polymer MEH-PPV causes a significant change on the MFC signal: an amplitude increase and a line-shape narrowing under light illumination at room temperature. However, no MFC signal was observed under dark conditions in either the pristine MEH-PPV or the radical-doped MEH-PPV. Furthermore, the magnitude increase and line-shape narrowing caused by the doped spin radicals are very similar to the phenomena induced by increasing the photoexcitation intensity. Our studies suggest that the MFC is essentially originated from the intermolecular excited states, namely, intermolecular electron-hole pairs, generated by a photoexcitation in the MEH-PPV. More importantly, by comparing the effects of spin radicals and electrically polar molecules on the MFC magnitude and line shape, we concluded that the doped spin radicals can have the spin interaction with intermolecular excited states and consequently affect the internal spin-exchange interaction within intermolecular excited states in the development of MFC. Clearly, our experimental results indicate that dispersing spin radicals forms a convenient method to enhance the magnetocapacitance effect in organic semiconducting materials. PMID:24144347 13. Entanglement Temperature and Entanglement Entropy of Excited States Wong, Gabriel; Zayas, Leopoldo A Pando; Vaman, Diana 2013-01-01 We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the \\emph{local} ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be interpreted as a state of local thermal equilibrium with a spatially varying "entanglement temperature." Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a generalized, local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally... 14. Internal-nuclear conversion of energy of nucleus excited state In the work an effect of penetration electrons of internal conversion showing in hindered M1-transitions was studied. At the moment of a nucleus transition from excited state in low state, electron of atomic shell can appear inside a nucleus and the internal conversion of electrons occur. For such transitions nuclear parameter do not equal zero. The analytical method of definition of nuclear parameter is offered from the relation of intensities L1/L2, L1/L3, L2/L3 of internal conversion of electrons. (authors) 15. Modular Hamiltonian for Excited States in Conformal Field Theory Lashkari, Nima 2016-07-01 We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Zn replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories. 16. Is the Z+(4430) a radially excited state of Ds? We present the interpretation that the recently discovered Z+(4430) by the Belle Collaboration can be a radial excitation of the cs-bar state, being consistent with an observed value of the product of branching ratios, B(B0→K±Z±(4430))xB(Z±(4430)→π±ψ')∼10-5. We give an explicit cs-bar candidate for this state by calculating the mass value in our semirelativistic quark potential model and also give a natural understanding for the facts that the decay mode Z→J/ψπ+ has not yet been seen while Z→ψ'π can be seen 17. Self-Scattering for Dark Matter with an Excited State Schutz, Katelin 2014-01-01 Self-interacting dark matter scenarios have recently attracted much attention, as a possible means to alleviate the tension between N-body simulations and observations of the dark matter distribution on galactic and sub-galactic scales. The presence of internal structure for the dark matter --- for example, a nearly-degenerate state in the spectrum that could decay, or be collisionally excited or de-excited --- has also been proposed as a possible means to address these discrepancies. Such internal structure can be a source of interesting signatures in direct and indirect dark matter searches, for example providing a novel explanation for the 3.5 keV line recently observed in galaxies and galaxy clusters. We analyze a simple model of dark matter self-scattering including a nearly-degenerate excited state, and develop an accurate analytic approximation for the elastic and inelastic $s$-wave cross sections, which is valid outside the perturbative regime provided the particle velocity is sufficiently low (this c... 18. Quantum Entanglement of Locally Excited States in Maxwell Theory Nozaki, Masahiro 2016-01-01 In 4 dimensional Maxwell gauge theory, we study the changes of (Renyi) entangle-ment entropy which are defined by subtracting the entropy for the ground state from the one for the locally excited states generated by acting with the gauge invariant local operators on the state. The changes for the operators which we consider in this paper reflect the electric-magnetic duality. The late-time value of changes can be interpreted in terms of electromagnetic quasi-particles. When the operator constructed of both electric and magnetic fields acts on the ground state, it shows that the operator acts on the late-time structure of quantum entanglement differently from free scalar fields. 19. Excited-State Properties of Molecular Solids from First Principles. Kronik, Leeor; Neaton, Jeffrey B 2016-05-27 Molecular solids have attracted attention recently in the context of organic (opto)electronics. These materials exhibit unique charge carrier generation and transport phenomena that are distinct from those of conventional semiconductors. Understanding these phenomena is fundamental to optoelectronics and requires a detailed description of the excited-state properties of molecular solids. Recent advances in many-body perturbation theory (MBPT) and density functional theory (DFT) have made such description possible and have revealed many surprising electronic and optical properties of molecular crystals. Here, we review this progress. We summarize the salient aspects of MBPT and DFT as well as various properties that can be described by these methods. These properties include the fundamental gap and its renormalization, hybridization and band dispersion, singlet and triplet excitations, optical spectra, and excitonic properties. For each, we present concrete examples, a comparison to experiments, and a critical discussion. PMID:27090844 20. Excited-State Properties of Molecular Solids from First Principles Kronik, Leeor; Neaton, Jeffrey B. 2016-05-01 Molecular solids have attracted attention recently in the context of organic (opto)electronics. These materials exhibit unique charge carrier generation and transport phenomena that are distinct from those of conventional semiconductors. Understanding these phenomena is fundamental to optoelectronics and requires a detailed description of the excited-state properties of molecular solids. Recent advances in many-body perturbation theory (MBPT) and density functional theory (DFT) have made such description possible and have revealed many surprising electronic and optical properties of molecular crystals. Here, we review this progress. We summarize the salient aspects of MBPT and DFT as well as various properties that can be described by these methods. These properties include the fundamental gap and its renormalization, hybridization and band dispersion, singlet and triplet excitations, optical spectra, and excitonic properties. For each, we present concrete examples, a comparison to experiments, and a critical discussion. 1. Self-scattering for Dark Matter with an excited state Self-interacting dark matter scenarios have recently attracted much attention, as a possible means to alleviate the tension between N-body simulations and observations of the dark matter distribution on galactic and sub-galactic scales. The presence of internal structure for the dark matter—for example, a nearly-degenerate state in the spectrum that could decay, or be collisionally excited or de-excited—has also been proposed as a possible means to address these discrepancies. Such internal structure can be a source of interesting signatures in direct and indirect dark matter searches, for example providing a novel explanation for the 3.5 keV line recently observed in galaxies and galaxy clusters. We analyze a simple model of dark matter self-scattering including a nearly-degenerate excited state, and develop an accurate analytic approximation for the elastic and inelastic s-wave cross sections, which is valid outside the perturbative regime provided the particle velocity is sufficiently low (this condition is also required for the s-wave to dominate over higher partial waves). We anticipate our results will be useful in incorporating inelastic self-scattering into N-body simulations, in order to study the quantitative impact of nearly-degenerate states in the dark matter spectrum on galactic structure and dynamics, and in computing the indirect signatures of multi-state dark matter 2. Systematic study of double beta decay to excited final states A systematic study of two-neutrino double beta (2νββ) decay to the final ground state and excited states is performed within a microscopic quasiparticle random phase approximation (QRPA) model. The excited states are assumed to have the structure of one or two QRPA phonons. This study of the 2νββ decay rates is complemented with the study of single-beta-decay feeding of the relevant nuclei taking part in the double beta process. The Woods-Saxon single-particle energies have been corrected near the Fermi surface by comparing the BCS quasi-particle energies with spectroscopic data of the relevant odd-mass nuclei. Pairing gaps, energy systematics of the Gamow-Teller-States and the available beta-decay data have been used to obtain effective, model-space adapted, two-body matrix elements starting from the G-matrix elements of the Bonn one-boson-exchange potential. This enables a parameter-free calculation of the double Gamow-Teller matrix elements and theoretical prediction of double-beta half lives. The harmonic two-phonon approximation has been used in the beta-decay analysis and the subsequent 2νββ calculations. (authors) 3. Output power of a quantum dot laser: Effects of excited states A theory of operating characteristics of quantum dot (QD) lasers is discussed in the presence of excited states in QDs. We consider three possible situations for lasing: (i) ground-state lasing only; (ii) ground-state lasing at first and then the onset of also excited-state lasing with increasing injection current; (iii) excited-state lasing only. The following characteristics are studied: occupancies of the ground-state and excited-state in QDs, free carrier density in the optical confinement layer, threshold currents for ground- and excited-state lasing, densities of photons emitted via ground- and excited-state stimulated transitions, output power, internal and external differential quantum efficiencies. Under the conditions of ground-state lasing only, the output power saturates with injection current. Under the conditions of both ground- and excited-state lasing, the output power of ground-state lasing remains pinned above the excited-state lasing threshold while the power of excited-state lasing increases. There is a kink in the light-current curve at the excited-state lasing threshold. The case of excited-state lasing only is qualitatively similar to that for single-state QDs—the role of ground-state transitions is simply reduced to increasing the threshold current 4. Excited state dynamics and isomerization in ruthenium sulfoxide complexes. King, Albert W; Wang, Lei; Rack, Jeffrey J 2015-04-21 Molecular photochromic compounds are those that interconvert between two isomeric forms with light. The two isomeric forms display distinct electronic and molecular structures and must not be in equilibrium with one another. These light-activated molecular switch compounds have found wide application in areas of study ranging from chemical biology to materials science, where conversion from one isomeric form to another by light prompts a response in the environment (e.g., protein or polymeric material). Certain ruthenium and osmium polypyridine sulfoxide complexes are photochromic. The mode of action is a phototriggered isomerization of the sulfoxide from S- to O-bonded. The change in ligation drastically alters both the spectroscopic and electrochemical properties of the metal complex. Our laboratory has pioneered the preparation and study of these complexes. In particular, we have applied femtosecond pump-probe spectroscopy to reveal excited state details of the isomerization mechanism. The data from numerous complexes allowed us to predict that the isomerization was nonadiabatic in nature, defined as occurring from a S-bonded triplet excited state (primarily metal-to-ligand charge transfer in character) to an O-bonded singlet ground state potential energy surface. This prediction was corroborated by high-level density functional theory calculations. An intriguing aspect of this reactivity is the coupling of nuclear motion to the electronic wave function and how this coupling affects motions productive for isomerization. In an effort to learn more about this coupling, we designed a project to examine phototriggered isomerization in bis-sulfoxide complexes. The goal of these studies was to determine whether certain complexes could be designed in which a single photon excitation event would prompt two sulfoxide isomerizations. We employed chelating sulfoxides in this study and found that both the nature of the chelate ring and the R group on the sulfoxide affect 5. Theoretical aspects of multiphoton ionization with many resonant excited states The variety of the parameters involved in multi-color multi-step ionization makes it a formidable job to obtain a theoretically comprehensible overview of the process. We examine these parameters of such processes as well as commonly used assumptions in theoretical investigations of multiphoton ionization with many resonantly excited levels. The density matrix formalism is adequate to treat resonant multiphoton ionization when the number of the resonant levels involved is not too large, solving the resonantly coupled states separately beyond the lowest order perturbation theory, while the rest of the states are treated perturbatively. An example of such formalism is given for a four-level system ionized with three lasers each of which resonantly couples the adjacent pairs of the atomic states. 6. Excited states in 146Sm and 147Sm The sup(144,146)Nd(α,xn) and sup(146,148)Nd(3He,xn) reactions with Esub(α) = 20 - 43 MeV and E3sub(He) = 19 - 27 MeV are used to investigate excited states in the isotopes 146Sm and 147Sm. The experiments involve measurements of singles γ-ray spectra and conversion electron spectra, γ-ray angular distributions and three parameter (E sub(γ)E sub(γ) time) coincidences. From these experiments information is obtained for states with spin up to I = 13+ and I = 27/2-, respectively, These states are interpeted within the framework of the cluster-vibration model (CVM) as well as the shell model. (author) 7. Excited states above the proton threshold in {sup 26}Si Komatsubara, T. [Institute for Basic Science (IBS), Rare Isotope Science Project, Yuseong-gu Daejeon (Korea, Republic of); Kubono, S.; Ito, Y. [RIKEN, Saitama (Japan); Hayakawa, T.; Shizuma, T. [Japan Atomic Energy Agency, Tokai, Ibaraki (Japan); Ozawa, A.; Ishibashi, Y. [University of Tsukuba, Institute of Physics, Tsukuba, Ibaraki (Japan); Moriguchi, T. [National Cerebral and Cardiovascular Center Research Institute, Suita, Osaka (Japan); Yamaguchi, H.; Kahl, D. [University of Tokyo, Wako Branch, Center for Nuclear Study (CNS), Wako, Saitama (Japan); Hayakawa, S. [Laboratori Nazionali del Sud-INFN, Catania (Italy); Nguyen Binh, Dam [Vietnamese Academy for Science and Technology, Institute of Physics, Hanoi (Viet Nam); Chen, A.A.; Chen, J. [McMaster University, Hamilton, Ontario (Canada); Setoodehnia, K. [University of Notre Dame, Department of Physics, Notre Dame, Indiana (United States); Kajino, T. [National Astronomical Observatory, Tokyo (Japan); University of Tokyo, Department of Astronomy, Graduate School of Science, Tokyo (Japan) 2014-09-15 The level scheme above the proton threshold in {sup 26}Si is crucial for evaluating the {sup 25}Al(p, γ){sup 26}Si stellar reaction, which is important for understanding the astrophysical origin of the long-lived cosmic radioactivity {sup 26}Al(T{sub 1/2} = 7.17 x 10{sup 5} y) in the Galaxy. The excited states in {sup 26}Si have been studied using an in-beam γ-ray spectroscopy technique with the {sup 24}Mg({sup 3}He, nγ){sup 26}Si reaction. γ-rays with energies up to 4.6 MeV emitted from excited states in {sup 26}Si have been measured using large volume HPGe detectors. The spin-parity of one of the most important states reported recently at 5890.0keV has been assigned as 0{sup +} by γ-γ angular correlation measurements in this work. (orig.) 8. Weighing excited nuclear states with a Penning trap mass spectrometer We report on high-accuracy mass measurements and isomer identification of 187Pb. In this nuclide, two close-lying isomeric states are known from α-decay studies. With the combined use of the ISOLDE resonance ionization laser ion source and the Penning trap mass spectrometer ISOLTRAP the energy difference of 187Pb and 187mPb was determined to be E = 33(13) keV. This is the lowest isomeric excitation energy ever determined by weighing nuclei. (orig.) 9. Coherence, energy and charge transfers in de-excitation pathways of electronic excited state of biomolecules in photosynthesis Bohr, Henrik; Malik, F. Bary 2013-01-01 The observed multiple de-excitation pathways of photo-absorbed electronic excited state in the peridinin–chlorophyll complex, involving both energy and charge transfers among its constituents, are analyzed using the bio-Auger (B-A) theory. It is also shown that the usually used F¨orster–Dexter... 10. Probing the Locality of Excited States with Linear Algebra. Etienne, Thibaud 2015-04-14 This article reports a novel theoretical approach related to the analysis of molecular excited states. The strategy introduced here involves gathering two pieces of physical information, coming from Hilbert and direct space operations, into a general, unique quantum mechanical descriptor of electronic transitions' locality. Moreover, the projection of Hilbert and direct space-derived indices in an Argand plane delivers a straightforward way to visually probe the ability of a dye to undergo a long- or short-range charge-transfer. This information can be applied, for instance, to the analysis of the electronic response of families of dyes to light absorption by unveiling the trend of a given push-pull chromophore to increase the electronic cloud polarization magnitude of its main transition with respect to the size extension of its conjugated spacer. We finally demonstrate that all the quantities reported in this article can be reliably approximated by a linear algebraic derivation, based on the contraction of detachment/attachment density matrices from canonical to atomic space. This alternative derivation has the remarkable advantage of a very low computational cost with respect to the previously used numerical integrations, making fast and accurate characterization of large molecular systems' excited states easily affordable. PMID:26574379 11. Excitation gap of fractal quantum hall states in graphene Luo, Wenchen; Chakraborty, Tapash 2016-01-01 In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter’s butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter’s butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation. 12. 3alpha clustering in the excited states of 16C Baba, T; Kimura, M 2014-01-01 The alpha cluster states of 16C are investigated by using the antisymmetrized molecular dynamics. It is shown that two different types of alpha cluster states exist: triangular and linear-chain states. The former has an approximate isosceles triangular configuration of alpha particles surrounded by four valence neutrons occupying sd-shell, while the latter has the linearly aligned alpha particles with two sd-shell neutrons and two pf-shell neutrons. It is found that the structure of the linear-chain state is qualitatively understood in terms of the 3/2 pi- and 1/2 sigma- molecular orbit as predicted by molecular-orbital model, but there exists non-negligible Be+alpha+2n correlation. The band-head energies of the triangular and linear-chain rotational bands are 8.0 and 15.5 MeV, and the latter is close to the He+Be threshold energy. It is also shown that the linear-chain state becomes the yrast sstate at J=10 with excitation energy 27.8 MeV owing to its very large moment-of-inertia comparable with hyperdeforma... 13. Kinetic studies following state-selective laser excitation We have made measurements of state-to-state deactivation cross sections and radiative lifetimes for Xe(6p,6p',7p) and Kr(5p) states in xenon and krypton buffer gases. These results are relevant to kinetic models and both excimer lasers and the infrared xenon laser; and they are a significant improvement in the precision of the known radiative lifetimes. This type of experiment can now be compared with recent calculations of state-to-state collisional relaxation in rare-gases by Hickman, Huestis, and Saxon. We have also made significant progress in the study of the electronic spectra of small molecules of the rare gases. Spectra have been obtained for Xe2, Xe3, Xe4, and larger clusters. As guidance for the larger clusters of the rare gases we have obtained the first multiphoton spectra for excitons in condensed xenon. In collaboration with research on the multiphoton spectra of the rare gases, we have continued experiments using synchrotron radiation in collaboration with the University of Hamburg. In experiments there we have observed excitation and fluorescence spectra for single xenon atoms at the surface, within the second layer, and within the bulk of large argon clusters 14. Observation of interference effects via four photon excitation of highly excited Rydberg states in thermal cesium vapor Kondo, Jorge M; Guttridge, Alex; Wade, Christopher G; De Melo, Natalia R; Adams, Charles S; Weatherill, Kevin J 2015-01-01 We report on the observation of Electromagnetically Induced Transparency (EIT) and Absorption (EIA) of highly-excited Rydberg states in thermal Cs vapor using a 4-step excitation scheme. The advantage of this 4-step scheme is that the final transition to the Rydberg state has a large dipole moment and one can achieve similar Rabi frequencies to 2 or 3 step excitation schemes using two orders of magnitude less laser power. Consequently each step is driven by a relatively low power infra-red diode laser opening up the prospect for new applications. The observed lineshapes are in good agreement with simulations based on multilevel optical Bloch equations. 15. A benchmark study of electronic excitation energies, transition moments, and excited-state energy gradients on the nicotine molecule Egidi, Franco, E-mail: [email protected]; Segado, Mireia; Barone, Vincenzo, E-mail: [email protected] [Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa (Italy); Koch, Henrik [Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim (Norway); Cappelli, Chiara [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi, 3 I-56124 Pisa (Italy) 2014-12-14 In this work, we report a comparative study of computed excitation energies, oscillator strengths, and excited-state energy gradients of (S)-nicotine, chosen as a test case, using multireference methods, coupled cluster singles and doubles, and methods based on time-dependent density functional theory. This system was chosen because its apparent simplicity hides a complex electronic structure, as several different types of valence excitations are possible, including n-π{sup }, π-π{sup }, and charge-transfer states, and in order to simulate its spectrum it is necessary to describe all of them consistently well by the chosen method. 16. A benchmark study of electronic excitation energies, transition moments, and excited-state energy gradients on the nicotine molecule In this work, we report a comparative study of computed excitation energies, oscillator strengths, and excited-state energy gradients of (S)-nicotine, chosen as a test case, using multireference methods, coupled cluster singles and doubles, and methods based on time-dependent density functional theory. This system was chosen because its apparent simplicity hides a complex electronic structure, as several different types of valence excitations are possible, including n-π, π-π, and charge-transfer states, and in order to simulate its spectrum it is necessary to describe all of them consistently well by the chosen method 17. Excited state properties of the astaxanthin radical cation: A quantum chemical study Dreuw, Andreas; Starcke, Jan Hendrik; Wachtveitl, Josef 2010-07-01 Using time-dependent density functional theory, the excited electronic states of the astaxanthin radical cation (AXT rad + ) are investigated. While the optically allowed excited D 1 and D 3 states are typical ππ∗ excited states, the D 2 and D 4 states are nπ∗ states. Special emphasis is put onto the influence of the carbonyl groups onto the excited states. For this objective, the excited states of four hypothetical carotenoids and zeaxanthin have been computed. Addition of a carbonyl group to a conjugated carbon double bond system does essentially not change the vertical excitation energies of the optically allowed ππ∗ states due to two counter-acting effects: the excitation energy should increase due to the -M-effect of the carbonyl group and at the same time decrease owing to the elongation of the conjugated double bond system by the carbonyl group itself. 18. Excited state properties of the astaxanthin radical cation: A quantum chemical study Dreuw, Andreas, E-mail: [email protected] [Institute of Physical and Theoretical Chemistry, Goethe-University Frankfurt, Max von Laue-Str. 7, 60438 Frankfurt am Main (Germany); Starcke, Jan Hendrik; Wachtveitl, Josef [Institute of Physical and Theoretical Chemistry, Goethe-University Frankfurt, Max von Laue-Str. 7, 60438 Frankfurt am Main (Germany) 2010-07-19 Using time-dependent density functional theory, the excited electronic states of the astaxanthin radical cation (AXT{sup {center_dot}+}) are investigated. While the optically allowed excited D{sub 1} and D{sub 3} states are typical {pi}{pi}* excited states, the D{sub 2} and D{sub 4} states are n{pi}* states. Special emphasis is put onto the influence of the carbonyl groups onto the excited states. For this objective, the excited states of four hypothetical carotenoids and zeaxanthin have been computed. Addition of a carbonyl group to a conjugated carbon double bond system does essentially not change the vertical excitation energies of the optically allowed {pi}{pi}* states due to two counter-acting effects: the excitation energy should increase due to the -M-effect of the carbonyl group and at the same time decrease owing to the elongation of the conjugated double bond system by the carbonyl group itself. 19. Excited state properties of the astaxanthin radical cation: A quantum chemical study Using time-dependent density functional theory, the excited electronic states of the astaxanthin radical cation (AXT·+) are investigated. While the optically allowed excited D1 and D3 states are typical ππ* excited states, the D2 and D4 states are nπ* states. Special emphasis is put onto the influence of the carbonyl groups onto the excited states. For this objective, the excited states of four hypothetical carotenoids and zeaxanthin have been computed. Addition of a carbonyl group to a conjugated carbon double bond system does essentially not change the vertical excitation energies of the optically allowed ππ* states due to two counter-acting effects: the excitation energy should increase due to the -M-effect of the carbonyl group and at the same time decrease owing to the elongation of the conjugated double bond system by the carbonyl group itself. 20. Ultrafast electronic relaxation of excited state vitamin B12 in the gas phase The time evolution of electronically excited vitamin B12 (cyanocobalamin) has been observed for the first time in the gas phase. It reveals an ultrafast decay to a state corresponding to metal excitation. This decay is interpreted as resulting from a ring to metal electron transfer. This opens the observation of the excited state of other complex biomimetic systems in the gas phase, the key to the characterisation of their complex evolution through excited electronic states 1. Breathing-like excited state of the Hoyle state in ${^{12}{\\rm C}}$ Zhou, Bo; Horiuchi, Hisashi; Ren, Zhongzhou 2016-01-01 The existence of the $0_3^+$ and $0_4^+$ states around 10 MeV excitation energy in ${^{12}{\\rm C}}$ is confirmed by a fully microscopic 3$\\alpha$ cluster model. Firstly, a GCM (generator coordinate method) calculation is performed by superposing optimized 2$\\alpha$+$\\alpha$ THSR (Tohsaki-Horiuchi-Schuck-R\\"{o}pke) wave functions with the radius-constraint method. The obtained two excited $0^+$ states above the Hoyle state are consistent with the recently observed states by experiment. Secondly, a variational calculation using the single 2$\\alpha$+$\\alpha$ THSR wave function orthogonalized to the ground and Hoyle states is made and it also supports the existence of the $0_3^+$ state obtained by the GCM calculation. The analysis of the obtained $0_3^+$ state is made by studying its 2$\\alpha$-$\\alpha$ reduced width amplitude, its 2$\\alpha$ correlation function, and the large monopole matrix element between this state and the Hoyle state, which shows that this $0_3^+$ state is a breathing-like excited state of th... 2. Electronic structure and excited state dynamics in optically excited PTCDA films investigated with two-photon photoemission Marks, M.; Sachs, S.; Schwalb, C. H.; Schöll, A.; Höfer, U. 2013-09-01 We present an investigation of the electronic structure and excited state dynamics of optically excited 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) thin films adsorbed on Ag(111) using two-photon photoemission spectroscopy (2PPE). 2PPE allows us to study both occupied and unoccupied electronic states, and we are able to identify signals from the highest occupied and the two lowest unoccupied electronic states of the PTCDA thin film in the 2PPE spectra. The energies for occupied states are identical to values from ultraviolet photoelectron spectroscopy. Compared to results from inverse photoelectron spectroscopy (IPES), the 2PPE signals from the two lowest unoccupied electronic states, LUMO and LUMO+1, are found at 0.8 eV and 1.0 eV lower energies, respectively. We attribute this deviation to the different final states probed in 2PPE and IPES and the attractive interaction of the photoexcited electron and the remaining hole. Furthermore, we present a time-resolved investigation of the excited state dynamics of the PTCDA film in the femtosecond time regime. We observe a significantly shorter inelastic excited state lifetime compared to findings from time-resolved photoluminescence spectroscopy of PTCDA single crystals which could originate from excitation quenching by the metal substrate. 3. Hemispherical Asymmetry from Parity-Violating Excited Initial States 2015-01-01 We investigate if the hemispherical asymmetry in the CMB is produced from parity-violating excited initial condition. We show that in the limit where the deviations from the Bunch-Davies vacuum is large and the scale of new physics is maximally separated from the inflationary Hubble parameter, the primordial power spectrum is modulated only by dipole and quadrupole terms. Requiring the dipole contribution in the power spectrum accounts for the observed power asymmetry, $A=0.07\\pm0.022$, we show that the amount of quadrupole terms is roughly equal to $A^2$, which is still consistent with the bounds from the CMB. The mean local bispectrum which gets enhanced for the excited initial states is within the $1\\sigma$ bound of Planck 2015 results, $f_{\\rm NL}\\simeq 4.17$, but reachable by future CMB experiments. The amplitude of the local non-gaussianity modulates around this mean value, approximately depending on the angle that the short wavelength mode makes with the preferred direction. The amount of variation max... 4. Excited states of quantum many-body interacting systems: A variational coupled-cluster description Xian, Y. 2007-01-01 We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin $\\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Ans... 5. Masses of ground and excited-state hadrons Roberts, H L L; Cloet, I C; Roberts, C D 2011-01-01 We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Delta masses and those of the dressed-quark and diquark correlations they contain. 6. Masses of Ground- and Excited-State Hadrons Roberts, Hannes L. L.; Chang, Lei; Cloët, Ian C.; Roberts, Craig D. 2011-07-01 We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Δ masses and those of the dressed-quark and diquark correlations they contain. 7. Chimera states and excitation waves in networks with complex topologies Schöll, Eckehard 2016-06-01 Chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desyn- chronized) dynamics are studied in networks of FitzHugh-Nagumo systems with complex topologies. To test the robustness of chimera patterns with respect to changes in the structure of the network, we study the following network topologies: Regular ring topology with R nearest neigbors coupled to each side, small-world topology with additional long-range random links, and a hierarchical geometry in the connectivity matrix. We find that chimera states are generally robust with respect to these perturbations, but qualitative changes of the chimera patterns in form of nested coherent and incoherent regions can be induced by a hierarchical topology. The suppression of propagating excitation waves by a small-world topology is also reviewed. 8. Ultrafast Spectroscopy of Delocalized Excited States of the Hydrated Electron Research under support of this grant has been focused on the understanding of highly delocalized ''conduction-band-like'' excited states of solvated electrons in bulk water, in water trapped in the core of reverse micelles, and in alkane solvents. We have strived in this work to probe conduction-band-like states by a variety of ultrafast spectroscopy techniques. (Most of which were developed under DOE support in a previous funding cycle.) We have recorded the optical spectrum of the hydrated electron for the first time. This was accomplished by applying a photo-detrapping technique that we had developed in a previous funding cycle, but had not yet been applied to characterize the actual spectrum. In the cases of reverse micelles, we have been investigating the potential role of conduction bands in the electron attachment process and the photoinduced detrapping, and have published two papers on this topic. Finally, we have been exploring solvated electrons in isooctane from various perspectives. All of these results strongly support the conclusion that optically accessible, highly delocalized electronic states exist in these various media 9. Suppression of Excited-State Contributions to Stellar Reaction Rates Rauscher, T 2013-01-01 It has been shown in previous work [Phys. Rev. Lett. 101, 191101 (2008); Phys. Rev. C 80, 035801 (2009)] that a suppression of the stellar enhancement factor (SEF) occurs in some endothermic reactions at and far from stability. This effect is re-evaluated using the ground-state contributions to the stellar reaction rates, which were shown to be better suited to judge the importance of excited state contributions than the previously applied SEFs. An update of the tables shown in Phys. Rev. C 80, 035801 (2009) is given. The new evalution finds 2350 cases (out of a full set of 57513 reactions) for which the ground-state contribution is larger in the reaction direction with negative reaction Q-value than in the exothermic direction, thus providing exceptions to the commonly applied Q-value rule. The results confirm the Coulomb suppression effect but lead to a larger number of exceptions than previously found. This is due to the fact that often a large variation in the g.s. contribution does not lead to a sizeable... 10. Foil dissociation of fast molecular ions into atomic excited states The intensity and polarizations of light emitted from atomic excited states of dissociated molecular ions were measured. The dissociations are induced when fast molecular ions (50 to 500 keV/amu) are transmitted through thin carbon foils. A calculation of multiple scattering and the Coulomb explosion gives the average internuclear separation of the projectile at the foil surface. Experimentally, the foil thickness is varied to give varying internuclear separations at the foil surface and observe the consequent variation in light yield and optical polarization. Using HeH+ projectiles, factors of 1 to 5 enhancements of the light yields from n = 3, 13P,D states of He I and some He II and H I emissions were observed. The results can be explained in terms of molecular level crossings which provide mixings of the various final states during dissociation of the molecular ions at the exit surface. They suggest a short range surface interaction of the electron pick-up followed by a slow molecular dissociation. Alignment measurements confirm the essential features of the model. Observations of Lyman α emission after dissociation of H2+ amd H3+ show rapid variations in light yield for small internuclear separations at the foil surface 11. Dynamics of the excited state intramolecular charge transfer The 6-dodecanoyl-2-dimethylaminonaphtalene (laurdan), a derivative of 6-propanoyl- 2-dimethylaminonaphthalene (prodan), has been used as a fluorescent probe in cell imaging, especially in visualizing the lipid rafts by the generalized polarization (GP) images, where GP=(I440-I490)/(I440+I490) with I being the fluorescence intensity. The fluorescence spectrum of laurdan is sensitive to its dipolar environment due to the intramolecular charge transfer (ICT) process in S1 state, which results in a dual emission from the locally excited (LE) and the ICT states. The ICT process and the solvation of the ICT state are very sensitive to the dipolar nature of the environment. In this work, the ICT of laurdan in ethanol has been studied by femtosecond time resolved fluorescence (TRF), especially TRF spectra measurement without the conventional spectral reconstruction method. TRF probes the excited states exclusively, a unique advantage over the pump/probe transient absorption technique, although time resolution of the TRF is generally lower than transient absorption and the TRF spectra measurement was possible only though the spectral reconstruction. Over the years, critical advances in TRF technique have been made in our group to achieve <50 fs time resolution with direct full spectra measurement capability. Detailed ICT and the subsequent solvation processes can be visualized unambiguously from the TRF spectra. Fig. 1 shows the TRF spectra of laurdan in ethanol at several time delays. Surprisingly, two bands at 433 and 476 nm are clearly visible in the TRF spectra of laurdan even at T = 0 fs. As time increases, the band at 476 nm shifts to the red while its intensity increases. The band at 433 nm also shifts slightly to the red, but loses intensity as time increases. The intensity of the 476 nm band reaches maximum at around 5 ps, where it is roughly twice as intense as that at 0 fs, and stays constant until lifetime decay is noticeable. The spectra were fit by two log 12. Carotenoid excited states: Mystery of the dark states and their roles in relaxation pathways Polívka, Tomáš Messina : Universitá di Messina, 2008. s. 36. [ESF Workshop on Ultrafast Excited-State Processes in Condensed Phases. 18.06.2008-21.06.2008, Santa Tecla] Institutional research plan: CEZ:AV0Z50510513 Keywords : carotenoids Subject RIV: BO - Biophysics 13. Study of excited states of mass=4 hypernuclei The excited states, J=1+, of the mirror hypernuclei sub(Λ)sup(4)H and sub(Λsup(4)He were observed by γ-spectroscopy. These hypernuclei were producted by K- absorption in 6Li and 7Li targets. Their identification was given by the detection and the energy measurement of the mesonic decay products: 53 MeV π- for sub(Λ)sup(4)H and 57 MeV π0 for sub(Λ)sup(4)He. A γ line at (1.04+-0.04) MeV has been observed in coincidence with charged pions in the energy range of 40 to 60 MeV then ascribed to a γ-transition in sub(Λ)sup(4)H. Whereas a second γ-line at (1.15+-0.04) MeV, in coincidence with neutral pions of 45 MeV to 75 MeV, has been ascribed to a γ transition in sub(Λ)sup(4)He. With these new experimental data, the phenomenological Λ-N potential for the S-state interaction was recalculated. It may be concluded that the CSB component of this Λ-N potential is spin-independant and that potentials with intrinsic range of 1.5 fm give the bast fit of the total low energy Λ - p elastic scattering cross-sections and to the experimental Bsub(Λ) value for sub(Λ)sup(3)H 14. Ground States and Excited States in a Tunable Graphene Quantum Dot WANG Lin-Jun; CAO Gang; TU Tao; LI Hai-Ou; ZHOU Cheng; HAO Xiao-Jie; GUO Guang-Can; GUO Guo-Ping 2011-01-01 We prepare an etched gate tunable quantum dot in single-layer graphene and present transport measurement in this system. We extract the information of the ground states and excited states of the graphene quantum dot, as denoted by the presence of characteristic Coulomb blockade diamond diagrams. The results demonstrate that the quantum dot in single-layer graphene bodes well in future quantum transport study and quantum computing applications.%@@ We prepare an etched gate tunable quantum dot in single-layer graphene and present transport measurement in this system.We extract the information of the ground states and excited states of the graphene quantum dot, as denoted by the presence of characteristic Coulomb blockade diamond diagrams.The results demonstrate that the quantum dot in single-layer graphene bodes well in future quantum transport study and quantum computing applications. 15. Ground States and Excited States in a Tunable Graphene Quantum Dot We prepare an etched gate tunable quantum dot in single-layer graphene and present transport measurement in this system. We extract the information of the ground states and excited states of the graphene quantum dot, as denoted by the presence of characteristic Coulomb blockade diamond diagrams. The results demonstrate that the quantum dot in single-layer graphene bodes well for future quantum transport study and quantum computing applications. (condensed matter: electronic structure, electrical, magnetic, and optical properties) 16. Excited state dipole moments of chloroanilines and chlorophenols from solvatochromic shifts in electronic absorption spectra: Support for the concept of excited state group moments Prabhumirashi, L. S.; Satpute, R. S. The dipole moments of isomeric o-, m- and p-chloroanilines and chlorophenols in electronically excited L a and L b states are estimated from solvent induced polarization shifts in electronic absorption spectra. It is observed that μ e( L a) > μ e( L b) > μ g, which is consistent with the general theory of polarization red shift. The μ es are found to be approximately co-linear with the corresponding μ gs. The concept of group moments is extended to aromatic molecules in excited states. This approach is found to be useful in understanding correlations among the excited states of mono- and disubstituted benzenes. 17. One-photon excitation and dissociation of both weakly bound rotational excited states and vibrational excited states of HD2+ and photofragment branching ratio D+/H+ of the final predissociative states The presence of weakly bound rotationally excited initial states of HD2+ lying just below the lowest dissociation limit has been observed as well as quasi-bound, predissociative final states above the dissociation limit resulting from one-photon excitation of those weakly bound states. The excitation of the initial weakly bound and possibly only few quasi-bound states took place with 1064 nm laser radiation. The possibility of one-photon excitation of the vibrationally excited initial HD2+ ions is considered. The centre-of-mass kinetic energy distributions of the D+ and H+ fragment were used to identify the possible initial and final states involved in the transitions leading to these fragments. The fragment ratio D+/H+ is shown to be critically dependent on the ion source pressure. A strong preference is observed for the D++HD dissociation channel over the H++D2 channel at high source gas pressures. The centre-of-mass energy of the resulting H+ and D+ fragments was found to agree with predicted theoretical values, and suggest that among initially excited HD2+ ions, only a few of these lie initially above the lowest dissociation limit. (author) 18. One-photon excitation and dissociation of both weakly bound rotational excited states and vibrational excited states of HD{sub 2}{sup +} and photofragment branching ratio D{sup +}/H{sup +} of the final predissociative states Yousif, F.B. [Centro de Ciencias Fisicas, UNAM, Cuernavaca, Morelos (Mexico)]. E-mail: [email protected]; Cisneros, C.; Urquijo, J. de; Alvarez, I. [Centro de Ciencias Fisicas, UNAM, Cuernavaca, Morelos (Mexico) 2001-03-14 The presence of weakly bound rotationally excited initial states of HD{sub 2}{sup +} lying just below the lowest dissociation limit has been observed as well as quasi-bound, predissociative final states above the dissociation limit resulting from one-photon excitation of those weakly bound states. The excitation of the initial weakly bound and possibly only few quasi-bound states took place with 1064 nm laser radiation. The possibility of one-photon excitation of the vibrationally excited initial HD{sub 2}{sup +} ions is considered. The centre-of-mass kinetic energy distributions of the D{sup +} and H{sup +} fragment were used to identify the possible initial and final states involved in the transitions leading to these fragments. The fragment ratio D{sup +}/H{sup +} is shown to be critically dependent on the ion source pressure. A strong preference is observed for the D{sup +}+HD dissociation channel over the H{sup +}+D{sub 2} channel at high source gas pressures. The centre-of-mass energy of the resulting H{sup +} and D{sup +} fragments was found to agree with predicted theoretical values, and suggest that among initially excited HD{sub 2}{sup +} ions, only a few of these lie initially above the lowest dissociation limit. (author) 19. TDDFT study on the excited-state proton transfer of 8-hydroxyquinoline: Key role of the excited-state hydrogen-bond strengthening Lan, Sheng-Cheng; Liu, Yu-Hui 2015-03-01 Density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations have been employed to study the excited-state intramolecular proton transfer (ESIPT) reaction of 8-hydroxyquinoline (8HQ). Infrared spectra of 8HQ in both the ground and the lowest singlet excited states have been calculated, revealing a red-shift of the hydroxyl group (-OH) stretching band in the excited state. Hence, the intramolecular hydrogen bond (O-H···N) in 8HQ would be significantly strengthened upon photo-excitation to the S1 state. As the intramolecular proton-transfer reaction occurs through hydrogen bonding, the ESIPT reaction of 8HQ is effectively facilitated by strengthening of the electronic excited-state hydrogen bond (O-H···N). As a result, the intramolecular proton-transfer reaction would occur on an ultrafast timescale with a negligible barrier in the calculated potential energy curve for the ESIPT reaction. Therefore, although the intramolecular proton-transfer reaction is not favorable in the ground state, the ESIPT process is feasible in the excited state. Finally, we have identified that radiationless deactivation via internal conversion (IC) becomes the main dissipative channel for 8HQ by analyzing the energy gaps between the S1 and S0 states for the enol and keto forms. 20. The Need, Benefits, and Demonstration of a Minimization Principle for Excited States Bacalis, Naoum C 2015-01-01 It is shown that the standard methods of computing excited states in truncated spaces must yield wave functions that, beyond truncation, are in principle veered away from the exact, and a remedy is demonstrated via a presented functional, F$_n$, obeying a minimization principle for excited states. It is further demonstrated that near avoided crossings, between two MCSCF 'flipped roots' the wave function that leads to the excited state has the lowest F$_n$. 1. Structural and excited-state properties of oligoacene crystals from first principles Rangel, Tonatiuh; Berland, Kristian; Sharifzadeh, Sahar; Brown-Altvater, Florian; Lee, Kyuho; Hyldgaard, Per; Kronik, Leeor; Neaton, Jeffrey B. 2016-01-01 Molecular crystals are a prototypical class of van der Waals (vdW) bound organic materials with excited state properties relevant for optoelectronics applications. Predicting the structure and excited state properties of molecular crystals presents a challenge for electronic structure theory, as standard approximations to density functional theory (DFT) do not capture long range vdW dispersion interactions and do not yield excited state properties. In this work, we use a combination of DFT in... 2. Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance Using pulsed optically detected magnetic resonance techniques, we directly probe electron-spin resonance transitions in the excited-state of single nitrogen-vacancy (NV) color centers in diamond. Unambiguous assignment of excited state fine structure is made, based on changes of NV defect photoluminescence lifetime. This study provides significant insight into the structure of the emitting 3E excited state, which is invaluable for the development of diamond-based quantum information processing. 3. Excited states in doubly-odd 98Rh Excited states in the 98Rh nucleus were populated in the 75As(28Si, 2p3n) fusion-evaporation reaction using the 120 MeV 28Si beam. The experiment was carried out at Inter University Accelerator Centre (IUAC), New Delhi. The 28Si projectiles were provided by the 15UD Pelletron accelerator. The target ∼ 3 mg/cm2 thick (ΔE ∼ 20 MeV) was prepared by vacuum evaporation of natural 75As on to ∼ 10 mg/cm2 natural Pb backing followed by rolling. The 103Ag compound nucleus produced in the present reaction is found to decay via several reaction channels associated with 5-particle emission, viz., p4n (98Pd), 2p3n (98Rh), and αp3n (95Ru) with relative population of ∼ 4%, 13%, and 2%, respectively, 4-particle emission, viz., p3n (99Pd), 2p2n (99Rh), and αp2n (96Ru) with relative population of ∼ 12%, 26%, and 20%, respectively, and 3-particle emission, viz., p2n (100Pd), α2n (97Rh), and 2αn (94Tc) with relative population of ∼ 9%, 6%, and 2%, respectively 4. Hertzian spectroscopy application to excited states in accelerated ion beams It is shown that accelerated ion beams enables the application of optical hertzian spectrometry methods to be extended to research on the excited states of free ionic systems. The photon beat method has proved especially simple to apply in beam foil geometry because of the unidirectional beam velocity while the beam gas device is suitable for experiments of the energy level crossing type. Only the resonance technique involving direct application of high-frequency magnetic fields poses serious problems because of the high HF powers necessary. So far structure intervals have been measured in ions carrying up to three charges (seven in the special case of Lamb shift measurements) with a precision of a few percent. The interest of these structure studies in free ions is emphasized particularly. The study of hydrogen-like or helium-like ions of high Z allows the fundamental calculations of quantum electrodynamics to be checked with regard to the Lamb shift or the spontaneous emission theory. In more complex electronic systems, optical spectroscopy of accelerated ion beams gives wavelengths with a resolution reaching 10-5, lifetimes with an accuracy better than 10% when the cascade effects are properly studied, and Lande factors with a precision of several % under present technical conditions. The photon beat method concerns hyperfine nuclear effects in light atoms of Z<=20. Another line of research study the hyperfine structure of a given configuration in an isoelectronic sequence 5. A Simple Hubbard Model for the Excited States of $\\pi$ Conjugated -acene Molecules 2015-01-01 In this paper we present a model that elucidates in a simple way the electronic excited states of $\\pi$ conjugated -acene molecules such as tetracene, pentacene, and hexacene. We use a tight-binding and truncated Hubbard model written in the electron-hole basis to describe the low lying excitations with reasonable quantitative accuracy. We are able to produce semi-analytic wavefunctions for the electronic states of the system, which allows us to compute the density correlation functions for various states such as the ground state, the first two singly excited states, and the lowest lying doubly excited state. We show that in this lowest lying doubly excited state, a state which has been speculated as to being involved in the singlet fission process, the electrons and holes behave in a triplet like manner. 6. The Structure of the Nucleon and its Excited States The past year has been an exciting and productive one for particle physics research at Abilene Christian University. The thrust of our experimental investigations is the study of the nucleon and its excited states. Laboratories where these investigations are presently being conducted are the AGS at Brookhaven, Fermilab and LAMPF. Some analysis of the data for experiments at the Petersburg Nuclear Physics Institute (Gatchina, Russia) is still in progress. Scheduling of activities at different laboratories inevitably leads to occasional conflicts. This likelihood is increased by the present budget uncertainties at the laboratories that make long-term scheduling difficult. For the most part, the investigators have been able to avoid such conflicts. Only one experiment received beam time in 1994 (E890 at the AGS). The situation for 1995-1996 also appears manageable at this point. E890 and another AGS experiment (E909) will run through May, 1995. El 178 at LAMPF is presently scheduled for August/September 1995. E866 at Fermilab is scheduled to start in Spring/Summer 1996. Undergraduate student involvement has been a key element in this research contract since its inception. Summer students participated at all of the above laboratories in 1994 and the same is planned in 1995. A transition to greater involvement by graduate students will provide cohesiveness to ACU involvement at a given laboratory and full-time on-site involvement in the longer running experiments at FNAL and BNL. Funds to support a full-time graduate student are requested this year. Finally, collaboration by Russian, Croatian and Bosnian scientists has proven to be mutually beneficial to these experimental programs and to the overall programs at the institutions involved. Past support has been augmented by other grants from government agencies and from the Research Council at Abilene Christian University. Additional funds are requested in this renewal to enable more programmatic support for these 7. Photodissociation path in H2 + induced by nonuniform optical near fields: Two-step excitation via vibrationally excited states Yamaguchi, Maiku; Nobusada, Katsuyuki 2016-02-01 In this paper, effects of the spatial nonuniformity of an optical near field (ONF) on the molecular photodissociation process are presented. The dissociation dynamics of H2 + was theoretically investigated by solving a non-Born-Oppenheimer Schrödinger equation. It was found that in addition to two dissociation mechanisms, which are one-photon and three-photon processes induced by uniform laser light excitation, the nonuniform ONF opens another dissociation path: two-step excitation mediated by vibrationally excited states. The nonuniformity of the ONF causes a transition between vibrational states that is forbidden according to conventional selection rules, leading to the dissociation path. The dependences of photodissociation on the intensity and nonuniformity of the ONF were calculated and the results validated the two-step dissociation mechanism. 8. Interplay between singlet and triplet excited states in a conformationally locked donor–acceptor dyad Filatov, Mikhail A. 2015-10-13 The synthesis and photophysical characterization of a palladium(II) porphyrin – anthracene dyad bridged via short and conformationally rigid bicyclo[2.2.2]octadiene spacer were achieved. A spectroscopic investigation of the prepared molecule in solution has been undertaken to study electronic energy transfer in excited singlet and triplet states between the anthracene and porphyrin units. By using steady-state and time-resolved photoluminescence spectroscopy it was shown that excitation of the singlet excited state of the anthracene leads to energy transfer to the lower-lying singlet state of porphyrin. Alternatively, excitation of the porphyrin followed by intersystem crossing to the triplet state leads to very fast energy transfer to the triplet state of anthracene. The rate of this energy transfer has been determined by transient absorption spectroscopy. Comparative studies of the dynamics of triplet excited states of the dyad and reference palladium octaethylporphyrin (PdOEP) have been performed. 9. Probing an Excited-State Atomic Transition Using Hyperfine Quantum Beat Spectroscopy Wade, Christopher G; Keaveney, James; Adams, Charles S; Weatherill, Kevin J 2014-01-01 We describe a method to observe the dynamics of an excited-state transition in a room temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the D2 transition, and continuous-wave driving of an excited-state transition from the 6P$_{3/2}$ state to the 7S$_{1/2}$ state. We observe quantum beats in the fluorescence from the 6P$_{3/2}$ state which are modified by the driving of the excited-state transition. The Fourier spectrum of the beat signal yields evidence of Autler-Townes splitting of the 6P$_{3/2}$, F = 5 hyperfine level and Rabi oscillations on the excited-state transition. A detailed model provides qualitative agreement with the data, giving insight to the physical processes involved. 10. Excited state lifetime during photostimulated desorption of no from a Pt surface Magkoev, T. T. 1998-07-01 We analyze the rotational energy distribution N(J) for NO molecules desorbed from a Pt (111) surface, taking into account the valence electron excitations, using a simple impulse model. We find a linear dependence between ln N(J) and (Er)1/2, where Er is the rotational energy of the desorbed molecules. The excited state lifetime and the critical residence time in the excited state, evaluated from the given dependences, are close to each other, and in order of magnitude are 10-15 s. We also estimate the frequency and amplitude of the tilting vibrations of the adsorbed molecules in the excited state. 11. A Dark Excited State of Fluorescent Protein Chromophores, Considered as Brooker Dyes Olsen, Seth 2010-01-01 The green fluorescent protein (GFP) chromophore is an asymmetric monomethine dye system. In the resonance color theory of dyes, a strong optical excitation arises from interactions of two valence-bond structures with a third, higher structure. We use correlated quantum chemistry to show that the anionic chromophore is a resonant Brooker dye, and that the third structure corresponds to a higher stationary electronic state of this species. The excitation energy of this state should be just below the first excitation energy of the neutral form. This has implications for excited state mechanism in GFPs, which we discuss. 12. Two-mode excited entangled coherent states and their entanglement properties Zhou Dong-Lin; Kuang Le-Man 2009-01-01 This paper introduces two types of two-mode excited entangled coherent states(TMEECSs)\|Ψ±(α,m,n)>,studies their entanglement characteristics,and investigates the influence of photon excitations on quantum entanglement.It shows that for the state\|Ψ+(α,m,m)>the two-mode photon excitations affect seriously entanglement character while the state \|Ψ-(α,m,m)>is always a maximally entangled state,and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements.It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number. 13. State-averaged Monte Carlo configuration interaction applied to electronically excited states Coe, J P 2014-01-01 We introduce state-averaging into the method of Monte Carlo configuration interaction (SA-MCCI) to allow the stable and efficient calculation of excited states. We show that excited potential curves for H$_{3}$, including a crossing with the ground state, can be accurately reproduced using a small fraction of the FCI space. A recently introduced error measure for potential curves [J. P. Coe and M. J. Paterson, J. Chem. Phys., 137, 204108 (2012)] is shown to also be a fair approach when considering potential curves for multiple states. We demonstrate that potential curves for LiF using SA-MCCI agree well with the FCI results and the avoided crossing occurs correctly. The seam of conical intersections for CH$_{2}$ found by Yarkony [J. Chem. Phys., 104, 2932 (1996)] is used as a test for SA-MCCI and we compare potential curves from SA-MCCI with FCI results for this system for the first three triplet states. We then demonstrate the improvement from using SA-MCCI on the dipole of the $2$ $^{1}A_{1}$ state of carbo... 14. Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions. The method is applied in a correlation function Monte Carlo calculation to compute ground- and excited-state energies of bosonic van der Waals clusters of up to seven particles. The calculations are performed using trial wave functions with general three-body correlations 15. Local density approximation for exchange in excited-state density functional theory Harbola, Manoj K.; Samal, Prasanjit 2004-01-01 Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies. 16. Ultrafast dynamics and excited state deactivation of [Ru(bpy)2Sq]+ (Ru-Sq) Excited state dynamics of Ru-Sq has been studied using time resolved transient absorption spectroscopy with a time resolution of about 100fs. [Ru(bpy)2Sq]+, where bpy is the bipyridyl and Sq is the semi quinone is known to have two ground state absorption bands corresponding to two different metal to ligand charge transfer (MLCT) states. The absorption band centered on 460 nm is assigned to Ru(d) to bpy (π) and the one on 890 nm is assigned to Ru(d) to Sq(π). Significantly different excited state relaxation dynamics for both the MLCT states have been observed exciting both the bands separately. (author) 17. Influence of multiple excitation of low lying states and giant resonances on heavy ion inelastic spectra The inelastic excitation probabilities of 40Ca, 90Zr and 208Pb impinged by 40Ca projectiles at bombarding energies between 10 and 100 MeV/nucleon are calculated in a model where the excitation amplitudes are evaluated along classical trajectories. The excited states are calculated in the random phase approximation and the nuclear and Coulomb excitations of both low lying states and giant resonances of the target and projectile are taken into account. A general feature of the calculated spectra for near grazing impact parameters and bombarding energies above 20 MeV/nucleon is the presence of broad regularly-spaced structures mainly due to the excitation of multiphonon states built with giant resonances. Cross section estimates for the inelastic excitations are given 18. A Doubles Correction to Electronic Excited States from Configuration Interaction in the Space of Single Substitutions Head-Gordon, Martin; Rico, Rudolph J.; Lee, Timothy J.; Oumi, Manabu 1994-01-01 A perturbative correction to the method of configuration interaction with single substitutions (CIS) is presented. This CIS(D) correction approximately introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS (D) excitation energies are size consistent and the calculational complexity scales with the fifth power of molecular size, akin to second-order Moller-Plesset theory for the ground state. Calculations on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS (D) is a uniform improvement over CIS. CIS(D) appears to be a promising method for examining excited states of large molecules, where more accurate methods are not feasible. 19. Exotic and excited-state meson spectroscopy and radiative transitions from lattice QCD Christopher Thomas 2010-09-01 We discuss recent progress in extracting the excited meson spectrum and radiative transition form factors using lattice QCD. We mention results in the charmonium sector, including the first lattice QCD calculation of radiative transition rates involving excited charmonium states, highlighting results for high spin and exotic states. We present recent results on a highly excited isovector meson spectrum from dynamical anisotropic lattices. Using carefully constructed operators we show how the continuum spin of extracted states can be reliably identified and confidently extract excited states, states with exotic quantum numbers and states of high spin. This spectrum includes the first spin-four state extracted from lattice QCD. We conclude with some comments on future prospects. 20. Self-Consistent Optimization of Excited States within Density-Functional Tight-Binding. Kowalczyk, Tim; Le, Khoa; Irle, Stephan 2016-01-12 We present an implementation of energies and gradients for the ΔDFTB method, an analogue of Δ-self-consistent-field density functional theory (ΔSCF) within density-functional tight-binding, for the lowest singlet excited state of closed-shell molecules. Benchmarks of ΔDFTB excitation energies, optimized geometries, Stokes shifts, and vibrational frequencies reveal that ΔDFTB provides a qualitatively correct description of changes in molecular geometries and vibrational frequencies due to excited-state relaxation. The accuracy of ΔDFTB Stokes shifts is comparable to that of ΔSCF-DFT, and ΔDFTB performs similarly to ΔSCF with the PBE functional for vertical excitation energies of larger chromophores where the need for efficient excited-state methods is most urgent. We provide some justification for the use of an excited-state reference density in the DFTB expansion of the electronic energy and demonstrate that ΔDFTB preserves many of the properties of its parent ΔSCF approach. This implementation fills an important gap in the extended framework of DFTB, where access to excited states has been limited to the time-dependent linear-response approach, and affords access to rapid exploration of a valuable class of excited-state potential energy surfaces. PMID:26587877 1. Ground and Excited States of Bipolarons in Two and Three Dimensions RUAN Yong-Hong; CHEN Qing-Hu 2007-01-01 The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The groundstate (GS) and excited-state energies of the Fr(o)hlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given. 2. Continuum excitations of $^{26}$O in a three-body model: $0^+$ and $2^+$ states Grigorenko, L V 2015-01-01 The structure and decay dynamics for $0^+$ and $2^+$ continuum excitations of $^{26}$O are investigated in a three-body $^{24}$O+$n$+$n$ model. Validity of a simple approximation for the cross section profile for long-lived $2n$ emission is demonstrated. Sequence of three $0^+$ monopole ("breathing mode" type) excited states is predicted. These states could probably be interpreted as analogues of Efimov states pushed into continuum by insufficient binding. The possible energies of the $2^+$ states are related to excitation spectrum of $^{25}$O. We discuss possible connection of predicted $^{26}$O spectrum with observations. 3. Protolytic dissociation of cyano derivatives of naphthol, biphenyl and phenol in the excited state: A review Szczepanik, Beata 2015-11-01 The excited state proton transfer (ESPT) has been extensively studied for hydroxyarenes, phenols, naphthols, hydroxystilbenes, etc., which undergo large enhancement of acidity upon electronic excitation, thus classified as photoacids. The changes of acidic character in the excited state of cyano-substituted derivatives of phenol, hydroxybiphenyl and naphthol are reviewed in this paper. The acidity constants pKa in the ground state (S0), pKa∗ in the first singlet excited state (S1) and the change of the acidity constant in the excited state ΔpKa for the discussed compounds are summarized and compared. The results of the acidity studies show, that the "electro-withdrawing" CN group in the molecules of naphthol, hydroxybiphenyl and phenol causes dramatic increase of their acidity in the excited state in comparison to the ground state. This effect is greatest for the cyanonaphthols (the doubly substituted CN derivatives are almost as strong as a mineral acid in the excited state), comparable for cyanobiphenyls, and smaller for phenol derivatives. The increase of acidity enables proton transfer to various organic solvents, and the investigation of ESPT can be extended to a variety of solvents besides water. The results of theoretical investigations were also presented and used for understanding the protolytic equilibria of cyano derivatives of naphthol, hydroxybiphenyl and phenol. 4. Excited triplet states as photooxidants in surface waters Canonica, S. 2012-12-01 The chromophoric components of dissolved organic matter (DOM) are generally the main absorbers of sunlight in surface waters and therefore a source of transient reactants under irradiation. Such short-lived species can be relevant for the fate of various classes of chemical contaminants in the aquatic environment. The present contribution focuses on the role of excited triplet states of chromophoric DOM, 3CDOM, as transient photooxidants initiating the transformation and degradation of organic chemical contaminants. An early study [1] indicated that 3CDOM may play a dominant role in the photo-induced transformation of electron-rich phenols, a conclusion which was later fortified by the results of transient absorption investigations using aromatic ketones as model photosensitizers [2] and by a recent careful analysis of the effect of oxygen concentration on transformation rates [3]. The variety of aquatic contaminants shown to be affected by triplet-induced oxidation has kept increasing, phenylurea herbicides [4], sulfonamide antibiotics [5] and some phytoestrogens [6] being prominent examples. Recent research has shown that the triplet-induced transformation of specific contaminants, especially aromatic nitrogen compounds, could be inhibited by the presence of DOM, very probably due to its antioxidant moieties [7]. While such moieties are not relevant for the quenching of 3CDOM, they are expected to react with it in a similar way as the studied contaminants. Analogous reactions can be postulated to occur in liquid or solid phases of the atmospheric environment, as demonstrated in the case of HONO formation [8]. References 1. Canonica, S.; Jans, U.; Stemmler, K.; Hoigné, J. Transformation kinetics of phenols in water: Photosensitization by dissolved natural organic material and aromatic ketones. Environ. Sci. Technol. 1995, 29 (7), 1822-1831. 2. Canonica, S.; Hellrung, B.; Wirz, J. Oxidation of phenols by triplet aromatic ketones in aqueous solution. J. Phys 5. Heme photolysis occurs by ultrafast excited state metal-to-ring charge transfer. Franzen, S.; Kiger, L.; Poyart, C; Martin, J.L. 2001-01-01 Ultrafast time-resolved resonance Raman spectra of carbonmonoxy hemoglobin (Hb), nitroxy Hb, and deoxy Hb are compared to determine excited state decay mechanisms for both ligated and unligated hemes. Transient absorption and Raman data provide evidence for a sequential photophysical relaxation pathway common to both ligated and unligated forms of Hb (photolyzed heme), in which the excited state 1Q decays sequentially: 1Q-->HbI-->HbII-->Hb ground state. Consistent with the observed kinetic... 6. Suppression of excited-state effects in lattice determination of nucleon electromagnetic form factors von Hippel, G M; Djukanovic, D; Hua, J; Jäger, B; Junnarkar, P; Meyer, H B; Rae, T D; Wittig, H 2014-01-01 We study the ability of a variety of fitting techniques to extract the ground state matrix elements of the vector current from ratios of nucleon three- and two-point functions that contain contaminations from excited states. Extending our high-statistics study of nucleon form factors, we are able to demonstrate that the treatment of excited-state contributions in conjunction with approaching the physical pion mass has a significant impact on the $Q^2$-dependence of the form factors. 7. Dual channel nitrogen laser useful for nanosecond excited state studies Shipman (1967) adapted the Blumlein discharge circuit to lasers and this method has proved highly useful in producing high peak pulses. The authors describe a double Blumlein producing two 250 kW pulses separated by 15 nanosecs. The dual channel nitrogen laser is designed for use in atomic spectroscopy, the first pulse excites the target atoms while the second pumps another laser whose output is used to study the levels. (U.S.) 8. Carbazole-containing light- emitting polymers: Properties of excited states 2003-01-01 A series of light-emitting conjugated polymers alternatively involving carbazole and bivinylene arylene moieties in the main chain were synthesized via Wittig-Horner type copolymerization. The photoinduced charge transfer process relating to these polymers was investigated by using the technique of fluorescence spectroscopy. The interaction between excited copolymers and C60 in benzene solution was studied. The fluorescence quenching can be well described by the "sphere-of-action" mechanism. It is believed that two basic steps are involved in the quenching process, i.e. the diffusion of excitation within the conjugated polymers and the dissociation of the exctions trapped by fullerene. The radius of the sphere-of-action can be related to the excitation diffusion length, which depends on the lifetime of the exciton. The dynamic fluorescence quenching of the copolymers by another quencher, 1,4-dicyanobenzene (DCB) was also surveyed. Copolymers with different chain conformations show different temperature effects in the dynamic quenching. A planar conformation is beneficial for the quenching via bimolecular collision. 9. Reconstruction of an excited-state molecular wave packet with attosecond transient absorption spectroscopy Cheng, Yan; Chini, Michael; Wang, Xiaowei; González-Castrillo, Alberto; Palacios, Alicia; Argenti, Luca; Martín, Fernando; Chang, Zenghu 2016-08-01 Attosecond science promises to allow new forms of quantum control in which a broadband isolated attosecond pulse excites a molecular wave packet consisting of a coherent superposition of multiple excited electronic states. This electronic excitation triggers nuclear motion on the molecular manifold of potential energy surfaces and can result in permanent rearrangement of the constituent atoms. Here, we demonstrate attosecond transient absorption spectroscopy (ATAS) as a viable probe of the electronic and nuclear dynamics initiated in excited states of a neutral molecule by a broadband vacuum ultraviolet pulse. Owing to the high spectral and temporal resolution of ATAS, we are able to reconstruct the time evolution of a vibrational wave packet within the excited B'Σ1u+ electronic state of H2 via the laser-perturbed transient absorption spectrum. 10. Characterization of ground state entanglement by single-qubit operations and excitation energies Giampaolo, S M; Illuminati, F; Verrucchi, P; Giampaolo, Salvatore M.; Illuminati, Fabrizio; Siena, Silvio De; Verrucchi, Paola 2006-01-01 We consider single-qubit unitary operations and study the associated excitation energies above the ground state of interacting quantum spins. We prove that there exists a unique operation such that the vanishing of the corresponding excitation energy determines a necessary and sufficient condition for the separability of the ground state. We show that the energy difference associated to factorization exhibits a monotonic behavior with the one-tangle and the entropy of entanglement, including non analiticity at quantum critical points. The single-qubit excitation energy thus provides an independent, directly observable characterization of ground state entanglement, and a simple relation connecting two universal physical resources, energy and nonlocal quantum correlations. 11. Mechanistic photodecarboxylation of pyruvic acid: Excited-state proton transfer and three-state intersection Photodissociation dynamics of pyruvic acid experimentally differs from that of commonly known ketones. We have employed the complete active space self-consistent field and its multi-state second-order perturbation methods to study its photodissociation mechanism in the S0, T1, and S1 states. We have uncovered four nonadiabatic photodecarboxylation paths. (i) The S1 system relaxes via an excited-state intramolecular proton transfer (ESIPT) to a hydrogen-transferred tautomer, near which an S1/S0 conical intersection funnels the S1 to S0 state. Then, some trajectories continue completing the decarboxylation reaction in the S0 state; the remaining trajectories via a reverse hydrogen transfer return to the S0 minimum, from which a thermal decarboxylation reaction occurs. (ii) Due to a small S1 −T1 energy gap and a large S1/T1 spin-orbit coupling, an efficient S1 → T1 intersystem crossing process happens again near this S1/S0 conical intersection. When decaying to T1 state, a direct photodecarboxylation proceeds. (iii) Prior to ESIPT, the S1 system first decays to the T1 state via an S1 → T1 intersystem crossing; then, the T1 system evolves to a hydrogen-transferred tautomer. Therefrom, an adiabatic T1 decarboxylation takes place due to a small barrier of 7.7 kcal/mol. (iv) Besides the aforementioned T1 ESIPT process, there also exists a comparable Norrish type I reaction in the T1 state, which forms the ground-state products of CH3CO and COOH. Finally, we have found that ESIPT plays an important role. It closes the S1-T1 and S1-S0 energy gaps, effecting an S1/T1/S0 three-state intersection region, and mediating nonadiabatic photodecarboxylation reactions of pyruvic acid 12. Bound states and entanglement in the excited states of quantum spin chains We investigate the entanglement properties of the excited states of the spin- (1/2) Heisenberg (XXX) chain with isotropic antiferromagnetic interactions, by exploiting the Bethe ansatz solution of the model. We consider eigenstates obtained from both real and complex solutions (‘strings’) of the Bethe equations. Physically, the former are states of interacting magnons, whereas the latter contain bound states of groups of particles. We first focus on the situation with few particles in the chain. Using exact results and semiclassical arguments, we derive an upper bound SMAX for the entanglement entropy. This exhibits an intermediate behaviour between logarithmic and extensive, and it is saturated for highly-entangled states. As a function of the eigenstate energy, the entanglement entropy is organized in bands. Their number depends on the number of blocks of contiguous Bethe–Takahashi quantum numbers. In the presence of bound states a significant reduction in the entanglement entropy occurs, reflecting that a group of bound particles behaves effectively as a single particle. Interestingly, the associated entanglement spectrum shows edge-related levels. At a finite particle density, the semiclassical bound SMAX becomes inaccurate. For highly-entangled states SA∝ Lc, with Lc the chord length, signalling the crossover to extensive entanglement. Finally, we consider eigenstates containing a single pair of bound particles. No significant entanglement reduction occurs, in contrast with the few-particle case. (paper) 13. Effects of crossed states on photoluminescence excitation spectroscopy of InAs quantum dots Lin Chien-Hung 2011-01-01 Full Text Available Abstract In this report, the influence of the intrinsic transitions between bound-to-delocalized states (crossed states or quasicontinuous density of electron-hole states on photoluminescence excitation (PLE spectra of InAs quantum dots (QDs was investigated. The InAs QDs were different in size, shape, and number of bound states. Results from the PLE spectroscopy at low temperature and under a high magnetic field (up to 14 T were compared. Our findings show that the profile of the PLE resonances associated with the bound transitions disintegrated and broadened. This was attributed to the coupling of the localized QD excited states to the crossed states and scattering of longitudinal acoustical (LA phonons. The degree of spectral linewidth broadening was larger for the excited state in smaller QDs because of the higher crossed joint density of states and scattering rate. 14. Effect of xanthophyll composition on the chlorophyll excited state lifetime in plant leaves and isolated LHCII Johnson, Matthew P.; Zia, Ahmad; Horton, Peter; Ruban, Alexander V. 2010-07-01 Xanthophyll excited states have been implicated by transient absorption and two-photon excitation studies in playing a key role in the regulation of photosynthetic light harvesting via photoprotective energy dissipation. For any proposed quenching mechanism to be effective it must reduce the chlorophyll excited state lifetime from 2 ns to ˜0.5-0.4 ns. In the presented study the effect of xanthophyll composition on the chlorophyll excited state lifetime in Arabidopsis leaves in the light harvesting ( F m) and photoprotective (NPQ) states was determined. The data was compared to the chlorophyll excited state lifetime of native isolated LHCII and CP26 in detergent micelles with varying xanthophyll composition. It was found that although the differences in xanthophyll composition between LHC complexes from various Arabidopsis mutants were sufficient to explain the varying F m lifetime (and varying PSII efficiency), they were not of a sufficient scale to fully explain the observed differences in the NPQ lifetimes. Only when the LHC complexes were exposed to a low detergent/low pH media, a condition known to mimic the conformational state of LHCII associated with NPQ in vivo, were variations in excited state lifetime large enough to explain the differences observed in leaves. Furthermore, the data reveal that the replacement of lutein by either zeaxanthin or violaxanthin in the internal xanthophyll binding sites of LHCII and CP26 reduces the efficiency of energy dissipation in the photoprotective state in leaves and isolated complexes. 15. $\\sigma$-SCF: A Direct Energy-targeting Method To Mean-field Excited States Ye, Hong-Zhou; Ricke, Nathan D; Van Voorhis, Troy 2016-01-01 The mean-field solutions of electronic excited states are much less accessible than ground state (e.g.\\ Hartree-Fock) solutions. Energy-based optimization methods for excited states, like $\\Delta$-scf, tend to fall into the lowest solution consistent with a given symmetry -- a problem known as "variational collapse". In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, $\\sigma$-scf, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find \\emph{all} excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states -- ground or excited -- are treated on an equal footing. Third, it provides an alternate approach to locate $\\Delta$-scf solutions that are otherwise inaccessible by the... 16. Ultrafast Excited State Relaxation of a Metalloporphyrin Revealed by Femtosecond X-ray Absorption Spectroscopy. Shelby, Megan L; Lestrange, Patrick J; Jackson, Nicholas E; Haldrup, Kristoffer; Mara, Michael W; Stickrath, Andrew B; Zhu, Diling; Lemke, Henrik T; Chollet, Matthieu; Hoffman, Brian M; Li, Xiaosong; Chen, Lin X 2016-07-20 Photoexcited Nickel(II) tetramesitylporphyrin (NiTMP), like many open-shell metalloporphyrins, relaxes rapidly through multiple electronic states following an initial porphyrin-based excitation, some involving metal centered electronic configuration changes that could be harnessed catalytically before excited state relaxation. While a NiTMP excited state present at 100 ps was previously identified by X-ray transient absorption (XTA) spectroscopy at a synchrotron source as a relaxed (d,d) state, the lowest energy excited state (J. Am. Chem. Soc., 2007, 129, 9616 and Chem. Sci., 2010, 1, 642), structural dynamics before thermalization were not resolved due to the ∼100 ps duration of the available X-ray probe pulse. Using the femtosecond (fs) X-ray pulses of the Linac Coherent Light Source (LCLS), the Ni center electronic configuration from the initial excited state to the relaxed (d,d) state has been obtained via ultrafast Ni K-edge XANES (X-ray absorption near edge structure) on a time scale from hundreds of femtoseconds to 100 ps. This enabled the identification of a short-lived Ni(I) species aided by time-dependent density functional theory (TDDFT) methods. Computed electronic and nuclear structure for critical excited electronic states in the relaxation pathway characterize the dependence of the complex's geometry on the electron occupation of the 3d orbitals. Calculated XANES transitions for these excited states assign a short-lived transient signal to the spectroscopic signature of the Ni(I) species, resulting from intramolecular charge transfer on a time scale that has eluded previous synchrotron studies. These combined results enable us to examine the excited state structural dynamics of NiTMP prior to thermal relaxation and to capture intermediates of potential photocatalytic significance. PMID:27286410 17. Semiclassical hyperspherical matrix elements for helium doubly excited states A classical description of the two-electron atom, analogous to the quantum adiabatic hyperspherical channel approach, is presented. The classical problems, analogue to the quantum eigenvalue problem for the great angular momentum operator, and the separated dynamical systems defined by each of the other constants of the motion of the non-interacting system are solved, using the Hamiltonian-Jacobi method. Some matrix elements of the Coulomb interaction terms of the Hamilton for doubly excited helium atom using the Heisenberg correspondence principle are calculated. (author). 26 refs, 4 tabs 18. Neutral Fermion Excitations in the Moore-Read state at \ Moller, Gunnar; Wojs, Arkadiusz; Cooper, Nigel R. 2010-01-01 We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux $N_\\phi=2N-3$ can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two qu... 19. Thermodynamical property of entanglement entropy for excited states. Bhattacharya, Jyotirmoy; Nozaki, Masahiro; Takayanagi, Tadashi; Ugajin, Tomonori 2013-03-01 We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two-dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy. PMID:23496702 20. Direct excitation of high-orbital-angular-momentum states of rare-gas atoms by electron impact Tarr, S.M.; Schiavone, J.A.; Freund, R.S. 1980-12-01 Narrow threshold peaks are observed in the excitation functions for high-Rydberg states of the rare-gas atoms. They are considered to be evidence for the direct excitation of high-orbital-angular-momentum (l) states. 1. The Millimeter-Wave Spectrum of Methacrolein. Torsion-Rotation Effects in the Excited States Zakharenko, Olena; Motiyenko, R. A.; Aviles Moreno, Juan-Ramon; Huet, T. R. 2015-06-01 Last year we reported the analysis of the rotational spectrum of s-trans conformer of methacrolein CH2=C(CH3)CHO in the ground vibrational state. In this talk we report the study of its low lying excited vibrational states. The study is based on room-temperature absorption spectra of methacrolein recorded in the frequency range 150 - 465 GHz using the spectrometer in Lille. The new results include assignment of the first excited torsional state (131 cm-1), and the joint analysis of the vt = 0 and vt = 1 states, that allowed us to improve the model in the frame of Rho-Axis-Method (RAM) Hamiltonian and to remove some strong correlations between parameters. Also we assigned the first excited vibrational state of the skeletal torsion mode (170 cm-1). The inverse sequence of A and E tunneling substates as well as anomalous A-E splittings observed for the rotational lines of vsk = 1 state clearly indicate a coupling between methyl torsion and skeletal torsion. However we were able to fit within experimental accuracy the rotational lines of vsk = 1 state using the RAM Hamiltonian. Because of the inversion of the A and E tunneling substates the rotational lines of the vsk = 1 states were assumed to belong to a virtual first excited torsional state. Finally, we assigned several low-Ka rotational transitions of the excited vibrational states above 200 cm-1 but their analysis is complicated by different rotation-vibration interactions. In particular there is an evidence of the Fermi-type resonance between the second excited torsional state and the first excited state of the in-plane skeletal bending mode (265 cm-1). Support from the French Laboratoire d'Excellence CaPPA (Chemical and Physical Properties of the Atmosphere) through contract ANR-10-LABX-0005 of the Programme d'Investissements d'Avenir is acknowledged. Zakharenko O. et al., 69th ISMS, 2014, TI01 2. Structural and excited-state properties of oligoacene crystals from first principles Rangel, Tonatiuh; Berland, Kristian; Sharifzadeh, Sahar; Brown-Altvater, Florian; Lee, Kyuho; Hyldgaard, Per; Kronik, Leeor; Neaton, Jeffrey B. 2016-03-01 Molecular crystals are a prototypical class of van der Waals (vdW) bound organic materials with excited-state properties relevant for optoelectronics applications. Predicting the structure and excited-state properties of molecular crystals presents a challenge for electronic structure theory, as standard approximations to density functional theory (DFT) do not capture long-range vdW dispersion interactions and do not yield excited-state properties. In this work, we use a combination of DFT including vdW forces, using both nonlocal correlation functionals and pairwise correction methods, together with many-body perturbation theory (MBPT) to study the geometry and excited states, respectively, of the entire series of oligoacene crystals, from benzene to hexacene. We find that vdW methods can predict lattice constants within 1% of the experimental measurements, on par with the previously reported accuracy of pairwise approximations for the same systems. We further find that excitation energies are sensitive to geometry, but if optimized geometries are used MBPT can yield excited-state properties within a few tenths of an eV from experiment. We elucidate trends in MBPT-computed charged and neutral excitation energies across the acene series and discuss the role of common approximations used in MBPT. 3. Inelastic WIMP-nucleus scattering to the first excited state in $^{125}$Te Vergados, J D; Kortelainen, M; Pirinen, P; Srivastava, P C; Suhonen, J; Thomas, A W 2016-01-01 The direct detection of dark matter constituents, in particular the weakly interacting massive particles (WIMPs), is considered central to particle physics and cosmology. In this paper we study transitions to the excited states, possible in some nuclei, which have sufficiently low lying excited states. Examples considered previously were the first excited states of $^{127}$I and $^{129}$Xe and $^{83}$Kr. Here we examine $^{125}$Te, which offers some advantages and is currently being considered as a target.In all these cases the extra signature of the gamma rays following the de-excitation of these states has definite advantages over the purely nuclear recoil and, in principle, such a signature can be exploited experimentally. A brief discussion of the experimental feasibility is given in the context of the CUORE experiment. 4. Hyperon and charmed baryon masses and nucleon excited states from lattice QCD Alexandrou, Constantia 2014-01-01 We discuss the status of current dynamical lattice QCD simulations in connection to the emerging results on the strange and charmed baryon spectrum, excited states of the nucleon and the investigation of the structure of scalar mesons. 5. Notes on entanglement entropy for excites holographic states in 2d 2016-01-01 In this work we revisit the problem of contributions of excited holographic states to the entanglement entropy in two-dimensional conformal field theories. Using the results of replica trick method we find three expressions for these contributions. First, we express the contribution of the excited states in terms of Aharonov invariants. It is shown that beside the Schwarzian, the one-point functions of descendants of energy-momentum also contribute. Given Schwarz-Christoffel map, the contributions to any order can be easily computed. The second expression relates the entanglement entropy of excited states to Faber polynomials and Grunsky coefficients. Based on the relation of Grunsky coefficiens to tau-funcion of dispersionless Toda hierarchy, we find the third expression for contributions of excited holographic states to the entanglement entropy. 6. Theoretical direct WIMP detection rates for inelastic scattering to excited states The recent WMAP and Planck data have confirmed that exotic dark matter together with the vacuum energy (cosmological constant) dominate in the flat Universe. Many extensions of the standard model provide dark matter candidates, in particular Weakly Interacting Massive Particles (WIMPs). Thus the direct dark matter detection is central to particle physics and cosmology. Most of the research on this issue has hitherto focused on the detection of the recoiling nucleus. In this paper we study transitions to the excited states, possible in some nuclei, which have sufficiently low lying excited states. Good examples are the first excited states of 127I and 129Xe. We find appreciable branching ratios for the inelastic scattering mediated by the spin cross sections. So, in principle, the extra signature of the gamma ray following the de-excitation of these states can, in principle, be exploited experimentally 7. Dark excited states of carotenoid in light harvesting complex probing with femtosecond stimulated Raman spectroscopy Sakai S. 2013-03-01 Full Text Available Vibrational dynamics of dark excited states in carotenoids have been investigated using tunable Raman pump pulses. The S1 state has same vibrational dynamics in light-harvesting complex (LH1 and solution. The S* state in LH1 has similar vibrational modes with the triplet state of carotenoid. However, the so-called S* state in solution does not have the modes and is concluded to be different from the S* state in LH1. 8. Excited-state absorption and radiative up-conversion in porphyrin-doped gels Wang, X.; Yates, L. M., III; Knobbe, Edward T. 1994-10-01 Optical absorption and emission behavior have been investigated in aluminosilicate sol-gel materials containing the sodium salt of tetra-4-sulfonatophenylporphyrinatocopper(II). Concentration-dependent nonlinear absorption was observed in the porphyrin-doped specimens. Up-converted optical emission from the second excited doublet band was studied, and a saturated behavior was observed as a function of incoming excitation energies. These phenomena have been attributed to excited state absorption from both doublet and quartet manifolds. Intersystem crossing and quartet-quartet absorption effects are believed to dominate the nonlinear processes, especially in the case of strong excitation. Rate equation analysis also suggests that the quartet manifold is extensively involved for intersystem relaxation and excited state absorption. Good agreement was obtained between experimental observations and the presented rate equations. 9. Mixed symmetry states and isospin excitation in N = Z nucleus 52Fe 2008-01-01 The interacting boson model with isospin (IBM-3) was applied to study the band structure and electromagnetic transition properties of the low-lying states in the even-even N = Z nucleus 52Fe. The isospin excitation states with T = 0, 1 and 2 were identified, and compared with the available data. The study shows that the 2+3 state is the lowest mixed symmetry state in 52Fe. The excitation energy of the second 0+2 state with T = 0 in nucleus 52Fe was identified. The model calculations with the data show a reasonably good agreement. 10. Multiple-Resonance Local Wave Functions for Accurate Excited States in Quantum Monte Carlo. Zulfikri, Habiburrahman; Amovilli, Claudio; Filippi, Claudia 2016-03-01 We introduce a novel class of local multideterminant Jastrow-Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to the bonding patterns of the different Lewis resonance structures of the molecule. We capitalize on the concept of orbital domains of local coupled-cluster methods, which is here applied to the active space to select the orbitals to correlate and construct the important transitions. The excitations are further grouped into classes, which are ordered in importance and can be systematically included in the Jastrow-Slater wave function to ensure a balanced description of all states of interest. We assess the performance of the proposed wave function in the calculation of vertical excitation energies and excited-state geometry optimization of retinal models whose π → π* state has a strong intramolecular charge-transfer character. We find that our multiresonance wave functions recover the reference values of the total energies of the ground and excited states with only a small number of excitations and that the same expansion can be flexibly used at very different geometries. Furthermore, significant computational saving can also be gained in the orbital optimization step by selectively mixing occupied and virtual orbitals based on spatial considerations without loss of accuracy on the excitation energy. Our multiresonance wave functions are therefore compact, accurate, and very promising for the calculation of multiple excited states of different character in large molecules. PMID:26761421 11. Counting the number of excited states in organic semiconductor systems using topology Catanzaro, Michael J. [Department of Mathematics, Wayne State University, 656 W. Kirby, Detroit, Michigan 48202 (United States); Shi, Tian [Department of Chemistry, Wayne State University, 5101 Cass Ave., Detroit, Michigan 48202 (United States); Tretiak, Sergei, E-mail: [email protected] [Theoretical Division, Center for Nonlinear Studies, and Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Chernyak, Vladimir Y., E-mail: [email protected] [Department of Mathematics, Wayne State University, 656 W. Kirby, Detroit, Michigan 48202 (United States); Department of Chemistry, Wayne State University, 5101 Cass Ave., Detroit, Michigan 48202 (United States) 2015-02-28 Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system. 12. Distribution of populations in excited states of electrodeless discharge lamp of Rb atoms TAO ZhiMing; WANG YanFei; HONG YeLong; WANG DongYing; ZHANG ShengNan; ZHUANG Wei; CHEN JingBiao 2013-01-01 The intensity of fluorescence spectral lines of Rb atoms in the region of 350-1110 nm is measured in eletrodeless discharge lamp.The population ratio between the excited states is calculated according to the spontaneous transition probabilities with rate equations.At the same time,the population density of energy level is also obtained.The results provide the potential applications of electrodeless discharge lamp in atomic filter and optical frequency reference at higher excited states without a pumping laser. 13. Sum rule analysis of vector and axial-vector spectral functions with excited states in vacuum Hohler, Paul M.; Rapp, Ralf 2012-01-01 We simultaneously analyze vector and axial-vector spectral functions in vacuum using hadronic models constrained by experimental data and the requirement that Weinberg-type sum rules are satisfied. Upon explicit inclusion of an excited vector state, viz. rho', and the requirement that the perturbative continua are degenerate in vector and axial-vector channels, we deduce the existence of an excited axial-vector resonance state, a1', in order that the Weinberg sum rules are satisfied. The resu... 14. Relativistic Hartree-Fock-Bogoliubov theory: ground states and excitations Long, Wen Hui; Meng, Jie; Giai, Nguyen Van The covariant density functional (CDF) theory with the Fock diagrams, the indivisible part of the effective nuclear interaction, is introduced, including both the relativistic Hartree-Fock and its extension -- the relativistic Hartree-Fock-Bogoliubov methods. The specific roles played by Fock diagrams, particularly for the new degrees of freedom associated with the π and ρ-tensor fields and the non-local mean fields, are discussed in determining the nuclear energy functional, the shell structure and the evolution, and nuclear isospin excitations. The existing problems and limits of the CDF theory with Fock terms are also discussed, and the perspective on a new algorithm of dealing with the non-local Fock terms is given. 15. First observation of excited states in 108Sb A spectroscopic study of 108Sb has been carried out as a part of a larger experiment where in total twenty-nine different residual nuclei were identified. This study gives the first information on excited levels in this nucleus. A low-lying two-quasi-particle multiplet together with some of the higher lying levels are discussed within the framework of the nuclear shell model. A rotational, strongly coupled, band is identified as, most likely, being built on the deformed πg9/2-1xνh11/2 configuration in accordance with total routhian surface calculations. Tentative spins and parities are presented as well as B(M1)/B(E2) ratios for some of the transitions in the strongly coupled band. ((orig.)) 16. Steady-state photoluminescent excitation characterization of semiconductor carrier recombination Photoluminescence excitation spectroscopy is a contactless characterization technique that can provide valuable information about the surface and bulk recombination parameters of a semiconductor device, distinct from other sorts of photoluminescent measurements. For this technique, a temperature-tuned light emitting diode (LED) has several advantages over other light sources. The large radiation density offered by LEDs from near-infrared to ultraviolet region at a low cost enables efficient and fast photoluminescence measurements. A simple and inexpensive LED-based setup facilitates measurement of surface recombination velocity and bulk Shockley-Read-Hall lifetime, which are key parameters to assess device performance. Under the right conditions, this technique can also provide a contactless way to measure the external quantum efficiency of a solar cell 17. High-energy excited states in {sup 98}Cd Braun, Norbert; Blazhev, Andrey; Jolie, Jan [Institut fuer Kernphysik, Universitaet Koeln (Germany); Boutachkov, Plamen; Gorska, Magda; Grawe, Hubert; Pietri, Stephane [GSI, Darmstadt (Germany); Brock, Tim; Nara Singh, B.S.; Wadsworth, Robert [Department of Physics, University of York, York (United Kingdom); Liu, Zhong [University of Edinburgh, Edinburgh (United Kingdom) 2009-07-01 Studies of isomerism in the proton-rich N {approx_equal}Z nuclei around {sup 100}Sn give important insights into the role of proton-neutron pairing and also serve as testing grounds for nuclear models. In summer 2008, an experiment on {sup 96,97,98}Cd was performed using the FRS fragment separator and the RISING germanium array at GSI. These exotic nuclei of interest were produced using fragmentation of a 850 MeV/u {sup 124}Xe beam on a 4 g/cm{sup 2} {sup 9}Be target and finally implanted into an active stopper consisting of 9 double-sided silicon strip detectors. In {sup 98}Cd, a new high-energy isomeric transition was identified. Preliminary results on {sup 98}Cd are presented and their implications for the high-excitation level scheme are discussed. 18. Steady-state photoluminescent excitation characterization of semiconductor carrier recombination Bhosale, J. S.; Moore, J. E.; Wang, X.; Bermel, P.; Lundstrom, M. S. 2016-01-01 Photoluminescence excitation spectroscopy is a contactless characterization technique that can provide valuable information about the surface and bulk recombination parameters of a semiconductor device, distinct from other sorts of photoluminescent measurements. For this technique, a temperature-tuned light emitting diode (LED) has several advantages over other light sources. The large radiation density offered by LEDs from near-infrared to ultraviolet region at a low cost enables efficient and fast photoluminescence measurements. A simple and inexpensive LED-based setup facilitates measurement of surface recombination velocity and bulk Shockley-Read-Hall lifetime, which are key parameters to assess device performance. Under the right conditions, this technique can also provide a contactless way to measure the external quantum efficiency of a solar cell. 19. A theoretical study of electronic excited states of photosynthetic reaction center in Rhodopseudomonas viridis 2006-01-01 The electronic singlet vertical excited states of photosynthetic reaction center (PSRC) in Rhodopseudomonas (Rps.) viridis were investigated by ZINDO and INDO/S methods. The effects of the interactions of pigment-pigment and pigment-protein on the electronic excitations were examined. The calculation results showed that the interactions of pigment-pigment and pigment-protein play an important role in reasonably assigning the experimental absorption and circular dichroism (CD) spectra of PSRC in Rps. virids. By comparing the theoretically computed excited states with the experimental absorption and CD spectra, satisfactory assignments of the experimental spectroscopic peaks were achieved. 20. Non-orthogonal configuration interaction for the calculation of multielectron excited states Sundstrom, Eric J., E-mail: [email protected]; Head-Gordon, Martin [Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States) 2014-03-21 We apply Non-orthogonal Configuration Interaction (NOCI) to molecular systems where multielectron excitations, in this case double excitations, play a substantial role: the linear polyenes and β-carotene. We demonstrate that NOCI when applied to systems with extended conjugation, provides a qualitatively correct wavefunction at a fraction of the cost of many other multireference treatments. We also present a new extension to this method allowing for purification of higher-order spin states by utilizing Generalized Hartree-Fock Slater determinants and the details for computing 〈S{sup 2}〉 for the ground and excited states. 1. Excited state evolution towards ligand loss and ligand chelation at group 6 metal carbonyl centres. Manton, Jennifer C; Amirjalayer, Saeed; Coleman, Anthony C; McMahon, Suzanne; Harvey, Emma C; Greetham, Gregory M; Clark, Ian P; Buma, Wybren Jan; Woutersen, Sander; Pryce, Mary T; Long, Conor 2014-12-21 The photochemistry and photophysics of three model "half-sandwich" complexes (η(6)-benzophenone)Cr(CO)3, (η(6)-styrene)Cr(CO)3, and (η(6)-allylbenzene)Cr(CO)3 were investigated using pico-second time-resolved infrared spectroscopy and time-dependent density functional theory methods. The (η(6)-benzophenone)Cr(CO)3 complex was studied using two excitation wavelengths (470 and 320 nm) while the remaining complexes were irradiated using 400 nm light. Two independent excited states were detected spectroscopically for each complex, one an unreactive excited state of metal-to-arene charge-transfer character and the other with metal-to-carbonyl charge transfer character. This second excited state leads to an arrested release of CO on the pico-second time-scale. Low-energy excitation (470 nm) of (η(6)-benzophenone)Cr(CO)3 populated only the unreactive excited state which simply relaxes to the parent complex. Higher energy irradiation (320 nm) induced CO-loss. Irradiation of (η(6)-styrene)Cr(CO)3, or (η(6)-allylbenzene)Cr(CO)3 at 400 nm provided evidence for the simultaneous population of both the reactive and unreactive excited states. The efficiency at which the unreactive excited state is populated depends on the degree of conjugation of the substituent with the arene π-system and this affects the efficiency of the CO-loss process. The quantum yield of CO-loss is 0.50 for (η(6)-allylbenzene)Cr(CO)3 and 0.43 for (η(6)-styrene)Cr(CO)3. These studies provide evidence for the existence of two photophysical routes to CO loss, a minor ultrafast route and an arrested mechanism involving the intermediate population of a reactive excited state. This reactive excited state either relaxes to reform the parent species or eject CO. Thus the quantum yield of the CO-loss is strongly dependent on the excitation wavelength. Time-dependent density functional theory calculations confirm that the state responsible for ultrafast CO-loss has significant metal-centred character while 2. Study on even-parity highly excited states of the Sm atom Zhao Yanhong; Dai Changjian; Ye Shiwei, E-mail: [email protected] [School of Science, Tianjin University of Technology, Tianjin 300384 (China) 2011-10-14 Spectra of even-parity highly excited states of the Sm atom have been systematically studied using the two-color three-step excitation and photoionization detection method. With three different excitation paths distinguished by three different intermediate states with the 4f{sup 6}6s6p configuration, the atom is resonantly excited to given highly excited states in the energy region between 30 040 and 38 065 cm{sup -1}, where it is detected by photoionization. The wavelength of the second laser is scanned from 440 to 700 nm, while that of the first laser is fixed at 638.96, 636.92 or 627.50 nm. Based on precise calibration of the wavelength, the energy levels of 198 even-parity states are determined with the relative line intensities of the related transitions. A unique value of J, the total angular momentum, is assigned to all detected states by comparing the three spectra obtained with the different excitation paths. Except that the energy levels of 113 states are confirmed in this work, the rest of the information mentioned above has not been previously reported. 3. The structure of the ground state and low excited states of quantum fluids The structure of the ground state of a quantum fluid is described in terms of the pair correlation function and pair-pair correlation function, which are the response functions to first and second order scattering respectively. Results are presented for the pair-pair correlation function of liquid 4He obtained using two methods; a Monte Carlo simulation and a hypernetted chain approximation. These results are used to obtain the solution of the Euler-Lagrange equation for the optimum Jastrow function for the ground state of liquid 4He. The Monte Carlo calculation is in good agreement with the augmented HNC approximation. General properties of the pair correlation function are discussed in terms of its Fourier transform, the liquid structure function. A critical review is given of the present status of the Jastrow theory ( and its generalizations) of the ground state of boson and fermion quantum fluids. The recent extension of the Jastrow theory to include three-body factors by Pandharipande is compared to the earlier theory of Campbell along with a parallel discussion of the theories of the low excited states of the boson fluid by Feynman and Cohen and by Jackson and Feenberg. The importance fo the three-body factors to the quantitative agreement between the theoretical and experimental phonon-roton spectrum of liquid 4He is discussed. (Auth.) 4. One Neutron Halo in a 12B Excited State 陈宝秋; 马中玉 2001-01-01 The nonlinear relativistic mean field (RMF) theory with a new effective interaction NL3 has been used to inves tigate the bulk properties of the 12B nucleus. The results obtained in the RMF predict one neutron halo in a 12Bexcited state. 12B does not show the neutron halo structure if it is in its ground state. 5. Photoionization spectra of even-parity states of Sm atom with multistep excitation Two-color stepwise excitation and photoionization schemes are adopted to study the spectra of bound even-parity high-lying states of the Sm atom with three different excitation paths via the 4f66s6p 7DJ (J=1, 2 and 3) intermediate states. In order to obtain the information of these high-lying states, the Sm atom in these high-lying states is photoionized with an extra photon. Among 231 states detected in the energy region between 35,545 and 44,225 cm-1, 108 states are newly discovered, while the rest can be identified as the same with the literature. In most cases, comparisons of the spectra corresponding to the three different excitation paths may partially determine the total angular momentum of the observed peaks with the selection rules. In addition, the relative intensities of all related transition lines are given. 6. On excited states in real-time AdS/CFT Botta-Cantcheff, Marcelo; Silva, Guillermo A 2015-01-01 The Skenderis-van Rees prescription, which allows the calculation of time-ordered correlation functions of local operators in CFT's using holographic methods is studied and applied for excited states. Calculation of correlators and matrix elements of local CFT operators between generic in/out states are carried out in global Lorentzian AdS. We find the precise form of such states, obtain an holographic formula to compute the inner product between them, and using the consistency with other known prescriptions, we argue that the in/out excited states built according to the Skenderis-Van Rees prescription correspond to {\\it coherent} states in the (large-$N$) AdS-Hilbert space. This is confirmed by explicit holographic computations. The outcome of this study has remarkable implications on generalizing the Hartle-Hawking construction for wave functionals of excited states in AdS quantum gravity. 7. Emergence of nontrivial magnetic excitations in a spin-liquid state of kagomé volborthite. Watanabe, Daiki; Sugii, Kaori; Shimozawa, Masaaki; Suzuki, Yoshitaka; Yajima, Takeshi; Ishikawa, Hajime; Hiroi, Zenji; Shibauchi, Takasada; Matsuda, Yuji; Yamashita, Minoru 2016-08-01 When quantum fluctuations destroy underlying long-range ordered states, novel quantum states emerge. Spin-liquid (SL) states of frustrated quantum antiferromagnets, in which highly correlated spins fluctuate down to very low temperatures, are prominent examples of such quantum states. SL states often exhibit exotic physical properties, but the precise nature of the elementary excitations behind such phenomena remains entirely elusive. Here, we use thermal Hall measurements that can capture the unexplored property of the elementary excitations in SL states, and report the observation of anomalous excitations that may unveil the unique features of the SL state. Our principal finding is a negative thermal Hall conductivity [Formula: see text] which the charge-neutral spin excitations in a gapless SL state of the 2D kagomé insulator volborthite Cu3V2O7(OH)2[Formula: see text]2H2O exhibit, in much the same way in which charged electrons show the conventional electric Hall effect. We find that [Formula: see text] is absent in the high-temperature paramagnetic state and develops upon entering the SL state in accordance with the growth of the short-range spin correlations, demonstrating that [Formula: see text] is a key signature of the elementary excitation formed in the SL state. These results suggest the emergence of nontrivial elementary excitations in the gapless SL state which feel the presence of fictitious magnetic flux, whose effective Lorentz force is found to be less than 1/100 of the force experienced by free electrons. PMID:27439874 8. Control of multiple excited Rydberg states around segmented carbon nanotubes Schmelcher, Peter; Sadeghpour, Hossein; Knoerzer, Johannes; Fey, Christian 2016-05-01 Electronic image Rydberg states around segmented carbon nanotubes can be confined and shaped along the nanotube axis by engineering the image potential. We show how several such image states can be prepared simultaneously along the same nanotube. The inter-electronic distance can be controlled a priori by engineering tubes of specific geometries. High sensitivity to external electric and magnetic fields can be exploited to manipulate these states and their mutual long-range interactions. These building blocks provide access to a new kind of tailored long-range interacting quantum systems. 9. Control of multiple excited image states around segmented carbon nanotubes Knörzer, J., E-mail: [email protected]; Fey, C., E-mail: [email protected] [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, Hamburg 22761 (Germany); Sadeghpour, H. R. [ITAMP, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138 (United States); Schmelcher, P. [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, Hamburg 22761 (Germany); The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, Hamburg 22761 (Germany) 2015-11-28 Electronic image states around segmented carbon nanotubes can be confined and shaped along the nanotube axis by engineering the image potential. We show how several such image states can be prepared simultaneously along the same nanotube. The inter-electronic distance can be controlled a priori by engineering tubes of specific geometries. High sensitivity to external electric and magnetic fields can be exploited to manipulate these states and their mutual long-range interactions. These building blocks provide access to a new kind of tailored interacting quantum systems. 10. Triplet excited state spectra and dynamics of carotenoids from the thermophilic purple photosynthetic bacterium Thermochromatium tepidum Niedzwiedzki, Dariusz; Kobayashi, Masayuki; Blankenship, R. E. 2011-01-13 Light-harvesting complex 2 from the anoxygenic phototrophic purple bacterium Thermochromatium tepidum was purified and studied by steady-state absorption, fluorescence and flash photolysis spectroscopy. Steady-state absorption and fluorescence measurements show that carotenoids play a negligible role as supportive energy donors and transfer excitation to bacteriochlorophyll-a with low energy transfer efficiency of ~30%. HPLC analysis determined that the dominant carotenoids in the complex are rhodopin and spirilloxanthin. Carotenoid excited triplet state formation upon direct (carotenoid) or indirect (bacteriochlorophyll-a Q{sub x} band) excitation shows that carotenoid triplets are mostly localized on spirilloxanthin. In addition, no triplet excitation transfer between carotenoids was observed. Such specific carotenoid composition and spectroscopic results strongly suggest that this organism optimized carotenoid composition in the light-harvesting complex 2 in order to maximize photoprotective capabilities of carotenoids but subsequently drastically suppressed their supporting role in light-harvesting process.	{"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": 0.8495563268661499, "perplexity": 3047.705226903598}, "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-2016-40/segments/1474738662336.11/warc/CC-MAIN-20160924173742-00027-ip-10-143-35-109.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/171595/hyper-birthday-paradox	There are $N$ buckets. Each second we add one new ball to a random bucket - so at $t=k$, there are a total of $k$ balls collectively in the buckets. At $t=1$, we expect that at least one bucket contains one ball. At $t=\sqrt{2N\ln{2}}$, due to birthday paradox, we expect that at least one bucket contains two balls. . . At $t=f(m)$, we expect at least one bucket to contain $m$ balls. What is the function $f(m)$? - Actually, the probability $p$ that there bucket with more than one ball occurs is first matched or exceeded at $t=\sqrt {2N\ln \frac 1{1-p}}$. – Roman Chokler Aug 25 '12 at 4:24 The birthday paradox is closer to $\sqrt{N\sqrt 2}$. The classic one is $23\approx \sqrt {365 \sqrt 2}$ A naive approach says you have $\frac {N(N-1)}2$ pairs, so when this is of the order of $1$ you should expect a match. – Ross Millikan Aug 25 '12 at 4:30 This is called the "balls in bins" problem, and there is huge amount known about it, because it is crucial to understanding the performance of computer hashing algorithms. You might try a web search for "balls in bins" and see what you find out. Or you might enjoy this. – MJD Aug 25 '12 at 4:37 This is not $\sqrt{2N\ln(2)}$ to obtain a 50% chance ? – Xoff Aug 29 '12 at 21:38 Firstly, for $m = 2$, the expected time $f(2)$ at which at least one bucket contains two balls is not $t = \sqrt{2N\ln 2}$. That is the time $t$ at which the probability that there is at least one bucket with two balls crosses $\frac12$. The actual expected time $t$ at which at least one bucket contains two balls is instead given by \begin{align} 1 + Q(N) &= 1 + 1 + \frac{N-1}{N} + \frac{(N-1)(N-2)}{N^2} + \cdots + \frac{(N-1)(N-2) \cdots 1}{N^{N-1}} \\ &\sim \sqrt{\frac{\pi N}{2}} + \frac{1}{3}+\frac{1}{12}\sqrt{\frac{\pi}{2N}}-\frac{4}{135N}+\cdots \end{align} where the $\sim$ denotes that these are the precise asymptotics. (Mildly related: this question and the methods of asymptotic analysis at this one.) For $m = 3$, see this question, where it is shown that the answer is $$f(3) = \int_0^\infty \left(1+{x\over N}+{x^2\over2N^2}\right)^N \,e^{-x}\,dx$$ which has asymptotics $$f(3) \sim 6^{1/3}\,\Gamma(4/3)\, N^{2/3} \approx 1.6226\,N^{2/3}.$$ For general $m$, the above question also says that the above answer generalizes to $$f(m) \sim \sqrt[m]{m!}\ \Gamma(1 + 1/m)\ N^{1-1/m}$$ (for fixed $m$ and asymptotically as $N \to \infty$). -	{"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9841392040252686, "perplexity": 424.3990361226397}, "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-2014-23/segments/1406510273663.2/warc/CC-MAIN-20140728011753-00419-ip-10-146-231-18.ec2.internal.warc.gz"}
https://cdsweb.cern.ch/collection/CMS%20Papers?ln=sv	# CMS Papers Senast inlagda poster: 2016-09-27 23:05 Search for long-lived charged particles in proton-proton collisions at $\sqrt{s}=$ 13 TeV Results are presented of a search for heavy stable charged particles produced in proton-proton collisions at $\sqrt{s} =$ 13 TeV using a data sample corresponding to an integrated luminosity of 2.5 fb$^{-1}$ collected in 2015 with the CMS detector at the CERN LHC. [...] CERN-EP-2016-204 ; CMS-EXO-15-010-003. - 2016. Additional information for the analysis - CMS AuthorList - Fulltext 2016-09-24 21:37 Inclusive search for supersymmetry using razor variables in pp collisions at $\sqrt{s} =$ 13 TeV An inclusive search for supersymmetry using razor variables is performed in events with four or more jets and no more than one lepton. [...] CERN-EP-2016-214 ; CMS-SUS-15-004-003. - 2016. Additional information for the analysis - CMS AuthorList - Fulltext 2016-09-19 19:09 Measurement of the WZ production cross section in pp collisions at $\sqrt{s} =$ 7 and 8 TeV and search for anomalous triple gauge couplings at $\sqrt{s} =$ 8 TeV / CMS Collaboration The WZ production cross section is measured by the CMS experiment at the CERN LHC in proton-proton collision data samples corresponding to integrated luminosities of 4.9 fb$^{-1}$ collected at $\sqrt{s} =$ 7 TeV, and 19.6 fb$^{-1}$ at $\sqrt{s} =$ 8 TeV. [...] arXiv:1609.05721 ; CERN-EP-2016-205 ; CMS-SMP-14-014. - 2016. - 44 p. Preprint - Full text 2016-09-18 10:28 Search for narrow resonances in dilepton mass spectra in proton-proton collisions at $\sqrt{s} =$ 13 TeV and combination with 8 TeV data / CMS Collaboration A search for narrow resonances in dielectron and dimuon invariant mass spectra has been performed using data obtained from proton-proton collisions at $\sqrt{s} =$ 13 TeV collected with the CMS detector. [...] arXiv:1609.05391 ; CERN-EP-2016-209 ; CMS-EXO-15-005. - 2016. - 32 p. Preprint - Full text 2016-09-17 23:40 Measurement of inclusive jet cross sections in pp and PbPb collisions at $\sqrt{s_{\mathrm{NN}}} =$ 2.76 TeV / CMS Collaboration Inclusive jet spectra from pp and PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV, collected with the CMS detector at the LHC, are presented. [...] arXiv:1609.05383 ; CERN-EP-2016-217 ; CMS-HIN-13-005. - 2016. - 34 p. Preprint - Full text 2016-09-17 15:52 Measurement and QCD analysis of double-differential inclusive jet cross-sections in pp collisions at $\sqrt{s} =$ 8 TeV and ratios to 2.76 and 7 TeV / CMS Collaboration A measurement of the double-differential inclusive jet cross section as a function of the jet transverse momentum $p_{\mathrm{T}}$ and the absolute jet rapidity $\|y\|$ is presented. [...] arXiv:1609.05331 ; CERN-EP-2016-196 ; CMS-SMP-14-001. - 2016. - 48 p. Preprint - Full text 2016-09-12 20:42 Studies of inclusive four-jet production with two b-tagged jets in proton-proton collisions at 7 TeV / CMS Collaboration Measurements are presented of the cross section for the production of at least four jets, of which at least two originate from b quarks, in proton-proton collisions. [...] CERN-EP-2016-191 ; CMS-FSQ-13-010-003 ; arXiv:1609.03489. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text 2016-09-08 23:41 Decomposing transverse momentum balance contributions for quenched jets in PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 2.76 TeV / CMS Collaboration Interactions between jets and the quark-gluon plasma produced in heavy ion collisions are studied via the angular distributions of summed charged-particle transverse momenta ($p_{\mathrm{T}}$) with respect to both the leading and subleading jet axes in high-$p_{\mathrm{T}}$ dijet events. [...] CERN-EP-2016-199 ; CMS-HIN-15-011-003 ; arXiv:1609.02466. - 2016. Additional information for the analysis - CMS AuthorList - Full text - Full text 2016-09-08 23:01 Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search / CMS Collaboration The results of a search are presented for the resonant production of high-mass photon pairs, specifically spin-0 and spin-2 resonances with an invariant mass between 0.5 and 4.5 TeV, and with a width, relative to the mass, between $1.4 \times 10^{-4}$ and $5.6 \times 10^{-2}$. [...] arXiv:1609.02507 ; CERN-EP-2016-216 ; CMS-EXO-16-027. - 2016. - 34 p. Full text - Full text 2016-09-04 18:43 The CMS trigger system / CMS Collaboration This paper describes the CMS trigger system and its performance during Run 1 of the LHC. [...] CERN-EP-2016-160 ; CMS-TRG-12-001-003 ; arXiv:1609.02366. - 2016. Additional information for the analysis - CMS AuthorList - Full text - 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": 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": 0.9965929388999939, "perplexity": 3042.1330464207576}, "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-2016-40/segments/1474738661289.41/warc/CC-MAIN-20160924173741-00167-ip-10-143-35-109.ec2.internal.warc.gz"}
http://cms.math.ca/cjm/kw/generalized%20Frobenius%20partition	Non-Existence of Ramanujan Congruences in Modular Forms of Level Four Ramanujan famously found congruences like $p(5n+4)\equiv 0 \operatorname{mod} 5$ for the partition function. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on $\Gamma_{1}(4)$ that is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored $F$-partitions. Keywords:modular form, Ramanujan congruence, generalized Frobenius partition, overpartition, crankCategories:11F33, 11P83	{"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": 0.8709318041801453, "perplexity": 695.7324052194344}, "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-2014-41/segments/1410657129407.88/warc/CC-MAIN-20140914011209-00310-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"}
https://electronics.stackexchange.com/questions/241238/the-physical-meaning-of-inductance	# The physical meaning of inductance What is the the physical meaning of inductance? We know that the resistance "R" of a conductor is how easily the electrons flow through it, etc., but what about the inductance "X"? • How many magnetic feild lines can be made per amp of current. – efox29 Jun 16 '16 at 2:06 • – Sredni Vashtar Feb 18 at 14:09 In addition to the other answers, the symbol for inductance is L, not X. The symbol for inductive reactance is $X_{L}$, and for capacitive reactance is $X_{C}$. What is the the physical meaning of inductance? Hugh Young, in his textbook University Physics [1], states the following: for a coil with $N$ turns of wire carrying current $i$, the current creates a magnetic flux $\Phi_{B}$ that passes through each turn. The coil's inductance $L$ (a.k.a. self-inductance) is given by $$L=\frac{N\, \Phi_{B}}{i}$$ Inductors store energy in a field of magnetic flux $\Phi_{B}$ whose magnitude is a function of the current flowing through the inductor: $$\Phi_{B}=\frac{L\, i}{N}$$ If an electric current flowing through an inductor changes with time $\frac{\mathrm{d} i}{\mathrm{d} t} \neq 0$, this changing current produces a changing magnetic field $\frac{\mathrm{d}\Phi_{B}}{\mathrm{d} t} \neq 0$, that in turn produces a non-zero electromotive force (emf) $\varepsilon$ across the inductor, measured in units of Volts, whose polarity opposes ("resists") the change in current [1]: $$\varepsilon = -L\frac{\mathrm{d}i}{\mathrm{d} t} = -N\frac{\mathrm{d}\Phi_{B}}{\mathrm{d} t}$$ This opposition to the change in current flow is the inductive reactance. If an electric current flowing through an inductor is constant (does not change with time, a.k.a., direct current) $\frac{\mathrm{d} i}{\mathrm{d} t}=0$, the field of magnetic flux $\Phi_{B}$ is not changing with time (its magnitude is constant) $\frac{\mathrm{d} \Phi_{B}}{\mathrm{d} t}=0$, then no emf is produced, $\varepsilon = 0$. Therefore, an ideal inductor (zero resistance) does not oppose direct current flowing through it. When an ideal inductor having inductance $L$ is driven with a sinusoidal current having radian frequency $\omega$ (or frequency f), the magnitude of the inductor's steady-state inductive reactance $X_{L}$ is given by $$X_{L}=j\omega L = j2\pi fL$$ where $j=\sqrt{-1}$. This equation is derived from a phasor transformation of the first order differential equation $$v_{L}(t)=L\, \frac{\mathrm{d}}{\mathrm{d} t}i_{L}(t)$$ where $v_{L}(t)$ is the instantaneous voltage across the inductor, and $i_{L}(t)$ is the instantaneous sinusoidal current through the inductor at time t: $$i_{L}(t) = I_{m} cos(\omega t + \phi)$$ References [1] H. Young. "Inductance," in University Physics, 8th ed. Reading, Massachusetts: Addison-Wesley, 1992, ch. 31, pp. 869-870. • Up you go, this is the best explaination of the inductance. – MathieuL Jun 17 '16 at 13:30 When we use the term 'inductance', we're usually shortening what should actually be called 'self-inductance'. When a current flows through a wire, a magnetic field is produced around that wire, with its field strength in proportion to the current strength, changing as the current changes. We also know that a changing magnetic field will induce a voltage over a wire in proportion to the strength of the field and the rate at which it changes. So, if we have a wire with a changing current flowing through it (think AC or DC with some ripple), then it will produce a changing magnetic field around itself. This changing magnetic field will then induce a voltage back across that same wire, but this induced voltage will be of the opposite polarity to the voltage of the original applied current. Since the induced voltage opposes the applied voltage/current, the apparent effect is an increased impedance (complex resistance, or resistance with a phase angle), and since the strength of the induced voltage increases in proportion with the frequency of the applied voltage/current (as frequency is the rate of change), the inductor's impedance increases with frequency. The inductance (with the unit Henrys) of an inductor is a measure of this self-inductance effect. (Self)inductance is increased by coiling the wire around so that the coils all contribute to and share the same magnetic field. Wrapping the coils around a magnetically permeable core also increases (self)inductance by 'concentrating' the magnetic field. • Voltage is induced not current and it is the induced voltage that counteracts the current that directly created the mag field. – Andy aka Jun 17 '16 at 8:03 • Both the inductor and capacitor oppose the input (exciting) voltage by an opposite voltage but in a different manner - the inductor opposition is maximum in the beginning while the capacitor opposition is maximum at the end (I mean the case of a DC input voltage). – Circuit fantasist Feb 18 at 16:46 If you expect an answer of the type "R" of a conductor is how easily the electrons flow through it (actually it should say how "difficult" instead of "easy") I'd say "L" is how difficult it is to change to current through the component. • Please explain more – Abdu Jun 15 '16 at 23:51 • V = R x I; V = L x di/dt. As L is bigger the voltage 'opposition' of the inductance to changes in current gets also bigger. – Claudio Avi Chami Jun 16 '16 at 0:36 Inductance is just "electron inertia." Adding inductance is like connecting a flywheel to the flowing charges. Or, it's like hanging larger weights on each moving electron. But also that's a bit of a simplification; it's not just inertia. For example, we can increase the inertia by making the wires longer. That's like increasing the water-inertia of plumbing, by adding longer pipes. Longer pipes, more fluid mass. But with conductors, if two conductors are placed side by side, they magnetically couple together, and their "inertia" increases! For this reason, whenever we double the number of turns in a simple hoop-coil of wire, the "inertia" (inductance) does not just double as one might expect. Instead it goes up 4x. The "flywheel mass" is not just a matter of electron-quantity within the conductors. For the ultra-simplified version which ignores these EM effects, just pretend that the wires are actually glass pipes full of filthy water, so you can see the suspended dirt moving inside the pipes. What do we get if we wind a coil of clear pipes? Then, whenever we pump a flow, the entire mass of water in the coil will all flow forward as a unit. The coil full of dirty water starts turning, as if the water was in a barrel. We've made a hydraulic flywheel: hard to get it moving, hard to make it stop, and it can store energy if we first get it spinning, then connect the hose-ends together to form a closed loop. (This reveals an important rule: to store energy in a coil, the terminals must be shorted, while storing energy in capacitors requires that the terminals be NOT-shorted.) If our spiral of transparent pipe was a one-turn shorted-out coil, it's definitely an "electron flywheel." But if it's multi-turns and shorted, then it's still a flywheel: one that has been sliced into a weird spiral-loop device. Notice that the "amp-turns" concept becomes visible, where gallons/sec flow rate through the loop is analogous to amperes. Then, add the induction concept: if we shove a single magnet pole into the center of the fluid-charges flywheel, the magnetic field gives the flywheel a spin, and the whole thing will keep turning until slowed by electric resistance. (Or, it just keeps spinning, if it's a superconductor ring.) When it slows and stops, then yank the magnet pole back out again, and the resistive "flywheel" will briefly spin in the opposite direction. The most common component that you would refer to as an "inductor" would be some sort of coil of wire. When you put a current through a coil, it creates a magnetic field. As the current increases, the field strength increases. There are a few ways of looking at it, but you could say that an inductor stores energy in its magnetic field, like a capacitor stores energy in its electric field. If you put a voltage across an inductor, at the beginning there will be a very small current. This will generate an increasingly large magnetic field. This changing field will impede the flow of current, slowing down the increase of the field strength, impeding the flow less and allowing faster change. This forms a kind of equilibrium, allowing the current to increase at a certain rate until some sort of limit is reached, either from the resistance of the inductor or the limits of the power supply. Equally, when you try to reduce the current, the magnetic field collapses, transferring the magnetic energy back into electrical energy, increasing the voltage. This forms another equilibrium until the current goes to 0. Inductance is a measure of how much voltage a change in current produces. More inductance means a bigger voltage change for a given current change. • Inductance is the relation between the flux created and the current you insert... Voltage appear in the picture because of an other electromagnetic concept: Faraday's law. – MathieuL Jun 17 '16 at 13:33 • Yeah, I originally said current, but then someone edited it – BeB00 Jun 17 '16 at 13:44 It may sound bizarre but I regard "inductance" as being defined by space (area within the coil) and shape (coil shape). This is for a single turn inductor in free-space (for simplicity) i.e. no interaction with other objects. It's easy to define inductance in terms of electrical terms such as the total flux produced per amp and there's nothing wrong in that. That is the usual definition. My version kind of tells me how inductance is increased by maximizing area (for a given wire length per turn) i.e. making a circle rather than making a square or rectangle. Hence I think of inductance in terms of area and shape. Resistance is the ratio of the voltage across a component to the direct current through the component. Inductance is the ratio of the voltage across a component to the rate of change of current through the component. (Here I am referring to the portion of the voltage that is produced by the rate of change of the current.) In general, most real physical components exhibit some of each effect. Resistors are designed to emphasize and have a well-defined value of resistance, while often having minimal inductance. On the other hand, inductors are designed to emphasize and have a well-defined value of inductance while generally having minimal resistance. Inductance is like a mass in the mechanical analogy, look into a frequency resonator to understand the coil. A whistle of a police officer at the train station is a good example for a resonator. Inside this whistle, there is a ball (weight) that moves inside a cavity, due to this weight the sound is produced. This weight is the L (coil) and the cavity is the C in an LC resonator circuit. • Exactly! The inductor stores something like kinetic energy while the capacitor stores something like potential energy. This intuitive notion about these energy-storing elements is sufficient to understand circuits. For example, see my Wikibooks story about LC tank. – Circuit fantasist Feb 18 at 16:35	{"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": 0.8829277753829956, "perplexity": 719.1072202654673}, "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/1627046154798.45/warc/CC-MAIN-20210804080449-20210804110449-00479.warc.gz"}
https://cs.stackexchange.com/questions/32043/fix-two-primes-p-and-q-given-input-a-number-of-the-form-paqb-find-the-imme	# Fix two primes p and q. Given input a number of the form $p^aq^b$, find the immediate next number of the same form As stated in the title: Fix two primes p and q. Given input a number of the form $p^aq^b$, find the immediate next number of the same form. For example: when $p = 2$ and $q = 3$ Next of $2^23=12$ is $2^3=16$ and after that is $23^2=18$ Question [edited]: Can this be done in poly-time of the representation of $a$ and $b$? I believe so and I do have a sketch for this, but I want to see what a "proper" answer to this question is. • I don't see how it could be done in constant time. As $a$ and $b$ get large, even producing the output would not be constant in time or memory. More speculatively, I don't think there is a simple relationship that would allow the determination of the answer quickly, my first-approximation guess is that this would take pseudopolynomial time (polynomial in the magnitude of $a$ and $b$, but maybe exponential in the size of their representation). – Luke Mathieson Oct 18 '14 at 11:22 • @LukeMathieson Fair suggestion. I am hoping to get it in time that is not exponential to the representation of $a$ and $b$ – InformedA Oct 18 '14 at 16:30 • If you have a sketch you should share it with us. Otherwise it's pointless to think about the question. This is not a puzzle site. – Yuval Filmus Oct 20 '14 at 4:06 • @YuvalFilmus I have a sketch, but I am not sure if that will be correct, so I refrain from writing it here. I have learnt the hard way that the real world is not like a school exam. You don't say anything to get partial credit. In the real world, wrong answers are not something with which you can be easy. – InformedA Oct 20 '14 at 4:17 • Have you empirically tested your algorithm? Do you have a candidate proof? – Yuval Filmus Oct 20 '14 at 11:46 Let $c = \log p$ and $d = \log q$. Then $\log (p^a q^b) = ca + db$. Define the set $S_{c,d} = \{ci+dj : i,j \in \mathbb{N}\}$. Your problem is equivalent to the following: Problem 1. Given $a,b \in \mathbb{N}$ and $c,d \in \mathbb{R}$, find $a',b' \in \mathbb{N}$ so that $ca' + db'$ is the next attainable real number in $S_{c,d}$ after $ca + db$. This is in turn equivalent to the following problem: Problem 2. Given $\alpha \in \mathbb{R}$ and $X,Y \in \mathbb{Z}$, find $x,y \in \mathbb{N}$ that minimizes $x+\alpha y$, subject to the requirements that $x \ge X$, $y \ge Y$, and $(x,y) \ne (0,0)$. (The equivalence can be seen by letting $\alpha = d/c$, $X=-a$, $Y=-b$, and $x=a'-a$, $y=b'-b$.) Problem 2 now amounts to finding the best rational approximation $x/y$ of $-\alpha$, subject to constraints on the size of $x,y$. There are many techniques for that, including continued fractions. You can also express this as the problem of finding a closest lattice point to $(0,0)$ in a certain two-dimensional lattice. There are many algorithms for closest lattice point search in lattices, also known as the closest vector problem; in two dimensions, I believe they run in polynomial time, if I remember correctly. See, e.g., https://mathoverflow.net/q/61897. • Hello, thank you very much for this response. I just want to note that I was hoping to put more focus on the fact that the 2 primes $p$ and $q$ are fixed. This means that any cost associated with only $p$, $q$ even exponential is considered a constant. – InformedA Oct 20 '14 at 1:41	{"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": 0.8143017292022705, "perplexity": 184.0554274737743}, "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-2021-25/segments/1623488269939.53/warc/CC-MAIN-20210621085922-20210621115922-00206.warc.gz"}
https://www.bartleby.com/solution-answer/chapter-15-problem-12p-college-physics-11th-edition/9781305952300/a-positive-charge-q1-270-c-on-a-frictionless-horizontal-surface-is-attached-to-a-spring-of-force/1c9aa43a-98d5-11e8-ada4-0ee91056875a	Chapter 15, Problem 12P ### College Physics 11th Edition Raymond A. Serway + 1 other ISBN: 9781305952300 Chapter Section ### College Physics 11th Edition Raymond A. Serway + 1 other ISBN: 9781305952300 Textbook Problem # A positive charge q1 = 2.70 μC on a frictionless horizontal surface is attached to a spring of force constant k as in Figure P15.12. When a charge of q2 = −8.60 μC is placed 9.50 cm away from the positive charge, the spring stretches by 5.00 mm, reducing the distance between charges to d = 9.00 cm. Find the value of k. To determine The value of spring constant. Explanation Given info: The two charges q1=2.70μC and q2=8.60μC The distance of separation (d) between the charges is 9.00 cm. The displacement (x) of the spring is 5.00 mm. Formula to calculate the spring force is, F=kx (I) • k is the spring constant. From Coulomb’s Law, F=ke\|q1\|\|q2\|d2 (II) • ke is the Coulomb constant. • q1 and q2 are the charges. • d is the distance of separation. The spring force equals the Coulomb force at equilibrium. From Equations (I) and (II) kx=ke\|q1\|\|q2\|d2 On Re-arranging, k=ke\|q1\|\|q2\|xd2 Substitute 8.99×109N.m2/C2 for ke , 2.70μC for q1 , 8 ### Still sussing out bartleby? Check out a sample textbook solution. See a sample solution #### The Solution to Your Study Problems Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees! Get Started	{"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": 0.9122552871704102, "perplexity": 4342.206000332729}, "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-2019-43/segments/1570987836368.96/warc/CC-MAIN-20191023225038-20191024012538-00082.warc.gz"}
http://fmoldove.blogspot.com/2015/08/where-does-hilbert-space-come-from.html	## Where does the Hilbert space come from? Continuing the discussion from last time, today we can put some of the pieces of the puzzle together. It is helpful to switch the discussion direction from classical to quantum and start for a moment from the quantum mechanics side to see where we want to arrive. Why do we use a Hilbert space in quantum mechanics? This is a big topic and we cannot cover it in one (or even several posts). Right away we will restrict ourselves to the finite dimensional degrees of freedom case, thus excluding the field theory considerations and avoiding the issues raised by Haag's theorem, or the breakdown of the Stone-von Neumann uniqueness theorem. We will also skip the treatment of unbounded operators which require the theory of rigged Hilbert spaces and we will stick with boring but well behaved bounded operators. For a bounded operator T on a Hilbert space it is easy to prove that $$\|\|T^{\dagger} T\|\| = {\|\|T\|\|}^2$$ as follows: $${\|\|T \Phi\|\|}^2 = \langle T \Phi, T \Phi\rangle = \langle T^{\dagger} T \Phi, \Phi\rangle \leq \|\|T^{\dagger} T\Phi \|\| \|\|\Phi\|\| \leq \|\|T^{\dagger} T \|\| {\|\|\Phi\|\|}^2$$ therefore $${\|\|T\|\|}^2 \leq \|\|T^{\dagger} T \|\|$$ and since $$\|\|T^{\dagger} T \|\| \leq \|\|T^{\dagger}\|\| \|\|T\|\| = {\|\|T\|\|}^2$$ we have: $${\|\|T\|\|}^2 \leq \|\|T^{\dagger} T \|\| \leq {\|\|T\|\|}^2$$ An algebra of bounded operators on a Hilbert space is the prototypical example of a C* algebra. A remarkable fact is the correspondence between states and representations of C* algebra given by the GNS construction. Here a representation is a linear map from the elements of the C* algebra to bounded operators on some Hilbert space. From categorical considerations one can obtain a C* algebra without the norm axioms. To distinguish math from physics one needs to be able to make experimental predictions and this is where the states enter the picture. A state on a C* algebra gives rise to a representation of the algebra as bounded linear operators on some Hilbert space and this is how Hilbert spaces are introduced. The key ingredient for this to work is the C* norm condition: $$\|\|T^{\dagger} T\|\| = {\|\|T\|\|}^2$$. However, this norm is unique and is given by the spectral radius - an algebraic concept! So there is hope we can arrive at quantum mechanics using only algebraic methods. Now we will show how. Coming back to the quantization discussion from the prior post, what we need to achieve is a prescription which constructs operators on a Hilbert space from functions on the phase space (also known as the cotangent bundle). Even better we should be able to start from either a Kahler, symplectic, or Poisson manifold. We can start with the simplest case where we replace the position $$q$$ and the momenta $$p$$ with the operators: $$x$$ and $$\frac{h}{i}\frac{\partial}{\partial x}$$ in any observable $$f(p, q)$$ provided $$f$$ contains no products $$pq$$ because the position and momenta operators in the Hilbert space do not commute and the order of the operators is ambiguous. The next level of sophistication is Weyl quantization procedure and the details can be found here. (Please excuse me for skipping typesetting it in LaTeX.) Weyl quantization tends to preserve well symmetry properties, but a better quantization prescription is Berezin quantization which work on all Kahler manifolds when positivity is guaranteed by the Kodaira embedding theorem. Erich Kahler A Kahler manifold is a truly outstanding mathematical object where three concepts meet: • a metric structure • a symplectic structure • a complex structure and any two define the third one. The main example is the complex projective space (endowed with the Fubini-Study metric) which is essential for quantum mechanics. It is very enlightening to see how it all works out in quantum mechanics and I'll attempt to show it below. In classical and quantum mechanics there are two products, one symmetric $$\sigma$$ and one anti-symmetric $$\alpha$$ corresponding to observables and generators as follows: Observables: $$\sigma$$ = regular function multiplication on phase space OR Jordan product Generators: $$\alpha$$ = Poisson bracket OR commutator There is also a 1-to-1 map $$J$$ between observable and generators called dynamic correspondence where $$J^2 = 0$$ for classical mechanics and $$J^2 = -1$$ for quantum mechanics. This map corresponds to Noether's theorem. Composing two physical systems 1 and 2 gives rise to the following fundamental composition relationship: $$\sigma_{12} = \sigma_1 \otimes \sigma_2 + J^2 \frac{\hbar^2}{4}\alpha_1 \otimes \alpha_2$$ $$\alpha_{12} = \sigma_1 \otimes \alpha_2 + \alpha_1 \otimes \sigma_2$$ and so the symmetry and anti-symmetry of the products is preserved. Now we want to deform the Poisson bracket and regular function multiplication of classical mechanics which respects the composition with $$J^2 = 0$$ into two products which respect $$J^2 = -1$$. We can do this term by term in powers of $$\hbar$$ preserving associativity at each step. This is the essence of deformation quantization. Without ado, here is the solution given by Moyal sine and cosine brackets in terms of the Poisson bracket $$\{ , \}$$ in the simplest case of a flat space: $$\alpha = \frac{2}{\hbar} sin (\frac{\hbar}{2} \{ , \})$$ $$\sigma = cos (\frac{\hbar}{2} \{ , \})$$ The star product is then $$\star= \sigma+ J\frac{\hbar}{2} \alpha$$ and we arrived at quantum mechanics in phase space. First a note: I demanded earlier to preserve associativity at each power of $$\hbar$$. This is a physical requirement to be able to compose experiments sequentially and not care where we draw the boundaries between them. But this has a very interesting consequence: we have freedom of pick how we carry out the quantization at each power of $$\hbar$$ step and this makes the subject of quantization non-trivial. In particular it turns out that the equivalence classes of star products on symplectic manifolds are in 1-to-1 correspondence with the second de Rham cohomology $$H^2_{dR} (M)$$! Second, we can see where the inner product is coming from. From the Moyal sine bracket we extract a symplectic form $$\omega^{IJ}$$ and construct it's inverse $$\Omega_{IJ}$$. So we have one of the three structures of a Kahler manifold: the symplectic structure. But we also have the complex structure as well because we have $$J^2 = -1$$. It can be shown that $$J$$ is actually a tensor or rank (1,1): $$J = J^{I }_{ J}$$ and from this we get a metric tensor $$g_{IJ}$$: $$g_{IJ} = \Omega_{IK} J^{K}_{ J}$$ The complex inner product is defined now by: $$g+ \sqrt{-1}\Omega$$: $$\langle X, Y \rangle = X^{T} g Y + i X^T \Omega Y$$ where X and Y are column vectors : $$q_1, q_2,...q_n, p_1, p_2, ..., p_n$$ Time evolution preserves $$J$$ and $$\Omega$$, meaning they preserve the metric structure by preserving a normalization constraint: $$\langle g \rangle - 1= X^I g_{IJ} X^J - 1 = 0$$ The constraint Hamiltonian motion which preserves the metric structure is nothing but the Schrodinger equation is disguise! I do not want to create the impression that this is all as simple as this. I only discussed the flat $$R^{2n}$$ case above. There are many subtle and hard problems, as well as open questions. As an example, there are Poisson manifolds which do not admit a Kahler structure, but all Poisson manifolds are quantizable. How would the quantization of such a system look like? Perhaps there are no bounded operators in this case, I don't know. Next time I'll present a concrete calculation of a standard problem in the phase space formalism of quantum mechanics. This will challenge the ontic interpretation of quantum mechanics.	{"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": 0.9419531226158142, "perplexity": 241.34476577345254}, "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-2020-24/segments/1590347409171.27/warc/CC-MAIN-20200530102741-20200530132741-00221.warc.gz"}
https://people.maths.bris.ac.uk/~matyd/GroupNames/288/C2.AGammaL(1,9).html	Copied to clipboard ## G = C2.AΓL1(𝔽9) order 288 = 25·32 ### 1st central extension by C2 of AΓL1(𝔽9) Aliases: C2.1AΓL1(𝔽9), S3≀C2⋊C4, C3⋊S3.D8, (C2×F9)⋊1C2, C32⋊C4.1D4, C32⋊(D4⋊C4), (C3×C6).1SD16, C2.PSU3(𝔽2)⋊1C2, (C2×C3⋊S3).1D4, (C2×S3≀C2).1C2, C32⋊C4.1(C2×C4), C3⋊S3.1(C22⋊C4), (C2×C32⋊C4).1C22, SmallGroup(288,841) Series: Derived Chief Lower central Upper central Derived series C1 — C32 — C32⋊C4 — C2.AΓL1(𝔽9) Chief series C1 — C32 — C3⋊S3 — C32⋊C4 — C2×C32⋊C4 — C2×F9 — C2.AΓL1(𝔽9) Lower central C32 — C3⋊S3 — C32⋊C4 — C2.AΓL1(𝔽9) Upper central C1 — C2 Generators and relations for C2.AΓL1(𝔽9) G = < a,b,c,d,e \| a2=b3=c3=d8=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=bc=cb, ebe=b-1c, dcd-1=b, ce=ec, ede=ad3 > Subgroups: 524 in 66 conjugacy classes, 16 normal (14 characteristic) C1, C2, C2 [×4], C3, C4 [×3], C22 [×5], S3 [×4], C6 [×3], C8, C2×C4 [×2], D4 [×3], C23, C32, D6 [×6], C2×C6, C4⋊C4, C2×C8, C2×D4, C3×S3 [×2], C3⋊S3 [×2], C3×C6, C22×S3, D4⋊C4, C32⋊C4 [×2], C32⋊C4, S32 [×3], S3×C6, C2×C3⋊S3, F9, S3≀C2 [×2], S3≀C2, C2×C32⋊C4, C2×C32⋊C4, C2×S32, C2.PSU3(𝔽2), C2×F9, C2×S3≀C2, C2.AΓL1(𝔽9) Quotients: C1, C2 [×3], C4 [×2], C22, C2×C4, D4 [×2], C22⋊C4, D8, SD16, D4⋊C4, AΓL1(𝔽9), C2.AΓL1(𝔽9) Character table of C2.AΓL1(𝔽9) class 1 2A 2B 2C 2D 2E 3 4A 4B 4C 4D 6A 6B 6C 8A 8B 8C 8D size 1 1 9 9 12 12 8 18 18 36 36 8 24 24 18 18 18 18 ρ1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 trivial ρ2 1 1 1 1 1 1 1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 linear of order 2 ρ3 1 1 1 1 -1 -1 1 1 1 -1 -1 1 -1 -1 1 1 1 1 linear of order 2 ρ4 1 1 1 1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 linear of order 2 ρ5 1 -1 -1 1 1 -1 1 -1 1 -i i -1 -1 1 -i -i i i linear of order 4 ρ6 1 -1 -1 1 1 -1 1 -1 1 i -i -1 -1 1 i i -i -i linear of order 4 ρ7 1 -1 -1 1 -1 1 1 -1 1 i -i -1 1 -1 -i -i i i linear of order 4 ρ8 1 -1 -1 1 -1 1 1 -1 1 -i i -1 1 -1 i i -i -i linear of order 4 ρ9 2 -2 -2 2 0 0 2 2 -2 0 0 -2 0 0 0 0 0 0 orthogonal lifted from D4 ρ10 2 2 2 2 0 0 2 -2 -2 0 0 2 0 0 0 0 0 0 orthogonal lifted from D4 ρ11 2 -2 2 -2 0 0 2 0 0 0 0 -2 0 0 √2 -√2 -√2 √2 orthogonal lifted from D8 ρ12 2 -2 2 -2 0 0 2 0 0 0 0 -2 0 0 -√2 √2 √2 -√2 orthogonal lifted from D8 ρ13 2 2 -2 -2 0 0 2 0 0 0 0 2 0 0 √-2 -√-2 √-2 -√-2 complex lifted from SD16 ρ14 2 2 -2 -2 0 0 2 0 0 0 0 2 0 0 -√-2 √-2 -√-2 √-2 complex lifted from SD16 ρ15 8 -8 0 0 2 -2 -1 0 0 0 0 1 1 -1 0 0 0 0 orthogonal faithful ρ16 8 8 0 0 -2 -2 -1 0 0 0 0 -1 1 1 0 0 0 0 orthogonal lifted from AΓL1(𝔽9) ρ17 8 8 0 0 2 2 -1 0 0 0 0 -1 -1 -1 0 0 0 0 orthogonal lifted from AΓL1(𝔽9) ρ18 8 -8 0 0 -2 2 -1 0 0 0 0 1 -1 1 0 0 0 0 orthogonal faithful Permutation representations of C2.AΓL1(𝔽9) On 24 points - transitive group 24T680 Generators in S24 (1 8)(2 5)(3 6)(4 7)(9 24)(10 17)(11 18)(12 19)(13 20)(14 21)(15 22)(16 23) (1 18 22)(2 19 23)(3 24 20)(5 12 16)(6 9 13)(8 11 15) (2 19 23)(3 20 24)(4 17 21)(5 12 16)(6 13 9)(7 10 14) (1 2 3 4)(5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24) (2 7)(4 5)(10 19)(11 15)(12 17)(14 23)(16 21)(18 22) G:=sub<Sym(24)\| (1,8)(2,5)(3,6)(4,7)(9,24)(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23), (1,18,22)(2,19,23)(3,24,20)(5,12,16)(6,9,13)(8,11,15), (2,19,23)(3,20,24)(4,17,21)(5,12,16)(6,13,9)(7,10,14), (1,2,3,4)(5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24), (2,7)(4,5)(10,19)(11,15)(12,17)(14,23)(16,21)(18,22)>; G:=Group( (1,8)(2,5)(3,6)(4,7)(9,24)(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23), (1,18,22)(2,19,23)(3,24,20)(5,12,16)(6,9,13)(8,11,15), (2,19,23)(3,20,24)(4,17,21)(5,12,16)(6,13,9)(7,10,14), (1,2,3,4)(5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24), (2,7)(4,5)(10,19)(11,15)(12,17)(14,23)(16,21)(18,22) ); G=PermutationGroup([(1,8),(2,5),(3,6),(4,7),(9,24),(10,17),(11,18),(12,19),(13,20),(14,21),(15,22),(16,23)], [(1,18,22),(2,19,23),(3,24,20),(5,12,16),(6,9,13),(8,11,15)], [(2,19,23),(3,20,24),(4,17,21),(5,12,16),(6,13,9),(7,10,14)], [(1,2,3,4),(5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24)], [(2,7),(4,5),(10,19),(11,15),(12,17),(14,23),(16,21),(18,22)]) G:=TransitiveGroup(24,680); On 24 points - transitive group 24T683 Generators in S24 (1 5)(2 6)(3 7)(4 8)(9 17)(10 18)(11 19)(12 20)(13 21)(14 22)(15 23)(16 24) (1 9 21)(3 11 23)(4 12 24)(5 17 13)(7 19 15)(8 20 16) (1 21 9)(2 10 22)(4 12 24)(5 13 17)(6 18 14)(8 20 16) (1 2 3 4 5 6 7 8)(9 10 11 12 13 14 15 16)(17 18 19 20 21 22 23 24) (2 8)(3 7)(4 6)(10 20)(11 15)(12 18)(14 24)(16 22)(19 23) G:=sub<Sym(24)\| (1,5)(2,6)(3,7)(4,8)(9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(16,24), (1,9,21)(3,11,23)(4,12,24)(5,17,13)(7,19,15)(8,20,16), (1,21,9)(2,10,22)(4,12,24)(5,13,17)(6,18,14)(8,20,16), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24), (2,8)(3,7)(4,6)(10,20)(11,15)(12,18)(14,24)(16,22)(19,23)>; G:=Group( (1,5)(2,6)(3,7)(4,8)(9,17)(10,18)(11,19)(12,20)(13,21)(14,22)(15,23)(16,24), (1,9,21)(3,11,23)(4,12,24)(5,17,13)(7,19,15)(8,20,16), (1,21,9)(2,10,22)(4,12,24)(5,13,17)(6,18,14)(8,20,16), (1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24), (2,8)(3,7)(4,6)(10,20)(11,15)(12,18)(14,24)(16,22)(19,23) ); G=PermutationGroup([(1,5),(2,6),(3,7),(4,8),(9,17),(10,18),(11,19),(12,20),(13,21),(14,22),(15,23),(16,24)], [(1,9,21),(3,11,23),(4,12,24),(5,17,13),(7,19,15),(8,20,16)], [(1,21,9),(2,10,22),(4,12,24),(5,13,17),(6,18,14),(8,20,16)], [(1,2,3,4,5,6,7,8),(9,10,11,12,13,14,15,16),(17,18,19,20,21,22,23,24)], [(2,8),(3,7),(4,6),(10,20),(11,15),(12,18),(14,24),(16,22),(19,23)]) G:=TransitiveGroup(24,683); Matrix representation of C2.AΓL1(𝔽9) in GL8(ℤ) -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 , 0 1 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 , -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 1 0 , 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 , 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 G:=sub<GL(8,Integers())\| [-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1],[0,-1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1,0],[0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0] >; C2.AΓL1(𝔽9) in GAP, Magma, Sage, TeX C_2.{\rm AGammaL}_1({\mathbb F}_9) % in TeX G:=Group("C2.AGammaL(1,9)"); // GroupNames label G:=SmallGroup(288,841); // by ID G=gap.SmallGroup(288,841); # by ID G:=PCGroup([7,-2,-2,-2,-2,-2,-3,3,28,421,219,100,4037,4716,2371,201,10982,4717,3156,622]); // Polycyclic G:=Group<a,b,c,d,e\|a^2=b^3=c^3=d^8=e^2=1,ab=ba,ac=ca,ad=da,ae=ea,dbd^-1=bc=cb,ebe=b^-1c,dcd^-1=b,ce=ec,ede=ad^3>; // generators/relations Export ׿ × 𝔽	{"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": 0.808854341506958, "perplexity": 344.05523747478776}, "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-2020-05/segments/1579251700675.78/warc/CC-MAIN-20200127112805-20200127142805-00029.warc.gz"}
http://mathhelpforum.com/calculus/188239-square-root-limit-print.html	# square root limit • September 17th 2011, 09:29 PM transgalactic square root limit $lim_{x->0}\frac{\sqrt{x^2+arctanx}}{x}$ when we put the x in the denominator inside the root we get absolute value so wee need to split into cases let us deal with only one case $lim_{x->0^+}\frac{\sqrt{1+\frac{arctan}{x^2}}}{1}$ so i have a member in side the root which is 0/0 can i solve this thing without lhopital? • September 17th 2011, 10:04 PM CaptainBlack Re: square root limit Quote: Originally Posted by transgalactic $lim_{x->0}\frac{\sqrt{x^2+arctanx}}{x}$ when we put the x in the denominator inside the root we get absolute value so wee need to split into cases let us deal with only one case $lim_{x->0^+}\frac{\sqrt{1+\frac{arctan}{x^2}}}{1}$ so i have a member in side the root which is 0/0 can i solve this thing without lhopital? $\lim_{x\to 0} \frac{\arctan(x)}{x}=1$ so: $\lim_{x\to 0} \frac{\arctan(x)}{x^2}=\infty$ CB • September 17th 2011, 10:11 PM transgalactic Re: square root limit Quote: Originally Posted by CaptainBlack $\lim_{x\to 0} \frac{\arctan(x)}{x}=1$ so: $\lim_{x\to 0} \frac{\arctan(x)}{x^2}=\infty$ CB why $\lim_{x\to 0} \frac{\arctan(x)}{x}=1$ ?? • September 17th 2011, 10:17 PM CaptainBlack Re: square root limit Quote: Originally Posted by transgalactic why $\lim_{x\to 0} \frac{\arctan(x)}{x}=1$ ?? For small $x$ we have $\tan(x)\sim x$, so put $y=\tan(x)$ and as $x$ is small so is $y$ and vice-versa and so for small $y$: $y\sim \arctan(y)$ CB • September 17th 2011, 10:29 PM transgalactic Re: square root limit its like sinx/x its a definition ? • September 18th 2011, 02:24 AM CaptainBlack Re: square root limit Quote: Originally Posted by transgalactic its like sinx/x its a definition ? It is not a definition, it is a consequence of the definition of the tan/arctan function/s. CB • September 18th 2011, 03:05 AM transgalactic Re: square root limit so i cant use it if its not a definition and i cant use your explanation because its based on approximation. and i cant do lopital only on one fracture so how to solve it ? • September 18th 2011, 04:11 AM HallsofIvy Re: square root limit Why can't you use it if it is not a definition? tan(x)= sin(x)/cos(x) so tan(x)/x= (sin(x)/x) cos(x). Now, both of those limits, as x goes to 0, should be easy. • September 18th 2011, 04:39 AM transgalactic Re: square root limit but its arctanx not tan ?	{"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": 17, "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": 0.8126144409179688, "perplexity": 3269.480140340572}, "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-2016-26/segments/1466783393093.59/warc/CC-MAIN-20160624154953-00035-ip-10-164-35-72.ec2.internal.warc.gz"}
https://ithems.riken.jp/en/events/symmetric-tornheim-double-zeta-functions	Date February 25 at 15:00 - 16:00, 2019 (JST) Speaker Dr. Takashi Nakamura (Tokyo University of Science) Venue Language English Let $s,t,u \in {\mathbb{C}}$ and $T(s,t,u)$ be the Tornheim double zeta function. We investigate some properties of symmetric Tornheim double zeta functions. As a corollary, we give explicit evaluation formulas for $T(s,t,u)$ in terms of series of the gamma function and Riemann zeta function.	{"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": 0.968520998954773, "perplexity": 831.7554822293384}, "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/1637964359073.63/warc/CC-MAIN-20211130201935-20211130231935-00571.warc.gz"}
https://www.futurelearn.com/courses/precalculus/6/steps/628245?main-nav-submenu=main-nav-courses	## Want to keep learning? This content is taken from the University of Padova's online course, Precalculus: the Mathematics of Numbers, Functions and Equations. Join the course to learn more. 2.18 ## Precalculus Skip to 0 minutes and 10 seconds We’ve talked about positive integer powers, negative integer powers. We’ve talked about n-th roots. It’s now time to put all of that together and more and talk about rational powers. Here’s some motivation. How should we define a to the power 1 over n? Well we would like the usual known properties of powers or exponents to hold. So, in particular, we’d like a to the power 1 over n, the whole thing raised to the n, to equal a. Therefore, we are forced really to define a to the power 1 over n as being the n-th root of a, which we do. Thus, the n-th root is actually a fractional power and vice versa. Skip to 1 minute and 1 second More generally, for any integers, m and n, where n is in the natural numbers and m can be a negative integer, we define a to the power m over n, which is a typical rational number, to be the n-th root of a to the m. Now we do this for positive numbers, a, only. In fact, if m is negative, we only do it for strictly positive numbers, a, in the base. For a greater than 0, we have defined a to the p for any rational number, p. Some facts that pertain to this definition are now given. Skip to 1 minute and 45 seconds We could prove all of these facts for these general rational numbers, but I immediately give you the same good news I gave you some time ago, these rules visually are exactly the same as they were say for positive integers. That’s good news. We don’t have to memorise a whole set of new rules. Some examples, x to the power of 1/2 is the square root of x. x to the power minus 3/5 turns out to be what I’ve written. Notice that the answer could be rationalised in the denominator if we so insisted. Another example, an exponent of minus 1/2 is undefined. We avoid negative numbers. Why should we avoid these negative bases, you say? Here’s an illustration of what can happen. Skip to 2 minutes and 42 seconds Suppose we did define minus 8 to the 1/3 as being minus 2. That’s not totally ridiculous because minus 2 cubed is equal to minus 8. But now, the usual exponential rules that we know so well don’t necessarily work. That is, minus 2 would be the cube root of minus 8, but that would be the same as minus 8 to the power 2 over 6 because, after all, 2 over 6 is the same as 1/3. And now, if we bring in the 2 as we do by the usual exponential rules, we get the cube root, the sixth root rather, of the number 64. Now 64 is 2 to the power 6, and, therefore, we wind up with 2. Skip to 3 minutes and 30 seconds And we have proved that minus 2 equals 2. That’s not a good sign. So you see, dangerous to define powers with negative bases, and I suggest that we avoid doing so. What are the graphs of these rational power functions going to look like? Well, by and large, they’re going to have the same general characteristics of some familiar graphs we’ve seen in the past. For example, when q is equal to 1, the function next to the q is an affine function, in fact, going through the origin called the linear function. When q is greater than 1, the graph looks rather like the graph of x squared. It has the increasingness on r plus, for example. Skip to 4 minutes and 17 seconds And when q is less than 1, it resembles the graph of the square root of x that we saw earlier. All these functions agree at x equal 1, of course, to give you the value 1. And for negative rational exponents, you get graphs that have this kind of characteristic, there you have decreasing functions of x. And, again, they’re defined only on r plus. It’s useful to know the general nature of these graphs, the monotonicity of the functions, for example, such as the following. Suppose you need to know which of these two numbers is greater than the other. How do you figure that out? Well you could say the following. Skip to 5 minutes and 2 seconds The function that to the argument x gives you the power minus 6.72 of x. That’s a strictly decreasing function by the graph that we saw just a moment ago. Why? Because the exponent is a negative number. We also observe that 1/2 is less than pi over 4. How do we prove that? Well we can cross multiply 1 times 4, 2 times pi. That’s equivalent to saying that 4 is less than 2 pi, cross multiplying. Is 4 less than 2 pi? Well that’s the same as saying 2 is less than pi, which is true because we know that pi is 3.14 something, something, and so on. Skip to 5 minutes and 50 seconds Now because of the decreasing nature of the negative power function that we have above, we deduce that 1/2 to that negative power is greater than pi over 4 to that same negative power. That’s clear from the graph because it’s a decreasing graph. So we have answered the question regarding the comparison. In fact, if we look at the graph and realise that both 1/2 and pi over 4 are less than 1, we can also add a further conclusion. Both our values here that we’re comparing are greater than 1. # Rational powers Basic properties, graphs, connection to radicals	{"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": 0.9072585701942444, "perplexity": 278.11698538613587}, "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-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00442.warc.gz"}
https://brilliant.org/problems/water-3/	# A number theory problem by Ralph Macarasig $\Large A =2017^{40^{640}} - 2017 \qquad \qquad B = 2017^{40^{544}} - 2017$ The greatest common divisor of $A$ and $B$ can be expressed in the form $\large 2017^{x^{y}} - 2017$, where $x$ and $y$ are integers. Submit your answer as $\overline{xy}$, which is the concatenation of the digits of $x$ and $y$. For example, if $x = 10$ and $y = 12$, then $\overline{xy} = 1012$. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 12, "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": 0.9850209355354309, "perplexity": 63.17749340629312}, "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-2019-47/segments/1573496668544.32/warc/CC-MAIN-20191114232502-20191115020502-00283.warc.gz"}
https://mathoverflow.net/questions/41784/roots-of-permutations	# Roots of permutations Consider the equation $$x^2=x_0$$ in the symmetric group $$S_n$$, where $$x_0\in S_n$$ is fixed. Is it true that for each integer $$n\geq 0$$, the maximal number of solutions (the number of square roots of $$x_0$$) is attained when $$x_0$$ is the identity permutation? How far may it be generalized? • I assume x_0 and x_o are the same? Also "identical permutation" means "identity permutation"? – JBL Oct 11 '10 at 13:52 • The number of $k$-th roots of a permutation is the number of ways to collect its cycles into tuples according to certain rules. At least for prime $k$, I think it follows immediately that the maximum is achieved at the identity permutation. – JBL Oct 11 '10 at 14:34 $$\DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\SL}{SL}$$ The maximum of the function counting square roots is attained at $$x_0=1$$ and this statement generalises quite well. Let $$s(\chi)$$ denote the Frobenius-Schur indicator of the irreducible character $$\chi$$. For the definition, see the edit below. One has $$s(\chi)=1$$ if the representation of $$\chi$$ can be realised over $$\mathbb{R}$$, $$s(\chi)=-1$$ if $$\chi$$ is real-valued but the corresponding representation is not realisable over $$\mathbb{R}$$, and $$s(\chi)=0$$ if $$\chi$$ is not real-valued. Then, the number of square roots of an element $$g$$ in any group is equal to $$\sum_\chi s(\chi)\chi(g),$$ where the sum runs over all irreducible characters of the group. See below for a reference and a quick proof of this identity. It follows from the usual theory of representations of $$S_n$$ that in this special case all Frobenius-Schur indicators are $$1$$, so the number of square roots of $$x_0$$ is just $$\sum_\chi \chi(x_0)$$. This proves that the maximal number of solutions is indeed attained by $$x_0 = 1$$, since each character value attains its maximum there. This generalises immediately to all groups for which every representation is either realisable over $$\mathbb{R}$$ or has non-real character, in other words has no symplectic (or sometimes called quaternionic) representations. That includes all abelian groups, all alternating groups, all dihedral groups, $$\GL_n(\mathbb{F}_q)$$ for all $$n\in \mathbb{Z}_{\geq 1}$$ and all prime powers $$q$$ (see [1, Ch. III, 12.6]), and many more. [1] A. Zelevinsky, Representations of Finite Classical Groups, Lecture Notes in Mathematics, Vol. 869, Springer-Verlag, New York/Berlin, 1981. Edit: One reference I have found for the identity expressing the number of square roots in terms of Frobenius-Schur indicators is Eugene Wigner, American Journal of Mathematics Vol. 63, No. 1 (Jan., 1941), pp. 57-63, "On representations of certain finite groups". Once you get used to the notation, you will recognise it in displayed formula (11). Since the notation is really heavy going, I will supply a quick proof here: Claim: If $$n(g)$$ is the number of square roots of an element $$g$$ of a finite group $$G$$, then we have $$n(g) = \sum_\chi s(\chi)\chi(g),$$ where the sum runs over all characters of $$G$$, and $$s(\chi)$$ denotes the Frobenius-Schur indicator of $$\chi$$, defined as $$s(\chi)=\frac{1}{\|G\|}\sum_{h\in G}\chi(h^2)$$. Proof: It is clear that $$n(g)$$ is a class function, so it is a linear combination of the irreducible characters of $$G$$. The coefficient of $$\chi$$ in this linear combination can be recovered as the inner products of $$n$$ with $$\chi$$. We can write $$n(g) = \sum_h \delta_{g,h^2}$$ (here $$\delta$$ is the usual Kronecker delta), so we obtain \begin{align} \left< n,\chi \right> &= \frac{1}{\|G\|}\sum_{g\in G}n(g)\chi(g) = \frac{1}{\|G\|}\sum_{g\in G}\sum_{h\in G}\delta_{g,h^2}\chi(g)=\\\\ &=\frac{1}{\|G\|}\sum_{h\in G}\sum_{g\in G}\delta_{g,h^2}\chi(g) = \frac{1}{\|G\|}\sum_{h\in G}\chi(h^2), \end{align} as claimed. Edit 2: I got curious and ran a little experiment. The proof above applies to all finite groups that have no symplectic representations. So the natural question is: what happens for those that do? Among the groups of size $$\leq 150$$, there are 1911 groups that have a symplectic representation, and for 1675 of them, the square root counting function does not attain its maximum at the identity! There are several curious questions that suggest themselves: is there a similar (representation-theoretic?) 2-line criterion that singles out those 300-odd groups that satisfy the conclusion but not the assumptions of the above proof? What happens for the others? Can we find a complete characterisation of the groups whose square root counting functions is maximised by the identity? Following Pete's suggestion, I have started two follow-up questions on this business: one on square roots and one on $$n$$-th roots. • Wow, neat: I didn't see that coming at all. Do you have a reference for your identity? – Pete L. Clark Oct 11 '10 at 14:55 • See also Exercise 7.69 of my book Enumerative Combinatorics, vol. 2. In particular, part (c) asserts that if $k$ is a positive integer and $r_k(w)$ is the number of $k$th roots of $w\in S_n$, then $r_k$ is a character of $S_n$. It follows that $r_k$ takes its maximum value at the identity permutation. – Richard Stanley Oct 11 '10 at 15:26 • @Alex: Your Edit 2 seems very interesting. I doubt it is getting optimal exposure here: please consider asking it as as a separate question. – Pete L. Clark Oct 13 '10 at 16:48 To your last question - "how far may it be generalized" - Richard Stanley answered when you fix the equation ($$X^2=c$$) and vary the group. You may also wonder about other equations. The situation is interesting: There are equations and groups with the property that the identity is not the RHS yielding the most solutions. This is so even though the LHS has no constants, just variables. One may rephrase the question as follows: given a word $$w=w(X_1,X_2,\ldots,X_r)$$ in the free group $$F_r$$ with variables $$X_1,\ldots,X_r$$, and given any finite group $$G$$, one may naturally consider $$w$$ as inducing a function $$G^r \to G$$ by plugging elements of $$G$$ as variables. This in turn defines a probability distribution on $$G$$: if you plug uniform random elements, what do you get? The most likely outcome is often, but not always, the identity. In fact, the probability of getting the identity can be made arbitrarily small iff the group is non-solvable. I circulated this as a conjecture some years ago and it was proven by Miklos Abert (for the non-solvable case) and Nikolov and Segal (for the solvable one). • In fact, Richard Stanley didn't fix the equation. He is talking about equations of the form $x^k = c$ in $S_n$. – Alex B. Oct 12 '10 at 8:39 • True. My answer attempts to generalize further into equations in several variables. – Alon Amit Oct 12 '10 at 18:44 For a general finite group $$G$$ and an arbitrary element $$y \in G,$$ there is a general way to use characters to compare the number of solutions of $$x^{2} = y$$ in $$G$$ with the number of solutions of $$x^{2} = 1$$ within $$C_{G}(y).$$ For notice that any element $$x$$ with $$x^{2} = y$$ already lies in $$C_{G}(y).$$ Hence (using the general formula mentioned in Alex's answer, but within the group $$C_{G}(y)$$) the number of solutions of $$y^{2} = x$$ is $$\sum_{ \mu \in {\rm Irr}(C_{G}(y)} \nu(\mu) \mu(y),$$ where $$\nu(\mu)$$ is the Frobenius-Schur indicator of $$\mu$$ ( which Alex denoted by $$s(\mu)$$). But now we note (using Schur's Lemma) that unless $$y{\rm ker} \mu$$ has order $$1$$ or $$2$$ in $$C_{G}(y)/{\rm ker}(\mu)$$ we have $$\nu(\mu) = 0$$ since $$\mu$$ is certainly not real-valued. Hence if $$y$$ has order $$m,$$ then we need only consider irreducible characters $$\mu$$ with $$y$$ in their kernel when $$m$$ is odd, and irreducible characters $$\mu$$ with $$y^{2}$$ in their kernel when $$m$$ is even. In any case, the contribution to the sum from those characters with $$y$$ in their kernel is the same as the number of square roots of the identity in $$C_{G}(y)/\langle y \rangle.$$ I won't give all details, but we may continue to deduce that the difference between the number of square roots of the identity in $$C_{G}(y)$$ and the number of square roots of $$y$$ in $$G$$ is given by the formula: $$\sum_{\mu \in {\rm Irr}(C_{G}(y)/\langle y^{2} \rangle) \backslash {\rm Irr}(C_{G}(y)/\langle y \rangle)} 2\nu(\mu)\mu(1).$$ Note that this number is non-negative unless $$C_{G}(y)$$ has an irreducible character $$\mu$$ with $$\nu(\mu) = -1$$ and with $$y^{2} \in {\rm ker} \mu$$ but $$y \not \in {\rm ker} \mu$$. Hence we may conclude in particular that for a general element $$y$$ of a general finite group $$G,$$ the number of square roots of $$y$$ in $$G$$ is already less that the number of solutions of square roots of the identity in $$C_{G}(y)$$ unless $$C_{G}(y)$$ has an irreducible character $$\mu$$ of Frobenius-Schur indicator $$-1$$ such that $$y{\rm ker} \mu$$ has order $$2$$ in $$C_{G}(y)/{\rm ker} \mu.$$ Latter edit: It is perhaps worth remarking that this argument shows that the number of square roots of $$y$$ in $$G$$ is the same as the number of square roots of $$yM$$ in $$C_{G}(y)/M$$, where $$M$$ is the normal subgroup $$\langle y^{2} \rangle$$ of $$C_{G}(y).$$ This reduces the computation of the number of square roots of $$y \in G$$ to the case that $$y$$ has order $$1$$ or $$2$$ and that $$y \in Z(G).$$ Returning to the (last part of the) original question, it means that each finite group $$G$$ for which the maximum number of square roots is not attained at the identity has a section (ie a factor group of a subgroup) $$H$$ such that $$Z(H)$$ such contains an involution $$u$$ with the number of elements of order four with square $$u$$ at least two greater that the number of involutions of $$H$$ ( here an involtion is considered to be an element of order exactly two). Furthermore, the section $$H$$ has the form $$C_{G}(y)/\langle y^{2} \rangle$$ where $$y$$ is an element of $$G$$ with the maximum number of square roots. Note also that if the identity element does not have the maximum number of square roots then the element $$y$$ attaining the maximum number necessarily has even order. Note that in the essential case that $$y \in Z(G)$$ is an involution, then $$y$$ has more square roots in $$G$$ than the identity does if and only if we have $$\sum_{ \{\chi \in {\rm Irr}(G) \backslash {\rm Irr}(G/\langle y \rangle): \nu(\chi) = -1 \}}\chi(1) > \sum_{ \{\chi \in {\rm Irr}(G) \backslash {\rm Irr}(G/\langle y \rangle): \nu(\chi) = +1 \} } \chi(1).$$ • That's nice! A data point, in particular in connection with my related question (link in my answer): out of the 1911 groups of order less than 150 that have a symplectic representation, in 236 the square root counting function takes its maximum at the identity. Out of those, 8 satisfy your criterion, i.e. there is no $y$ and $\mu\in {\rm Irr}_{C_G(y)}$ with Frobenius-Schur indicator $-1$ and such that $y{\rm ker}\mu$ has order $2$ in $C_G(y)/{\rm ker}\mu$. All 8 are groups of order $128$. – Alex B. Mar 14 '19 at 11:57 • Are there any general results regarding Frobenius-Schur indicators of element centralisers in finite groups? In particular, are there any infinite families of groups that may have symplectic representations but for which your criterion kicks in? – Alex B. Mar 14 '19 at 11:57 • Not sure if you have now seen the new edit, which reduces the problem to the essential case of a central involution which has strictly more square roots than the identity. For groups like ${\rm SL}(2,q)$ ($q$ odd) I think it's obvious that the central involution has more square roots than the identity since the identity has only two square roots,whereas there are already at least six elements of order $4$ in the Sylow $2$-subgroup. But the character theoretic condition also shows this easily too. – Geoff Robinson Mar 14 '19 at 12:33 • Our comments overlapped, we had been typing at the same time. I had also noticed that among the aforementioned small groups, in the vast majority of them (all but 23), the square root counting function attains its maximum at a central element. Your argument offers an explanation of this observation. – Alex B. 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https://www.physicsforums.com/threads/statics-question.173486/	# Statics question 1. Jun 10, 2007 ### JoshuaR 1. The problem statement, all variables and given/known data This is the diagram of the question. There are 3 wooden beams nailed together and supported at A,D, and F. Assuming only vertical forces, what are the vertical reactions at A, D, and F? The solution uses this diagram to make three basic equations: (1) for BEF, F=2/3(P+E)=2B (2) for ECD, D=2/3C=2E (3) for ABC, A=2/3B=2C For (2), why is it D=2/3C=2E and not D=2/3C=2(P+E)? Why doesn't P come into the equation? Isn't it acting at point E? I understand the solution completely except for this one point. Thank you. Using algebra I can get the solution of D=1/13P, F=9/13P, A=3/13P But only if D=2E rather than D=2(P+E) 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 2. Jun 10, 2007 ### JoshuaR Someone suggests that force P may be only applied to beam BEF, not on beam DCE. Would that make it work? 3. Jun 10, 2007 ### PhanthomJay That is not quite correct, force P is applied as shown, to the system of beams, at the intersection of the 2 beams BEF and DCE. Draw a Free Body Diagram of beam DCE. Isolate it such that you cut the beam with your Free Body Diagram immediately to the right of joint E, such that P, the applied force, does not enter into the diagram, and therefore the given solution appears correct.	{"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": 0.8748026490211487, "perplexity": 1931.2657087096225}, "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-2016-44/segments/1476988719041.14/warc/CC-MAIN-20161020183839-00559-ip-10-171-6-4.ec2.internal.warc.gz"}
https://ipm.ac.ir/ViewPaperInfo.jsp?PTID=7828&school=Physic	## “School of Physic” Back to Papers Home Back to Papers of School of Physic Paper IPM / Physic / 7828 School of Physics Title: Casimir Densities for A Spherical Brane in Rindler-Like Spacetimes Author(s): 1 A.A. Saharian 2 M.R. Setare Status: Published Journal: Nucl. Phys. B Vol.: 724 Year: 2005 Pages: 406-422 Supported by: IPM Abstract: Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are evaluated for a scalar field obeying mixed boundary condition on a spherical brane in (D+1)-dimensional Rindler-like spacetime Ri×SD−1, where Ri is a two-dimensional Rindler spacetime. This spacetime approximates the near horizon geometry of (D+1) -dimensional black hole in the large mass limit. The vacuum expectation values are presented as the sum of boundary-free and brane-induced parts. Further we extract from the Wightman function for the boundary-free geometry the corresponding function in the bulk R2×SD−1. For the latter geometry the vacuum expectation values of the field square and the energy-momentum tensor do not depend on the spacetime point. For the renormalization of these quantities we use zeta regularization technique. Various limiting cases of the brane-induced vacuum expectation values are investigated.	{"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": 0.9170324802398682, "perplexity": 3134.4947294070566}, "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-2023-06/segments/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00305.warc.gz"}
https://oa.journalfeeds.online/2022/08/23/methods-to-derive-the-magnetopause-from-soft-x-ray-images-by-the-smile-mission-geoscience-letters/	# Methods to derive the magnetopause from soft X-ray images by the SMILE mission – Geoscience Letters #### ByChi Wang and Tianran Sun Aug 23, 2022 Solar wind charge exchange (SWCX) occurs when highly ionized species in the solar wind interact with neutral atoms such as the exospheric (geocoronal) hydrogen. SWCX was first proposed by Cravens (1997) to explain observations of X-ray emissions from the comet. An electron from the neutrals is transferred to the ion initially in a highly excited state, for example O(^{6+}), O(^{7+}), C(^{5+}), etc. On relaxation to the ground state one or more photons are emitted, producing soft X-ray of 0.5–2.0 keV band. These highly ionized solar wind ions originate in the solar atmosphere, and, for the most part, do not enter the magnetospheric cavity (magnetosphere) and thus are mainly present in the magnetosheath and cusps. Earth’s atmosphere does not contain highly ionized ions due to its lower temperature. Therefore, soft X-ray emissions mainly come from outside of the magnetopause, and rarely from the inside of the magnetopause, creating a sharp boundary. The SMILE SXI is a widefield lobster-eye telescope equipped with CCD detectors, developed by the University of Leicester, UK. The latest design of the SXI has a field of view of 16(^o) by 27(^o). It will perform soft X-ray observations of the subsolar magnetopause and cusps. The soft X-ray flux is given by the integral of (P = alpha _{cx} n_H n_{sw} V_{rel}) along the line of sight, where (alpha _{cx}) is an efficiency factor dependent on the ion abundance, interaction cross-sections, branching ratios, etc. Typical value for (alpha _{cx}) is about (6 times 10^{-16}) to (6 times 10^{-15}) (Cravens 2000). (n_H) is the density of neutral particles, usually estimated as (25 (text{cm}^{-3})(10(R_E)/r)^3) (Cravens et al. 2001). (n_{sw}) is the density of solar wind protons with typical values as 5–12 (text{cm}^{-3}) (Wilson et al. 2021), and (V_{relv}) is their relative velocities typically several hundred km/s. The SXI will basically take 2D soft X-ray image of the intended target, with its FOV keeping changing as the spacecraft moves along orbit. It is essential to identify the exact location of the magnetopause, and will be a challenging task to to reconstruct the 3-dimensional surface of the magnetopause from 2-dimensional images. So far, four approaches have been developed to derive the 3-D magnetopause position from X-ray images, namely the tangential direction approach (TDA), boundary fitting approach (BFA), tangent fitting approach (TFA), and computerized tomography approach (CTA). They will be introduced in the following sub-sections. ### Tangential direction approach (TDA) The tangent vector plays a central role in differential geometry, which can be used to define global geometry of the magnetopause. Under a broad range of conditions, the peak soft X-ray emission corresponds to the tangent to the boundary surface such as magnetopause, the so-called limb brightening phenomenon (Collier et al. 2014). The viewing angle that touches the edge of the magnetopause has the longest path length through the emission region in the magnetosheath (Collier and Connor 2018). More emission occurs along this direction, producing a bright edge. To determine the validity of the assumption that the local peaks in the observed SWCX soft X-ray flux coincide with the line-of-sight tangents to the magnetopause, Collier and Connor (2018) performed MHD simulations using OpenGGCM (e.g., Raeder et al. 2008). The MHD models were run and then line-of-sight integrations were calculated to determine the total soft X-ray flux observed in that direction due to the solar wind SWCX with exospheric neural hydrogen. Figure 2 shows an example of the results from MHD simulation for a southward interplanetary magnetic field (IMF) of 5 nT, a solar wind density of 10 cm(^{-3}), and a flow speed of 400 km s(^{-1}). In this case, the spacecraft was orbiting in the geocentric solar ecliptic (GSE) YZ plane (GSE X = 0). The top left panel in Fig. 2 shows the local soft X-ray emission at each point in this plane, and the top right panel shows the plasma density. Although densities peak in the outermost magnetosheath, emissions peak in the inner magnetosheath, since the total observed soft X-ray intensity depends not only on plasma density, but also on the exospheric neutral density and effective velocity. The lines in these two panels originate at the spacecraft location and show both the direction of the local peak in the soft X-ray emission (black) and the direction of the tangent to the magnetopause location (red). The lower panel in Fig. 2 shows that the direction of the peak emission ((theta _{XR})) and the direction tangent to the magnetopause ((theta _text{MP})) coincide to each other with an accuracy higher than one degree by plotting the line-of-sight integrated emission versus the line-of-sight angle. As expected, the difference between the two angles increases as the observation point gets closer to Earth. This appears to be a general property, namely, that a local peak in the observed soft X-ray flux occurs coincident with the geometric tangent line of sight to the surface. To derive the general formula for reconstruction of the magnetopause from the spacecraft position, (vec {s}), parameterized by tangent angle (theta ), Fig. 3 illustrates the geometry. The point O is an arbitrary origin, (vec {r}) is the line-of-sight tangent direction unit vector, (vec {s}) is the vector define the spacecraft (for example, SMILE) location relative to O, (theta ) is the observed angle between the line-of-sight tangent and the positive x direction. As derived by Collier and Connor (2018), the general formula is: begin{aligned} vec {p} = \|frac{dvec {s}}{dtheta }cdot hat{theta }\|vec {r}+vec {s}. end{aligned} (1) The magnetopause location can then be determined by the derivative of the spacecraft position with respect to the angle of the tangent direction. Figure 4 shows the application of the reconstruction algorithm to a case in which the spacecraft executes a circular orbit in the GSE YZ plane of 20 Re radius (black). The top panel shows the relationship between the spacecraft location, and the angle at which the maximum soft X-ray flux is observed ((theta )). The middle panel shows (\|ds/dtheta \|), the derivative of the spacecraft position with respect to the observation angle of peak soft X-ray intensity. The bottom panel shows the magnetopause reconstruction resulting from the soft X-ray emission simulation (red, blue, and green) using equation 1 superimposed on the MHD plasma density results (shading). The black and yellow lines indicate the spacecraft orbit and the magnetopause locations calculated from the MHD model, respectively. The algorithm reconstructs the magnetopause location with reasonable accuracy. The root-mean-square (rms) difference between the position of the magnetopause based on the MHD simulation and the position calculated from the reconstruction algorithm is about 0.18 Re. In fact, the reconstruction algorithm manages to even reproduce the outer cusp shape viewing from satellite positions in the XZ plane (not shown here). There are, however, limitations inherent in this reconstruction approach, for example, the assumption of time stationarity and the offset between the peak density gradient and the maximum soft X-ray emission. The first limitation could be alleviated by orbit binning the data according the desired solar wind conditions and then reconstructing the magnetopause from the data subsets corresponding to these conditions. ### Boundary fitting approach (BFA) Jorgensen et al. (2019a) developed an method to extract the large-scale structures such as the magnetopause, and the bow shock from the soft X-ray images by fitting parameterized models to the images, so we called it boundary fitting approach (BFA). The models consist of a boundary model used for the magnetopause and the bow shock and a emission model used for the regions between the boundaries. The boundary model is a generalization of the model by Shue et al. (1997) and has the following form: begin{aligned} r(theta ,phi )=frac{r_y(theta )r_z(theta )}{sqrt{[r_z(theta )cosphi ]^2+[r_y(theta )sinphi ]^2}}, end{aligned} (2) where in accordance with Shue et al. (1997), begin{aligned} r_y(theta )=r_0(frac{2}{1+costheta })^{alpha _y}, end{aligned} (3) and begin{aligned} r_z(theta )=r_0(frac{2}{1+costheta })^{alpha _z}, end{aligned} (4) where (theta ) is the angle to the X-axis and (phi ) is the azimuthal angle in a right-hand sense around the X-axis starting from the Y-axis. The emissions model consists of three regions separated by the magnetopause and bow shock, both represented by the above equation with different parameters (r_0), (alpha _y), and (alpha _z) for each. The three regions are the solar wind region sunward (+X) of the bow shock boundary; the magnetosheath between the bow shock and the magnetopause, and the magnetosphere inside the magnetopause. The model is as follows: begin{aligned} F(vec {r})={ begin{array}{ll} 0 &{} text {inside MP} \ (A_1+Bsin^8theta )(frac{r}{r_{ref}})^{-(alpha +beta sin^2theta )} &{} text {between MP and BS}\ A_2(frac{r}{r_{ref}})^{-3} &{} text {outside BS}. end{array} end{aligned} (5) The images used in the fit are then computed from the analytical model based on Eq. 5 for the soft X-ray emissions and Eq. 2 for each of the magnetopause and bow shock. The cost function is the mean-absolute deviation begin{aligned} e=frac{1}{N}sum _{i=1}^{N}\|f_{i,model}-f_{i,data}\|, end{aligned} (6) because it typically produces better results (in the sense that it looks like a better fit to the eye) than the least-squares fit when the model and data are not exact matches. For finding the cost-function minimum, the the simplex approach by Nelder and Mead (1965) has been used. Since it is not a global minimization algorithm, the starting point for the minimizer should be carefully picked. The 11 parameters ((A_1, B, alpha ,beta ,A_2, r_0^{mp},alpha _y^{mp},alpha _z^{mp},r_0^{bs},alpha _y^{bs}), and (alpha _z^{bs})) are varied until an optimal match with a minimum cost function has been reached. In the same way as above, we simulate the SWCX soft X-ray emissions by running the global MHD model, namely PPMLR (Hu et al. 2007; Wang et al. 2013). Figure 5a shows a simulated noise-free image, whereas Fig. 5b–d shows the same image with average pixel count rates of 1, 0.1, and 0.01 counts, assuming Poisson statics. The simulated image can be used to mimic the soft X-ray observations from SMILE. The fitted images from the boundary model and emission model are shown in Fig. 6. Comparing the images in Fig. 6 with those in Fig. 5 suggests that this is a close fit for the region imaged. Jorgensen et al. (2019a, b) also discussed the effect of photon noise and model-fitting noise when extracting the 3D structures from 2D images by applying this boundary fitting approach. It is found that the reconstruction accuracy depends on pixel counts as expected. At lower count rates, the uncertainty becomes higher. The uncertainties obtained depend on viewing geometries. Generally, the more of a boundary that is contained in the image, the smaller the uncertainty on the parameters of that boundary. The fitted model parameters do not vary much with the viewing geometry except when the FOV misses essential elements such as the subsolar point of the magnetopause and bow shock. In future work, it is worthwhile to consider other functional forms for the boundaries as well as the emission distribution in the magnetosheath and to a less extend the emission distribution in the solar wind. The emission from the cusps should be also taken into account. ### Tangent fitting approach (TFA) Combining the advantages of TDA and DFA, Sun et al. (2020) developed a new method to derive the 3D magnetopause from a single X-ray image. The basic idea is similar to BFA in Jorgensen et al. (2019a, b) as introduced above, which compares the information provided by the X-ray image as well as a parameterized magnetospheric system in order to find the best match. However, instead of comparing the X-ray intensity at each pixel inside the FOV, TFA compares the tangent directions of the magnetopause. Specifically, as the first step, tangent directions of the magnetopause are derived by finding the location with maximum intensity of the X-ray image (Collier and Connor 2018). For the second step, a parameterized functional form for the magnetopause has been assumed, providing a set of reasonable magnetopause profiles. For each profile, the tangent directions can be calculated numerically. Finally, the magnetopause is reconstructed by finding the best match of the tangent directions analyzed from the soft X-ray image and the magnetopause function. In the second step, the functional form of magnetopause used by Sun et al. (2020) is also the modified Shue et al. (1997) model, shown by Eqs. (2)–(4). By changing (r_0), (alpha _y), and (alpha _z) within reasonable ranges, a set of magnetopause profiles can be obtained. TFA has also been validated by using PPMLR-MHD simulation. Figure 7a is the simulated soft X-ray image ’observed’ by a hypothetical X-ray telescope, with a typical viewing geometry designed for SMILE. By searching for the maximum intensity, the black curve is derived and marked to show the tangent directions of the magnetopause. The tangent directions are also calculated for each possible magnetopause profile, by allowing the three parameters ((r_0), (alpha _y), and (alpha _z)) in the magnetopause function to float within reasonable ranges. Then the optimum match with the black curve has been found and plotted as the red curve. The parameters corresponding to the red curve are: (r_0) = 8.0 (R_E), (alpha _y) = 0.8 and (alpha _z) = 0.2, which help to portray the reconstructed magnetopause in Fig. 7c. To better evaluate the TFA result, 2D views of the reconstructed magnetopause are marked in Fig. 7(b1)–(b4) by the red curves, in comparison with the original MHD boundary shown by the white curves. The reconstruction result is in good accordance with the MHD boundary. TFA is further validated with different viewing geometries on a candidate SMILE orbit. It is concluded that there is no apparent orbital bias while utilizing TFA to derive the 3D magnetopause position, as all the three variables show reasonable agreement with the MHD result. Nevertheless, the fitting error tends to increase while the satellite gets closer to the magnetopause boundary as expected. Since it is not able to obtain tangent directions from a point inside the magnetopause, TFA becomes invalid after the satellite enters the magnetosphere. Based on TFA, we are able to derive the 3D magnetopause position from a single X-ray image, and therefore, TFA is applicable to events under fast solar wind variations. TFA only requires the assumption of the magnetopause function, and thus the number of free variables is apparently reduced compared to that in BFA, which has 11 parameters from the magnetopause, bow shock and magnetosheath emissivity models. Therefore, TFA tends to avoid possible false minima caused by inaccurate initial guess of the parameters. The application of TFA does not rely on simultaneous solar wind observations, which is used to provide well evaluated initial conditions. ### Computerized tomography approach (CTA) Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions. The impact of this technique in diagnostic medicine has been revolutionary. Computed tomography (CT) allows physicians to view internal organs non-invasively and scientists to evaluate compound materials non-destructively (Kak and Slaney 1987). The fundamental principle of X-ray CT is to reconstruct an object from its known line integrals or projection. CT image reconstruction algorithms have been extensively studied (see e.g., Kak and Slaney 1987 for a book description). In the field of space research, CT technique was first applied to image the electron density distribution in the ionosphere (Austen et al. 1988). Li et al. (2009) proposed using this method to reconstruct the global density of Earth plasmasphere from the line integrals of the EUV radiation. SMILE will record a large enough number of images from different viewing geometries, so the CT technique may be applicable if the magnetosphere remains unchanging which requires constant solar wind conditions. This is rare in the real situations. However, we could take superposed-epoch approach using images widely spaced in time but for similar solar wind conditions and dipole tilts. Jorgensen et al. (2022) conducted a theoretical study of the tomographic reconstruction of the magnetosheath X-ray emissions, with (0.125 R_E) spatial resolution. Generally, begin{aligned} A bar{u} = bar{p}, end{aligned} (7) where (bar{u}) of length n represents the real soft X-ray emission, (bar{p}) of length m is the imaged soft X-ray data, denoting all of the pixels in all of the images, and A is the system matrix with m rows and n columns which may be determined by the data collection geometry of the X-ray sensor. Tomographic reconstruction then solves the inverse problem of determining (bar{u}) from (bar{p}) given a known geometry matrix A. One of the earliest and simplest reconstruction techniques is the Algebraic Reconstruction Technique (ART) (Gordon et al. 1970). The main idea of ART is to make the estimated image satisfy one equation at a time. At each iteration, k, cycling through the rays, (i in [1;m]) and the next emissions distribution, (bar{u}^{k+1}) is computed as: begin{aligned} bar{u}^{k+1}=bar{u}^{k}+lambda _{k}frac{p_i – overline{A}_{i} cdot bar{u}^{k}}{parallel overline{A_i} parallel ^2} overline{A}_{i}^{T}, end{aligned} (8) where (overline{A}_{i}) is now i of A. (p_i) is the measured data from the ith soft X-ray image. (bar{u}^k) is the estimation of the image by the kth iteration. For many practical cases the ART procedure is nonetheless capable of producing an adequate reconstruction of the original volume distribution, with 180(^circ ) full coverage. However, for more complex volume distributions, when there is noise present in the images, or to improve the accuracy of the reconstruction with partial angular coverage, additional constraints can be introduced. Jorgensen et al. (2022) employs a denoising algorithm called total variation (TV) minimization which can reduce the total pixel-to-pixel variation in the image (Rudin et al. 1992). The TV algorithm is run after every pixel in every image has been visited in the ART algorithm. In the same way as described above, the MHD simulation results are used to mimic the realistic soft X-ray emissions for a nominal designed orbit of SMILE. Figure 8 shows examples of images for a modeled apogee pass of the SMILE spacecraft not long after launch. Figure 9 shows the reconstruction using 100 images with ART and TV. The magnetosheath is reconstructed and that a portion of the cusp is reconstructed as well. As expected, the resulting reconstruction show much less pixel-to-pixel variation with more times TV iteration. Jorgensen et al. (2022) also compared the reconstruction with 10 images and 1000 images, and concluded that 100 images is sufficient for proper reconstruction.	{"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": 0.8968928456306458, "perplexity": 1636.4867004286302}, "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-2023-06/segments/1674764500273.30/warc/CC-MAIN-20230205161658-20230205191658-00544.warc.gz"}
https://brilliant.org/problems/counting-surjective-functions/	# Counting surjective functions Let $$I_7=\{1,2,3,4,5,6,7\}$$. Let $$N$$ be the number of surjective functions $$f:I_7\to I_7$$ such that $$f(f(a))\neq a$$ for all values of $$a$$. What are the last three digits of $$N$$? Details and assumptions A function $$f:A \to B$$ is surjective if for each $$b \in B$$, there exists $$a\in A$$ such that $$f(a)=b$$. ×	{"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": 0.97965407371521, "perplexity": 87.06961116869456}, "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/1500549423769.10/warc/CC-MAIN-20170721102310-20170721122310-00404.warc.gz"}
http://physics.stackexchange.com/tags/voltage/hot	# Tag Info 123 Why is mains frequency 50Hz and not 500 or 5? Engine efficiency, rotational stress, flicker, the skin effect, and the limitations of 19th century material engineering. 50Hz corresponds to 3000 RPM. That range is a convenient, efficient speed for the steam turbine engines which power most generators and thus avoids a lot of extra gearing. 3000 RPM is ... 43 In addition to the other answers, here is something for the intuition: $$V=RI$$ More "pressure" $V$ (more correctly: higher "pressure" difference from one side to the other) is required to keep the flow $I$ of charges constant when the flow is resisted by $R$. A thin wire has higher resistance than a thick wire, $R=\rho L/A$) analogous to a "bottleneck" ... 33 Ohm's Law is not a construct which can be derived. It is essentially a generalized observation. It is only useful for a few materials (conductors and medium resistivity), and even then virtually all of those materials show deviations from the ideal, such as temperature coefficients and breakdown voltage limits. Rather, Ohm's Law is an idealization of the ... 25 In the end, the choice of a single specific number comes from the necessity to standardize. However, we can make some physical observations to understand why that final choice had to fall in a certain range. Frequency Why a standard? First of all, why do we even need a standard? Can't individual appliances convert the incoming electricity to whatever ... 23 You could start from Drude in zero magnetic field, that equates the derivative of the momentum $\vec p$ by the electrostatic force $\vec F_{el} = q \vec E$ as a product of charge $q$ and electric field $\vec E$ minus a scattering term (with time constant $\tau$; compared to Newtons second law that does not feature the latter, crystal term): $~~~~~~\dot ... 23 Suppose you are using a waterwheel to do some form of work (e.g. grind corn). You need a head of water to make the wheel move, and you could use either 1kg of water at a height of a million metres or you could use a million kg of water at a height of one metre. In both cases the water would do the same amount of work as it flowed through your wheel. The ... 20 The identity $$V = K \frac{dV}{dt}$$ is only guaranteed with a constant$K$if your assumptions actually hold. The first identity$V=RI$only holds for a resistor, while the other holds for a capacitor. So in this sense, the letters$V,I$in these equations mean something else. In one of them, it's the current through (or voltage on) a particular resistor, ... 17 Perhaps I can clarify what I'm trying to get at with the famous waterwheel analogy 99 years ago, Nehemiah Hawkins published what I think is a marginally better analogy: Fig. 38. — Hydrostatic analogy of fall of potential in an electrical circuit. Explanation of above diagram In this diagram, a pump at bottom centre is pumping water from right to ... 14 For static charges, the relationship is V (voltage) = Q (charge) / C (capacitance). Capacitance is a function of the shape, size and distance between objects, which are all continuous values. (Well, I suppose you could argue that shape and size are quantized to the atomic spacing of the object's material, but you can't say the same thing for distance.) So ... 12 The two other answers address the frequency issue. The voltage issue is much simpler. If the voltage is too high, you run the risk of arcs between conductors. The minimum distance between conductors before an arc appears is proportional to voltage. At 240V, you arc at a distance of a few millimeters in air, depending on humidity. More voltage gets clearly ... 10 firstly, you hooked up the red wire to negative and the black wire to positive--you got it backwards. secondly, computer fans operate at 12V, so you are short of several batteries. with luck, some fans might start spinning at 7V . 10 There are various ways to decide which of the assumptions are primary and which of them are their consequences but$E=VQ$may be most naturally interpreted as the definition of the potential. The potential energy is a form of energy and the potential (and therefore voltage, when differences are taken) is defined as the potential energy (or potential energy ... 10 What makes it a good idea to use RMS rather than peak values The rms value, not the peak value, is the equivalent DC value that gives the same average power. Recall that power is the product of voltage and current:$p(t) = v(t) \cdot i(t)$For a resistor, we have:$p(t) = R[i(t)]^2$To find the average power, we must take the time average of both ... 9 does this mean that Ohm's law just fails in this case Ohm's law is not universal. The ideal resistor circuit element is defined by Ohm's law but not all circuit elements obey Ohm's law; Ohm's law only applies to ohmic devices. Physical resistors and conductors approximately obey Ohm's law but, for example, semiconductor diodes, transistors, ... 9 Think of plumbing for a close analogy. Voltage is how hard you are pushing, and current is how much flows. The relationship writes itself: why would you get more or less flow from the same pump? The measure of how much effort is used to get flow (it makes more sense as the reciprical: how much flows for a unit of effort) is the interesting property, and ... 8 This isn't really an answer, because your question doesn't provide enough information for an answer. However it explains what you need to do. In fact this is exactly what I did (back in 1983!) to measure the resistivity of evaporated silver films. If you have the film formed on some substrate you need to score two lines to leave a long narrow track like ... 8 EDIT: Put simply, potential difference is the work done by electrostatic force on a unit charge, while EMF is the work done by anything other than electrostatic force on a unit charge. I don't like the term "voltage". It seems to mean anything measured in volts. I'd rather say electric potential and electromotive force. And the two are fundamentally ... 8 1) If you are thinking of harmonics as sinusoidal waves, well yes, ALL waveforms are (can be described as) sum of harmonics. This is essentially the idea of the Fourier analysis. The problem is that to exactly reproduce a desired waveform you need in general an infinite number of harmonics. This is for instance the case of square waves. So in reality you ... 8 Let me first comment that the statement electric fields cancel while the electric potentials just add up algebraically is not actually correct. Electric fields add due to the principle of superposition (see the section on superposition in the wikipedia article). However, when two electric field vectors are of the same magnitude but point in ... 7 What flows is not the voltage but the charge, and that flow is called current. Voltage can be without a current, if you have a single charge, that charge induces a voltage in all space, even if it's empty. Voltage, in the most physical way, is a scalar field that determines the potential energy per unit charge at every point in space. Now, you can't have ... 7 Your analogy with water flow through a pipe is correct. In that analogy a voltage source corresponds to a pump that generates a specific pressure, and a current source corresponds to a pump that generates a specific water displacement (volume per second). 7 I've found this to be the case, too. Generally, my shop lights will flicker when turning on, especially when it is colder outside . There are two basic phases to this kind of light bulb: a start-up phase, and an operating phase. The start-up requires more voltage, because you are initiating the plasma stream between the terminals of the bulb. So, these ... 7 Voltage is a continuous function. If you are a certain distance from a (point) charge$q$, the potential is $$V=\frac{q}{4\pi\epsilon_0 r}$$ By adjusting the value of$r$to anything you want (not quantized), you can get any potential you want. And so yes, when you do any analog-to-digital conversion, you will "destroy" a certain amount of information. ... 7 This is true but strictly limited to RC circuits without external sources: that is, a resistor hooked up to a capacitor with nothing else in between. In that case,$V$is indeed proportional to$\dot V$, with a crucial minus sign in between: $$\dot V=-\frac1\tau V,$$ where$\tau>0$is some constant. This equation implies that$V(t)=V(0)e^{-t/\tau}$, ... 7 The physical meaning of the capacitance is precisely given by$\mathrm{d}Q=C\cdot \mathrm{d}V$:$C$tells you how much charge there will be in the capacitor per voltage applied. For all capacitors, the linearity holds fairly well. Generally speaking, capacitance is given by a Q-V curve, which may consist of a linear region, a saturation region and a ... 7 Voltage (Joule per coulomb) is a measure of electric potential energy gained by a positive test charge, or the work done in moving a positive test charge from infinity to a point in a positive electric field. This energy gained is due to the conservative electrostatic force between charge. When a charge gains potential it naturally does work equal to its ... 7 Another possibility is that you are having to break through the oxide film that all Aluminium has in air. The voltage needed to do that can vary considerably. You might need to use sharp steel electrodes that will punch through the oxide and contact the metal directly. 7 Have you looked at Drude's model? I was taught something like that back at school and have kept it in mind as a intuitive way of understanding it. We want to understand why the current (rate of flow of charge) should be linear with the potential difference. The Drude idea is, as you noted, related to friction. Firstly, the EM field is linear in the ... 6 A negative voltage means that you have hooked your power supply across your device backwards. Purely resistive devices, like resistors and lamp filaments, don't care which way current flows through them, only how much current flows. Such devices will always have current-voltage curves which are "odd" functions, with$I(-V) = -I(V)\$, as in your graph. It is ... 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https://www.answers.com/Q/How_many_galaxies_are_there	Galaxies # How many galaxies are there? 133134135 ###### 2015-06-16 01:55:59 No one really knows for sure, but there have been estimates that there are more than there are grains of sand. Hundreds of billions might be a reasonable "guesstimate". • Astronomers now estimate that the observable universe contains anywhere between 100 and 300 billion galaxies. However, if space time is flat on large scales (as it seems to be), the universe is infinite in size and contains an infinite number of galaxies in total, they are just so far away that their light has not had time to reach us since the beginning of the universe. In fact, because the universe is expanding, we will never see most of these galaxies ever! • The answer to your question is unknown. The universe is infinite containing billions and billions of galaxies as it expands. Roughly 150-200 billion galaxies though. • It is not definite how many galaxies there are but there could be up to 500 billion galaxies! I think that was found out by a German organization. • There are millions of galaxies that we can observe from Earth, but there are millions more that we cannot observe. • About 100,000,000,000 (a hundred billion) and still expanding! • Let's not forget the galaxies that are not in the observable Universe! Add up all the galaxies in the entireUniverse (including the part we can't see) and the number of galaxies could be in the trillions or larger! Humans can't even conceive huge numbers like that so knowing this has little effect on most of us. It is truly mind boggling how many galaxies could be out there. 🙏 0 🤨 0 😮 0 😂 0 ###### 2020-07-02 09:06:39 WHAT THE 100 BILLION!!!!!! 🙏 0 🤨 0 😮 0 😂 0 ## Related Questions That is related to their past history. Many galaxies have undergone collisions with other galaxies; this takes out most of the interstellar gas, and the galaxies can no longer form new stars. If I remember correctly, such galaxies will change into elliptical galaxies.That is related to their past history. Many galaxies have undergone collisions with other galaxies; this takes out most of the interstellar gas, and the galaxies can no longer form new stars. If I remember correctly, such galaxies will change into elliptical galaxies.That is related to their past history. Many galaxies have undergone collisions with other galaxies; this takes out most of the interstellar gas, and the galaxies can no longer form new stars. If I remember correctly, such galaxies will change into elliptical galaxies.That is related to their past history. Many galaxies have undergone collisions with other galaxies; this takes out most of the interstellar gas, and the galaxies can no longer form new stars. If I remember correctly, such galaxies will change into elliptical galaxies. There are no types of basic galaxies. There are galaxies of different nature such as spiral, barred spiral, lenticular and irregular galaxies. Galaxy clusters typically have anywhere from 50 to 1,000 galaxies. Spiral galaxies account for about 60% of all the galaxies. There are an estimated 100 billion galaxies in the observable Universe. So there about 60 billion spiral galaxies. Approximately 60% of all galaxies are spiral 5 galaxies in each dome... 6 domes... 7 hidden galaxies... 3 trials... 70 galaxies. Do you know how many galaxies are in space?It is never ending just like space. Yes, galaxies frequently collide, our own milky way is a result of many galaxies colliding and merging. There are Ten Billion Galaxies in outer space Yes, many galaxies rotate around a center or core. The majority of all of the known galaxies rotate around a core. They study distant galaxies because they want to know whats out in other galaxies and how many planets it has It's not known to any degree of accuracy, but about 66% of all spiral galaxies are barred and about 60% of galaxies in the local Universe are spiral galaxies. There is no way to find out how many galaxies are documented, but according to the NASA Extragalactic database, there are 4 million named. It is estimated that there are hundreds of billions of galaxies in space. All galaxies are massive clusters of stars scattered across the universe. Many galaxies take the same form, for instance, spiral and elliptical galaxies. Some galaxies also have a black hole in their center. The milky way is the name of our galaxy, there are no other galaxies in it. It is believed that there are over 170 billion galaxies in the observable universe. There are no smaller galaxies in the Andromeda galaxy. In the Local group of galaxies to which Andromeda and the Milky Way are part of, there are around 30 smaller galaxies, Not just dwarf galaxies. Giant elliptical galaxies lie likely the result of many galaxies, small and large, merging. Elliptical galaxies are called so because of their peculiar shape. The number of stars in these galaxies may change galaxy to galaxy. So there is no saying how many stars. A Galaxy Cluster can contain between 50 and a 1,000 galaxies. ###### ScienceAstronomyHistory of SciencePlanetary ScienceGalaxiesGame Consoles and Gaming HardwareAndromeda Galaxy Copyright © 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.	{"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": 0.8176872730255127, "perplexity": 902.4148893460266}, "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/1600402123173.74/warc/CC-MAIN-20200930075754-20200930105754-00749.warc.gz"}
http://www.quantumdiaries.org/2008/11/25/how-tracking-works/	## View Blog \| Read Bio ### How Tracking Works Author’s note: I didn’t mean for this to end up so complicated that it had equations, figures, and footnotes, but that’s how it turned out. I do apologize for the inconvenience, and if it’s any compensation I can assure you that about half the footnotes are funny. I’ve written before about how a pixel detector works, but at the time I left as a “topic for another day” the broader question of what a pixel detector is for. I’m going to answer one part of that question today, and discuss the tracking system, of which a pixel detector is one possible component.1 I’ll have to leave the question of the specific advantages of using pixels, as opposed to other tracking technologies, for another other day. Regardless of the technology used, the basic idea of a tracker is to put together a bunch of stuff that measures the path a charged particle has taken. The “stuff” could be silicon, in which electron-hole pairs are separated as the charged particle passes through, and can be used to produce a current, as I explained in my pixel detector entry. It could also be gas, in which case electron-ion pairs are separated and produce a current in wires; this is the technology used in the ATLAS Transition Radiation Tracker. If you want to “track” a baseball through the stands, the “stuff” is people: even if you can’t see the baseball in the crowd on other side of the stadium, you can see where it’s gone by who stands up or jumps down and starts grabbing under the seats. An individual jumping person, or silicon pixel producing a current, is what we call a hit. Our primary interest actually isn’t in how particles move through the detector, even though that’s what we directly measure. So let me take a step back now and describe what we are measuring, first and foremost: momentum. Momentum: What It’s Really All About The best way I can think of to describe momentum in a few words is to quote Newton and call it the “quantity of motion.”2 It reflects not just the speed and direction (i.e. velocity) of an object, but also the amount of stuff (i.e. mass) that makes up that object. In ordinary life, if you double the mass then you double the momentum, and if you double the velocity you get double the momentum too; in other words: • p = mv where m is the mass, v is the velocity, and p is the momentum.3 Unfortunately, things get a little more complicated when the particle goes really fast, which they usually do in our detectors; then the equation doesn’t work anymore. We’ll get to one that does in a minute. Momentum intuitively seems the same as energy of motion, but technically the ideas aren’t exactly the same, and it just so happens that the difference is important to how the LHC detectors work. One way to think of the energy of a particle is as follows: if you slammed the particle into a big block of metal and then extracted all the ensuing vibrations of the metal’s atoms4 and put them in a usable form, it’s the amount of mechanical work you could do. In fact, that’s exactly what a detector’s calorimeter does, up to a point. It’s made of big blocks of metal that absorb the particle’s energy, and then it samples that energy and turns it into an electrical current — not so we can do any kind of work with it, but just so we know how much energy there was in the first place. So the calorimeter is the piece of ATLAS or CMS that measures the energy of particles and absorbs them; the tracker, by contrast, measures the momentum of particles and lets them pass through. These two pieces of information are related by the following equation: • E2 = p2c2 + m2c4 where p and m are still momentum and mass, E is the energy, and c is the speed of light. The intuitive understanding of this equation is that the energy of a particle is partially due to its motion and partially due to the intrinsic energy of its mass. The application to particle detectors is that if you know the mass of a particular particle, or if it’s going so fast that its energy and momentum are both huge so that the mass can be roughly ignored, then knowing the energy tells you the momentum and vice versa — and knowing at least one of the two is critical for analyzing where a particle might have come from and understanding the collision as a whole. We have both kinds of systems because they have different strengths — for example, some kinds of particles don’t get absorbed by the calorimeter, and some kinds of particles (the uncharged ones) can’t be seen in the tracker — and together, they cover almost everything. (By the way, the second equation is relativistic; that is, it’s compatible with Einstein’s Theory of Relativity. That means it always works for any particle at any speed — it might assume that space is reasonably flat or that time really exists, but these are very reasonable assumptions for experimental physicists working on Earth. For those who haven’t seen the equation before and enjoy algebra problems: what famous equation do you get if you take the special case of a particle that isn’t moving, i.e. with a momentum of zero?) Particle Motion and Momentum The next ingredient you need to understand what a tracker does is something I haven’t mentioned yet: the whole thing is enclosed in a huge solenoid magnet, which produces a more-or-less uniform magnetic field pointing along the direction of the LHC beam. As a charged particle moves through a magnetic field, the force exerted on it by the field works at a right angle to both the direction of motion and the field — I tried to illustrate this in figure 1, where the magnetic field is pointing into your screen if you assume the particle is positively charged.5 This means that as the charged particle flies from the center of the detector, it curves (figure 2). The amount it curves by is inversely proportional to the momentum, which means that higher-momentum particles curve less. Along its path, it leaves hits in the detecting material, as I discussed above (red dots, figure 3). Finally, in a process called track reconstruction, our software “connects the dots” and produces a track — which is just our name for “where we think the particle went” (figure 4). You’ll notice that figure 2 looks a lot like figure 4, but the conceptual difference is a very important one. The red line in figure 2 is the actual path followed by the particle, which we don’t see directly, while the black line in figure 4 is our track as determined by detector hits. If we do our job right, the red line and black line should be almost exactly the same, but that job is complex indeed — literally thousands of person-years have been put into it, including two or three Seth-years6 spent on detector calibration and writing automated tools for making sure the tracking software works properly. The detector is shown here with only three layers. Although this would be enough to find a particle’s path in ideal circumstances, we actually have many more: this allows us to still make good measurements even when one layer somehow doesn’t see the particle, and to get a final result for the path that’s more accurate. And don’t forget that there will actually be many particles passing through the detector at the same time — so we need lots of measurements to be sure that we’re seeing real tracks and not just a bunch of “dots” that happen to “line up”…! More Than Just Momentum If you measure the path of a particle, you can do more than just find its momentum; you can also see where it came from, or at least whether it could have come from the same place as another particle. Pixel detectors excel at making accurate measurements to figure out this kind of thing, but as I said already, to do that subject justice will require another entry. So there you have it. In a very broad sense, that’s what I’m working toward when I talk about calibrating the pixel detector. Tracking provides critical basic information about every charged particle that passes through our detector; combined with data from the calorimeter and the muon systems, this information is what will let ATLAS and CMS measure the properties of the new particles that we hope the LHC will produce. 1 Both ATLAS and CMS have one, but many other detectors at colliders do not, because the technology is complex, relatively new, and expensive. 2 See Corollary III here for what he says about it, if you like your science extra-opaque. 3 I’m really not sure why we always use p for momentum, although a good guess seems to be that it’s related to impetus or impulse. 4 A friend of mine, who has the mysterious superpower of understanding how bulk matter works rather than just mucking about with individual particles, looked at a draft of this and was very concerned that I’m implying that all the energy from such a happening would end up as atomic vibrations. So let the record show that this probably isn’t true. And now, if you’d be so kind, can we pretend it is true? It will make illustrating my point very much easier. Thanks! 5 The particle is definitely not actual size, and don’t ask me why it’s green. 6 A Seth-year doesn’t make nearly as big a contribution as a year of work by any of our real experts, but they do happen to be of particular interest to me. • Nonnormalizable Hey Seth, if this whole LHC thing doesn’t work out, you can totally look forward to an excellent career as a science popularizer/author. Cool! Thanks for the info, I can actually understand what you’re talking about, well written. What do you use to calibrate the detectors? I’ll take a guess at known low energy particles? I think I remember someone saying you use cosmic rays to do some of the calibration. Very interesting. • kate I like the baseball analogy a lot, that explains it really well. • Didi Mouse Yes, what Nonn said. This was the perfect level of technical detail. BTW, who gets to name the new particles? • Jmom Really good explanation! You have the gift of explaining, which is part of the art of teaching. My daughter is a “you” at CMS, so I try to learn what she does. Knowledge comes in layers, and bits and pieces. This was very helpful. • Jacques Hi Seth Although not a physicist, I may have the answer to the origin of the “p” symbol for momentum. It might come from the french, assuming that p = mv means: poids (weight) = masse (mass) x vitesse (velocity) Worth checking maybe with native french speaking colleagues of yours at CERN. Cheers! 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http://persiavisit.ir/css/peter-harrison-zlv/archive.php?page=hazard-function-calculator-bfa990	The hazard function is the density function divided by the survivor function. Statistical Its graph resembles the shape of the hazard rate curve. Given the survival function, we can always differentiate to obtain the density and then calculate the hazard using Equation 7.3. asked Feb 13 '13 at 18:22. Evans, M.; Hastings, N.; and Peacock, B. The first link you provided actually has a clear explanation on the theory of how this works, along with a lovely example. Weisstein, Eric W. "Hazard Function." Distributions, 3rd ed. calculate the hazard ratio, which is a conventional e ect size to evaluate clinical relevance of treatment e ects. Your -stcox- model, however is semi-parametric and is constrained by the assumption of proportional hazards between the two groups shown in your graph. For example, many mechanical items that are prone to stress or fatigue have an increased risk of failure over the lifetime of the product. I create a set of hazard functions that perfectly satisfy the proportional hazards assumption. Canada V5A 1S6. In addition to estimating the hazard rate, quantifying the e ects of covariates on time to failure is usually of interest. Indicates that items are more likely to fail with time. The baseline hazard function can be estimated in R using the "basehaz" function. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Hazard Hazard Hazard Rate We de ne the hazard rate for a distribution function Fwith density fto be (t) = f(t) 1 F(t) = f(t) F (t) Note that this does not make any assumptions about For f, therefore we can nd the Hazard rate for any of the distributions we have discussed so far. Both hazard quotient (HQ) and risk quotient (RQ) are very important concepts in chemical risk assessment. They are used by regulatory authorities such as US EPA to describe the risk category of a chemical substance. You often want to know whether the failure rate of an item is decreasing, constant, or increasing. at week #6 there is one censored observation in group A. That is, for any two such functions h i and h j, there exists a constant c i,j such that h i (t) = c i,j h j (t) for all t >=0. if your research aims to improve pregnancy rates then the events in the control group can be live births while "number at risk" is actually the couples still trying to get to that stage who have not dropped from the study for other reasons. The smoothed estimate is based on B-splines from the perspective of generalized linear mixed models. If you’re not familiar with Survival Analysis, it’s a set of statistical methods for modelling the time until an event occurs.Let’s use an example you’re probably familiar with — the time until a PhD candidate completes their dissertation. The hazard function is related to the probability density function, f(t), cumulative distribution function, F(t), and survivor function, S(t), as follows: Note that the number at risk should contain the number who were at risk at the beginning of the period, minus the censored observations. Property 3: 6 Responses to Estimating the Baseline Hazard Function. It is the integral of h(t) from 0 to t, or the area under the hazard function h(t) … The hazard ratio calculator will output: hazard ratio, two-sided confidence interval, left-sided and right-sided confidence interval, two-sided p-value and Χ2 statistic. We are not to be held responsible for any resulting damages from proper or improper use of the service. Hazard ratio. If the hazard ratio estimate is less than one, this means that the hazard function for the first group is smaller than that for the second group. Canada V5A 1S6. https://www.gigacalculator.com/calculators/hazard-ratio-calculator.php Relationship Summary An example will help x ideas. The hazard function is also known as the failure rate or hazard rate. The hazard plot shows the trend in the failure rate over time. If one inspects the code, it's clearly the cumulative hazard function from a survfit object. By Property 2, it follows that. In many medical, epidemiological and economic analyses you can see an average hazard ratio for the difference between two groups being reported. Make sure you exclude any column headers and that each row should contain exactly 5 values, separated by commas, spaces or tabs. Different hazard functions are modeled with different distribution models. Therefore it is important to use the right kind of interval: see below for more on this. The hazard function depicts the likelihood of failure as a function of how long an item has lasted (the instantaneous failure rate at a particular time, t). Walk through homework problems step-by-step from beginning to end. Hazard Function The hazard function at any time tj is the number of deaths at that time divided by the number of subjects at risk, i.e. Hazard ratio vs. Risk Ratio (Relative Risk), Standard error and confidence interval formula for hazard ratios, https://www.gigacalculator.com/calculators/hazard-ratio-calculator.php. The cumulative hazard function (CHF), is the total number of failures or deaths over an interval of time. The results from this simple calculation are very close to or identical with results from the more complex Cox proportional hazard regression model which is applicable when we want to take into account other confounding variables. However, these values do not correspond to probabilities and might be greater than 1. Compute the hazard function using the definition as conditional probability: The hazard function is a ratio of the PDF and the survival function : The hazard rate of an exponential distribution is constant: Estimating the Survival Function. [3] Sashegyi A., Ferry D. (2017) "On the Interpretation of the Hazard Ratio and Communication of Survival Benefit" The oncologist, 22(4):484-486, [4] Stare J., Maucort-Boulch D. (2016) "Odds Ratio, Hazard Ratio and Relative Risk" Metodološki zvezki, 13(1):59-67, [5] Georgiev G.Z. survival. If a hazard function is assumed to be constant during the follow-up period [0, T], then it can be ... (7.6_sample_size__time_.sas) This is a program that illustrates the use of PROC POWER to calculate sample size when comparing two hazard functions. Since the hazard is defined at every time point, we may bring up the idea of a hazard function, h(t) — the hazard rate as a function of time. (eg UN number and hazard classification). Given the survival function, we can always differentiate to obtain the density and then calculate the hazard using Equation 7.3. The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models that treat the log of the HR as a function of a baseline hazard () and a linear combination of explanatory variables: Use dot as a decimal notation. The hazard function may assume more a complex form. However, the notes I'm following calculate the hazard function like this: \begin{align} h(t) &= 1-0.458^{1/3} \\ &= 0.2292 \end{align} The lack of parentheses and the different power confuse me. The CHF is H(t) = Rt 0 r(t)dt = -ln(S(t)) The CHF describes how the risk of a particular outcome changes with time. The hazard ratio is the ratio of the hazard functions between two population groups. Hazard Rate Functions General Discussion De nition. A one-sided hazard ratio interval in which one side is plus or minus infinity is appropriate when we have a null / want to make statements about a hazard ratio value lying either above or below the top / bottom bound [5]. Hints help you try the next step on your own. The problem with your code is that you are taking this definition at face value and doing a simple division operation; when both the numerator and the denominator are very small values (on the order of 1e-300), which happens in the tail of the distribution, this operation becomes numerically unstable. The tool only has one input field for your raw data and one to specify the confidence level for your confidence interval. bshazard-package Nonparametric Smoothing of the Hazard Function Description The function estimates the hazard function non parametrically from a survival object (possibly adjusted for covariates). true hazard function shape. [1] Altman D.G., (1991) "Practical Statistics for Medical Research", London, Chapman and Hall. The hazard function always takes a positive value. Functions to calculate power and sample size for testing main effect or interaction effect in the survival analysis of epidemiological studies (non-randomized studies), taking into account the correlation between the covariate of the interest and other covariates. (2017) "One-tailed vs Two-tailed Tests of Significance in A/B Testing", [online] http://blog.analytics-toolkit.com/2017/one-tailed-two-tailed-tests-significance-ab-testing/ (accessed Apr 28, 2018). An example will help fix ideas. By Property 2, it follows that. You can find the Workbook: www.hazardoussubstances. If there is censored data, it should be reflected by decreasing the number at risk, as shown in the example, e.g. Rodrigo says: September 17, 2020 at 7:43 pm Hello Charles, Would it be possible to add an example for this? Some calculations also take into account the competing risks and stratified analysis. ), Column 2: events in treatment group, Column 3: number at risk in treatment group, Column 4: events in control group, Column 5: number at risk in the control group. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. Definition of the hazard ratio. Given the hazard, we can always integrate to obtain the cumulative hazard and then exponentiate to obtain the survival function using Equation 7.4. calculate the hazard using Equation 7.3. I'm trying to calculate the hazard function for a type of mechanical component, given a dataset with the start and failure times of each component. Written by Peter Rosenmai on 11 Apr 2014. 1.2 Common Families of Survival Distributions While confidence intervals are customarily given in their two-sided form, this can often be misleading if we are interested if a particular value below or above the interval can be excluded at a given significance level. Join the initiative for modernizing math education. By Property 1 of Survival Analysis Basic Concepts, the baseline cumulative hazard function is. HR, a.k.a. In survival analysis, the hazard function is a useful way to describe the distribution of survival times. Terms and conditions © Simon Fraser University The hazard function (also known as the failure rate, hazard rate, or force of mortality) is the ratio of the probability The failure rate (or hazard rate) is denoted by $$h(t)$$ ... dt $$be the Cumulative Hazard Function, we then have $$F(t) = 1 - e^{H(t)}$$. Terms and conditions © Simon Fraser University Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. There are a number of popular parametric methods that are used to model survival data, and they differ in terms of the assumptions that are made about the distribution of survival times in the population. Rodrigo says: September 17, 2020 at 7:43 pm Hello Charles, Would it be possible to add an example for this? Additional comments on this program: Note the curve statements indicate points on the survival curves. Despite often being mistaken for being the same thing, relative risk and hazard ratios are nothing alike [3,4]. Most often what is computed in research papers is the mean hazard ratio across all time slices, which reflects the differences in two survival curves. If the hazard ratio is 2.0, then the rate of deaths in one treatment group is twice the rate in the other group. The hazard ratio compares two treatments. No shape assumption is imposed other than that the hazard function is a smooth function. assessment address only the individual risks and hazards; calculation of population risks and hazards is not required. In the dataset, all components eventually fail. The nonparametric approach to estimate hazard rates for lifetime data is ﬂexible, model-free and data-driven. Calculating the failure rate for ever smaller intervals of time results in the hazard function (also called hazard rate), {\displaystyle h (t)}. When the interval length L is small enough, the conditional probability of failure is approximately h(t)L. H(t) is the cumulative hazard function. Finally, the program lists the baseline cumulative hazard H 0 (t), with the cumulative hazard and survival at mean of all covariates in the model. The hazard is modeled as:where X1 ... Xk are a collection of predictor variables and H0(t) is t… I need to estimate baseline hazard function \lambda_0(t) in a time dependent Cox model \lambda(t) = \lambda_0(t) \exp(Z(t)'\beta) While I took Survival course, I remember that the direct derivative of cumulative hazard function (\lambda_0(t) dt = d\Lambda_0(t)) would not be a good estimator because Breslow estimator gives a step function. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. (Thank you for this, it is a nice resource I will use in my own work.) Here's some R code to graph the basic survival-analysis functions—s(t), S(t), f(t), F(t), h(t) or H(t)—derived from any of their definitions.. For example: Thus, the resulting curve of the three failure periods frequently resembles the shape of a bathtub. Use this hazard ratio calculator to easily calculate the relative hazard, confidence intervals and p-values for the hazard ratio (HR) between an exposed/treatment and control group. Survival models are used to analyze sequential occurrences of events governed by probabilistic laws. Two other useful identities that follow from these formulas are:$$ h(t) = - \frac{d \mbox{ln} R(t)}{dt} H(t) = - \mbox{ln} R(t) \,\, . If you perform the reverse comparison, the reverse of these statements are true. In this video, I define the hazard function of continuous survival data. 2000, p. 13). The hazard ratio quantifies the difference between the hazard of two groups and it is calculated as the ratio between the ratios of observed events and expected events under the null hypothesis of no difference between the two groups. Using these additional tools it is easy to spot that the graph on the right depicts significantly better performance than the one on the left. Here is example input - first how it seems in a spreadsheet and then how it looks when the data is copied to our calculator: Click here to load the example data into the calculator and see the output. To use the curve function, you will need to pass some function as an argument. https://mathworld.wolfram.com/HazardFunction.html. If we denote the observed event rate in group A at time t as ObsA, the expected event rate at time t as ExpA, the observed event rate in group B at time t as ObsB and the expected event rate in group B at time t as ExpB, then the formula is [1]: This is the math equation used in this hazard ratio calculator. You need to follow an exact order of columns in order for the tool to work as expected: Column 1: time (number of days, weeks, months, years, etc. In such cases it is better to use the appropriate one-sided interval instead, to avoid confusion. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. What is a hazard ratio / relative hazard? 8888 University Drive Burnaby, B.C. Additional metrics such as the median and mean or restricted mean need to be considered as well as visual representation which would depict the actual survival curves. The latter is what relative risk measures and which would be the metric of interest if durable benefit is what you want to measure. Left truncated and right censoring data are allowed. From MathWorld--A Wolfram Web Resource. Hazard Function The formula for the hazard function of the exponential distribution is $$h(x) = \frac{1} {\beta} \hspace{.3in} x \ge 0; \beta > 0$$ The following is the plot of the exponential hazard function. If T is an absolutely continuous non-negative random variable, its hazard rate function h(t); t 0, is de ned by h(t) = f(t) S(t); t 0; where f(t) is the density of T and S(t) is the survival function: S(t) = R 1 t f(u)du. The relative risk (RR) at any point t is a decreasing function of t with a value equal to 1 - HR only at t=0 [3,4]. I use the apply_survival_function(), defined above, to plot the survival curves derived from those hazard functions. The following shape parameter characteristics are noted: E.g. When the interval length L is small enough, the conditional probability of failure is approximately h(t)L. H(t) is the cumulative hazard function. The hazard rate refers to the rate of death for an item of a given age (x). This becomes the instantaneous failure rate or we say instantaneous hazard rate as {\displaystyle \Delta t} approaches to zero: In the system, the two functions calculate an employee-specific compensation for occupational hazard as follows: The P3312 function reads the compensation model that the employee is assigned to from the Occupational Hazard SA (3312) infotype and retrieves the corresponding model definition from the Customizing settings (see Prerequisites). Unlimited random practice problems and answers with built-in Step-by-step solutions. 8888 University Drive Burnaby, B.C. The graph produced by -sts graph- is the result of a fully non-parametric model. Graphing Survival and Hazard Functions. a Z-score of 1.6448 is used for a 0.95 (95%) one-sided confidence interval and a 90% two-sided interval, while 1.956 is used for a 0.975 (97.5%) one-sided confidence interval and a 0.95 (95%) two-sided interval. The hazard function describes the ‘intensity of death’ at the time tgiven that the individual has already survived past time t. There is another quantity that is also common in survival analysis, the cumulative hazard function. See our full terms of service. [2] Spruance S.L., Reid J.E., Grace M., Samore M. (2004) "Hazard ratio in clinical trials", Antimicrobial agents and chemotherapy, 48(8):2787-92. The cumulative hazard function is H(t) = Z t 0 h(s)ds: 5-1. hazard function H(x), which describes the overall risk rate from the onset to time x. I The mean residual lifetime at age x, mrl(x), is the mean time to the event of interest, given the event has not occurred at x. Wenge Guo Chapter 2 Basic Quantities and Models. In this hazard ratio calculator we use the log-rank test to calculate the Χ2 statistics, the p-value, and the confidence intervals. 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http://mathhelpforum.com/geometry/16639-finding-x-usin-algebraic-method.html	# Math Help - Finding X usin an algebraic method 1. ## Finding X usin an algebraic method Hi can somebody help me find X in this diagram using an algebraic method? Please also explain how its done! Firstly the shape is a sqaure, and a line has been attached to 3 corners of the square from a random dot inside the square, the smallest line is 3 units, the mid one is 4 units and the largest is 5 units large. 2. I have a method, but it might be messy. The sum of those areas of those three peices equals to the area of the square. That gives you just an equation in terms of x. By "Heron's Formula" 3. Hello, hossein! I have an approach . . . but is it acceptable? Firstly the shape is a sqaure. Lines have been drawn to 3 corners of the square from a point inside the square. The smallest line is 3 units, the mid one is 4 units, and the largest is 5 units. Place the square on a coordinate system. Let the side of the square be $a$. Code: (0,a) (a,a) A * - - - - - - - * B \| \| \| * P \| \| (x,y) \| \| \| \| \| \| \| - C * - - - - - - - * D - (0,0) (a,0) Using the Distance Formula, we have: . . $\begin{array}{ccccc}PA = 3: & x^2 + (y-a)^2 & = & 9 & {\bf (1)} \\ PB = 4: & (x-a)^2 + \,(y-a)^2 & = & 16 & {\bf(2)} \\ PC = 5: & x^2 + \,y^2 & = & 25 & {\bf(3)}\end{array}$ Subtract (1) from (3): . $y^2 - (y-a)^2 \:=\:16$ . . which simplifies to: . $y \:=\:\frac{a^2+16}{2a}$ . (4) Subtract (1) from (2): . $(x-a)^2-x^2 \:=\:7$ . . which simplifies to: . $x \:=\:\frac{a^2-7}{2a}$ .(5) Substitute (4) and (5) into (3): . $\left(\frac{a^2-7}{2a}\right)^2 + \left(\frac{a^2+16}{2a}\right)^2\:=\:25$ . . which simplifies to: . $2a^4 - 82a^2 + 305 \:=\:0$ . . . a quadratic in $a^2$. Quadratic Formula: . $a^2 \;=\;\frac{-(\text{-}82) \pm\sqrt{(\text{-}82)^2 - 4(2)(305)}}{2(2)} \;=\;\frac{82 \pm \sqrt{4284}}{4}\;=\;\frac{41 \pm\sqrt{1071}}{2}$ Then: . $a \;=\;\sqrt{\frac{41 \pm\sqrt{1071}}{2}}\;=\;\begin{Bmatrix}6.07149637 \\ 2.033944893 \end{Bmatrix}$ . . The second root is too small be the side of the square. Therefore, the side of the square is about $6.07$ units. Edit: corrected errors in last four lines. . 4. hey Soroban! I kindda undrestand wut u did, but I dont think its a right answer.because if u draw it out using a protractor the side turns out to be 5.8 .so in a way I know the answer is 5.8 but I still have to show where I got it from. and the HINT that we got was that we have to use the method that we learned in grade 10 math. 5. Originally Posted by hossein hey Soroban! I kindda undrestand wut u did, but I dont think its a right answer.because if u draw it out using a protractor the side turns out to be 5.8 .so in a way I know the answer is 5.8 but I still have to show where I got it from. and the HINT that we got was that we have to use the method that we learned in grade 10 math. you mind being more specific about what method you used. depending on what country you are from--and what part of the country--there are many different things you could learn in this respect 6. A similar solution as the Soroban's, but without using coordinates. Let $ABCD$ be the square and $P$ the point inside such as $AP=3,BP=4,DP=5$. Draw a line through $P$ parallel with $AB$ which intersects $AD, \ BC$ in $M$ and $N$. Draw a line through $P$ parallel with $AD$ which intersects $AB, \ DC$ in $P$ and $Q$. Let $AB=x,MP=y,AM=z$. Then $PB=x-y,MD=x-z$. Applying Pitagora in triangles where $AP,BP,DP$ are hypotenuses, we have the following system: $\displaystyle \left\{\begin{array}{lll}y^2+z^2=9\\z^2+(x-y)^2=16\\y^2+(x-z)^2=25\end{array}\right.$ From here you can follow the solution of Soroban. 7. Originally Posted by Soroban Hello, hossein! I have an approach . . . but is it acceptable? Place the square on a coordinate system. Let the side of the square be $a$. Code: (0,a) (a,a) A * - - - - - - - * B \| \| \| * P \| \| (x,y) \| \| \| \| \| \| \| - C * - - - - - - - * D - (0,0) (a,0) Using the Distance Formula, we have: . . $\begin{array}{ccccc}PA = 3: & x^2 + (y-a)^2 & = & 9 & {\bf (1)} \\ PB = 4: & (x-a)^2 + \,(y-a)^2 & = & 16 & {\bf(2)} \\ PC = 5: & x^2 + \,y^2 & = & 25 & {\bf(3)}\end{array}$ Subtract (1) from (3): . $y^2 - (y-a)^2 \:=\:16$ . . which simplifies to: . $y \:=\:\frac{a^2+16}{2a}$ . (4) Subtract (1) from (2): . $(x-a)^2-x^2 \:=\:7$ . . which simplifies to: . $x \:=\:\frac{a^2-7}{2a}$ .(5) Substitute (4) and (5) into (3): . $\left(\frac{a^2-7}{2a}\right)^2 + \left(\frac{a^2+16}{2a}\right)^2\:=\:25$ . . which simplifies to: . $2a^4 - 82a^2 + 305 \:=\:0$ . . . a quadratic in $a^2$. Quadratic Formula: . $a^2 \;=\;\frac{-(\text{-}82) \pm\sqrt{(\text{-}82)^2 - 4(2)(305)}}{2(2)} \;=\;\frac{84 \pm \sqrt{4284}}{4}\;=\;\frac{42 \pm\sqrt{1071}}{2}$ Then: . $a \;=\;\sqrt{\frac{42 \pm\sqrt{1071}}{2}}\;=\;\begin{Bmatrix}6.112533695 \\ 2.153353624 \end{Bmatrix}$ . . The second root is too small be the side of the square. Therefore, the side of the square is about $6.11$ units. i thought about doing this, but like you, i wasn't sure it would be acceptable for some reason 8. the canadian skool system, ONTARIO..does that help?? 9. Okay, I'll try again . . . Are you allowed to use the Pythagorean Theorem? Let the side of the square be $a$. From $P$ draw perpendicular $PE$ to $AB\!:\;\;h = PE$ . . Let $x \,= \,AE$, then $a-x \:=\:EB$ Code: x E a-x A * - - - + - - - - - - * B \| * : * \| \| 3* :h 4 \| \| : * \| \| * \| \| P \| In right triangle $AEP$, we have: . $x^2 + h^2 \:=\:3^2$ . [1] In right triangle $BEP$, we have: . $(a-x)^2 + h^2 \:=\:4^2$ .[2] Subtract [1] from [2]: . $(a-x)^2 - x^2 \:=\:7\quad\Rightarrow\quad x \:=\:\frac{a^2-7}{2a}$ . [3] From $P$ draw perpendicular $PF$ to $AD$; $x = PF$ . . Let $y \,= \,AF$, then: $a-y \:= \:FD$ Code: A * - - - - - - - \| * y \| 3 \| F + - - - * P \| x * \| * \| * a-y \| 5 \| \| * \|* D * - - - - - - - In right triangle $PFA\!:\;x^2 + y^2 \:=\:3^2$ . [4] In right triangle $PFD\!:\;x^2 + (a-y)^2 \:=\:5^2$ . [5] Subtract [4] from [5]: . $(a-y)^2 - y^2 \:=\:16\quad\Rightarrow\quad y \:=\:\frac{a^2-16}{2a}$ . [6] Substitute [3] and [6] into [4]: . $\left(\frac{a^2-7}{2a}\right)^2 + \left(\frac{a^2-16}{2a}\right)^2 \:=\:9$ . . which simplifies to: . $2a^4-82a^2 + 305\:=\:0$ . . . the same equation as before. I think I just repeated red_dog's solution . . . sigh Also, I see a typo and the end of my original post. . . I'll correct it . . . 10. thanx guys I GOT THE right answer!! thanx 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": 1, "img_math": 0, "codecogs_latex": 63, "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": 0.8674944043159485, "perplexity": 821.3455160613788}, "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/1406510271862.24/warc/CC-MAIN-20140728011751-00476-ip-10-146-231-18.ec2.internal.warc.gz"}
https://mathemerize.com/find-the-normal-to-the-hyperbola-x2over-16-y2over-9-1-whose-slope-is-1/	# Find the normal to the hyperbola $$x^2\over 16$$ – $$y^2\over 9$$ = 1 whose slope is 1. ## Solution : We have, $$x^2\over 16$$ – $$y^2\over 9$$ = 1 Compare given equation with $$x^2\over a^2$$ – $$y^2\over b^2$$ = 1 a = 4 and b = 3 Since the normal to the given hyperbola whose slope is ‘m’, is y = mx $$\mp$$ $${m(a^2+b^2)}\over \sqrt{a^2 – m^2b^2}$$ Hence, required equation of normal is y = x $$\mp$$ $${25}\over \sqrt{7}$$. ### Similar Questions Angle between asymptotes of hyperbola xy=8 is Find the asymptotes of the hyperbola $$2x^2 + 5xy + 2y^2 + 4x + 5y$$ = 0. Find also the general equation of all the hyperbolas having the same set of asymptotes. Find the equation of the tangent to the hyperbola $$x^2 – 4y^2$$ = 36 which is perpendicular to the line x – y + 4 = 0 The eccentricity of the conjugate hyperbola to the hyperbola $$x^2-3y^2$$ = 1 is If the foci of a hyperbola are foci of the ellipse $$x^2\over 25$$ + $$y^2\over 9$$ = 1. If the eccentricity of the hyperbola be 2, then its equation is :	{"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": 0.8684197664260864, "perplexity": 234.6752428405042}, "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/1656103915196.47/warc/CC-MAIN-20220630213820-20220701003820-00509.warc.gz"}
http://cogsci.stackexchange.com/questions/7642/is-rapport-a-cognitive-phenomenon	# Is rapport a cognitive phenomenon? "Building rapport" is often mentioned as one of the most fundamental sales techniques, but I had a hard time understanding the cognitive mechanism behind this. Is this really a state of awareness that can be analysed via cognitive science tools, or just a salespeople buzzword? -	{"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": 0.8506332039833069, "perplexity": 868.8876473139101}, "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-2014-49/segments/1416931006593.41/warc/CC-MAIN-20141125155646-00208-ip-10-235-23-156.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/tension-between-3-blocks.268504/	# Tension between 3 blocks 1. Oct 31, 2008 ### ScullyX51 1. The problem statement, all variables and given/known data Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force F_vec. (Intro 1 figure) The magnitude of the tension in the string between blocks B and C is T = 3.00 N. Assume that each block has mass m = 0.400 kg What is the magnitude F of the force? What is the tension T:AB in the string between block A and block B? 2. Relevant equations F=ma 3. The attempt at a solution I am unsure of how to approach the first part of the problem. For the second part, since t is the only force acting this the block, I have: T=ma I solve for A from the first part of the equation where t is given as follows: t=ma 3=.400a a=3/.4 a=7.5 m/s^2 I plugged this into to solve for the other tension as follows: t=ma t=.47.5 t=3 Mastering physics is saying the tension and the acceleration is wrong. Where did I screw up? 2. Oct 31, 2008 ### LowlyPion What is the order of your blocks? T <---{A}--{B}--{C} Generally, whatever your force is, the acceleration will be F/(3m) and then the intermediate tensions would be whatever force is needed to keep the blocks remaining moving with that acceleration. In the example above that would be 2/3F between A:B and 1/3F between B:C	{"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": 0.9532418847084045, "perplexity": 732.1096767578861}, "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-2017-17/segments/1492917122174.32/warc/CC-MAIN-20170423031202-00377-ip-10-145-167-34.ec2.internal.warc.gz"}
http://mathhelpforum.com/discrete-math/95438-arrangements-help-print.html	# arrangements help • July 18th 2009, 12:38 AM flyinhigh123 arrangements help Prove from the defintion of nPr (as in nPr = n!/(n-r)!) that (n+1)/Pr = nPr + r.nP(r-1) and show that nPr = (n-2)Pr + 2r. (n-2)P(r-1) + r(r-1) x (n-2)P(r-2) if anyone could give me some techniques or some help solving these types of questions i would really appreciate it ! thankyou =D • July 18th 2009, 01:30 AM red_dog $P_n^r+rP_n^{r-1}=\frac{n!}{(n-r)!}+r\cdot\frac{n!}{(n-r+1)!}=$ $=\frac{n!(n-r+1)}{(n-r+1)!}+\frac{n!r}{(n-r+1)!}=\frac{n!(n-r+1+r)}{(n-r+1)!}=\frac{(n+1)!}{(n-r+1)!}=P_{n+1}^r$ Now we use this formula to prove the second identity. $P_n^r=P_{n-1}^r+rP_{n-1}^{r-1}=P_{n-2}^r+rP_{n-2}^{r-1}+r(P_{n-2}^{r-1}+(r-1)P_{n-2}^{r-2})=$ $=P_{n-2}^r+2rP_{n-2}^{r-1}+r(r-1)P_{n-2}^{r-2}$ • July 18th 2009, 10:32 PM flyinhigh123 thanx so much for your help !	{"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": 0.9031660556793213, "perplexity": 4930.341215499071}, "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-2016-07/segments/1454701148758.73/warc/CC-MAIN-20160205193908-00090-ip-10-236-182-209.ec2.internal.warc.gz"}
https://en.m.wikiversity.org/wiki/Damped_oscillation	# Damped oscillation An oscillator is anything that has a rhythmic periodic response. A damped oscillation means an oscillation that fades away with time. Examples include a swinging pendulum, a weight on a spring, and also a resistor - inductor - capacitor (RLC) circuit. Suppose we have an RLC circuit, which has a resistor + inductor + capacitor in series.When the switch closes at time t=0 the capacitor will discharge into a series resistor and inductor. Now, the voltages and current in this circuit can be given by {\displaystyle {\begin{aligned}I(t)&={\frac {V_{0}}{\beta L}}e^{-at}\sin(\beta t)\\V_{c}(t)&=V_{0}e^{-at}\cos(\beta t)\end{aligned}}} where {\displaystyle {\begin{aligned}\beta &={\sqrt {{\frac {1}{LC}}-{\frac {R^{2}}{4L^{2}}}}}\\a&={\frac {R}{2L}}\end{aligned}}} and V= initial voltage C = capacitance (farads) R = resistance (ohms) L = inductance (henrys) e = base of natural log (2.71828...) The above equation is the current for a damped sine wave. It represents a sine wave of maximum amplitude (V/BL) multiplied by a damping factor of an exponential decay. The resulting time variation is an oscillation bounded by a decaying envelope. Critical Damping We can use these equations to discover when the energy fades out smoothly (over-damped) or rings (under-damped). Look at the term under the square root sign, which can be simplified to: R2C2-4LC • When R2C2-4LC is positive, then α and β are real numbers and the oscillator is over-damped. The circuit does not show oscillation • When R2C2-4LC is negative, then α and β are imaginary numbers and the oscillations are under-damped. The circuit responds with a sine wave in an exponential decay envelope. • When R2C2-4LC is zero, then α and β are zero and oscillations are critically damped. The circuit response shows a narrow peak followed by an exponential decay.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "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": 0.9080638885498047, "perplexity": 1739.7360081952027}, "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-2020-50/segments/1606141188899.42/warc/CC-MAIN-20201126171830-20201126201830-00425.warc.gz"}
https://thewindingnumber.blogspot.com/p/2202.html	### MAR2202: Variant calculi Multiplicative and fractional calculus covered in variant calculi (note that this has nothing to do with the calculus of variations -- this is covered under "Advanced Classical Physics") Multiplicative calculus Fractional calculus	{"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": 0.9655963778495789, "perplexity": 2264.226640805614}, "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/1552912202572.29/warc/CC-MAIN-20190321193403-20190321215403-00076.warc.gz"}
https://science.sciencemag.org/content/346/6211/831	Report # The structure of interfacial water on gold electrodes studied by x-ray absorption spectroscopy See allHide authors and affiliations Science 14 Nov 2014: Vol. 346, Issue 6211, pp. 831-834 DOI: 10.1126/science.1259437 ## Abstract The molecular structure of the electrical double layer determines the chemistry in all electrochemical processes. Using x-ray absorption spectroscopy (XAS), we probed the structure of water near gold electrodes and its bias dependence. Electron yield XAS detected at the gold electrode revealed that the interfacial water molecules have a different structure from those in the bulk. First principles calculations revealed that ~50% of the molecules lie flat on the surface with saturated hydrogen bonds and another substantial fraction with broken hydrogen bonds that do not contribute to the XAS spectrum because their core-excited states are delocalized by coupling with the gold substrate. At negative bias, the population of flat-lying molecules with broken hydrogen bonds increases, producing a spectrum similar to that of bulk water. ## Dissecting the electrical double layer The structure of water within a nanometer of an electrode surface is known as the electrical double layer. This layer creates a strong electrical field that can affect electrochemical reactions. Velasco-Velez et al. explored the structure of the electrical double layer at a bare gold electrode. With no applied potential and at positive potentials, the layer is highly structured (resembling ice) with few dangling hydrogen bonds. However, at negative potentials, the layer was more like bulk water, and half of the water molecules lie flat on the surface. Science, this issue p. 831 View Full Text	{"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": 0.8197382092475891, "perplexity": 2782.6635813543953}, "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-2021-21/segments/1620243991737.39/warc/CC-MAIN-20210514025740-20210514055740-00547.warc.gz"}
https://science.sciencemag.org/content/298/5596/1213	Report # Superconductivity in Dense Lithium See allHide authors and affiliations Science 08 Nov 2002: Vol. 298, Issue 5596, pp. 1213-1215 DOI: 10.1126/science.1078535 ## Abstract Superconductivity in compressed lithium is observed by magnetic susceptibility and electrical resistivity measurements. A superconducting critical temperature (T c) is found ranging from 9 to 16 kelvin at 23 to 80 gigapascals. The pressure dependence of T csuggests multiple phase transitions, consistent with theoretical predictions and reported x-ray diffraction results. The observed values for T c are much lower than those theoretically predicted, indicating that more sophisticated theoretical treatments similar to those proposed for metallic hydrogen may be required to understand superconductivity in dense phases of lithium. • * To whom correspondence should be addressed. E-mail: struzhkin{at}gl.ciw.edu View Full Text	{"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": 0.9159362316131592, "perplexity": 2499.3246702712117}, "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-2019-30/segments/1563195524522.18/warc/CC-MAIN-20190716095720-20190716121720-00321.warc.gz"}
http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.101.181301	# Synopsis: Cosmic consistency check #### Consistency Tests for the Cosmological Constant Caroline Zunckel and Chris Clarkson Published October 31, 2008 The leading interpretation of why the expansion of the Universe is apparently accelerating is the presence of dark energy. Long before the supernova observations that indicated an accelerating Universe, Einstein proposed the idea of a cosmological constant, which says that dark energy homogeneously fills all of space as a constant energy density. Numerous other ideas, involving the variation of dark energy in time and space, have gained substantial interest. However, it is difficult to distinguish among them with either present data or those expected to be available in the next few years. The main sources of these data are measurements of how the luminosity of supernovae depends on redshift and therefore distance. To interpret these data with dark-energy theories requires necessarily oversimplified parametrizations and assumptions (based on inferences from other data) about the matter density and curvature of the Universe. In a paper appearing in Physical Review Letters, Caroline Zunckel of Oxford University and Chris Clarkson of the University of Cape Town develop a new approach, which could more independently distinguish among dark-energy theories. They introduce a new measure, based only on luminosity-distance data, which does not require knowledge of the cosmic matter density and would be zero if the cosmological constant is correct. Conversely, finding a nonzero value would indicate that some other explanation of dark energy must be valid. This test alone would be unable to firmly establish the cosmological constant as the unique picture of dark energy, but it would considerably narrow the possibilities. – Stanley Brown	{"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": 0.8336793184280396, "perplexity": 854.264300180625}, "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-2014-23/segments/1406510270399.7/warc/CC-MAIN-20140728011750-00354-ip-10-146-231-18.ec2.internal.warc.gz"}
https://www.solidot.org/translate/?nid=140578	Distributionally Robust Transmission Expansion Planning: a Multi-scale Uncertainty Approach. (arXiv:1810.05212v1 [math.OC]) In this paper, we present a distributionally robust optimization (DRO) approach for the transmission expansion planning (TEP) problem, considering both long- and short-term uncertainties on the system load and renewable generation. Long-term uncertainty is represented on two interrelated levels. At the first level, as is customary in industry applications, the deep uncertainty faced in economic, political, environmental, and technological development is addressed based on plausible visions of long-term future scenarios (trends), traced by current experts beliefs. Subsequently, uncertainty-related parameters defining the probability distributions of the uncertain factors are partially refined for each long-term scenario, thereby inducing an ambiguity set. Finally, for each long-term scenario and induced ambiguity set, the inherent risk model for the short-term uncertainty is described by means of conditional probability distributions. The mathematical problem is formulated as a distribu查看全文 Solidot 文章翻译你的名字留空匿名提交你的Email或网站用户可以联系你标题简单描述内容 In this paper, we present a distributionally robust optimization (DRO) approach for the transmission expansion planning (TEP) problem, considering both long- and short-term uncertainties on the system load and renewable generation. Long-term uncertainty is represented on two interrelated levels. At the first level, as is customary in industry applications, the deep uncertainty faced in economic, political, environmental, and technological development is addressed based on plausible visions of long-term future scenarios (trends), traced by current experts beliefs. Subsequently, uncertainty-related parameters defining the probability distributions of the uncertain factors are partially refined for each long-term scenario, thereby inducing an ambiguity set. Finally, for each long-term scenario and induced ambiguity set, the inherent risk model for the short-term uncertainty is described by means of conditional probability distributions. The mathematical problem is formulated as a distribu	{"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": 0.8906261920928955, "perplexity": 1831.029378391811}, "config": {"markdown_headings": false, "markdown_code": false, "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-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00491.warc.gz"}
http://mathhelpforum.com/algebra/9857-complex-fraction-help.html	1. ## complex fraction! help!! here's the tricky little problem.. i have no idea how to solve this! x-(x+h) ----------- 2(x+h)(x) ---------------- h 2. There's nothing to solve. What's the question? Is it the following fraction? $ \frac{{\frac{{x - \left( {x + h} \right)}}{{2\left( {x + h} \right)x}}}}{h} $ Then you can simplify: $ \frac{{\frac{{x - \left( {x + h} \right)}}{{2\left( {x + h} \right)x}}}}{h} = \frac{{ - h}}{{2\left( {x + h} \right)x}}\frac{1}{h} = \frac{{ - 1}}{{2\left( {x + h} \right)x}} $	{"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": 2, "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": 0.9398185610771179, "perplexity": 3077.0727779255717}, "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-2016-36/segments/1471983001995.81/warc/CC-MAIN-20160823201001-00188-ip-10-153-172-175.ec2.internal.warc.gz"}
https://www.bydletespokojene.cz/06a5qic/page.php?tag=system-of-linear-equations-matrix-62b127	3. 12. 2020 Domů / Inspirace a trendy / system of linear equations matrix # system of linear equations matrix ] ] 2 There are multiple ways to solve such a system, such as Elimination of Variables, Cramer's Rule, Row Reduction Technique, and the Matrix Solution. y 3 Understand the definition of R n, and what it means to use R n to label points on a geometric object. Minor of order 1 is every element of the matrix. Find the number of non-zero rows in A and [A : B] to find the ranks of A and [A : B] respectively. If all lines converge to a common point, the system is said to be consistent and has a solution at this point of intersection. ( ) 3 x Solution for Solve the system of linear equations using matrices. − [ x + 3 ] and In a similar way, for a system of three equations in three variables, a Find the determinant of the matrix. y Check It Out. b . 5 The same techniques will be extended to accommodate larger systems. If \|A\| = 0, then the systems of equations has infinitely many solutions. y y If \|A\| ≠ 0, then the system is consistent and x = y = z = 0 is the unique solution. We discuss what systems of equations are and how to transform them into matrix notation. Varsity Tutors does not have affiliation with universities mentioned on its website. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Minor of order $$2=\begin{vmatrix} 1 & 3 \\ 1 & 2 \end{vmatrix}=2-3=-1\neq 0$$. [ Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to solve system of linear equations using inverse matrix method. The two numbers in that order correspond to the first and second equations, and therefore take the places at the first and the second rows in the constant matrix. 3 Systems of Linear Equations. z c . 1 2 x b A system of linear equations can be represented in matrix form using a coefficient matrix, a variable matrix, and a constant matrix. The variables we have are We can generalize the result to x Substitute into equation (7) and solve for x. Part 6 of the series "Linear Algebra with JavaScript " Source Code. Solve the following system of equations, using matrices. Abstract- In this paper linear equations are discussed in detail along with elimination method. Now let us understand what this representation means. If the rows of the matrix represent a system of linear equations, then the row space consists of all linear equations that can be deduced algebraically from those in the system. x For example, Y = X + 1 and 2Y = 2X + 2 are linearly dependent equations because the second one can be obtained by taking twice the first one. Matrix A: which represents the variables; Matrix B: which represents the constants; A system of equations can be solved using matrix multiplication. x ] Solving a System of Linear Equations Using the Inverse of a Matrix Solving a system of linear equations using the inverse of a matrix requires the definition of two new matrices: \displaystyle X X is the matrix representing the variables of the system, and \displaystyle B B is the matrix representing the constants. ( a y d Scroll To Top	{"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": 0.8280545473098755, "perplexity": 224.50350812856163}, "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-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00015.warc.gz"}
http://www.zentralblatt-math.org/zmath/en/search/?q=an:1045.60026	Language: Search: Contact Zentralblatt MATH has released its new interface! For an improved author identification, see the new author database of ZBMATH. # Simple Search Query: Enter a query and click »Search«... Format: Display: entries per page entries Zbl 1045.60026 Bolthausen, Erwin Large deviations and interacting random walks. (English) [A] Bolthausen, Erwin et al., Lectures on probability theory and statistics. Ecole d'été de probabilités de Saint-Flour XXIX - 1999, Saint-Flour, France, July 8--24, 1999. Berlin: Springer. Lect. Notes Math. 1781, 1-124 (2002). ISBN 3-540-43736-3 In these lecture notes the author presents three closely related topics on random walks with self-interactions or with interactions with a wall. All topics have version for Brownian motions, but not in all cases both versions have been proved. \par The first part of the lectures originates from an outstanding open problem in probability theory. This is the determination of the mean end to end distance of a standard self-avoiding random walk on the $d$-dimensional lattice $\Bbb{Z}^d$ for $d=2,3,4$. The author discusses mainly the results for the very weakly interactive case for dimension $d= 3$. Here all paths in the set $\Omega_n$ of paths $\omega$ of length $n$ receive positive weight, but the ones with many interactions are punished''. This is given by the Gibbsian formalism as the following transformed path measure $$\widehat{P}_{n,\beta}(\omega)=\exp\left.\left[-\frac{\beta}{2}\sum\limits_{i,j=1}^n 1_{\{\omega_i=\omega_j\}}\right]\right/Z_{n,\beta}.$$ This can also be written as a sum over the whole lattice of the square of the discrete local time. This is called Domb-Joyce model. The corresponding set-up for Brownian motions leads to difficulties because evidently even the expectation under the Wiener measure is divergent for $d\ge 2$. Thus different techniques may apply here. One is the so-called gap regularization, where one replaces the $\delta$ function by some smoothed version, with some parameter $\varepsilon >0$ and integrating over time with gap $\varepsilon$ between the two time scales. Removing this regularization is possible, shown in Theorems 1.1 and 1.2. Next the skeleton inequalities and boundedness properties are presented as the main techniques for the proof. \par The second part is devoted to random walks with self-attracting path interactions which are all closely related to large deviation theory. For technical reasons continuous time Markov processes with discrete state space are considered. The interaction is given by the following transformed path measure where the corresponding interaction (attraction) is decaying with time: $$\widehat P_{T,\beta}(d\omega)=\exp\left[\frac{\beta}{T}\int\limits_0^Tds\int\limits_0^Tdt 1_{\{\omega_t=\omega_s\}}\right]P(d\omega)/Z_{T,\beta}.$$ For $d=1$ and in all other dimensions if $\beta$ is large enough, the path measure is localized. But for $d\ge 2$ collapse transition occurs, where the measure behaves diffusively if $\beta$ is small. A related model for Brownian motion is the Wiener sausage in such a way that large volumes are suppressed. After providing basic large deviation theory tools the author discusses the maximum entropy principle first for simple examples and then for the transformed path measures. In two further subsections the diffusive and collapsed phase is discussed. The last two subsections of this part deal with Wiener sausage, first the large deviation for the volume and the droplet construction and then second some moderate deviation results. \par In the last third part of the notes wetting transitions for one-dimensional random walks are discussed. For example one works with the tied down random walk, i.e., $\Omega_{n,0}=\{\omega\in\Omega_n:\omega_{2n}=0\}$. The attraction to the wall'' $(0,\ldots,0)$ is again given by a transformed path measure for some coupling parameter $\beta > 0$ as $$\widehat{P}_{2n,\beta}(\omega)=\frac{1}{Z_{2n,\beta}}\exp\left[\beta\sum\limits_{i=1}^{2n-1}1_{\{\omega_i=0\}}\right]P^0_{2n}(\omega).$$ Localization is then proved for this model. In another model the interaction of the random walk (the hetero-polymer'') with the wall is produced by a random environment. MSC 2000: *60F10 Large deviations 82B41 Random walks, etc. (statistical mechanics) 60J25 Markov processes with continuous parameter Keywords: random walks; Brownian motion; Edwards' model; local time; large deviation; polymer measure; self-attracting random walks; pinning-depinning transition Highlights Master Server	{"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": 0.9147301912307739, "perplexity": 723.7838116775205}, "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/1368705097259/warc/CC-MAIN-20130516115137-00047-ip-10-60-113-184.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/102136/can-i-manipulate-the-rounded-ness-of-blocks	# Can I manipulate the rounded-ness of blocks? I'm creating a beamertemplate (for beamerposter, actually) and I want to increase the radius of a block. According to the beamer manual (12.3) I can pass the [rounded] option to a block or the beamertemplate blocks in order to make the borders round. But the rounded corners look really small, so I'd like to play around with the radius of the circle that specifies the round corner. How can I do that? - The document class beamer internally uses \pgfpathqmoveto, \pgfpathqcurveto and \pgfpathlineto to build the rounded boxes, so you can play with the values used in the original definition (it can be found in the file beamerbaseboxes.sty). In the code below I show a variation in which I changed the values for the rounded corners for the upper part of the blocks (these changes have to be made in the definition of \beamerboxesrounded, which builds the upper part of the blocks); the original definitions appear commented out and marked with % original at the end of the lines; the modified lines appear right afterwards and are marked with % NEW. To change the rounded corners for the bottom of the blocks you will have to make similar changes in some lines of \endbeamerboxesrounded (which builds the lower part of the blocks); the lines in which changes will have to be made are marked with % original:change. \documentclass{beamer} \usetheme{Warsaw} \setbeamertemplate{blocks}[rounded] \makeatletter \renewcommand\beamerboxesrounded[2][]{% \global\let\beamer@firstlineitemizeunskip=\relax% \vbox\bgroup% \setkeys{beamerboxes}{#1}% {% \usebeamercolor{\bmb@lower}% \globalcolorstrue% \colorlet{lower.bg}{bg}% }% {% \usebeamercolor{\bmb@upper}% \globalcolorstrue% \colorlet{upper.bg}{bg}% }% % % \vskip4bp \setbox\bmb@box=\hbox{% \begin{minipage}[b]{\bmb@width}% \usebeamercolor[fg]{\bmb@upper}% #2% \end{minipage}}% \ifdim\wd\bmb@box=0pt% \setbox\bmb@box=\hbox{}% \ht\bmb@box=1.5pt% \bmb@prevheight=-4.5pt% \else% \wd\bmb@box=\bmb@width% \bmb@temp=\dp\bmb@box% \ifdim\bmb@temp<1.5pt% \bmb@temp=1.5pt% \fi% \setbox\bmb@box=\hbox{\raise\bmb@temp\hbox{\box\bmb@box}}% \dp\bmb@box=0pt% \bmb@prevheight=\ht\bmb@box% \fi% \bmb@temp=\bmb@width% \hbox{% \begin{pgfpicture}{0bp}{+-\ht\bmb@box}{0bp}{+-\ht\bmb@box} \ifdim\wd\bmb@box=0pt% \color{lower.bg}% \else% \color{upper.bg}% \fi% % \pgfpathqmoveto{-4bp}{-1bp}% original % \pgfpathqcurveto{-4bp}{1.2bp}{-2.2bp}{3bp}{0bp}{3bp}% original \pgfpathqmoveto{-4bp}{-6bp}% NEW \pgfpathqcurveto{-4bp}{-0.8bp}{-1.2bp}{2bp}{5bp}{3bp}% NEW % \pgfpathlineto{\pgfpoint{\bmb@temp}{3bp}}% original \pgfpathlineto{\pgfpoint{\bmb@temp-6pt}{3bp}}% NEW \pgfpathcurveto% % {\pgfpoint{\bmb@dima}{3bp}}% original % {\pgfpoint{\bmb@dimb}{1.2bp}}% original % {\pgfpoint{\bmb@dimb}{-1bp}}% original {\pgfpoint{\bmb@dima-2bp}{1bp}}% NEW {\pgfpoint{\bmb@dimb-2bp}{-1.2bp}}% NEW {\pgfpoint{\bmb@dimb}{-6bp}}% NEW \bmb@dima=-\ht\bmb@box% \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfpathlineto{\pgfpoint{-4bp}{\bmb@dima}} \pgfusepath{fill} \end{pgfpicture}% \copy\bmb@box% }% \nointerlineskip% \vskip-1pt% \ifdim\wd\bmb@box=0pt% \else% \hbox{% \begin{pgfpicture}{0pt}{0pt}{\bmb@width}{6pt} \bmb@dima=\bmb@width% \pgfpathrectangle{\pgfpoint{-4bp}{-1bp}}{\pgfpoint{\bmb@dima}{8bp}} \pgfusepath{clip} \end{pgfpicture}% }% \nointerlineskip% \vskip-0.5pt% \fi% \fi% \setbox\bmb@colorbox=\hbox{{\pgfpicturetrue\pgfsetcolor{lower.bg}}}% \setbox\bmb@box=\hbox\bgroup\begin{minipage}[b]{\bmb@width}% \vskip2pt% \usebeamercolor[fg]{\bmb@lower}% \colorlet{beamerstructure}{upper.bg}% \colorlet{structure}{upper.bg}% %\color{.}% } \def\endbeamerboxesrounded{% \end{minipage}\egroup% \wd\bmb@box=\bmb@width% \bmb@temp=\dp\bmb@box% \setbox\bmb@box=\hbox{\raise\bmb@temp\hbox{\box\bmb@box}}% \dp\bmb@box=0pt% \bmb@temp=\wd\bmb@box% \hbox{% \begin{pgfpicture}{0bp}{0bp}{0bp}{0bp} \begin{pgfscope} {% \pgfpathrectangle{\pgfpoint{\bmb@temp}{-7bp}}{\pgfpoint{9bp}{9bp}}% \pgfusepath{clip} }% \end{pgfscope} \begin{pgfscope} \pgfpathrectangle{\pgfpoint{4bp}{-7bp}}{\pgfpoint{\bmb@temp}{5bp}} \pgfusepath{clip} \end{pgfscope} \begin{pgfscope} \bmb@dima=\ht\bmb@box% \pgfpathrectangle{\pgfpoint{\bmb@temp}{1bp}}{\pgfpoint{4bp}{\bmb@dima}} \pgfusepath{clip} \pgfpathrectangle{\pgfpoint{\bmb@temp}{1bp}}{\pgfpoint{4bp}{\bmb@dima}} \pgfusepath{clip} {\pgftransformshift{\pgfpoint{\bmb@temp}{-3bp}}% \pgftransformrotate{90}% \end{pgfscope} \fi% \unhbox\bmb@colorbox% \pgfpathqmoveto{-4bp}{1bp}% original:change \pgfpathqcurveto{-4bp}{-1.2bp}{-2.2bp}{-3bp}{0bp}{-3bp}% original:change \pgfpathlineto{\pgfpoint{\the\bmb@temp}{-3bp}}% original:change \pgfpathcurveto% {\pgfpoint{\the\bmb@dima}{-3bp}}% original:change {\pgfpoint{\the\bmb@dimb}{-1.2bp}}% original:change {\pgfpoint{\the\bmb@dimb}{1bp}}% original:change { \bmb@dima=\ht\bmb@box% \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfpathlineto{\pgfpoint{-4bp}{\bmb@dima}} \pgfusepath{fill} } { \color{black!50!bg} \pgfsetlinewidth{0pt} \pgfpathmoveto{\pgfpoint{\bmb@dimb}{-.5bp}} \bmb@dima=\ht\bmb@box% \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfusepath{stroke} \bmb@temp=\bmb@dima \color{black!31!bg} \pgfpathmoveto{\pgfpoint{\bmb@dimb}{\bmb@temp}} \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfusepath{stroke} \color{black!19!bg} \pgfpathmoveto{\pgfpoint{\bmb@dimb}{\bmb@temp}} \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfusepath{stroke} \color{black!6!bg} \pgfpathmoveto{\pgfpoint{\bmb@dimb}{\bmb@temp}} \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfusepath{stroke} \color{bg} \pgfpathmoveto{\pgfpoint{\bmb@dimb}{\bmb@temp}} \pgfpathlineto{\pgfpoint{\bmb@dimb}{\bmb@dima}} \pgfusepath{stroke} } \fi \end{pgfpicture}% \box\bmb@box% }% \vskip4bp minus 2bp% \else% \vskip2bp% \fi% \egroup% of \vbox\bgroup } \makeatother \begin{document} \begin{frame} \begin{exampleblock}{test} test \end{exampleblock} \end{frame} \end{document} - Great answer. Thank you! I suppose there is no way to do this without redefining the entire command, right? – bitmask Mar 13 '13 at 2:48 @bitmask there's another possibility and it is to patch the commands using, for example, the xpatch package. – Gonzalo Medina Mar 13 '13 at 12:52	{"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": 0.9398989081382751, "perplexity": 1780.8944693176654}, "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/1432207932182.13/warc/CC-MAIN-20150521113212-00168-ip-10-180-206-219.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-solve-2-3b-4-8b-11	Algebra Topics # How do you solve 2(3b-4)=8b-11? Jun 17, 2015 $b = \frac{3}{2}$ #### Explanation: You start multiplying $2$ times the bracket: $6 b - 8 = 8 b - 11$ Take all the $b s$ on the left and the numbers on the right changing sign when moving them: $6 b - 8 b = 8 - 11$ $- 2 b = - 3$ take $- 2$ to the right: $b = \frac{- 3}{-} 2 = \frac{3}{2}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.8435618281364441, "perplexity": 1211.26282865449}, "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/1568514572491.38/warc/CC-MAIN-20190916060046-20190916082046-00053.warc.gz"}
https://www.wikiplanet.click/enciclopedia/en/Kronecker_delta	# Kronecker delta In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: ${\displaystyle \delta _{ij}={\begin{cases}0&{\text{if }}i\neq j,\\1&{\text{if }}i=j.\end{cases}}}$ This latter case is for convenience. ## Properties The following equations are satisfied: {\displaystyle {\begin{aligned}\sum _{j}\delta _{ij}a_{j}&=a_{i},\\\sum _{i}a_{i}\delta _{ij}&=a_{j},\\\sum _{k}\delta _{ik}\delta _{kj}&=\delta _{ij}.\end{aligned}}} Therefore, the matrix δ can be considered as an identity matrix. Another useful representation is the following form: ${\displaystyle \delta _{nm}={\frac {1}{N}}\sum _{k=1}^{N}e^{2\pi i{\frac {k}{N}}(n-m)}}$ This can be derived using the formula for the finite geometric series. Other Languages	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "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": 0.9509603977203369, "perplexity": 3109.773837636856}, "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/1539583512504.64/warc/CC-MAIN-20181020034552-20181020060052-00032.warc.gz"}
http://math.stackexchange.com/questions/637286/what-is-symmetric-square-root-of-matrix/637296	# What is symmetric square root of matrix? In one publication I found a following part: $\textbf R^{-1/2}$ is a symmetric square root of matrix $\textbf R^{-1}$ I know what is a square root of matrix, but what exactly is symmetric square root of matrix? The matrix $\textbf R$ is symmetric and invertible. - For a symmetric real positive definite matrix $A$ there is a symmetric square root $Q$ such that $Q^2=A=Q^{1/2}Q^{1/2}$. - So it just means that matrix Q is also symmetric? – Gacek Jan 13 '14 at 19:38 Yes. So in your example $R^{1/2}$ would be the square root of $R$ which is symmetric (in this case) and $R^{-1/2}$ is its inverse (also symmetric). – John U Jan 13 '14 at 19:41 Great, thank you. – Gacek Jan 13 '14 at 19:42 Do you mean $A^{1/2}A^{1/2}$ on the right hand side or does $Q^2=Q$? – Matta May 18 '15 at 11:15 This is just saying that the square root is also symmetric. For a matrix $A$, there may exist more than one matrix $Q$ such that $QQ = A$. Not all $Q$ are symmetric, but if there is a $Q$ that is symmetric, then so must be $A$, since $A^T = Q^TQ^T = QQ = A$. One of the easy ways to find $Q$ is to use the eigendecomposition of $A$. If $Q$ needs to be a real matrix, then $A$ has to be real and positive semidefinite. In the case that $A$ is positive semidefinite, you can take powers of $A$ to get the inverse, or the inverse square root, etc., like for $R$ in your example. -	{"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": 0.9219911694526672, "perplexity": 174.6610392396568}, "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/1469257831770.41/warc/CC-MAIN-20160723071031-00086-ip-10-185-27-174.ec2.internal.warc.gz"}
https://quant.stackexchange.com/questions/40527/how-should-i-convert-fx-volatility-surface-from-one-base-currency-to-another	# How should I convert FX Volatility Surface from one base currency to another? This might be a very simple question but I wanted to understand how to convert FX volatility surface points which are quoted in one base currency to another currency? Eg I have fx vol quoted in EUR base currency. I want to use USD base currency instead. Do I need to build correlation matrix and/or use triangle methodology to compute Fx implied volatility? Any guide is appreciated. There is no simple way and you have to make correlation assumptions. For instance say you have a volatility surface for $\text{EURUSD}$ and another volatility surface for $\text{USDJPY}$ and you want to build a volatility surface for $\text{EURJPY}$. You start from the observation that a call with maturity $T$ and strike $K$ on $\text{EURJPY}$ with payoff in JPY is equivalent to an option to exchange a quantity of $\text{EURUSD}_T$ USD for a quantity of $K \text{JPYUSD}_T$ USD so that $$D_{\text{JPY}}(T)E^{Q_{\text{JPY}}}[(\text{EURJPY}_T - K)^+] = D_{\text{USD}}(T)\text{USDJPY}_0 E^{Q_{\text{USD}}}[(\text{EURUSD}_T - K \text{JPYUSD}_T)^+]$$ where $Q_{\text{JPY}}$ is the JPY forward measure and $Q_{\text{USD}}$ is the USD forward measure. Next you can use a copula function to mix the marginals of $\text{EURUSD}_T$ and $\text{JPYUSD}_T$ under $Q_{\text{USD}}$: • You obtain the marginal of $\text{EURUSD}_T$ by differentiating with respect to strike a call option on $\text{EURUSD}$, priced from the $\text{EURUSD}_T$ volatility surface. • likewise you obtain the marginal of $\text{JPYUSD}_T$ by differentiating with respect to strike a call option on $\text{JPYUSD}_T$ with payoff in USD, which is equivalent to a put option on $\text{USDJPY}_T$ with payoff in JPY and inverse strike, priced from the $\text{USDJPY}$ volatility surface • you assume a correlation $\rho$ between $\text{EURUSD}_T$ and $\text{JPYUSD}_T$, which you plug in your copula function (for instance a Gaussian copula) You now have a bivariate model to price any $\text{EURJPY}$ option, from which you can infer (by applying inverse Black-Scholes) the $\text{EURJPY}$ volatility surface. As you can see the methodology relies strongly on the estimation for the correlation $\rho$. In fact, it often works the reverse way: from the 3 volatility surfaces for $\text{EURUSD}$, $\text{USDJPY}$ and $\text{EURJPY}$ and the approach above, one can infer an implied correlation $\rho$, and use this correlation for other purposes, such as computing the quanto drift adjustment for a quanto $\text{EURUSD}$ option with payoff in JPY. There are some papers on this methodology. See for instance http://eprints.lancs.ac.uk/45612/1/10.pdf. • Thanks for that answer, I found this question really interesting and had never encountered or considered it, but at least my instinct was right that it was indeed quite complicated! – Attack68 Jun 28 '18 at 10:51 I don't know the answer to this and am just thinking aloud here but if you were to assume that, say, $$EURJPY = E_j \sim \mathcal{N}(0,\sigma^2)$$ i.e. the volatility of EURJPY here is $\sigma$, but instead you want USDJPY, then you know that: $$USDJPY = U_j = E_j U_e$$ where $U_e$ is the random variable of USDEUR. Now, your intended random variable is the product of two (possible correlated?) random variables for which you have data. If you take the simple case that they are assumed to be (joint) normally distributed then the distribution of USDJPY, or $U_j$, is quite a complex matter [see https://mathoverflow.net/questions/11800/what-is-the-probability-distribution-function-for-the-product-of-two-correlated]. Unless I'm having a bad evening and thinking poorly!	{"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": 0.9272454380989075, "perplexity": 631.2505621548091}, "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/1566027318421.65/warc/CC-MAIN-20190823130046-20190823152046-00018.warc.gz"}
https://optimization-online.org/2021/03/8305/	# Lower Bounds on the Size of General Branch-and-Bound Trees A \emph{general branch-and-bound tree} is a branch-and-bound tree which is allowed to use general disjunctions of the form $\pi^{\top} x \leq \pi_0 \,\vee\, \pi^{\top}x \geq \pi_0 + 1$, where $\pi$ is an integer vector and $\pi_0$ is an integer scalar, to create child nodes. We construct a packing instance, a set covering instance, and a Traveling Salesman Problem instance, such that any general branch-and-bound tree that solves these instances must be of exponential size. We also verify that an exponential lower bound on the size of general branch-and-bound trees persists when we add Gaussian noise to the coefficients of the cross polytope, thus showing that polynomial-size smoothed analysis'' upper bound is not possible. The results in this paper can be viewed as the branch-and-bound analog of the seminal paper by Chv\'atal et al.~\cite{chvatal1989cutting}, who proved lower bounds for the Chv\'atal-Gomory rank.	{"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": 0.9810187816619873, "perplexity": 289.8631780175987}, "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-2022-49/segments/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00607.warc.gz"}
https://www.jamelsaadaoui.com/fourier-df-unit-root-test-for-rd-intensity-of-g7-countries/	Fourier DF unit root test for R&D intensity of G7 countries NEW WORKING PAPER: According to the Schumpeterian endogenous growth theory, the efficacy of R&D is lowered by the proliferation of products. To be consistent with empirical data, the ratio between innovative activity and product variety (also called R&D intensity) must be stationary. In this perspective, our contribution investigates whether the R&D intensity series are stationary when structural breaks are considered. Our sample of G7 countries is examined over the period spanning from 1870 to 2016. Our results indicate that traditional unit root tests (ADF, DF-GLS and KPSS) conclude that the R&D intensity series are non-stationary in contradiction with the Schumpeterian endogenous growth theory. The conclusions of these traditional unit root tests may be misleading, as they ignore the presence of structural breaks. Indeed, we use several types of Fourier Dickey-Fuller tests to consider the presence of structural breaks. In the Fourier Dickey-Fuller unit root tests using double frequency and fractional frequency, the R&D intensity is significantly stationary at least at the 5% level for Canada, France, Germany, Italy, Japan and the U.K. when a deterministic trend is included in the tests. Nevertheless, the R&D intensity is non-stationary for the US, even when we consider structural breaks. Indeed, the integration analyses aimed at discriminating between competing theories of endogenous growth should be careful of the presence of structural breaks. Especially when historical data are used, traditional unit root tests may lead to erroneous economic interpretations. These findings may help to understand the true nature of long-run economic growth and may help to formulate sound policy recommendations.	{"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": 0.8017720580101013, "perplexity": 1521.5991792326913}, "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-2022-21/segments/1652662538646.33/warc/CC-MAIN-20220521045616-20220521075616-00085.warc.gz"}
https://infoscience.epfl.ch/record/189198	Infoscience Journal article # On the rate of convergence in the martingale central limit theorem Consider a discrete-time martingale, and let V-2 be its normalized quadratic variation. As V-2 approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian distribution. For any p >= 1, (Ann. Probab. 16 (1988) 275-299) gave a bound on the rate of convergence in this central limit theorem that is the sum of two terms, say A(p) + B-p, where up to a constant, A(p) = parallel to V-2 - 1 parallel to(p/(2p+1))(p). Here we discuss the optimality of this term, focusing on the restricted class of martingales with bounded increments. In this context, (Ann. Probab. 10 (1982) 672-688) sketched a strategy to prove optimality for p = 1. Here we extend this strategy to any p >= 1, thereby justifying the optimality of the term A(p). As a necessary step, we also provide a new bound on the rate of convergence in the central limit theorem for martingales with bounded increments that improves on the term B-p, generalizing another result of (Ann. Probab. 10 (1982) 672-688).	{"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": 0.9652131199836731, "perplexity": 374.1779890994489}, "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-2016-50/segments/1480698541950.13/warc/CC-MAIN-20161202170901-00007-ip-10-31-129-80.ec2.internal.warc.gz"}
https://infoscience.epfl.ch/record/135791	Infoscience Journal article # Dynamics of surface migration in the weak corrugation regime We report a systematic study for metal-on-metal surface migration in the weak corrugation regime, i.e., with migration barriers falling below approximate to 100 meV. The migration characteristics are elucidated by variable-temperature scanning tunneling microscopy observations in the 50-200 K temperature range, which are analyzed by means of nucleation theory. The results demonstrate that, upon entering the weak corrugation regime, the dynamics of the systems are characterized by increasingly reduced effective preexponential factors, while Arrhenius behavior prevails.	{"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": 0.8189325332641602, "perplexity": 3957.1286732727626}, "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-2016-44/segments/1476988720475.79/warc/CC-MAIN-20161020183840-00349-ip-10-171-6-4.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/403616/solving-an-integral-involving-a-bessel-function-laguerre-function-and-gaussian	# Solving an integral involving a Bessel function, Laguerre function and Gaussian We want to calculate the expectation value $$\langle q^2\rangle$$ in polar coordinates which gives us the following integral, for integer values of $$p$$: $$$$\int_0^\infty dq~q^3 \left(\int_0^\infty dr~ J_{0}(q r) e^{-r^2/2} L_{p}^{1}(r^2) r^2\right)^2.$$$$ With Bessel function of the first kind $$J_n(x)$$ and generalized Laguerre polynomial $$L_{p}^{l}(x)$$. We can't solve it because we don't find a nice form of the Fourier-Bessel transform of our waves: (with $$l\geq1$$) $$$$\psi_p^l(q)=\int_0^\infty dr~ J_{l-1}(q r) e^{-r^2/2} L_{p}^{l}(r^2)r^{l+1}.$$$$ In the literature (http://hdl.handle.net/1794/3778, Eq. 3.26) we find a form which is similar but not quite the same. $$$$\int_0^\infty dr~ J_{l}(q r) e^{-r^2/2} L_{p}^{l}(r^2)r^{l+1}=(-1)^p q^l L_p^l(q^2) e^{-q^2/2}.$$$$ Can anyone help us to solve the first or second integral? • I'm not sure, but integrating out the $q$ variable using Hankel transform en.wikipedia.org/wiki/Hankel_transform might be possible. I did some calculations and it seems $\int_0^\infty q^3J_0(qr_1)J_0(qr_2)dq=-\frac{\delta'(r_1-r_2)}{r_1^2}-\frac{\delta''(r_1-r_2)}{r_1}$. Then one of the $r$ variables can be integrated from the delta function, and the resulting integral over the second $r$ would be equal to a finite sum. Sep 10 at 11:24 • The majestic, royal, use of the plural of the first person has not passed unnoticed... Sep 10 at 12:23 • @Nemo Thanks, this helped a lot, I can now solve it! By the way, there should be a "+" instead of a "-" in front of the second delta function. Sep 11 at 12:43 • I will post the full solution tomorrow. Sep 11 at 12:44 This is my solution. Might still contain mistakes. Hope this helps others too! ## The bessel function Using the following properties $$$$\int_0^\infty dq q J_v(q \rho_1) J_v(q \rho_2)= \frac{\delta(r_1-r_2)}{r_1}$$$$ $$$$J'_v(z)=- J_{v+1}(z)+\frac{v}{z}J_{v}(z)$$$$ $$$$J_0'(z)=-J_1(z)$$$$ $$$$J_{-n}=(-1)^n J_{n}.$$$$ Therefore; $$$$q^3 J'_{-1}(q \rho_1) J'_{-1}(q \rho_2)= q^3 J_0(q \rho_1) J_0(q \rho_2)+ q \frac{1}{\rho_1 \rho_2} J_{-1}(q\rho_1)J_{-1}(q\rho_2)+q^2\left( \frac{1}{\rho_2}J_0(q \rho_1) J'_0(q \rho_2)+\frac{1}{\rho_1}J'_0(q \rho_1) J_0(q \rho_2) \right)$$$$ This gives $$$$\int_0^\infty dq q^3 J_0(q \rho_1) J_0(q \rho_2)=\left(\partial_{\rho_1}\partial_{\rho_2}-\frac{1}{\rho_1 \rho_2}-\frac{\partial_{\rho_1}}{\rho_1}-\frac{\partial_{\rho_2}}{\rho_2}\right)\frac{\delta(\rho_1-\rho_2)}{\rho_1}$$$$ ## Solving the integral $$$$I=\int_0^\infty d \rho f(\rho) \left(-\frac{\partial^2_{\rho}}{\rho}+\frac{3\partial_{\rho}}{\rho^2}-\frac{3}{\rho^3} \right)f(\rho).$$$$ define $$x\equiv \rho^2$$. $$$$I=-\int_0^\infty dx f(x)\left[ 2\partial^2_x-2\frac{\partial_x}{x}+\frac{3}{2x^2}\right] f(x).$$$$ Using the identities $$$$\partial_x(x L^1_p(x))=(p+1) L_{p}^0$$$$ $$$$\partial_x(L_p^0)=-L_{p-1} (\text{for}~ p\geq1) ~(=0~ \text{otherwise})$$$$ the derivatives to $$f(x)=x L_p^1(x) e^{-x/2}$$ are $$$$\partial_x f(x)=(- \frac{x}{2} L_p^1(x)+(p+1)L_p^0(x) ) e^{x/2}$$$$ $$$$\partial^2_x f(x)=(\frac{x}{4} L_p^1(x)-(p+1)L_p^0(x)-L^1_{p-1}(!)) e^{x/2}$$$$ where the $$(!)$$ points out that this term is only there is $$p\geq1$$. This gives the following integral $$$$I=-\int_0^\infty dx e^{-x} \left[L_p^1(x)L_p^1(x)(\frac{3}{2}+x+\frac{x^2}{2}) -x (p+1) L_p^0(x) L_p^1(x)- 2 x L_{p-1}^1(x) L_{p}^1(x)\right]$$$$ ## Orthogonality conditions Making us of the orthogonality conditions $$$$\int_0^\infty dx x^a e^{-x} L_n^a L_m^a =\frac{(n+a)!}{n!} \delta_{n,m}$$$$ $$$$\int_0^\infty dx x^{a+1} e^{-x} (L_n^a(x))^2 =\frac{(n+a)!}{n!} (2n+a+1)$$$$ and $$$$L_p^1=\sum_{i=0}^p L_{i}^0(x)$$$$ $$$$L_n^a=L_n^{a+1}-L_{n-1}^{a+1}.$$$$ then $$$$I=-(3p/2+(p+1)+(p+1)(2p+1+1)/2-(p+1)(p+1)-0)=-\frac{5p}{2}-1$$$$	{"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": 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": 30, "wp-katex-eq": 0, "align": 0, "equation": 21, "x-ck12": 0, "texerror": 0, "math_score": 0.9516577124595642, "perplexity": 2044.8590721534822}, "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-20211127223710-20211128013710-00098.warc.gz"}
https://cstheory.stackexchange.com/questions/42248/whats-the-fastest-known-algorithm-for-finding-the-diameter-of-a-graph	What's the fastest known algorithm for finding the diameter of a graph? Given a positively weighted graph what's the fastest algorithm for finding the diameter for that graph? • Currently the fastest deterministic algorithm for diameter in general should be Chan-Williams which runs in $n^3/2^{\Omega(\sqrt{\log n})}$ time, matching the previous randomized algorithm by Williams. But there are better algorithms when the graph is special, or if you accept approximated solutions. – Hsien-Chih Chang 張顯之 Jan 21 at 17:54 • I guess the OP could've searched a little more to find the answer to his question, but I am still surprised this question is getting buried so much – Sasho Nikolov Jan 22 at 1:16 • I think there's interesting, recent literature on this question besides the fast algorithms for APSP that Hsien-Chih mentions. I.e., see people.csail.mit.edu/virgi/diam.pdf which gives approximation algorithms and fine-grained complexity results. – Huck Bennett Jan 22 at 1:44 • @Hsien-ChihChang張顯之, HuckBennett, these comments seem like reasonable answers to the question, would you consider posting them as answers? – a3nm Jan 22 at 10:42	{"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": 0.9561711549758911, "perplexity": 982.8610784499616}, "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-2019-51/segments/1575540499389.15/warc/CC-MAIN-20191207105754-20191207133754-00144.warc.gz"}
https://onepetro.org/ISOPEPACOMS/proceedings-abstract/PACOMS14/All-PACOMS14/ISOPE-P-14-110/26058	Abstract Unsteady hydroelastic waves generated by impulsively-starting surface and submerged concentrated loads in a fluid with an underlying uniform current are studied analytically. The fluid is assumed to be homogeneous, incompressible, inviscid, and of finite depth. For the case of irrotational motion with small-amplitude deflections, linear potential-flow theory is employed. The Laplace equation is the governing equation, with the dynamic condition representing a balance among the hydrodynamic, elastic, inertial forces and the downward applied load. It is shown that the analytical solution, obtained by the Laplace-Fourier integral transform, consists of steady-state and transient responses. For the steady response, an explicit expression is further derived by the residue theorem, while the transient response is obtained by the stationary-phase method. These expressions allow the effects of various physical parameters on the hydroelastic responses to be studied in detail. It is found that the flexural-gravity wave motion depends on the ratio of current speed to phase or group speeds. This content is only available via 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": 0.9508204460144043, "perplexity": 803.1753411451691}, "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-2021-43/segments/1634323585916.29/warc/CC-MAIN-20211024081003-20211024111003-00228.warc.gz"}
http://mathoverflow.net/questions/107565/using-function-terminology-for-functors	# Using Function Terminology for Functors? The analogy between functions from a set to set, and functors from a category to a category is obvious. But transferring terminology from functions to functors can be a tricky business. I would like to ask if the following is acceptable: For $B$ a subcategory of $A$, and $D$ a subcategory of $C$, and $F:A \to C$ a functor, is the following statement clear in meaning, and well-defined? It holds that the image of $B$ under $F$ lies in $D$. If not, then how should it be phrased? - Presumably you mean that the objects $F(b)$ for $b$ an object of $B$ are all objects of $D$. Do you mean the same for the morphisms? – Jon Beardsley Sep 19 '12 at 13:54 Yes in both cases. – Mihail Matrix Sep 19 '12 at 13:59 Analogy? A function is a functor (between discrete categories). – Qiaochu Yuan Sep 19 '12 at 16:15 It seems still unclear. @Mihail: May I ask you to clarify if the intended meaning of your statement is the one explained by Andreas and Todd, or the one suggested by me? – Fred Rohrer Sep 19 '12 at 20:40 @Theo: Of course. The point is the distinction between "is" and "is equivalent to". For example, the last "are" in your comment is of the latter type (supposing our definitions of "functor" coincide, and supposing we have a similar set theory). And in that case it is indeed appropriate to speak of analogy. – Fred Rohrer Sep 20 '12 at 5:13 Andreas's answer is very much to the point. I'd like to add to it and give some accepted terminology. As he was saying, the naive image doesn't work. Consider the arrow category $2 = \{0 \to 1 \}$, and take the functor $2 \to Set$ which maps both objects to the natural numbers $\mathbb{N}$ and the arrow to the successor function $s: \mathbb{N} \to \mathbb{N}$. Now ask yourself if the "image" of this functor is actually a subcategory! The notion you really want is called the essential image. - If you use James Cranch's suggestion, namely to say that the image is a subcategory of $D$, you should make sure that it's actually true in your situation, because it might not be in general. $B$ might contain morphisms $f:x\to y$ and $g:z\to w$, and your functor might have $F(y)=F(z)$, so that $F(f)$ and $F(g)$ are composable morphisms in $D$. Yet, if $y\neq z$ and so $f$ and $g$ are not composable in $A$, then the composite $F(g)F(f)$ might not be in the image of $F$. - As proven by Jon's comment, the statement is not clear in meaning. A precise statement is the following, but it is of course unclear whether it is equivalent to the statement you had in mind: $F$ induces by restriction and coastriction a functor from $B$ to $D$. (The very useful word "coastriction" seems to be not so well-known, but it is explained in this answer.) - I think this is well-defined. You mean that the images of objects and morphisms in $B$ under $F$ all lie within $D$. It might be slightly clearer to say, "... is a subcategory of $D$" rather than "... lies in $D$" (to avoid a reader thinking that the image has to be a single point for some stupid reason) but this is almost pedantic. -	{"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": 0.8647042512893677, "perplexity": 329.277062739009}, "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-2015-18/segments/1430458524551.85/warc/CC-MAIN-20150501053524-00046-ip-10-235-10-82.ec2.internal.warc.gz"}
https://socratic.org/questions/a-5-25-gram-sample-of-a-cobalt-chloride-hydrate-is-heated-until-dried-the-anhydr	Chemistry Topics # A 5.25 gram sample of a cobalt chloride hydrate is heated until dried. The anhydrous sample has a mass of 3.00 gram. What is the percent water by mass of the original hydrate? Dec 27, 2015 42.9% #### Explanation: So, you're dealing with a $\text{5.25-g}$ sample of a cobalt(II) chloride hydrate, let's say $\text{CoCl"_2 * color(blue)(n)"H"_2"O}$. You know that the mass of the anhydrous salt, which is what remains after all the water of crystallization was driven off by heating, is equal to $\text{3.00 g}$. Assuming the all the water of crystallization was indeed driven off, you can say that since ${m}_{\text{hydrate" = m_"anhydrous salt" + m_"water}}$ you will have ${m}_{\text{water" = "5.25 g" - "3.00 g" = "2.25 g}}$ This means that your initial sample of cobalt(II) chloride hydrate contained $\text{3.00 g}$ of anhydrous cobalt(II) chloride and $\text{2.25 g}$ of water of crystallization. The percent composition of water in the hydrate will thus be (2.25 color(red)(cancel(color(black)("g"))))/(5.25color(red)(cancel(color(black)("g")))) xx 100 = color(green)("42.9% H"_2"O") Here is a similar lab with analysis conducted using copper (II) sulfate. Hope this helps! ##### Impact of this question 4676 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "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": 0.8441117405891418, "perplexity": 4419.568920051306}, "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-2022-05/segments/1642320299894.32/warc/CC-MAIN-20220129002459-20220129032459-00564.warc.gz"}
http://mathterms.blogspot.com/	## Monday, June 10 ### Multiple Determinism Determinism is the philosophical view that every event, including human cognition, behavior, decision, and action, is casually determined by the environment. It is, in essence, the view that one's life is predetermined before one is even born. Determinism proposes there is a predetermined unbroken chain of prior occurrences back to the origin of the universe. Determinists believe the universe is fully governed by causal laws resulting in only one possible state at any point in time. With numerous historical debates, many varieties and philosophical positions on the subject of determinism exist, most prominently the free will disputes involving compatibilism and incompatibilism. In other words, determinism necessarily entails that humanity or individual humans may not change the course of the future and its events (a position known as fatalism).However, some theorists believe that the extent to which human beings have influence over their future is itself merely dependent on present and past. Causal determinism is associated with, and relies upon, the ideas of materialism ## Multiple determinism The Principle of Multiple Determinism The principle of multiple determinism specifes that a target event at one level of organization, but particularly at molar (e.g., social) levels of organization, may have multiple antecedents within or across levels of organization. For example, consider the multiple factors that contribute to drug abuse. Onthe biological level, researchers identi®ed the contribution of individual differences in the susceptibility of the endogenous opiod receptor system while on the social level investigators have noted the important role of social context. Both operate, and our understanding of drug abuse is incomplete if either perspective is excluded. A corollary to this principle is that the mapping between elements across levels of organization becomes more complex (e.g., many-to-many) as the number of intervening levels of organization increases. One implication is that the likelihood of complex and potentially obscure mappings increases as one skips levels of organizations. ### Preparation for Inverse Exponential Function The exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex equals its own derivative. The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. (Source from Wikipedia).It is otherwise Written as exp(x).Here we are going to see about preparation about inverse exponential function and its example problems. Preparation for finding the inverse of the function: • First we got to to replace f(x) with y • Switch x‘s y‘s • Solve for y • Replace y of f(x) ## Preparation problems for preparation for inverse exponential function: pro1 : Find the inverse function of the following y = 3x+1 Sol : The given function is y = 3x +1 Following the above procdure to find the inverse of the function First we have to Interchange x and y value x=3y+1 Then now solve for y Add both sides -1 then the equation will be x-1 =3y + 1 -1 x-1=3y Divide both sides 3 we get , y = `(x-1) / (3)` Therefore the inverse function is (x-1) / (3) ## Example for inverse of exponential function: Pro 2: Find the inverse of the following exponential function, y = 5. 6 (3x-4) +7 Sol : Interchange the x and y value then the equation will be, x= 5. 6 (3y-4) +7 Now we solve for y Add both sides -7 we get x-7 = 5. 6 (3y-4) +7-7 x-7 = 5. 6 (3y-4) Divide both sides 5 we get, `(x-7) / (5)` = `(5. 6 (3y-4)) / (5)` `(x-7) / (5)` = 6 (3y-4) Take both sides log then the equation will be , Log 6 `((x-7) / (5))` = log 6 6 (3y-4) Log 6 `((x-7) / (5))` = 3y-4 Log 6 `((x-7) / (5))` + 4 = 3y Both sides divide 3 we get `{Log 6 ((x-7) / (5) + (4))} / (3)``(3y) / (3)` `{Log 6 ((x-7) / (5) + (4))} / (3)` = y Therefore the inverse exponential function is `{Log 6 ((x-7) / (5) + (4))} / (3)` = y Hence the preparation of inverse exponential function is explained, ### Figure Segment of a Circle In geometry, a circular segment also circle segment. It is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord. The circle segment constitutes the part between the secant and an arc, excluding the circle's center.It is shown in figure bellow. ## Example of figure segment of a circle: Example 1 Radius of the circle is 15 cm, angle of the Segment of a circle is 45 degree. Find the area of the Segment of a circle is shown in figure. Solution: Area of the circle = `1/2` r2`theta` - sin `theta` = `1/2` r2( `pi/180` `theta` - sin `theta`) =0.5152(`pi/180` 45-(sin 45)) =112.5(0.785-0.7071) Area of the Segment of a circle=8.77 cm2 Example 2 Radius of the circle is 10 cm, angle of the Segment of a circle is 55 degree. Find the area of the Segment of a circle is shown in figure. Solution: Area of the circle = `1/2` r2`theta` - sin `theta` = `1/2` r2( `pi/180` `theta` - sin `theta`) =0.5102(`pi/180` 50-(sin 50)) =50(0.873-0.766) Area of the Segment of a circle=5.53 cm2 Example 3 Radius of the circle is 15 cm, angle of the Segment of a circle is 85 degree. Find the area of the Segment of a circle is shown in figure. Solution: Area of the circle = `1/2` r2`theta` - sin `theta` = `1/2` r2( `pi/180` `theta` - sin `theta`) =0.5152(`pi/180` 85-(sin 85)) =112.5(1.484-0.996) Area of the Segment of a circle=54.9 cm2 Example 4 Radius of the circle is 15 cm, angle of the Segment of a circle is 105 degree. Find the area of the Segment of a circle is shown in figure. Solution: Area of the circle = `1/2` r2`theta` - sin `theta` = `1/2` r2( `pi/180` `theta` - sin `theta`) =0.5152(`pi/180` 105-(sin 105)) =112.5(1.833-0.9659) Area of the Segment of a circle= 97.54 cm2 Example 5 Radius of the circle is 15 cm, angle of the Segment of a circle is 110 degree. Find the area of the Segment of a circle is shown in figure. Solution: Area of the circle = `1/2` r2`theta` - sin `theta` = `1/2` r2( `pi/180` `theta` - sin `theta`) =0.5152(`pi/180` 110-(sin 110)) =112.5(1.92-0.9396) Area of the Segment of a circle=110.29 cm2 ## Friday, June 7 ### Distribution of the Sample Means A sample mean is a numerical set which is an average value of a particular portion of a number in a certain group. A sample mean is expressed as x.suppose if we take a sample of size n and there is a n independent variables x1,x2…xn and each value is respect to one randomly selected observation, then the distribution of the population of these variables has the mean value mhu and the standard deviation sigma. Then the sample value is, X=1/n(x1+x2+…..xn) ## Mean and variance of the distribution of the sample means: Using the mean and variance property of the random variable ,the mean and variance of the sample mean is given below. µx= µ sigmax=sigma/sqrt(n)` therefore the mean value of the sample mean is similar to the mean of the population distribution and the variance is smaller than the variance of the population distribution. For example: In population distribution where the mean value µ=20 and the standard deviation σ=2 that means ( N(20,2).then we have the simple random sample of 100 students ,then what is the mean and variance of the sample mean distribution? µx= µ µx=20 σx=σ/`sqrt(n)` σx =2/`sqrt(100)` σx =2/10 σx =0.2 ## shape property of the distribution of the sample means: It may be in the following shapes like normal, skewed, bimodal. Explanation for distribution of the sample means: If the population distribution is normal,then the distribution of the sample mean is normal. If in the population distribution the mean and variance value is respectively (µ, σ), then the mean and variance for the distribution of the sample mean is(µ, σ/`sqrt(n)` ). For linearcombination the sample mean x=(1/n)(x1+x2+..x n) By using the above all concept the following theorem is illustrated. Central Limit Theorem- distribution of the sample mean: Theorem definition: If we take a population with a mean μ and a variance σ2, then the sampling distribution of the mean approach a normal distribution with a mean of μ and a variance of σ2/N as N means increases value of the sample size. ### Irregular Triangle A closed figure contains the three line of the segments that join end to end. The triangle is the three side polygon. The irregular triangle is the scalene triangle. Scalene triangles are abnormal in that they are distinct by what they are not. The majority triangles drained at chance would be scalene. The angles of the interior of the scalene triangle are normally all different. ## Irregular triangle: In the triangle all the sides are dissimilar length. The sides are not equal and angles are not equal. The triangle is the general shape of geometry. This is containing the line segment. In the Euclidean geometry three non collinear positions is the represented to the unique triangle and unique or the unique plane. The right triangle is the other name for the right angled triangle. Hypotenuse triangle is the larger size of the right triangle. The length of the square is the equal to the length of the square of the hypotenuse. Area of the irregular triangle: The area of a triangle is usually computed as area = bh /2 Where b means base length and h means base height. Calculating the length the side using the formula: S= (a +b +c)/2 Irregular triangle fact: Shortest side is opposite to the small angle: • The straight side is constantly differing the minimum interior angle. • The greatest side is constantly opposite the maximum interior angle. Longest side is opposite to the largest angle: • The straight side is constantly differing the nominal interior angle. • The top side is forever differing the main interior angle. ## Example 1: Triangle EFG shown below is inscribed inside a square of side 40 cm. Find the area of the triangle. Solution: Area of triangle = (1/2) base = (1/2)(40)(40) = 800 cm 2 Problem Calculating the third side from the specified right scalene triangle Solution: GI2=GH2+HI2 150=62+HI2 150-36=HI2 114=HI2 HI2 = `sqrt(114)` HI = 10.67 Problem 3: Fine the area of scalene triangle the problem, the given data : s=6, a=5, b=3, c=4 Solution: Area formula = `sqrt(s(s-a)(s-b)(s-c))` = sqrt(6(6-5)(6-3)(6-4))` =sqrt(6(1)(3)(2))` =sqrt(36)` = 6 The area is 6cm. ## Thursday, June 6 ### Pitch Diameter Formula When cutting screw threads the mechanic must have some way to check the threads. Threads should be measured at the pitch diameter. The pitch diameter is a point along the flank or angular surface of the thread . The thread pitch micrometer is an excellent and easy way to measure threads, but one pitch micrometer will not measure all of the different thread types and sizes. The thread ring gage will tell you whether the thread is right or wrong, but it will not give you an accurate account of the thread depth. The three-wire method is considered to be one of the most accurate and versatile ways of measuring threads. The three-wire method uses three lapped and polished wires and a micrometer to measure the pitch diameter of the thread The wires are placed in the threads and a micrometer is used to measure over the top of the wires. Different thread types and thread sizes require different size wires. The three-wire method of thread measurement can be used for all types of threads including Unified, Acme, and Buttress thread forms. To help you understand the three-wire method of thread measurement, we will use an example thread of 1.250-5 ACME-2G . The first piece of information we need to acquire is the "best wire size." The best wire size is the size of the wire that will contact the thread at the pitch diameter. The best wire size can be calculated using a formula, Begin by looking in the index under Thread, Acme, wire method of testing. Turn to this section and find the table which gives the wire sizes for measuring Acme threads with lead angles less than 5 degrees. Now look for the column that shows 5 threads per inch. You should find that the table gives you 0.10329 as the best wire size. The table also gives you minimum and maximum wire size limits. Make a note of the best wire size. Now we need to find out what the measurement over the wires should be. Within the same unit you will find a paragraph entitled Three Wire Measurement of Acme and Stub Acme Thread Pitch Diameters. Within this paragraph it will tell you where to find the Approximate Three Wire Formula. The Approximate Three Wire Formula "SIMPLIFIED VERSION" should read as follows: M = E - 0.86603P + 3W Where: M = the measurement over the wires E = the pitch diameter P = the pitch or (1 divided by the number of threads per inch) W= the wire size We really only need to find the pitch diameter to solve the formula. We have the wire size. We know the pitch is 1/5 or 0.2 . To find the pitch diameter, go back to the index in the Machinery’s Handbook. Look in the index for Screw threads and threads systems. Under Screw threads and threads systems find Acme. Turn to this section and find the table that gives the Limiting Dimension for American National Standards for General Purpose Acme Single-Start Screw threads. In this table find the Class 2G, Pitch Diameter, Maximum and Minimum limiting diameters for the 1.250-5 ACME-2G thread. You should find that the table gives you 1.1210 as the minimum size and 1.1410 as the maximum size for the pitch diameter calculation. We will use the median dimension of 1.1310 for our formula calculation. Now that we have all of the information, let's plug the numbers into the formula. M = E - 0.86603P + 3W M = 1.131-(0.86603 X 0.2) + (3 X 0.10329) M = 1.131 - 0.173206 + 0.30987 M = 1.268 (micrometer measurement over the wires) ### Isosceles Triangle Proof In an isosceles triangle, two sides are equal in length. An isosceles triangle also has two angles of the same measure; namely, the angles opposite to the two sides of the same length; this fact is the content of the Isosceles triangle theorem. Some mathematicians define isosceles triangles to have only two equal sides, whereas others define that an isosceles triangle is one with at least two equal sides. The latter definition would make all equilateral triangles isosceles triangles. (Source : WIKIPEDIA) ## Things need to remember for Proofs of isosceles triangle: For proving isosceles triangle we need to know the following information about isosceles triangle, There are two types of isosceles triangles, 1.Normal isosceles triangle 2.Right isosceles triangle. Properties: Properties of parts of isosceles triangle: 1.The two sides of the isosceles tringles are equal. 2.Two base angles has same measure. 3. Angle ratio of the right isosceless triangle is 45:90:45. 4.The side ratio of the isosceles triangle is 1:1:`sqrt(2)` ## Problems on isosceles triangle proof: Problem 1: Prove that the following triangle is isosceles triangle. Proof: Given , The angle We know that the sum of the angles are 180. So 100 + x +x = 180 100 + 2x = 180 Subtract 100 0n both sides. 2x =180 -100 2x = 80 Divide by x on both sides, x = 40 The base anles are equal two 40 . According to the properties of isosceles triangle,we can determine that the given triangle is isosceles triangle. Hence the proof. Problem 2: Prove that the triangle with the sides 5 : 5 : 5`sqrt(2)` is an isosceles right triangle triangle. Proof: Given,The sides of the triangle is 5 , 5 ,5`sqrt(2)` We know that in a right Angle triangle,the hypotenuse is greater then the legs and it satisfies the pythagorean theorem, 5`sqrt(2)` > 5 , 5 52+52 = (5`sqrt(2)` )2 25+25 = 25 *2 50 = 50 So the given sides satisfies the pythagoren theorem.So we can say that it is a right triangle. The given sides are in the ratio of 1:1:`sqrt(2)` so the given triangle is isosceles triangle. Hence the proof.	{"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": 0.8499608039855957, "perplexity": 2443.4339185998315}, "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-2015-06/segments/1422115855561.4/warc/CC-MAIN-20150124161055-00077-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.albert.io/learn/gmat/question/keeping-an-objective-stance-while-teaching	Limited access Directions This question presents a sentence, part of which or all of which is underlined. Beneath the sentence, you will find five ways of phrasing the underlined part. The first of these repeats the original; the other four are different. If you think the original is best, choose the first answer; otherwise, choose one of the others. One of the most difficult elements of teaching is to keep an objective stance when students are writing papers that, however indirectly, criticizes stances or choices that the teacher has taken in life; however, it is crucial that the teacher assess such papers fairly rather than allowing personal opinion and prejudice affect the grade. A to keep an objective stance when students are writing papers that, however indirectly, criticizes stances or choices that the teacher has taken in life; however, it is crucial that the teacher assess such papers fairly rather than allowing personal opinion and prejudice affect the grade. B keeping an objective stance when students write papers that, however indirectly, criticize stances or choices that the teacher is taking in life; however, it is crucial that the teacher assess such papers fairly rather than allowing personal opinion and prejudice to effect the grades. C keeping an objective stance when students write papers that, however indirectly, criticize stances or choices that the teacher has taken in life; however, it is crucial that the teacher assess such papers fairly rather than allowing personal opinion and prejudice to affect the grades. D keeping an objective stance, when students write a paper that, however indirectly, criticizes stances or choices that the teacher has taken in life; although, it is crucial that he assess such papers fairly rather than allowing personal opinion and prejudice to affect the grades. E to keep an objective stance even when students write papers, that, however indirectly, criticize stances or choices that the teacher has taken in life; however, he or she should assess such papers fairly rather than allowing personal, opinion, and prejudice affect the grades. Select an assignment template	{"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": 0.9615208506584167, "perplexity": 2856.1361939983885}, "config": {"markdown_headings": true, "markdown_code": false, "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-2017-17/segments/1492917123172.42/warc/CC-MAIN-20170423031203-00129-ip-10-145-167-34.ec2.internal.warc.gz"}
https://lqp2.org/node/473	# Combinatorial Quantization of the Hamiltonian Chern-Simons Theory II Anton Yu Alekseev, Harald Grosse, Volker Schomerus August 17, 1994 This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [AGS]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathe- matically rigorous definition of the algebra of observables ${\cal A}_{CS}$ of the Chern Simons model. It is a *-algebra of functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional $\omega$ (integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [FoRo], the algebra ${\cal A}_{CS}$ provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.	{"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": 0.924765408039093, "perplexity": 393.98282953646645}, "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-2020-10/segments/1581875145529.37/warc/CC-MAIN-20200221111140-20200221141140-00021.warc.gz"}
https://ita.skanev.com/04/problems/04.html	# Problem 4.4 ## Fibonacci numbers This problem develops properties of the Fibonacci numbers, which are defined by recurrence (3.22). We shall use the technique of generating functions to solve the Fibonacci recurrence. Define the generating function (or formal power series) $\mathcal{F}$ as \begin{align} \mathcal{F}(z) &= \sum_{i=0}^{\infty}F_iz^i \\ &= 0 + z + z^2 + 2z^3 + 3z^4 + 5z^5 + 8z^6 + 13z^7 + 21z^8 + \ldots, \end{align} where $F_i$ is the $i$th Fibonacci number. 1. Show that $\mathcal{F}(z) = z + z\mathcal{F}(z) + z^2\mathcal{F}$. 2. Show that \begin{align} \mathcal{F}(z) &= \frac{z}{1 - z - z^2} \\ &= \frac{z}{(1 - \phi z)(1 - \hat\phi z)} \\ &= \frac{1}{\sqrt5}\Big(\frac{1}{1 - \phi z} - \frac{1}{1 - \hat{\phi} z}\Big) \end{align} where $$\phi = \frac{1 + \sqrt5}{2} = 1.61803\ldots \\ \hat\phi = \frac{1 - \sqrt5}{2} = -0.61803\ldots$$ 3. Show that $$\mathcal{F}(z) = \sum_{i=0}^{\infty}\frac{1}{\sqrt5}(\phi^i - \hat{\phi}^i)z^i$$ 4. Use part (c) to prove that $F_i = \phi^i / \sqrt5$ for $i > 0$, rounded to the nearest integer. (Hint: Observe that $\|\hat{\phi}\| < 1$.) ### Part 1 \begin{align} & z + z\mathcal{F}(z) + z^2\mathcal{F}(Z) = \\ & = z + z\sum_{i=0}^{\infty}F_iz^i + z^2\sum_{i=0}^{\infty}F_iz^i \\ & = z + \sum_{i=1}^{\infty}F_{i-1}z^i + \sum_{i=2}^{\infty}F_{i-2}z^i \\ & = z + F_1z + \sum_{i=2}^{\infty}(F_{i-1} + F_{i-2})z^i \\ & = z + F_1z + \sum_{i=2}^{\infty}F_iz^i \\ & = \mathcal{F}(z) \end{align} ### Part 2 Let's just note that $\phi - \hat\phi = \sqrt5$, $\phi + \hat\phi = 1$ and $\phi\hat\phi = - 1$ (just calculate them): \begin{align} \mathcal{F}(z) &= \frac{\mathcal{F}(z)(1 - z - z^2)}{1 - z - z^2} \\ &= \frac{\mathcal{F}(z) - z\mathcal{F}(z) - z^2\mathcal{F}(z) - z + z}{1 - z - z^2} \\ &= \frac{\mathcal{F}(z) - \mathcal{F}(z) + z}{1 - z - z^2} \\ &= \frac{z}{1 - z - z^2} \\ &= \frac{z}{1 - (\phi + \hat\phi)z + \phi\hat\phi z^2} \\ &= \frac{z}{(1 - \phi z)(1 - \hat\phi z)} \\ &= \frac{\sqrt5 z}{\sqrt5 (1 - \phi z)(1 - \hat\phi z)} \\ &= \frac{(\phi - \hat\phi)z + 1 - 1}{\sqrt5 (1 - \phi z)(1 - \hat\phi z)} \\ &= \frac{(1 - \hat\phi z) - (1 - \phi z)}{\sqrt5 (1 - \phi z)(1 - \hat\phi z)} \\ &= \frac{1}{\sqrt5}\Big(\frac{1}{1 - \phi z} - \frac{1}{1 - \hat\phi z}\Big) \\ \end{align} ### Part 3 We have that: $$\frac{1}{1 - x} = \sum_{k=0}^{\infty}x^k \quad\text{when } \|x\| < 1$$ Thus: \begin{align} \mathcal{F}(n) &= \frac{1}{\sqrt5}\Big(\frac{1}{1 - \phi z} - \frac{1}{1 - \hat\phi z}\Big) \\ &= \frac{1}{\sqrt5}\Big(\sum_{i=0}^{\infty}\phi^i z^i - \sum_{i=0}^{\infty}\hat{\phi}^i z^i\Big) \\ &= \sum_{i=0}^{\infty}\frac{1}{\sqrt5}(\phi^i - \hat{\phi}^i) z^i \end{align} ### Part 4 $$\mathcal{F}(z) = \sum_{i=0}^{\infty}\alpha_iz^i \quad\text{ where } \alpha_i = \frac{\phi^i - \hat{\phi}^i}{\sqrt5}$$ From this follows that $\alpha_i = F_i$, that is: $$F_i = \frac{\phi^i - \hat{\phi}^i}{\sqrt5} = \frac{\phi^i}{\sqrt5} - \frac{\hat{\phi}^i}{\sqrt5}$$ For $i = 0$, $\phi/\sqrt5 = (\sqrt5 + 5)/10 > 0.5$. For $i > 2$, $\|\hat{\phi}^i\| < 0.5$.	{"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": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 1776.1722946998552}, "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-2018-05/segments/1516084887621.26/warc/CC-MAIN-20180118210638-20180118230638-00071.warc.gz"}
http://mathhelpforum.com/algebra/34248-integers-fractions-print.html	# integers and fractions • April 12th 2008, 07:06 PM not happy jan integers and fractions Can I please have help with these problems? 2/5 divided by 5/6= (+4)-(-5)= (+18)divided by(-3)= • April 12th 2008, 07:18 PM topher0805 $\frac {2}{5}\div \frac {5}{6}$ Remember when dividing fraction just flip and multiply: $\frac {2}{5}\div \frac {5}{6}=\frac {2}{5}\cdot \frac {6}{5}$ Then just multiply the numerator by the numerator and the denominator by the denominator. $(4)-(-5)$ Remember that subtracting a negative number is the same as adding that number: $(4)-(-5)=4+5$ $18\div (-3)$ $18\div (-3)=-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": 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": 0.9198021292686462, "perplexity": 3296.8916780606296}, "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/1469257829320.91/warc/CC-MAIN-20160723071029-00167-ip-10-185-27-174.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-domain-and-range-of-y-log-5x	Precalculus Topics # How do you find the domain and range of y = log_5x? Jul 19, 2015 $f \left(x\right) = {\log}_{5} x$ is the inverse of the function $e \left(x\right) = {5}^{x}$ which has domain $\left(- \infty , \infty\right)$ and range $\left(0 , \infty\right)$. So the domain of ${\log}_{5} x$ is $\left(0 , \infty\right)$ and range is $\left(- \infty , \infty\right)$ #### Explanation: The domain of $e \left(x\right) = {5}^{x}$ is the whole of $\mathbb{R}$, that is $\left(- \infty , \infty\right)$, but its range is $\left(0 , \infty\right)$. So the domain of its inverse $y = {\log}_{5} x$ is $\left(0 , \infty\right)$ and its range is $\left(- \infty , \infty\right)$ ##### Impact of this question 538 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 14, "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": 0.9107696413993835, "perplexity": 230.83723030577377}, "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-2020-16/segments/1585370490497.6/warc/CC-MAIN-20200328074047-20200328104047-00535.warc.gz"}
http://mathhelpforum.com/calculus/93249-covergence-series.html	# Math Help - Covergence of series 1. ## Covergence of series Hi I want to determine if this series is convergent or divergent. Can anyone give me a hint on which theorem to use here? $\displaystyle\sum_{k=1}^{\infty} \; ln(1+\frac{1}{k})$ thx 2. Can I use $ln(1+\frac{1}{k}) \geq ln(\frac{1}{k})$ And $\displaystyle\sum_{k=1}^{\infty} \; ln(\frac{1}{k})$ is divergent , so my original series is also diverging? 3. $\ln\left(\frac{1}{k}\right)\leq \ln\left(1+\frac{1}{k}\right)$ Study $\ln\left(\frac{1}{k}\right)=\ln(1)-\ln(k)$ and see that it diverges. EDIT: Uhm, you got it. 4. Hello, Originally Posted by Twig Hi I want to determine if this series is convergent or divergent. Can anyone give me a hint on which theorem to use here? $\displaystyle\sum_{k=1}^{\infty} \; ln(1+\frac{1}{k})$ thx $1+\frac 1k=\frac{k+1}{k}$ So $\ln\left(1+\frac 1k\right)=\ln(k+1)-\ln(k)$ So this is a telescoping series and finally, $\sum_{k=1}^\infty \ln\left(1+\frac 1k\right)=\lim_{n\to\infty} \sum_{k=1}^n \ln\left(1+\frac 1k\right)=\lim_{n\to\infty} \ln(n+1)-\ln(1)=\infty$ 5. In general the series... $\sum_{n=1}^{\infty} \ln (1+a_{n})$ ... converges if and only if converges the series... $\sum_{n=1}^{\infty} a_{n}$ Kind regards $\chi$ $\sigma$ 6. Hello chisigma, I thought $\frac {1}{k}$ converges? 7. Originally Posted by calc101 Hello chisigma, I thought $\frac {1}{k}$ converges? It´s diverging. The n:th term approaches zero as n approaches infinity, but $\displaystyle\sum_{k=1}^{\infty} \frac{1}{k}$ is diverging. You know about the integral test? $\displaystyle\lim_{R\to \infty} \int_{1}^{R} \frac{1}{x} \, dx = ln(R)-ln(1) = \infty$ Note: $\displaystyle\sum_{k=1}^{\infty} \frac{1}{k^{1.000001}}$ is convergent. 8. No, I meant the sequence $\frac {1}{k}$ converges to 0? Not the function $\frac {1}{x}$ 9. Yes, the sequence $(a_{n})_{n=1}^{\infty} = \frac{1}{n}$ converges to 0.	{"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": 0.993029773235321, "perplexity": 1348.539335994826}, "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/1464049276564.72/warc/CC-MAIN-20160524002116-00138-ip-10-185-217-139.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/matter-wave-quantum-stuff.44130/	# Matter wave / quantum stuff 1. Sep 22, 2004 ### tyco05 G'day guys, Just looking for a bit of help.... I'm not sure that I fully understand the question here either.... but here goes: a) Using the Fourier integral, $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}a(k)e^{ikx}dk$$ Show that a matter wave having a wave-vector distribution given in the diagram below (see attached), has the form: $$\Psi(x)=\sqrt{\frac{\Delta k}{2\pi}} \frac{\sin{\frac{\Delta kx}{2}}}{\frac{\Delta kx}{2}} e^{ik_0 x}$$ (note that $\Delta k$ is a constant in the above diagram (attached)) b) Calculate the probability of finding a particle given by the above wavefunction in the region $-\infty<x<+\infty$ For part a) I'm just assuming that I am supposed to work out the Fourier integral for the given function a(k), and that should work out to what's above right??.... Whenever I do that, however I can't get it! Is this the right way to approach this? Or is there simply a mistake somewhere in my workings? (My maths is a bit scratchy at the moment) Here it is..... (I'm new to this LaTex game too by the way, so please be gentle) $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty}a(k)e^{ikx}dk$$ $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\left[\int_{-\infty}^{k_0 -\frac{\Delta k}{2}}a(k)e^{ikx}dk + \int_{k_0 -\frac{\Delta k}{2}}^{k_0 +\frac{\Delta k}{2}}a(k)e^{ikx}dk + \int_{k_0 +\frac{\Delta k}{2}}^{+\infty}a(k)e^{ikx}dk\right]$$ $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\left[\int_{-\infty}^{k_0 -\frac{\Delta k}{2}}(0)e^{ikx}dk + \int_{k_0 -\frac{\Delta k}{2}}^{k_0 +\frac{\Delta k}{2}}(1)e^{ikx}dk + \int_{k_0 +\frac{\Delta k}{2}}^{+\infty}(0)e^{ikx}dk\right]$$ $$\Psi(x)=\frac{1}{\sqrt{2\pi}} \int_{k_0 -\frac{\Delta k}{2}}^{k_0 +\frac{\Delta k}{2}}e^{ikx}dk$$ $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\left[\frac{1}{ix}e^{ikx}\right]_{k_0 -\frac{\Delta k}{2}}^{k_0 +\frac{\Delta k}{2}}$$ Am I making the mistake here? ^^^ Is the integral correct? $$\Psi(x)=\frac{1}{\sqrt{2\pi}}\left[\frac{1}{ix}\left(e^{i(k_0 +\frac{\Delta k}{2})x}-e^{i(k_0 -\frac{\Delta k}{2})x}\right)\right]$$ $$\Psi(x)=\frac{1}{ix\sqrt{2\pi}}\left(e^{ik_0 x +i\frac{\Delta k x}{2}}-e^{ik_0 x -i\frac{\Delta k x}{2}}\right)$$ $$\Psi(x)=\frac{1}{ix\sqrt{2\pi}}\left(e^{ik_0 x}e^{i\frac{\Delta k x}{2}}}-e^{ik_0 x}e^{-i\frac{\Delta k x}{2}}}\right)$$ $$\Psi(x)=\frac{1}{ix\sqrt{2\pi}}\left[e^{ik_0 x}\left(e^{i\frac{\Delta k x}{2}}}-e^{-i\frac{\Delta k x}{2}}}\right)\right]$$ $$\Psi(x)=\frac{1}{ix\sqrt{2\pi}}\left[e^{ik_0 x}\left(\sin{\frac{\Delta k x}{2}}\right)\right]$$ Where do I go from here? This is obviously not correct, but I just don't know what is going on....... I would love some guidance! I haven't attempted part b) yet, but I'm assuming the solution will come from $$\int_{-\infty}^{+\infty}\mid\Psi(x)\mid^2dx$$ and should equal 1 ?? Any help would be great, thanks, Ty #### Attached Files: • ###### wave-vector distribution.bmp File size: 15.3 KB Views: 80 Last edited: Sep 22, 2004 2. Sep 22, 2004 ### stunner5000pt SInce most of the problms you see in this forum are based on elementary physics, i suggest try posting in the quantum forum you may be more successful with getting a response. 3. Sep 22, 2004 ### HallsofIvy Staff Emeritus To stunner5000p: No, if the is homework, then it should be here, not in "Quantum Physics". (In fact, if he posted it there, it would probably get moved here.) To Tyco05: $sin(a)= \frac{e^{ix}- e^{-ix}}{2i}$. You should not have that "i" in the denominator of your final answer. Other than that, you answer is exactly the same as $$\Psi(x)=\sqrt{\frac{\Delta k}{2\pi}} \frac{\sin{\frac{\Delta kx}{2}}}{\frac{\Delta kx}{2}} e^{ik_0 x}$$ except for that $$\sqrt{\Delta k}$$ You have only $\Delta k$ without the square root. Check the answer again. 4. Sep 22, 2004 ### tyco05 Thanks HallofIvy, I just made that sin(x) identity incorrectly...... oh well, some things get past us.... but the $\sqrt{\Delta k}$ is definitely in the question I was given. Maybe it is a typo, or perhaps a genuine mistake? When I worked it through I also got what you said, just $\Delta k$ . I'll leave it as is unless you have any other suggestions, and just see what happens! Cheers 5. Sep 22, 2004 ### tyco05 Hey again, Just checked another source (Serway, Moses and Moyer. Modern Physics.) and it is definitely a typo or mistake. Instead of what was written on the assignment: $$\Psi(x)=\sqrt{\frac{\Delta k}{2\pi}} \frac{\sin{\frac{\Delta kx}{2}}}{\frac{\Delta kx}{2}} e^{ik_0 x}$$ It should have been : $$\Psi(x)=\frac{\Delta k}{\sqrt{2\pi}} \frac{\sin{\frac{\Delta kx}{2}}}{\frac{\Delta kx}{2}} e^{ik_0 x}$$ Thanks again. 6. Sep 22, 2004 ### tyco05 OK, this question is getting on my nerves now. I tried part b), only to have to integrate by parts over and over and over and over again. It won't stop. What's going on??...... $$P(x)=\int_{-\infty}^{+\infty}\mid\Psi(x)\mid^2dx$$ Where $$\Psi(x)=\frac{\Delta k}{\sqrt{2\pi}} \frac{\sin{\frac{\Delta kx}{2}}}{\frac{\Delta kx}{2}} e^{ik_0 x}$$ Now, I found that : $$\mid\Psi(x)\mid^2 = \frac{2}{\pi x^2} \sin^2{\frac{\Delta k x}{2}}$$ so, $$P(x)=\int_{-\infty}^{+\infty}\frac{2}{\pi x^2} \sin^2{\frac{\Delta k x}{2}}dx$$ $$P(x)=\frac{2}{\pi}\int_{-\infty}^{+\infty}\frac{1}{x^2}\sin^2{\frac{\Delta k x}{2}}dx$$ $$P(x)=\frac{1}{\pi}\int_{-\infty}^{+\infty}\frac{1}{x^2}(1-\cos{\Delta k x})dx$$ $$P(x)=\frac{1}{\pi}\left[\int_{-\infty}^{+\infty}\frac{1}{x^2}dx-\int_{-\infty}^{+\infty}\frac{1}{x^2}\cos{\Delta k x}dx\right]$$ Is there something I should realise about these integrals?.... The one on the right is the one that just goes on and on and on.... The one on the left seems easy enough, but what about the limits.... ? Can it be evaluated ? 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https://link.springer.com/article/10.1186%2Fs13660-019-1975-0	# Solvability of some classes of singular integral equations of convolution type via Riemann–Hilbert problem • Pingrun Li Open Access Research ## Abstract In this paper, we study methods of solution for some kinds of convolution type singular integral equations with Cauchy kernel. By means of the classical boundary value problems for analytic functions and of the theory of complex analysis, we deal with the necessary and sufficient conditions of solvability and obtain the general solutions and the conditions of solvability for such equations. All cases as regards the index of the coefficients in the equations are considered in detail. Especially, we discuss some properties of the solutions at the nodes. This paper will be of great significance for the study of improving and developing complex analysis, integral equation and boundary value problems for analytic functions (that is, Riemann–Hilbert problems). Therefore, the classical theory of integral equations is extended. ## Keywords Singular integral equations Riemann–Hilbert problems Integral operators Convolution type ## MSC 45E05 45E10 30E25 ## 1 Introduction There were rather complete investigations on the method of solution for integral equations of Cauchy type and integral equations of convolution type [1, 2, 3, 4, 5]. The solvability of a singular integral equation (SIE) of Wiener–Hopf type with continuous coefficients was considered in [6, 7]. For operators with Cauchy principal value integral and convolution, the conditions of their Noethericity were discussed in [8, 9]. Recently, Li [10, 11, 12, 13, 14, 15, 16] studied some classes of SIEs with convolution kernels and gave the Noether theory of solvability and the general solutions in the cases of normal type. It is well known that integral equations of convolution type, mathematically, belong to an interesting subject in the theory of integral equations. In this paper, we study the solvability and the explicit solutions for several classes of SIEs with Cauchy kernel and convolution kernel, in which include equations with one or two convolution kernels, equation of Wiener–Hopf type, and dual equations. Here, we give the new methods of solution for these equations, and our approach of solving the equations is novel and effective, different from the ones in classical cases. Thus, the results in this paper generalize ones in Refs. [1, 2, 10, 11, 12], and improve the theory of SIEs and boundary value theory. Our study of the following equations is motivated by continuous efforts of those studies as well as a sufficiently long list of the above-mentioned materials. Now we consider the following some classes of SIEs of convolution type with Cauchy kernel. 1. (1) SIEs of dual type $$\textstyle\begin{cases} a_{1}\omega (t)+\frac{b_{1}}{\pi i}\int _{\mathbb{R}}\frac{\omega ( \tau )}{\tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k _{1}(t-\tau )\omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}^{+}; \\ a_{2}\omega (t)+\frac{b_{2}}{\pi i}\int _{\mathbb{R}}\frac{\omega ( \tau )}{\tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k _{2}(t-\tau )\omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}^{-}. \end{cases}$$ 2. (2) SIE of Wiener–Hopf type $$a\omega (t)+\frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t-\tau ) \omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}^{+}.$$ 3. (3) SIEs with one convolution kernel $$a\omega (t)+\frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t-\tau ) \omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}.$$ 4. (4) SIEs with two convolution kernels \begin{aligned} &a\omega (t)+ \frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}^{+}}k_{1}(t- \tau )\omega (\tau )\,d\tau \\ &\quad{}+\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R} ^{-}}k_{2}(t-\tau )\omega (\tau )\,d\tau =g(t), \quad t\in \mathbb{R}, \end{aligned} where a, b ($$b\neq 0$$), $$a_{j}$$, $$b_{j}$$ are constants and $$b_{j}$$ are not equal to zero simultaneously. For these equations, we will discuss their Noether theory and methods of solution in a different class of function, that is, these equations are transformed by integral transformation into Riemann–Hilbert problems with nodes. Some special kinds of Riemann–Hilbert problems with discontinuous coefficients appear in the course of solution, which are solved in the same time. Actually, the problem to find their solutions is very important in practical applications. ## 2 Definitions and lemmas The concepts of classes $$\{\{0\}\}$$ ($$((0))$$, $$\langle \!\langle 0 \rangle \!\rangle$$) and $$\{0\}$$ ($$(0)$$, $$\langle0\rangle$$) are introduced as follows. ### Definition 2.1 A function $$F(s)$$ belongs to $$\{\{0\}\}$$, if the following two conditions are fulfilled: 1. (1) $$F(s)\in \hat{H}$$, that is, it satisfies the Hölder condition on $$\mathbb{R}\cup \{\infty \}$$ (for the notation Ĥ, cf. [2]). 2. (2) $$F(s)\in L^{2}(\mathbb{R})$$. ### Definition 2.2 A function $$f(t)\in \{0\}$$, if its Fourier transform \begin{aligned} F(s)=\mathbb{F}f(t)=\frac{1}{\sqrt{2\pi }} \int _{ \mathbb{R}}f(t)e^{ist}\,dt, \quad s \in \mathbb{R,} \end{aligned} (2.1) belongs to $$\{\{0\}\}$$. ### Definition 2.3 Let $$F(s)$$ be a continuous function on $$\mathbb{R}$$. If (1) $$F(s)\in \hat{H}$$. (2) $$F(s)=O(\|s\|^{-\rho })$$, $$\rho >\frac{1}{2}$$, where $$\|s\|$$ is sufficiently large. Then we write $$F(s)\in ((0))$$ or $$((0))^{\rho }$$. If $$F(s)\in ((0))$$ or $$((0))^{\rho }$$, we write $$f(t)\in (0)$$ or $$(0)^{\rho }$$. ### Definition 2.4 If (1) $$F(s)\in \hat{H}$$; (2) $$F(s)\in H^{ \rho }(N_{\infty })$$, $$\rho >\frac{1}{2}$$, i.e., it belongs to H in the neighborhood $$N_{\infty }$$ of ∞, and $$F(\infty )=0$$. Then we write $$F(s)\in \langle \!\langle 0 \rangle \!\rangle$$ or $$\langle \!\langle 0 \rangle \!\rangle ^{\rho }$$, and $$f(t)\in \langle0\rangle$$ or $$\langle0\rangle ^{\rho }$$. Let $$H_{1}=\{F(s)\|F(s)\in L^{2}(\mathbb{R})\}$$, $$H_{2}=\{F(s)\|F(s)=O(\|s\|^{- \rho }), \rho >\frac{1}{2}\}$$, and $$H_{3}=\biggl\{ F(s)\|F(s)\in H^{\rho }(N_{\infty }),\rho > \frac{1}{2}\biggr\} .$$ Obviously, $$H_{3} \subset H_{2} \subset H_{1}$$, hence $$\langle \!\langle 0 \rangle \!\rangle \subset ((0))\subset \{\{0\}\}$$, and $$\langle0\rangle \subset (0)\subset \{0\}$$. We denote by $$H_{0}$$ the class of Hölder continuous functions on any closed interval exterior to $$s=0$$. For two functions $$k(t)$$ and $$f(t)$$, their convolution is defined by the formula \begin{aligned} k\ast f(t)=\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t-\tau )f( \tau )\,d\tau , \quad t \in \mathbb{R}. \end{aligned} (2.2) It is well known that $$\mathbb{F}(k\ast f)=KF$$, where K, F are the Fourier transforms of k, f, respectively. Lemma 2.1 is obvious fact and we omit its proof here. ### Lemma 2.1 1. (1) If$$k,f\in \{0\}$$ ($$\langle0\rangle$$), then$$k\ast f \in \{0\}$$ ($$\langle0\rangle$$). 2. (2) If$$f\in \{0\}$$and$$k\in (0)$$ ($$\langle0\rangle$$), then$$k\ast f\in (0)$$ ($$\langle0\rangle$$). We also introduce the Cauchy operatorT: \begin{aligned} Tf(t)=\frac{1}{\pi i} \int _{\mathbb{R}}\frac{f(\tau )}{\tau -t}\,d\tau , \quad t \in \mathbb{R}. \end{aligned} (2.3) It follows from [15, 16] thatTmaps$$\{0\}$$and$$\langle0\rangle$$into themselves, respectively, and$$T^{2}=I$$ (identity). We define the operators N and S as follows: \begin{aligned} Nf(t)=f(-t), \qquad Sf(t)=f(t)\operatorname{sgn}t, \end{aligned} (2.4) obviously, $$N^{2}=S^{2}=I$$, and $$SN=-NS$$. For the inverse Fourier transform operator $$\mathbb{F}^{-1}$$: \begin{aligned} \mathbb{F}^{-1}F=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R}}F(s)e^{-ist}\,ds, \quad t \in \mathbb{R}. \end{aligned} (2.5) It is evident that \begin{aligned} \mathbb{F}^{-1}=N\mathbb{F}=\mathbb{F}N, \quad \mathbb{F}^{2}=N, \end{aligned} (2.6) and for any $$f \in \{0\}$$, we have \begin{aligned} \mathbb{F}Sf=T\mathbb{F}f. \end{aligned} (2.7) Lemma 2.2 plays an important role in our paper. ### Lemma 2.2 Let$$f(t)\in \{0\}$$, $$F(s)=\mathbb{F}f(t)$$, then$$\mathbb{F}[Tf(t)]=-SF(s)$$, that is, \begin{aligned} \mathbb{F}\biggl[\frac{1}{\pi i} \int _{\mathbb{R}}\frac{f(\tau )}{\tau -t}\,d\tau \biggr]=-F(s) \operatorname{sgn}s. \end{aligned} (2.8) ### Proof Since \begin{aligned}[b] \mathbb{F}\bigl[Tf(t)\bigr] &= \frac{1}{\sqrt{2\pi }} \int _{\mathbb{R}}\biggl[\frac{1}{ \pi i} \int _{\mathbb{R}}\frac{f(\tau )}{\tau -t}\,d\tau \biggr] e^{ist}\,dt \\ &=-\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}\biggl[\frac{1}{\pi i} \int _{\mathbb{R}}\frac{e^{ist}}{t- \tau }\,dt\biggr]f(\tau )\,d\tau , \end{aligned} (2.9) by the extended residue theorem [1], we have $$\frac{1}{\pi i} \int _{\mathbb{R}}\frac{e^{ist}}{t-\tau }\,dt= \textstyle\begin{cases} e^{is\tau }, &\mbox{if } s>0, \\ 0, & \mbox{if } s=0, \\ -e^{is\tau },&\mbox{if } s< 0. \end{cases}$$ (2.10) Substituting (2.10) into (2.9), we obtain $$\mathbb{F}\bigl[Tf(t)\bigr]=-\operatorname{sgn}s\cdot \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}f(t)e^{ist}\,dt=-\operatorname{sgn}sF(s).$$ (2.11) □ ### Lemma 2.3 If$$f\in \{0\}$$and$$F(0)=0$$, then$$Tf\in \{0\}$$. ### Proof Since $$f\in \{0\}$$, then $$F=\mathbb{F}f\in \{\{0\}\}$$ and $$F\in C(\mathbb{R})$$. By $$F(0)= 0$$ and $$F(s)\in L^{2}(\mathbb{R})$$, we have $$F(s)\operatorname{sgn}s \in C(\mathbb{R}) \cup L^{2}(\mathbb{R})$$. For any two points $$s_{1}$$, $$s_{2}$$ in the neighborhood of +∞ (or −∞), that is, there exists a sufficiently large constant M such that $$s_{j}> M$$ (or $$s_{j}<- M$$). Since $$\bigl\vert F(s_{1})\operatorname{sgn}s_{1}-F(s_{2}) \operatorname{sgn}s_{2} \bigr\vert = \bigl\vert F(s_{1})-F(s _{2}) \bigr\vert ,$$ (2.12) we can obtain $$F(s)\operatorname{sgn}s\in {H^{\rho }}$$ from $$F(s)\in {H^{ \rho }}$$, where ρ is the Hölder exponent. On the other hand, for any $$s_{1},s_{2} \in [-M, M]$$, when $$s_{1}s _{2}>0$$, (2.12) is fulfilled; when $$s_{1} s_{2} \leq 0$$, since \begin{aligned}[b] \bigl\vert F(s_{1}) \operatorname{sgn}s_{1}-F(s_{2})\operatorname{sgn}s_{2} \bigr\vert &= \bigl\vert F(s_{1})+F(s_{2}) \bigr\vert \\ & = \bigl\vert F(s_{1})-F(0)+F(s_{2})-F(0) \bigr\vert \\ &\leq \bigl\vert F(s_{1})-F(0) \bigr\vert + \bigl\vert F(s_{2})-F(0) \bigr\vert \\ & \leq D_{1} \vert s_{1} \vert ^{\rho _{1}}+ D_{2} \vert s_{2} \vert ^{\rho _{2}}\leq (D_{1}+ D _{2}) \vert s_{1}-s_{2} \vert ^{\rho }, \end{aligned} (2.13) $$F(s)\operatorname{sgn}s\in \hat{H}$$, where $$D_{j}$$ ($$j=1,2$$) are positive constants, and $$\rho = \textstyle\begin{cases} \max\{\rho _{1}, \rho _{2}\}, & \mbox{if } \vert s_{1}-s_{2} \vert \geq 1, \\ \min\{\rho _{1}, \rho _{2}\}, & \mbox{if } \vert s_{1}-s_{2} \vert < 1. \end{cases}$$ Through the above discussion, we obtain $$F(s)\operatorname{sgn}s\in \{\{0\}\}$$ and then $$Tf\in \{0\}$$. □ In Lemma 2.3, note that $$F(0)=0$$ is a necessary condition, otherwise the lemma is invalid. Similarly, we can prove that, if $$f\in (0)$$ ($$\langle0\rangle$$), and $$F(0)=0$$, then $$Tf\in (0)$$ ($$\langle0\rangle$$). In order to transform the above-mentioned SIEs into Riemann–Hilbert problems, we give Lemma 2.4. ### Lemma 2.4 Let$$\omega (t)\in \{0\}$$, $$\varOmega (x)=\mathbb{F} \omega (t)$$, and$$\tilde{\varOmega }(z)=\frac{1}{2 \pi i}\int _{ \mathbb{R}}\frac{\varOmega (s)}{s-z}\,ds$$, then, we have 1. (1) $$\operatorname{Im}z>0$$, $$\tilde{\varOmega }(z)=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}\omega (t) e^{i t z}\,dt$$. 2. (2) $$\operatorname{Im}z<0$$, $$\tilde{\varOmega }(z)=-\frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R^{-}}}\omega (t) e^{i t z}\,dt$$. 3. (3) $$\operatorname{Im}z=0$$, $$\tilde{\varOmega }(z)=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R}}\omega (t) e^{i t z} \operatorname{sgn}t \,dt$$. ### Proof Since $$\omega (t)\in \{0\}$$, we have \begin{aligned}[b] \tilde{\varOmega }(z) &= \frac{1}{2 \pi i} \int _{\mathbb{R}}\frac{1}{s-z}\biggl[\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}\omega (t) e^{is t}\,dt\biggr]\,ds \\ &=\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R^{-}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds+\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds. \end{aligned} (2.14) Let $$\varTheta =\frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds$$. By the generalized residue theorem, when $$\operatorname{Im} t>0$$, we have $$\varTheta = \textstyle\begin{cases} e^{itz}, \quad \operatorname{Im}z>0, \\ 0, \qquad \operatorname{Im}z< 0; \end{cases}$$ (2.15) and when $$\operatorname{Im} t<0$$, $$\varTheta = \textstyle\begin{cases} -e^{-itz}, & \operatorname{Im}z< 0, \\ 0, &\operatorname{Im}z>0. \end{cases}$$ (2.16) Therefore, when $$\operatorname{Im}z>0$$, we get $$\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{-}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds=0$$ and $$\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds=\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R^{+}}}\omega (t) e^{i t z}\,dt;$$ when $$\operatorname{Im}z<0$$, we have $$\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds=0$$ and $$\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{-}}}\omega (t)\,dt \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{ e^{is t}}{s-z}\,ds=-\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R^{-}}}\omega (t) e^{i t z}\,dt;$$ when $$\operatorname{Im}z=0$$, by applying Plemelj formula [12], we find $$\tilde{\varOmega }^{+}(x)=\frac{1}{2}\varOmega (x)+ \tilde{\varOmega }(x), \qquad \tilde{\varOmega }^{-}(x)=-\frac{1}{2} \varOmega (x)+ \tilde{\varOmega }(x),$$ (2.17) therefore, $$\tilde{\varOmega }(x)=\frac{1}{2}\bigl[\tilde{\varOmega }^{+}(x)+ \tilde{\varOmega }^{-}(x)\bigr]$$ (2.18) and $$\tilde{\varOmega }^{+}(x)=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}\omega (t) e^{i t x}\,dt; \qquad \tilde{\varOmega } ^{-}(x)=-\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{-}}}\omega (t) e ^{i t x}\,dt.$$ (2.19) Then, we have \begin{aligned}[b] \tilde{\varOmega }(x) &= \frac{1}{2 \pi i} \int _{\mathbb{R}} \frac{\varOmega (s)}{s-x}\,ds =\frac{1}{\sqrt{2\pi }} \int _{ \mathbb{R^{+}}}\omega (t) e^{i t x}\,dt-\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{-}}}\omega (t) e^{i t x}\,dt \\ &=\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}\omega (t) e^{i t x} \operatorname{sgn}t \,dt. \end{aligned} (2.20) □ ### Remark 2.1 If $$\omega (t)\in L^{1}(\mathbb{R})$$, then $$\varOmega (0)=0$$ if and only if $$\int _{\mathbb{R}}\omega (t)\,dt=0$$. ### Remark 2.2 Note that, for the class $$(0)$$ or $$\langle0\rangle$$, the index ρ is invariant, provided $$\frac{1}{2}<\rho <1$$. In Sects. 36, we shall study the Noether theory of solvability and methods of solution for some classes of SIEs of convolution type with Cauchy kernel. ## 3 Dual equations Let us consider the following SIEs of dual type: $$\textstyle\begin{cases} a\omega (t)+\frac{b}{\pi i}\int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k_{1}(t- \tau )\omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}^{+}; \\ a\omega (t)+\frac{b}{\pi i}\int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k_{2}(t- \tau )\omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}^{-}, \end{cases}$$ (3.1) where a, b are constants and $$b\neq 0$$. The given functions $$k_{j}, g\in \{0\}$$ ($$j=1,2$$), and an unknown function $$\omega \in \{0 \}$$, then their Fourier transforms belong to class $$\{\{0\}\}$$. In order to solve Eq. (3.1), we rewrite it as $$\textstyle\begin{cases} a\omega (t)+\frac{b}{\pi i}\int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k_{1}(t- \tau )\omega (\tau )\,d\tau =g(t)-f_{-}(t); \\ a\omega (t)+\frac{b}{\pi i}\int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }}\int _{\mathbb{R}}k_{2}(t- \tau )\omega (\tau )\,d\tau =g(t)+f_{+}(t), \end{cases}\displaystyle t\in \mathbb{R},$$ (3.2) where $$f \in \{0\}$$ is an undetermined function. $$f_{+}(t)= \textstyle\begin{cases} f(t), & t\geq 0, \\ 0, & t< 0; \end{cases}\displaystyle \qquad f_{-}(t)= \textstyle\begin{cases} 0, & t\geq 0, \\ -f(t), & t< 0 \end{cases}$$ (3.3) and $$f(t)=f_{+}(t)-f_{-}(t)$$. Taking Fourier transforms in both sides of (3.2), by Lemmas 2.1 and 2.2 we obtain $$\textstyle\begin{cases} a\varOmega (s)-b\operatorname{sgn}s \varOmega (s)+K_{1}(s)\varOmega (s)=G(s)+F^{-}(s); \\ a\varOmega (s)-b\operatorname{sgn}s \varOmega (s)+K_{2}(s)\varOmega (s)=G(s)+F^{+}(s), \end{cases}$$ (3.4) where $$K_{j}(s)=\mathbb{F}k_{j}(t)$$, $$\varOmega (s)=\mathbb{F}\omega (t)$$, $$G(s)=\mathbb{F}g(t)$$, $$F^{\pm }(s)=\mathbb{F}f_{\pm }(t)$$, $$j=1,2$$. By Lemma 2.4, we know that $$F^{\pm }(s)$$ are the boundary values of the Cauchy type integral $${F}(z)=\frac{1}{2 \pi i} \int _{\mathbb{R}}\frac{F(\tau )}{\tau -z}\,d\tau , \quad \operatorname{Im}z \neq 0,$$ and it is well known that $$F^{\pm }(s)$$ also are the one-sided Fourier transforms of $$f(t)$$, that is, $${F}^{+}(s)=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{+}}}f(t) e^{i t s}\,dt; \qquad {F}^{-}(s)=-\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R^{-}}}f(t) e ^{i t s}\,dt.$$ It is evident that $$F(s)=F^{+}(s)-F^{-}(s)$$. Since $$\varOmega (s)$$ is continuous at $$s=0$$, thus $$\varOmega (0)=0$$ by (3.4). We assume $$K_{j}(s)\neq \textstyle\begin{cases} - (a-b), & 0< s < +\infty , \\ - (a+b), & -\infty < s < 0, \end{cases}\displaystyle \quad j=1,2,$$ (3.5) which is called the normal case of (3.1). By eliminating $$\varOmega (s)$$ in (3.4) we get $$\bigl[a-b\operatorname{sgn}s+K_{1}(s)\bigr] \bigl[G(s)+F^{+}(s)\bigr]=\bigl[a-b\operatorname{sgn}s+K_{2}(s) \bigr] \bigl[G(s)+F ^{-}(s)\bigr],$$ (3.6) so that (3.6) may be written as the following Riemann–Hilbert problems with discontinuous coefficients: $$F^{+}(s)=\varPhi (s)F^{-}(s)+\varUpsilon (s),\quad s\in \mathbb{R},$$ (3.7) where $$\varPhi (s)=\frac{a-b\operatorname{sgn}s+K_{2}(s)}{a-b\operatorname{sgn}s+K_{1}(s)},\qquad \varUpsilon (s)= \frac{[K_{2}(s)-K_{1}(s)]G(s)}{a-b\operatorname{sgn}s+K_{1}(s)}.$$ (3.8) We remark that the Riemann boundary value problem (3.7) can be directly solved by the methods in [1] under certain conditions through Fredholm integral equations (see also Muskhelishvili [17]). But in this paper we shall apply Fourier theory to solve (3.7), which may enable us to deal with other equations. Since $$K_{j}(s)\in \{\{0\}\}$$, then $$K_{j}(\infty )=0$$ ($$j=1,2$$), so $$\varPhi (\infty )=1$$ and $$\varUpsilon (\infty )=0$$. Thus $$s=\infty$$ is not a nodal point of (3.7), and its unique nodal point is $$s=0$$. Note that $$F(s)$$ is continuous on the whole real axis and $$F(\infty )=0$$. We take a continuous branch of $$\log \varPhi (s)$$ such that it is continuous at $$s=\infty$$, e.g., $$\log \varPhi (\infty )=0$$, and denote $$\frac{1}{2\pi i}\bigl\{ \log \varPhi (+0)-\log {\varPhi (-0)} \bigr\} = \gamma _{0}=\delta _{0}+i\eta _{0}.$$ (3.9) We choose an integer κ such that $$0\leq \delta =\delta _{0}- \kappa <1$$, and call κ the index of (3.7). The homogeneous problem of (3.7) is denoted by $$F^{+}(s)=\varPhi (s)F^{-}(s),\quad s\in \mathbb{R}.$$ (3.10) Without loss of generality, we take the fixed point $$z_{0}$$ such that $$\operatorname{Im} z_{0}> 0$$, and $$\bar{z}_{0}$$ denotes the conjugate complex number of $$z_{0}$$. In order to solve (3.10), we define the following sectionally holomorphic function: $$V(z)= \textstyle\begin{cases} (z-\bar{z}_{0})^{-\kappa } e^{\varGamma (z)}, & \operatorname{Im}z>0; \\ (z-z_{0})^{-\kappa } e^{\varGamma (z)}, & \operatorname{Im}z< 0, \end{cases}$$ (3.11) where $$\varGamma (z)=\frac{1}{2\pi i} \int _{\mathbb{R}}\frac{\log \varPhi _{0}(t)}{t-z}\,dt,$$ (3.12) and $$\varPhi _{0}(t)=\biggl(\frac{t-z_{0}}{t-\bar{z}_{0}} \biggr)^{-\kappa } \varPhi (t),$$ (3.13) in which we have taken the definite branch of $$\log \varPhi _{0}(t)=-k\log \frac{t-z_{0}}{t-\bar{z} _{0}}+\log \varPhi (t),$$ (3.14) provided that we have chosen $$\log \frac{t-z_{0}}{t-\bar{z}_{0}}\|_{t= \infty }=0$$, or, which is the same, $$\log \frac{t-z_{0}}{t-\bar{z} _{0}}\|_{t=\operatorname{Re}z_{0}}=\pm i\pi$$. From (3.11) and (3.12), we have $$V^{+}(s)=\varPhi (s)V^{-}(s), \quad s\in \mathbb{R}.$$ Since $$\frac{F^{+}(s)}{V^{+}(s)}=\frac{F^{-}(s)}{V^{-}(s)},$$ $$D(z)=\frac{F(z)}{V(z)}$$ is analytic on $$\mathbb{R}^{2}$$ and has the order $$\kappa -1$$ at ∞. By the generalized Liouville theorem [14], we can get a general solution of (3.10), $$F(z)=V(z)P_{\kappa -1}(z),$$ (3.15) and when $$\kappa >0$$, $$P_{\kappa -1}(z)=e_{0}+e_{1}z+\cdots +e_{ \kappa -1}z^{\kappa -1}$$ is a polynomial of degree $$\kappa -1$$; when $$\kappa \leq 0$$, $$P_{\kappa -1}(z)\equiv 0$$, that is, (3.10) only has zero solution. Next, we consider the solutions and the conditions of solvability for (3.7). To do this, we define $$Y(z)$$ as follows: $$Y(z)= \textstyle\begin{cases} e^{\varGamma (z)}, & \operatorname{Im}z>0; \\ (\frac{z-z_{0}}{z-\bar{z}_{0}})^{-\kappa }e^{\varGamma (z)},& \operatorname{Im}z< 0. \end{cases}$$ (3.16) According to the method used in [17, 18, 19], (3.7) can be transformed into $$\frac{F^{+}(s)}{Y^{+}(s)}=\frac{F^{-}(s)}{Y^{-}(s)}+\frac{ \varUpsilon (s)}{Y^{+}(s)}.$$ (3.17) We again define the following sectionally holomorphic function: $$\varPsi (z)=\frac{1}{2\pi i} \int _{\mathbb{R}}\frac{\varUpsilon (t)}{Y ^{+}(t)(t-z)}\,dt,\quad z\,\bar{\in }\,\mathbb{R}.$$ (3.18) By applying Plemelj’s formula to $$\varPsi (z)$$ in (3.18), we rewrite (3.17) as $$\frac{F^{+}(s)}{Y^{+}(s)}-\varPsi ^{+}(s)=\frac{F^{-}(s)}{Y ^{-}(s)}-\varPsi ^{-}(s).$$ (3.19) It is easily seen that, $$D(z)=\frac{F(z)}{Y(z)}-\varPsi (z)$$ is possibly analytic exterior to $$z=\bar{z}_{0}$$. In order to guarantee that $$D(z)$$ is bounded at $$z=\bar{z}_{0}$$, we have that $$(z-\bar{z}_{0})^{\kappa }D(z)=P_{\kappa -1}(z).$$ Thus, the general solution of Eq. (3.7) is given by formula $$F(z)=Y(z)\biggl[\varPsi (z)+\frac{P_{\kappa -1}(z)}{(z-\bar{z}_{0})^{ \kappa }}\biggr], \quad \kappa >0,$$ (3.20) and $$P_{\kappa -1}(z)=e_{0}+e_{1}z+\cdots +e_{\kappa -1}z^{\kappa -1},$$ which is a polynomial of degree $$\kappa -1$$ with arbitrary complex coefficients. If $$\kappa \leq 0$$, then $$P_{\kappa -1}(z)\equiv 0$$, in this case, (3.7) has the unique solution $$F(z)=Y(z)\varPsi (z).$$ (3.21) And when $$\kappa \leq -1$$, (3.7) is solvable if the conditions $$\int _{\mathbb{R}}\frac{\varUpsilon (t)}{Y^{+}(t)}(z-\bar{z} _{0})^{-j} \,dt=0,\quad j=1,2,\ldots ,-\kappa$$ (3.22) are also satisfied. By taking the boundary values to $$Y(z)$$ in (3.16), we have $$Y^{+}(t)=\sqrt{\varPhi _{0}(t)}e^{\varGamma (t)}, \qquad Y^{-}(t)=\frac{1}{\sqrt{ \varPhi _{0}(t)}}e^{\varGamma (t)},$$ (3.23) where $$\sqrt{\varPhi _{0}(t)}=\exp \{\frac{1}{2}\log \varPhi _{0}(t)\}$$ has definite value. By applying the Plemelj formula to (3.20), we get \begin{aligned} &F^{+}(s)=\frac{1}{2} \varUpsilon (s)+Y^{+}(s)\biggl[\varPsi (s)+\frac{Q_{k-1}(s)}{(s- \bar{z}_{0})^{k}}\biggr]; \\ &F^{-}(s)=-\frac{1}{2}\frac{\varUpsilon (s)}{ \varPhi (s)}+Y^{-}(s) \biggl[\varPsi (s)+\frac{Q_{k-1}(s)}{(s-\bar{z}_{0})^{k}}\biggr]. \end{aligned} (3.24) Therefore, the general solution of (3.7) may also be written in the following form: $$F(s)=\frac{1+ \varPhi (s)}{2 \varPhi (s)} \varUpsilon (s)+\bigl[Y^{+}(s)-Y ^{-}(s)\bigr] \biggl[\varPsi (s)+\frac{Q_{k-1}(s)}{(s-\bar{z}_{0})^{k}}\biggr].$$ (3.25) Since $$Y^{\pm }(s)$$ are bounded and nonzero on $$\mathbb{R}$$, we can prove that $$F^{\pm }(s),F(s)\in L^{2}(\mathbb{R})\cap H_{0}$$. In order to guarantee that $$F^{\pm }(s)$$, $$F(s)\in \{\{0\}\}$$, we need to consider some properties of $$F^{\pm }(s)$$, $$F(s)$$ at $$s=0$$. Now we discuss the behaviors of the solution near $$s=0$$. (1) Let $$s=0$$ be an ordinary node. Then, $$0<\delta <1$$, $$\gamma =\gamma _{0}-\kappa =\delta +i\eta _{0}\neq 0$$ and $$e^{\gamma \pi i}\neq 1$$. It is easy to verify that, in the neighborhood of $$s=0$$, $$Y^{+}(s)=\sqrt{\varPhi _{0}(s)}s^{\gamma }e^{\varGamma _{0}(s)}, \quad \varGamma _{0}(s) \in H,$$ where $$\varGamma _{0}(s)=\varGamma (s)-\gamma \ln s$$. Moreover, we can prove that, \begin{aligned} & \sqrt{\varPhi _{0}(\pm 0)}= \exp \frac{1}{2}\bigl[\pm \kappa \pi i+\log \varPhi (\pm 0)\bigr]; \\ & \sqrt{\varPhi _{0}(-0)}=e^{\gamma \pi i} \sqrt{\varPhi _{0}(+0)}. \end{aligned} (3.26) Similar to the discussion in [12, 20, 21], when $$s>0$$, we have \begin{aligned} \varPsi (s)=\frac{i \csc \gamma \pi }{2 s^{\gamma } e^{\varGamma _{0}(s)}}\biggl[e ^{-\gamma \pi i}\frac{\varUpsilon (-0)}{\sqrt{\varPhi _{0}(-0)}}-\cos \gamma \pi \frac{\varUpsilon (+0)}{\sqrt{\varPhi _{0}(+0)}}\biggr]+A(s), \end{aligned} (3.27) where $$A(s)=\frac{\varPsi ^{\ast }(s)}{\|s\|^{\delta '}}$$ ($$0<\delta '< \delta$$) and $$\varPsi ^{\ast }(s)\in H$$. We apply (3.26) to simplify (3.24) and obtain \begin{aligned} F^{+}(+0)=\frac{i \csc \gamma \pi }{2 e^{2 \gamma \pi i}}\bigl[\varUpsilon (-0)-e ^{3\gamma \pi i} \varUpsilon (+0)\bigr]. \end{aligned} (3.28) When $$s<0$$, we have \begin{aligned} \varPsi (s)=\frac{i \csc \gamma \pi }{2 s^{\gamma } e^{\varGamma _{0}(s)}}\biggl[ \cos \gamma \pi \frac{\varUpsilon (-0)}{\sqrt{\varPhi _{0}(-0)}}-e^{\gamma \pi i} \frac{\varUpsilon (+0)}{\sqrt{\varPhi _{0}(+0)}}\biggr]+A(s), \end{aligned} (3.29) and then \begin{aligned} F^{+}(-0)=\frac{i \csc \gamma \pi }{2 e^{ \gamma \pi i}}\bigl[\varUpsilon (-0)-e ^{3\gamma \pi i} \varUpsilon (+0)\bigr]. \end{aligned} (3.30) By comparing (3.28) with (3.30), we know that $$F(s)$$ is continuous at $$s=0$$ if and only if $$\varUpsilon (-0)=e^{3\gamma \pi i}\varUpsilon (+0).$$ (3.31) Therefore, we obtain $$F^{+}(0)=F^{-}(0)=0$$ (3.32) and $$F(0)=0.$$ (3.33) By (3.4), we also have $$\varOmega (0)=0$$ (3.34) and $$G(0)=0.$$ (3.35) Conversely, if (3.35) is fulfilled, then (3.32) and (3.33) are valid, and $$F^{\pm }(s), F(s) \in H$$ in the neighborhood of $$s=0$$. Therefore, we have $$F^{\pm }(s), F(s) \in \{\{0\}\}$$. In conclusion, it is necessary that $$G(0)=0$$. (2) Let $$s=0$$ be a special node. In this case, $$\delta =0$$ and $$\gamma =i\eta _{0}$$. If $$\eta _{0}=0$$, that is, $$\gamma =0$$, then $$\varPhi (s)$$ must be continuous at $$s=0$$. It follows from $$b\neq 0$$ that $$K_{1}(0)=K_{2}(0)=0$$, so $$E(0)=1$$, $$\varUpsilon (0)=0$$, and $$F(0)=0$$. Thus, $$F(s)$$ is continuous at $$s=0$$, and $$s=0$$ is not a nodal point at all. There is no boundary value problem in this case. If $$\eta _{0}\neq 0$$, then (3.27) and (3.29) remain valid. We can prove that $$A(s)\in H_{0}$$ and $$A(\pm 0)$$ exist, thus we have $$F^{+}(+0)=\frac{ i \csc \gamma \pi }{2e^{2\gamma \pi i}}\bigl[ \varUpsilon (-0)-e^{3\gamma \pi i}\varUpsilon (+0)\bigr]+ \lim_{s\rightarrow +0} \sqrt{\varPhi _{0}(+0)}e^{\varGamma _{0}(0)} s^{i\eta _{0}}\bigl[A(s)+B_{0} \bigr],$$ (3.36) where $$B_{0}=(\bar{z}_{0})^{\kappa }e_{0}$$ when $$\kappa >0$$; and $$B_{0}=0$$ when $$\kappa \leq 0$$. And a similar formula for $$F^{+}(-0)$$ can be obtained, that is, $$F^{+}(-0)=\frac{ i \csc \gamma \pi }{2e^{2\gamma \pi i}}\bigl[ \varUpsilon (-0)-e^{3\gamma \pi i}\varUpsilon (+0)\bigr]+ \lim_{s\rightarrow -0} \sqrt{\varPhi _{0}(-0)}e^{\varGamma _{0}(0)} s^{i\eta _{0}}\bigl[A(s)+B_{0} \bigr].$$ (3.37) In order that $$F^{+}(\pm 0)$$ exist, we should have $$A(\pm 0)= \textstyle\begin{cases} (\bar{z}_{0})^{\kappa }e_{0}, & \kappa >0; \\ 0, &\kappa \leq 0. \end{cases}$$ By (3.28), (3.30) and (3.31), we get (3.35) again. Once (3.35) is fulfilled, then $$\varUpsilon (0)=0$$ and $$\varPsi (s)\in H$$ near $$s=0$$. Since we require $$F^{+}(s)$$ is continuous at $$s=0$$, thus, when $$\kappa > 0$$, the constant term $$e_{0}$$ of $$P_{\kappa -1}(z)$$ should take the value \begin{aligned} e_{0}= \frac{(-1)^{\kappa -1}(\bar{z}_{0})^{\kappa }}{2\pi i} \int _{\mathbb{R}}\frac{\varUpsilon (t)}{Y^{+}(t)t}\,dt; \end{aligned} (3.38) and when $$\kappa \leq 0$$, the following condition of solvability must be satisfied: $$\int _{\mathbb{R}}\frac{\varUpsilon (t)}{Y^{+}(t)t}\,dt=0.$$ (3.39) Once (3.38) and (3.39) are fulfilled, we can readily verify $$F^{\pm }(0)=F(0)=0$$. In all of the above cases, it is easy to see that $$F^{\pm }(s), F(s) \in \{\{0\}\}$$. Moreover, we have the following results. ### Theorem 3.1 Assume that (3.5) and (3.35) are fulfilled. 1. (1) Let$$s=0$$be an ordinary node, when$$\kappa \geq 0$$, (3.1) always has a solution; when$$\kappa <0$$, provided that (3.22) are fulfilled, (3.1) has the unique solution (3.21). 2. (2) Let$$s=0$$be a special node, when$$K_{1}(0)=K_{2}(0)$$, the results obtained in (1) remain true; when$$K_{1}(0)\neq K_{2}(0)$$, if$$\kappa > 0$$and (3.38) is fulfilled, (3.1) has a solution; if$$\kappa \leq 0$$, when (3.22) and (3.39) are fulfilled, (3.1) is solvable. Under the above suppositions, Eq. (3.1) is solvable in class $$\{0\}$$ and has the solution $$\omega (t)=\mathbb{F}^{-1}\varOmega (s)$$, where $$\varOmega (s)$$ is given by (3.6). Obviously, $$F(s) \in \{\{0\}\}$$ and so $$\omega (t)\in \{0\}$$. ### Remark 3.1 In Eq. (3.1), if $$k_{j}\in \{0\}$$ ($$j=1,2$$), $$g\in (0)$$, then $$\omega \in (0)$$; if $$k_{j},g\in \langle0\rangle$$ ($$j=1,2$$), then $$\omega \in \langle0\rangle$$. Similarly, we can also obtain that, if $$k_{j}, g \in (0)^{\rho }$$ ($$j=1,2$$), then $$\omega \in (0)^{\rho }$$, and if $$k_{j},g\in \langle0\rangle ^{\rho }$$ ($$j=1,2$$), then $$\omega \in \langle0\rangle ^{\rho }$$, provided $$0<\rho <1$$. ## 4 Equation of Wiener–Hopf type In this section, we discuss method of solution for the following SIE of Wiener–Hopf type: $$a\omega (t)+\frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t-\tau ) \omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R^{+}},$$ (4.1) where a, b are as the above, $$k(t),g(t)\in (0)^{\rho }$$ ($$\frac{1}{2}< \rho <1$$) and $$\omega (t)$$ is required to be in $$\{0\}$$. Extending t in (4.1) to $$t \in \mathbb{R}$$, the right-hand side of (4.1) is augmented with an unknown function $$-\omega _{-}(t)$$. Rewrite (4.1) as $$a\omega _{+}(t)+\frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega _{+}( \tau )}{\tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t- \tau )\omega _{+}(\tau )\,d\tau =g(t)- \omega _{-}(t),\quad t\in \mathbb{R}.$$ (4.2) Taking Fourier transformations on both sides of (4.2), we get by Lemma 2.2 $$a \varOmega ^{+}(s)-b\operatorname{sgn}s \varOmega ^{+}(s)+K(s)\varOmega ^{+}(s)=G(s)+ \varOmega ^{-}(s),$$ (4.3) that is, $$\varOmega ^{+}(s)=\varPhi (s)\varOmega ^{-}(s)+W(s),$$ (4.4) where $$\varPhi (s)=\frac{1}{a-b\operatorname{sgn}s+K(s)},\qquad W(s)= \frac{G(s)}{a-b\operatorname{sgn}s+K(s)}.$$ (4.5) Note that $$\varOmega ^{\pm }(s)$$, $$G(s)$$ belong to class $$\{\{0\}\}$$ on $$\mathbb{R}$$. Here we only consider the case of normal type, that is, $$K(s)\neq \textstyle\begin{cases} - (a-b), & 0< s < +\infty , \\ - (a+b), & -\infty < s < 0. \end{cases}$$ (4.6) Denote \begin{aligned}[b] &\frac{1}{2\pi i}\bigl\{ \log \varPhi (+\infty )-\log {\varPhi (-\infty )}\bigr\} \\ &\quad =\frac{1}{2\pi i}\bigl\{ \log (a-b)-\log (a+b)\bigr\} \\ &\quad = \delta _{\infty }+i\eta _{\infty }=\gamma _{\infty }, \end{aligned} (4.7) where $$\log \varPhi (s)$$ is taken to be continuous branch for $$s>0$$ and $$s<0$$ respectively such that it is continuous at $$s=\infty$$, and $$0\leq \delta _{\infty }<1$$. Since $$b\neq 0$$, thus $$\gamma _{\infty } \neq 0$$. We again denote $$\frac{1}{2\pi i}\bigl\{ \log \varPhi (+0)-\log {\varPhi (-0)} \bigr\} = \delta _{0}+i\eta _{0}=\gamma _{0}.$$ (4.8) Then we choose an integer κ, the index of (4.4), such that $$0\leq \delta =\delta _{0}-\kappa <1$$. Denote $$\gamma =\gamma _{0}- \kappa =\delta +i\eta _{0}$$. Note that $$\varOmega ^{+}(\infty )=0$$, then we also have $$\varOmega ^{-}(\infty )=\varOmega (\infty )=0$$. Therefore, it is necessary that $$\varOmega (\infty )=0$$. Since $$b\neq 0$$, we get $$\gamma \neq 0$$. It is seen from the above discussion that both $$s=0$$ and $$s=\infty$$ are nodes of (4.4). Similar to the discussion in [17, 22, 23] and Sect. 3, we can obtain the general solution of (4.4) $$\varOmega (z)=Y(z)\biggl[M(z)+\frac{P_{\kappa -1}(z)}{(z-\bar{z}_{0})^{ \kappa }}\biggr],$$ (4.9) where $$M(z)=\frac{1}{2\pi i} \int _{\mathbb{R}}\frac{z-\bar{z}_{0}}{t- \bar{z}_{0}}\frac{W(t)}{Y^{+}(t)(t-z)}\,dt, \quad z \,\bar{\in }\,\mathbb{R},$$ (4.10) when $$\kappa >0$$, $$P_{\kappa -1}(z)=e_{0}+e_{1}z+\cdots +e_{\kappa -1}z ^{\kappa -1}$$ is an arbitrary polynomial of degree $$\kappa -1$$, and $$Y(z)$$, $$z_{0}$$ are still given by (3.16); when $$\kappa \leq 0$$, $$P_{\kappa -1}(z)\equiv 0$$, and the following conditions of solvability must be fulfilled: $$\int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t-\bar{z}_{0})^{j}}\,dt=0, \quad j=1,2,\ldots ,-\kappa +1.$$ (4.11) Note that, in (4.10), since $$k,g \in (0)$$, then $$W(\infty )=0$$, by [12] we get $$M(s)=\frac{M_{\ast }(s)}{ \vert s \vert ^{\delta '}}, \quad 0< \delta '< \delta ,$$ where $$M_{\ast }(s)\in H$$. Therefore, a factor $$\frac{z-\bar{z}_{0}}{t- \bar{z}_{0}}$$ should be multiplied in the integrand of (4.10). And we also have $$Y^{-}(s)=\frac{\xi (s)}{s^{\gamma _{\infty }}}$$, here $$\xi (s)\in H_{2}$$. Taking the boundary values for $$\varOmega (z)$$ in (4.9), we have $$\varOmega ^{+}(s)=\frac{1}{2} W(s)+Y^{+}(s) \biggl[M(s)+\frac{P_{ \kappa -1}(s)}{(s-\bar{z}_{0})^{\kappa }}\biggr]$$ (4.12) and $$\varOmega ^{-}(s)=-\frac{1}{2} \frac{W(s)}{E(s)}+Y^{-}(s)\biggl[M(s)+\frac{P _{k-1}(s)}{(s-\bar{z}_{0})^{k}}\biggr].$$ (4.13) In the following, we consider some properties of the solutions at nodes. First, we consider the situation near $$s=\infty$$. 1. (1) Let $$s=\infty$$ be an ordinary node, we have the following two cases. 1. (a) When $$0\leq \delta _{\infty }\leq \frac{1}{2}$$, we easily find that $$W(s)[Y(s)]^{-1}$$$$\in H_{2}$$ since $$W(s)\in H_{2}$$. In order to guarantee that $$\varOmega (s)\in \{\{0\}\}$$, when $$\kappa \geq 0$$, the constant term $$e_{0}$$ of $$P_{\kappa -1}(z)$$ should take the value $$e_{0}=-\frac{1}{2 \pi i} \int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t- \bar{z}_{0})}\,dt;$$ (4.14) and when $$\kappa < 0$$, we have the following conditions of solvability: $$\int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)t(t-\bar{z}_{0})^{j}}\,dt=0, \quad j=1,2,\ldots, {-}\kappa .$$ (4.15) 2. (b) When $$\frac{1}{2}<\delta _{\infty }<1$$, if $$\rho \leq \delta _{ \infty }$$, by [20] we have $$Y(s)M(s)=O\bigl( \vert s \vert ^{-\delta _{\infty }+\varepsilon }\bigr),$$ where $$\varepsilon >0$$ is arbitrarily small such that $$\delta _{\infty }-\varepsilon >\frac{1}{2}$$; if $$\rho >\delta _{\infty }$$, then $$M(s)$$ is bounded and so $$Y(s)M(s)=O\bigl( \vert s \vert ^{-\delta _{\infty }}\bigr)$$ near $$s=\infty$$. Thus we also obtain $$\varOmega ^{\pm }(s) \in H_{2}$$ and so $$\varOmega (s)\in H_{2}$$. In conclusion, in any case, we have $$F(s)=O(\|s\|^{-\mu })$$, where $$\mu =\min \{\rho , \delta _{\infty }- \varepsilon \}$$, obviously, $$\mu >\frac{1}{2}$$. 2. (2) Let $$s=\infty$$ be a special node, then $$\delta _{\infty }=0$$ and $$\gamma _{\infty }=i\eta _{\infty }\neq 0$$. In this case, the discussion is the same as that in (1), and we can obtain $$\varOmega (s)\in H$$ and $$\varOmega (s)\in H_{2}$$. Next, we consider the behavior of the solution near $$s=0$$. Since $$\varOmega (s)$$ is continuous at $$s=0$$, similar to the discussion in Sect. 3, we may get $$W(+0)=e^{-3\gamma \pi i}W(-0)$$. From (4.5), we have $$W(\pm 0)=G(0)\varPhi (\pm 0)$$. Therefore, we can obtain $$G(0)\bigl[\varPhi (-0)-e^{3\gamma \pi i}\varPhi (+0)\bigr]=0.$$ (4.16) Note that $$\varPhi (+0)=e^{2\gamma _{0} \pi i}\varPhi (-0)$$ and $$\gamma = \gamma _{0}-\kappa \neq 0$$, so $$\varPhi (-0)-e^{3\gamma \pi i}\varPhi (+0)=\varPhi (-0) \bigl(1-e^{5 \gamma _{0} \pi i}\bigr)\neq 0,$$ (4.17) and by (4.16) and (4.17), we get $$G(0)=0$$ again. Moreover, in the case $$\delta _{\infty }>\frac{1}{2}$$, when $$\kappa \geq 0$$, for the constant term $$e_{0}$$ of $$P_{\kappa -1}(s)$$ must be taken the value $$e_{0}=\frac{(-1)^{\kappa }(\bar{z}_{0})^{\kappa +1}}{2 \pi i} \int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t-\bar{z}_{0})t}\,dt;$$ (4.18) when $$\kappa \leq -1$$, there is the following condition of solvability: $$\int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t-\bar{z}_{0})t}\,dt=0.$$ (4.19) It is seen from the above discussions that $$\varOmega (0)=0$$, $$\varOmega (s) \in \{\{0\}\}$$. In fact, when $$\delta _{\infty }>\frac{1}{2}$$, we can get $$\varOmega (s)\in ((0))$$ and hence $$\omega (t)\in (0)$$. Now we can formulate the main results about the solutions of Eq. (4.1) in following form. ### Theorem 4.1 Under condition (4.6), the necessary condition of the existence of solution to Eq. (4.1) is$$G(0)=0$$in class$$\{0\}$$. 1. (1) Let$$s=0$$be a node, if$$\frac{1}{2}<\delta _{\infty }<1$$, when$$\kappa \geq 0$$, (4.1) always has a solution, and the constant term of$$P_{\kappa -1}(s)$$takes value as (4.18); and when$$\kappa <0$$, (4.11) and (4.19) should be supplemented, then Eq. (4.1) has a solution. If$$0\leq \delta _{\infty }\leq \frac{1}{2}$$, when$$\kappa \geq 0$$, the constant term of$$P_{\kappa -1}(s)$$should be taken as (3.34); when$$\kappa <0$$, the conditions of solvability (3.22) and (3.35) are fulfilled. 2. (2) Let$$s=\infty$$be a node, if$$\frac{1}{2}<\delta _{\infty }<1$$, when$$\kappa \geq 0$$, (4.1) has a solution; when$$\kappa <0$$, provided that (4.11) are satisfied, (4.1) is solvable. If$$0\leq \delta _{ \infty }\leq \frac{1}{2}$$, when$$\kappa \geq 0$$, (4.1) has the solution; when$$\kappa <0$$, the conditions of solvability (4.15) must be augmented. Assume that the above (1) and (2) are fulfilled, then (4.1) has the following general solution: $$\omega ^{+}(t)=\mathbb{F}^{-1}\varOmega ^{+}(s),$$ where $$\varOmega ^{+}(s)$$ is given by (4.12). ### Remark 4.1 We should note that $$M(z)$$ cannot be separated as, in general, \begin{aligned} M(z)=\frac{1}{2\pi i} \int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t-z)}\,dt-\frac{1}{2 \pi i} \int _{\mathbb{R}}\frac{W(t)}{Y^{+}(t)(t-\bar{z}_{0})}\,dt, \end{aligned} (4.20) because two integrals in (4.20) may be divergent. But, in case (1) of Theorem 4.1, when $$\delta _{\infty }\leq \frac{1}{2}$$, (4.20) becomes valid, and the integrals in (4.20) are convergent now. In this case, we also have $$Y(s)\varPsi (s)\in H_{2}$$. ### Remark 4.2 In Eq. (4.1), if $$a\neq 0$$ is real, b is purely imaginary, and $$k_{1}(t)$$, $$k_{2}(t)$$ are real functions, then (4.1) is a real equation. In this case, $$s=0$$ is an ordinary node of (4.1). It is also easily seen that the characteristic feature is for $$\delta _{\infty }>\frac{1}{2}$$ or $$\delta _{\infty }\leq \frac{1}{2}$$. By (4.7), when $$\delta _{\infty }>\frac{1}{2}$$, we have $$\pi < \arg (a+b)-\arg (a-b)< 2\pi ,$$ then, $$a+b$$ lies in the quadrant 2 or 4; when $$\delta _{\infty }< \frac{1}{2}$$, $$0< \arg (a+b)-\arg (a-b)< \pi ,$$ and $$a+b$$ lies in the quadrant 1 or 3. ## 5 Equations with two convolution kernels The above method is applicable to solving the SIEs with two convolution kernels \begin{aligned}[b] &a\omega (t)+ \frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}^{+}}k_{1}(t- \tau )\omega (\tau )\,d\tau \\ &\quad +\frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R} ^{-}}k_{2}(t-\tau )\omega (\tau )\,d\tau=g(t), \quad t\in \mathbb{R}, \end{aligned} (5.1) where a, b are as the above, $$k_{1}, k_{2}, g \in \langle0\rangle$$ and the unknown function $$\omega \in \{0\}$$. Taking the Fourier transform on both sides of (5.1), we obtain $$(a-b\operatorname{sgn}s)\varOmega (s)+K_{1}(s)\varOmega ^{+}(s)-K_{2}(s)\varOmega ^{-}(s)=G(s),$$ (5.2) where $$\varOmega ^{\pm }(s)$$ are respectively the Fourier transforms of $$\omega _{\pm }(t)$$. In fact, $$\varOmega ^{\pm }(s)$$ also are the boundary values of the holomorphic function $$\varOmega (z)=\frac{1}{\sqrt{2\pi }} \int _{\mathbb{R}}\omega (t) e^{itz}\,dt$$ (5.3) in the upper and the lower half planes, respectively. In order to guarantee that $$\varOmega ^{\pm }(s)$$, $$\varOmega (s)$$ are continues at $$s=0$$, it is necessary that $$\varOmega (0)=0$$, that is, $$\varOmega ^{+}(0)=\varOmega ^{-}(0)$$. Restricted to the case of normal type, i.e., $$K(s)$$ satisfying (4.6). From (5.2), we get the following Riemann–Hilbert problem: $$\varOmega ^{+}(s)=\varPhi (s)\varOmega ^{-}(s)+W(s), \quad s\in \mathbb{R},$$ (5.4) in which we have put $$\varPhi (s)=\frac{a-b\operatorname{sgn}s+K_{2}(s)}{a-b\operatorname{sgn}s+K_{1}(s)},\qquad W(s)=\frac{G(s)}{a-b\operatorname{sgn}s+K _{1}(s)}.$$ (5.5) Similarly, we easily verify that $$s=\infty$$ is not a nodal point of (5.4), and $$s=0$$ is its unique nodal point. The solution of (5.4) be discussed by using the same method as shown in Sect. 3. The remaining discussions will be omitted also. ## 6 Equations with one convolution kernel Finally, we solve SIEs with one convolution kernel \begin{aligned} a\omega (t)+ \frac{b}{\pi i} \int _{\mathbb{R}}\frac{\omega (\tau )}{ \tau -t}\,d\tau + \frac{1}{\sqrt{2 \pi }} \int _{\mathbb{R}}k(t-\tau ) \omega (\tau )\,d\tau =g(t),\quad t\in \mathbb{R}, \end{aligned} (6.1) where a, b are as the above, $$k, g\in \{0\}$$ and the unknown function $$\omega \in \{0\}$$. Taking Fourier transforms on both sides of (6.1), we get by Lemma 2.2 $$a\varOmega (s)-b\operatorname{sgn}s \varOmega (s)+K(s)\varOmega (s)=G(s).$$ (6.2) Note that (6.2) is not a Riemann–Hilbert problem. Without loss of generality, we only discuss the function $$a-b\operatorname{sgn}s+K(s)\neq 0$$ ($$s \in \mathbb{R}$$). From (6.2) we get $$\varOmega (s)=\frac{G(s)}{a-b\operatorname{sgn}s+K(s)}.$$ (6.3) Since $$G(s)$$ is continuous at $$s=0$$ and $$G(0)=0,$$ (6.4) thus $$G(s)\in \{\{0\}\}$$. Note that $$a-b\operatorname{sgn}s+K(s)$$ is bounded and non-zero on $$\mathbb{R}$$, we get $$\varOmega (s)\in \{\{0\}\}$$ and hence $$\omega (t)=\mathbb{F}^{-1}\varOmega (s)$$ is the solution of (6.1) in $$\{0\}$$. Thus, we obtain the following conclusions. ### Theorem 6.1 If$$k(t),g(t)\in \{0\}$$, in the case of normal type, that is, (4.6) is valid, then (6.1) is solvable if and only if (6.4) is satisfied. Assume that this is fulfilled, (6.1) has a solution $$\omega (t)=\mathbb{F}^{-1}\varOmega (s)$$ in$$\{0\}$$, where$$\varOmega (s)$$is given by (6.3). After simplification, $$\omega (t)$$ may be written as \begin{aligned} \omega (t)=q(t)-p\ast q(t), \end{aligned} (6.5) where $$p(t)=\mathbb{F}^{-1}P(s)$$, $$q(t)=\mathbb{F}^{-1}Q(s)$$, in which $$P(s)=\frac{K(s)}{a-b\operatorname{sgn}s+K(s)}, \qquad Q(s)=\frac{G(s)}{a-b\operatorname{sgn}s }.$$ (6.6) Noting that, although $$P(s)$$ is discontinuous at $$s=0$$, it would not influence the property $$p\ast q\in \{0\}$$ since $$G(0)=0$$. Here, we shall discuss the equations of dual type in the more general case $$\textstyle\begin{cases} a_{1}\omega (t)+b_{1}T\omega (t)+k_{1}\omega (t)=g(t),& t\in \mathbb{R}^{+}; \\ a_{2}\omega (t)+b_{2}T\omega (t)+k_{2}\omega (t)=g(t),& t\in \mathbb{R}^{-}, \end{cases}$$ (7.1) where $$a_{j}$$, $$b_{j}$$ are constants and all the functions appeared belong to $$\{0\}$$. Assume $$b_{1}$$, $$b_{2}$$ are not equal to zero simultaneously. Actually, (3.1) is a special case of (7.1). In order to solve Eq. (7.1), we rewrite (7.1) as $$\textstyle\begin{cases} a_{1}\omega (t)+b_{1}T\omega (t)+k_{1}\omega (t)=g(t)-f_{-}(t); \\ a_{2}\omega (t)+b_{2}T\omega (t)+k_{2}\omega (t)=g(t)+f_{+}(t), \end{cases}\displaystyle t\in \mathbb{R},$$ (7.2) where $$f_{\pm }(t)$$ are as the above. Taking Fourier transforms in both sides of (7.2), we obtain $$\textstyle\begin{cases} [a_{1}-b_{1}\operatorname{sgn}s+K_{1}(s)]\varOmega (s)=G(s)+F^{-}(s); \\ [a_{2}-b_{2}\operatorname{sgn}s+K_{2}(s)]\varOmega (s)=G(s)+F^{+}(s). \end{cases}$$ (7.3) In the case of normal type, that is, $$K_{j}(s)\neq \textstyle\begin{cases} - (a_{j}-b_{j}), & 0 < s < +\infty , \\ - (a_{j}+b_{j}), & -\infty < s< 0 \end{cases}$$ (7.4) for any $$j=1,2$$. By eliminating $$\varOmega (s)$$ in (7.3), it gives rise to $$F^{+}(s)=\varPhi (s)F^{-}(s)+\varUpsilon (s),\quad s\in \mathbb{R},$$ (7.5) where $$\varPhi (s)=\frac{a_{2}-b_{2}\operatorname{sgn}s+K_{2}(s)}{a_{1}-b_{1}\operatorname{sgn}s+K_{1}(s)}$$ and $$\varUpsilon (s)=\frac{[a_{2}-a_{1}-(b_{2}-b_{1})\operatorname{sgn}s+K_{2}(s)-K_{1}(s)]G(s)}{a _{1}-b_{1}\operatorname{sgn}s+K_{1}(s)}.$$ Equation (7.5) is a Riemann–Hilbert problem with discontinuous coefficients and nodes $$s=0$$, ∞, and its method of solution may be made fully analogous to those in Sect. 4. In order that $$\varOmega (s)$$ is continuous at $$s=0$$, it is necessary that $$F(s)$$ is continuous at $$s=0$$ and $$F^{\pm }(0)=-G(0)$$. Since $$F^{+}(s)$$ is continuous at $$s=0$$, we should again get $$G(0)=0$$. Hence all the results as stated in Theorem 4.1 remain true and $$\omega (t)=\mathbb{F}^{-1}\varOmega (s)$$, in which $$\varOmega (s)$$ is given by (7.3). The only difference lies in that $$\gamma _{\infty }$$ and γ may be zero, for instance, when $$a_{1}=a_{2}$$, $$b_{1}=b_{2}$$, we have $$\gamma _{\infty }=0$$, then this case may be transformed to that in Sect. 3. Here, we will not elaborate on the solving method of (7.5). ## 8 Conclusions In this paper, we study some classes of SIEs with convolution kernels and Cauchy kernels in the different classes of functions. By Fourier transform, these equations are transformed into Riemann–Hilbert problems with discontinuous coefficients. The general solutions denoted by integrals and the solvable conditions are obtained for the equations. Here, our method is different from the classical ones, and it is novel and effective. Thus, this paper generalizes the theory of the classical Riemann–Hilbert problems and SIEs. Meanwhile, we remark that the methods of this paper may be used to solving the above equations in the non-normal case. Indeed, it is possible to study the above-mentioned equation in Clifford analysis, which is similar to that in [24, 25, 26, 27, 28]. Further discussion is omitted here. ## Notes ### Acknowledgements The author is very grateful to the anonymous referees for their valuable suggestions and comments, which helped to improve the quality of the paper. This research is supported by the Science and Technology Plan Project of Qufu Normal University (xkj 201606). Not applicable. ### Authors’ contributions This entire work has been completed by the author. Analytical solutions were determined by him. The author read and approved the final manuscript. ### Funding This work was supported by the Science and Technology Plan Project of Qufu Normal University (xkj 201606). ### Competing interests The author declares to have no competing interests. ## References 1. 1. Lu, J.K.: Boundary Value Problems for Analytic Functions. World Scientific, Singapore (2004) Google Scholar 2. 2. 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Math. 181(1), 39–113 (2010)	{"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": 2, "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": 0.9978259801864624, "perplexity": 982.2846463894944}, "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-2019-09/segments/1550247484928.52/warc/CC-MAIN-20190218094308-20190218120308-00589.warc.gz"}
https://cs.stackexchange.com/questions/3295/hardness-of-counting-solutions-to-np-complete-problems-assuming-a-type-of-reduc	# Hardness of counting solutions to NP-Complete problems, assuming a type of reduction The $\text{NP-Complete}$ class of problems is defined w.r.t Karp Reductions, which are polytime many-one reductions. However, they need not necessarily preserve the number of solutions. A more restrictive type: polytime one-one reductions do indeed preserve the number of solutions. Suppose $f:\Sigma^{\ast}\to \mathbb{N}$ is a counting function in $\text{#P}$ and the decision problem $f_{ > 0}$ defined as: Is $f(x) > 0$ ? is in $NP$. Now if $f_{> 0}$ is in $\text{NP-Complete}$, can we immediately tell that $f$ is in $\text{#P-Complete}$ or, do we could only say so, if the reduction map (showing $\text{NP-Completeness}$) was one-one. • Up to my (poor :-) knowledge it is an open problem, i.e. an example of a polytime many-one reduction that cannot be made parsimonious (polytime one-one) has not been found yet. I think that further details can be found in J. Simon. On the difference between one and many – Vor Aug 23, 2012 at 9:54 • ps: we know that the reverse direction does not hold (unless strange things happens in complete theory, i.e. P=NP) since the counting version of Matching is #P-complete while the search version can be solved in polytime so decision version is in P. Aug 23, 2012 at 12:19 • @Kaveh: you are right, even "parsimonious reduction" (I used my comment above) is not correct. #P-hardness is defined using weakly parsimonious reductions (counting reductions). From Algebraic Techniques for Satisfiability Problems: "... In the constraint context, there are satisfiability problems, where the problem if a given formula has a solution at all is NP-complete, but the corresponding counting problem is not complete for #P under parsimonious reductions. ..." – Vor Aug 23, 2012 at 13:57 • @Vor, actually I am not sure that is the standard definition of #P-hardness, e.g. see Arora and Barak, definition 17.8, or #P-complete on Wikipedia. The definition in Valiant's paper is as follows: $A$ is #P-hard iff $\mathsf{FP}^A$ contains #P. The definition doesn't talk about preserving the number of solutions, however the proof of #P-completeness of #3SAT satisfies the condition. Aug 23, 2012 at 15:36 • @Kaveh: I was only trying to express that the definition of #P-hardness under counting reductions (which I found in some papers) seems stronger than the Valiant's definition of #P-hardness. – Vor Aug 23, 2012 at 23:21	{"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": 0.9015417098999023, "perplexity": 748.6181279733811}, "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/1659882571745.28/warc/CC-MAIN-20220812170436-20220812200436-00089.warc.gz"}
https://hal.archives-ouvertes.fr/hal-01779804	New interface # On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2 Abstract : Let t be an integer ≥ 3 such that t ≡ 1 mod 4. The absolute irreducibility of the polynomial ϕt(x,y)=xt+yt+1+(x+y+1)t(x+y)(x+1)(y+1) (over F2) plays an important role in the study of APN functions. We prove that this polynomial is absolutely irreducible under the assumptions that the largest odd integer which divides t − 1 is large enough and can not be written in a specific form. Keywords : Document type : Journal articles Domain : https://hal.archives-ouvertes.fr/hal-01779804 Contributor : Alicia Benson-Rumiz Connect in order to contact the contributor Submitted on : Friday, April 27, 2018 - 12:09:02 AM Last modification on : Wednesday, March 9, 2022 - 11:46:08 PM ### Citation Eric Férard. On the irreducibility of the hyperplane sections of Fermat varieties in P3 in characteristic 2. Advances in Mathematics of Communications, 2014, 8 (4), pp.497-509. ⟨10.3934/amc.2014.8.497⟩. ⟨hal-01779804⟩ 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": 0.8013668060302734, "perplexity": 1294.483948905374}, "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-2022-49/segments/1669446708010.98/warc/CC-MAIN-20221126144448-20221126174448-00633.warc.gz"}
http://wiki.forecastverification.com/doku.php?id=metrics:reliability_plot	# forecastverification.com ### Sidebar References References Verification software Miscellaneous LateX users metrics:reliability_plot # Reliability plot One desired property of probabilistic forecasts is that forecasted event probabilities $f$ coincide with observed relative frequencies $F$. This is visualized in reliability plots that plot the latter variable versus the former, $$F_i = \dfrac{\sum o\|f=i}{J_i}$$ where $F$ is the observed relative frequency, $i$ is one of eleven allowable values of the forecast $f$: $i~\in~\lbrace~0,0.1,0.2,\ldots,1~\rbrace$, $o$ is an indicator variable that is assigned a value of 1 if the event was observed and a value of 0 if the event was not observed, $f$ is the forecasted probability of event occurrence and $J_i$ is the total number of forecasts made within bin $i$ [wilks_statistical_2011].	{"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9567912220954895, "perplexity": 790.3507729244567}, "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/1656104675818.94/warc/CC-MAIN-20220706151618-20220706181618-00760.warc.gz"}
http://mathhelpforum.com/algebra/104150-finding-equation-lines.html	# Thread: Finding the equation of lines 1. ## Finding the equation of lines A bit confused on this: 1. Find the equation of the line between the points (9, -9) and (-5, -2). m=y2-y1 -2 - -9 7 = -1 --------- (over) --------- ---- ---- x2-x1 -5 - -9 -14 2 y=-1/2x+b ... How would I find b, the y-intercept then? 2. Find the equation of the line with an x-intercept of -2 and a y-intercept of 7. That's the points (-2, 0) and (0, 7), so m=y2-y1/x2-x1 again, or 7-0/0--2 = 7/2....which would be y=7/2x+b and the y-intercept is 7 so the final equation would be y=7/2x+7 ? just checking. 3. Find the equation of the line that has the same x-intercept as x-4y=3 and the same y-intercept as 2x-3y=9. x-4y=3 rearranges to x=4y+3, and to find the x-int you would substitute 0 in right for y so x=4(0)+3 or x=4+3, or x=7... so the x-intercept is 7. For the y-intercept, 2x-3y=9 you substitute 0 in for x, so 2(0)-3y=9 would be 0-3y=9 or just -3y=9... or y=-3. I guess the equation so far would be y=mx-3... but I don't know how I would find the slope at this point to finish the equation. 4. Finally... (the most important question) If A(1,2), B(-2,5) and C(3, 4), find the equation of the line perpendicular to AB and through C. I know the slope of the line perpendicular to something is the negative reciprocal... but I don't know what to do here. If I found the slope of A and B, that would be 2-5/-2-1 or -3/-3 or 1 I guess, so then would the slope of the new line be -1/2? What impact does "through C" have? The equation so far if that's right of the new line would be y=-1/2x+b... b being the y-intercept again, but I don't know what to do from this point on. Thanks for reading! My math skills aren't great... or even "good" for that matter 2. Q1 is to mashed up for me to understand. Originally Posted by ~NeonFire372~ A bit confused on this: 1. Find the equation of the line between the points (9, -9) and (-5, -2). m=y2-y1 -2 - -9 7 = -1 --------- (over) --------- ---- ---- x2-x1 -5 - -9 -14 2 y=-1/2x+b ... How would I find b, the y-intercept then? 2. Find the equation of the line with an x-intercept of -2 and a y-intercept of 7. That's the points (-2, 0) and (0, 7), so m=y2-y1/x2-x1 again, or 7-0/0--2 = 7/2....which would be y=7/2x+b and the y-intercept is 7 so the final equation would be y= (7/2) x + 7 ? just checking. Mr F says: Correct. Note the brackets .... 3. Find the equation of the line that has the same x-intercept as x-4y=3 and the same y-intercept as 2x-3y=9. x-4y=3 rearranges to x=4y+3, and to find the x-int you would substitute 0 in right for y so x=4(0)+3 or x=4+3, or x=7... so the x-intercept is 7. Mr F says: 4(0)+3 = 0 + 3 = 3. For the y-intercept, 2x-3y=9 you substitute 0 in for x, so 2(0)-3y=9 would be 0-3y=9 or just -3y=9... or y=-3. Mr F says: Correct. I guess the equation so far would be y=mx-3... but I don't know how I would find the slope at this point to finish the equation. Mr F says: Substitute (3, 0) into y = mx - 3 and solve for m. 4. Finally... (the most important question) If A(1,2), B(-2,5) and C(3, 4), find the equation of the line perpendicular to AB and through C. I know the slope of the line perpendicular to something is the negative reciprocal... but I don't know what to do here. If I found the slope of A and B, that would be 2-5/-2-1 or -3/-3 or 1 Mr F says: NO. (2 - 5)/(1 -(-2)) = -3/3 = -1. I guess, so then would the slope of the new line be -1/2? Mr F says: No. The gradient of the perpendicular is (and you should know this) the negative reciprocal of -1, that is, 1. What impact does "through C" have? The equation so far if that's right of the new line would be y=-1/2x+b... b being the y-intercept again, but I don't know what to do from this point on. Mr F says: Substitute m = 1 to get the required equation as y = x + c. Now substitute the given point (3, 4) and solve for c. Thanks for reading! My math skills aren't great... or even "good" for that matter .. 3. Sorry, I tried to write question 1 but I guess the formatting didn't work out right... It's Find the equation fo the line between the points (9, -9) and (-5, -2)... so I tried to find the slope, which is m=y2-y1/x2-x1 or -2 - -9/-5-9 or 7/-14 or -1/2... so the equation so far is y=mx+b - y=-1/2x+b, but I don't know how to find b, the y-intercept. 4. Originally Posted by ~NeonFire372~ Sorry, I tried to write question 1 but I guess the formatting didn't work out right... It's Find the equation fo the line between the points (9, -9) and (-5, -2)... so I tried to find the slope, which is m=y2-y1/x2-x1 or -2 - -9/-5-9 or 7/-14 or -1/2... so the equation so far is y=mx+b - y=-1/2x+b, but I don't know how to find b, the y-intercept. Two choices: Substitute (9, -9) into y = -(1/2) x + b and solve for b. Substitute (-5, -2) into y = -(1/2) x + b and solve for b. 5. Originally Posted by mr fantastic Two choices: Substitute (9, -9) into y = -(1/2) x + b and solve for b. Substitute (-5, -2) into y = -(1/2) x + b and solve for b. Thanks again for the help. That was so obvious but didn't come to mind for some reason. I just tried the last question you helped with (the find the equation of the line perpendicular to AB and through C one), it ended off with y=1x+b right, 1 being the slope, so I substituted it in like this: 4=1(3)+b 4=3+b 1=b The final equation being y=1x+1 Is that right? Just making sure. Thanks again! 6. Originally Posted by ~NeonFire372~ Thanks again for the help. That was so obvious but didn't come to mind for some reason. I just tried the last question you helped with (the find the equation of the line perpendicular to AB and through C one), it ended off with y=1x+b right, 1 being the slope, so I substituted it in like this: 4=1(3)+b 4=3+b 1=b The final equation being y=1x+1 Is that right? Just making sure. Thanks again! Looks OK. I'd write it as y = x + 1. 7. Thanks for all the help! Edit: My final answer for 1 is y=-1/2x - 9 is that right?	{"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": 0.8683428764343262, "perplexity": 972.9857509585374}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2016-50/segments/1480698544140.93/warc/CC-MAIN-20161202170904-00253-ip-10-31-129-80.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/summation-of-sin.163688/	# Summation of sin 1. Apr 2, 2007 ### svensl Hello, Can anyone give some hints on how to solve this: $$\sum_{n=0}^{K-1}\frac{sin(2\pi n^2\Delta)}{n}$$ It's just the n^2 that complicates things. I tried re-writing it as $$Im\sum_{n=0}^{K-1}\frac{e^{j n^2 x}}{n}$$, where $$x=2\pi \Delta$$ but I cannot solve this either. Thanks, svensl Last edited: Apr 2, 2007 2. Apr 2, 2007 ### d_leet What is delta? If it is an integer than sin(2pik) for any integer k is equal to 0. 3. Apr 2, 2007 ### svensl Delta is a number between (0, 1(. BTW, K will later be taken to infinity if that makes a difference. 4. Apr 2, 2007 ### AlphaNumeric Perhaps some well choosen function which has poles at certain places in the complex plane to give that summation as residues might be useful? Then you can use a contour integral and Jordans lemma to turn that sum into an integral along the Reals somehow? That's without putting pen to paper so I might be way off. Similar Discussions: Summation of sin	{"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": 0.9785549640655518, "perplexity": 1959.074228095367}, "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-2017-17/segments/1492917123590.89/warc/CC-MAIN-20170423031203-00008-ip-10-145-167-34.ec2.internal.warc.gz"}
https://plainmath.net/72123/i-have-the-following-samples-data	# I have the following 2 samples data 1 : 59.09 59.17 59.27 59.13 59.10 59.14 59.54 59. I have the following 2 samples data 1 : 59.09 59.17 59.27 59.13 59.10 59.14 59.54 59.90 data 2: 59.06 59.40 59.00 59.12 59.01 59.25 59.23 59.564 And I need to check whether there is differentiation regarding the mean and the variance between the 2 data samples at significance level a=0.05 I think that the first thing I need to do is to check whether the samples come from a normal distribution in order to infer whether i should proceed using parametric or non marametric tests... However using lillietest in matlab returned that both samples do not follow the normal distribution... Any ideas on how should I proceed with checking the differentiation tests ? Should I perform ttest ? Or should I proceed by using something like Wilcoxon ? (p.s please confirm that that both data samples do not follow normal distribution...) You can still ask an expert for help • Questions are typically answered in as fast as 30 minutes Solve your problem for the price of one coffee • Math expert for every subject • Pay only if we can solve it Raiden Williamson For a t-test, you need the samples to follow a normal distribution, so you're right to check this assumption first. I did a Shapiro-Wilk to test the normality, and it is rejected for the first sample, but it is not for the second sample. Thus you can't use a t-test. The alternative is to use the Wilcoxon test, which is non-parametric. Here is the code I have used with R : data1 <- c(59.09, 59.17, 59.27, 59.13, 59.1, 59.14, 59.54, 59.9) data2 <- c(59.06, 59.4, 59, 59.12, 59.01, 59.25, 59.23, 59.564) shapiro.test(data1) # P-value = 0.007987. Normality is rejected. shapiro.test(data2) # P-value = 0.3873. Normality is not rejected. wilcox.test(data1, data2) # P-value = 0.5054. No significative difference.	{"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": 0.8070361614227295, "perplexity": 698.2480942619753}, "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/1652662545548.56/warc/CC-MAIN-20220522125835-20220522155835-00401.warc.gz"}
http://www.gradesaver.com/textbooks/math/calculus/calculus-10th-edition/chapter-3-differentiation-3-2-exercises-page-174/15	## Calculus 10th Edition Rolle's Theorem can be applied; $c=\sqrt{5}-2.$ While $f(x)$ is not continuous at $x=-2$, the specified interval does not include $x=-2$ and hence $f(x)$ is continuous for all the values of $x$ in the closed interval and differentiable at every value of $x$ in the open interval. $f(-1)=f(3)=0.$ Since $f(x)$ is continuous over $[-1 ,3 ]$ and differentiable over $(-1, 3)$, applying Rolle's Theorem over the interval $[-1, 3]$ guarantees the existence of at least one value $c$ such that $-1\lt c\lt3$ and $f'(c)=0.$ Using the quotient rule: $f’(x)=(\frac{u(x)}{v(x)})'=\frac{u'(x)v(x)-v'(x)u(x)}{(v(x))^2}$ $u(x)=x^2-2x-3; u'(x)=2x-2$ $v(x)=x+2; v'(x)=1$ $f'(x)=\dfrac{(2x-2)(x+2)-(x^2-2x-3)(1)}{(x+2)^2}=\dfrac{x^2+4x-1}{(x+2)^2}$ $f'(x)=0\to \dfrac{x^2+4x-1}{(x+2)^2}=0\to x^2+4x-1=0\to$ Using the Quadratic equation, we get $c=\sqrt{5}-2$ or $c=-\sqrt{5}-2$ (which is rejected since $c\gt-1$)	{"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": 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": 0.9936065673828125, "perplexity": 55.20741745591952}, "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-2018-17/segments/1524125937780.9/warc/CC-MAIN-20180420120351-20180420140351-00492.warc.gz"}
http://www.ck12.org/algebra/One-Step-Equations-and-Inverse-Operations/lesson/Equations-with-Variables-on-One-Side-Honors/r10/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> You are viewing an older version of this Concept. Go to the latest version. # One-Step Equations and Inverse Operations ## Add and subtract like terms as a step to solve equations. 0% Progress Practice One-Step Equations and Inverse Operations Progress 0% Equations with Variables on One Side Erin, Jillian, Stephanie and Jacob went to the movies. The total bill for the tickets and snacks came to $72.00. What is an equation that represents this situation? How much should each teen pay to split the bill evenly? ### Watch This ### Guidance When solving any equation, your job is to find the value for the letter that makes the equation true. Solving equations with variables on one side can be done with the help of models such as a balance or algebra tiles. When solving equations with variables on one side of the equation there is one main rule to follow: whatever you do to one side of the equals sign you must do the same to the other side of the equals sign. For example, if you add a number to the left side of an equals sign, you must add the same number to the right side of the equals sign. #### Example A Solution: The problem can be solved if you think about the problem in terms of a balance. You know that the two sides are equal so the balance has to stay horizontal. You can place each side of the equation on each side of the balance. In order to solve the equation, you have to get the variable all by itself. Always remember that you need to keep the balance horizontal. This means that whatever you do to one side of the equation, you have to do to the other side. First subtract 2 from both sides to get rid of the 2 on the left. Since 5 is multiplied by , you can get by itself (or isolate it) by dividing by 5. Remember that whatever you do to one side, you have to do to the other. If you simplify this expression, you get: Therefore . You can check your answer to see if you are correct by substituting your answer back into the original equation. #### Example B Solution: Again, you can solve the problem if you think about the problem in terms of a balance (or a seesaw). You know that the two sides are equal so the balance has to stay horizontal. You can place each side of the equation on each side of the balance. In order to solve the equation, you have to get the variable all by itself. Always remember that you need to keep the balance horizontal. This means that whatever you do to one side of the equation, you have to do to the other side. First add 7 from both sides to get rid of the 7 on the left. Since 7 is multiplied by , you can get by itself (or isolate it) by dividing by 7. Remember that whatever you do to one side, you have to do to the other. If you simplify this expression, you get: Therefore . You can check your answer to see if you are correct. #### Example C This same method can be extended by using algebra tiles. If you let rectangular tiles represent the variable, square tiles represent one unit, green tiles represent positives numbers, and white tiles represent the negative numbers, you can solve the equations using an alternate method. The green algebra tiles represent variables; therefore, there are 3 blocks for the equation. The other green blocks represent the numbers or constants. There is a 2 on the left side of the equation so there are 2 square green blocks. There is an 11 on the right side of the equation so there are 11 square green blocks on the right side of the equation. Solution: To solve, add two negative tiles to the right and left hand sides. The same rule applies to this problem as to all of the previous problems. Whatever you do to one side you have to do to the other. This leaves us with the following: You can reorganize these to look like the following: Organizing the remaining algebra tiles allows us to realize the answer to be or for your example . Let’s do your check as with the previous two problems. #### Concept Problem Revisited There are four teens going to the movies (Erin, Jillian, Stephanie, and Jacob). The total bill was$72.00. Therefore your equation is . you divide by 4 to find your answer. Therefore each teen will have to pay \$18.00 for their movie ticket and snack. ### Vocabulary Constant A constant is a numerical coefficient. For example in the equation , the 72 is a constant. Equation An equation is a mathematical statement with expressions separated by an equals sign. Numerical Coefficient In mathematical equations, the numerical coefficients are the numbers associated with the variables. For example, with the expression , 4 is the numerical coefficient and is the variable. Variable A variable is an unknown quantity in a mathematical expression. It is represented by a letter. It is sometimes referred to as the literal coefficient. ### Guided Practice 1. Use a model to solve for the variable in the equation . 2. Use a different model to solve for the variable in the equation . 3. Solve for in the equation . Answers: 1. Therefore, . 2. First you have to subtract 9 from both sides of the equation in order to start to isolate the variable. Now, in order to get all by itself, you have to divide both sides by 3. This will isolate the variable . Therefore, . 3. You can use any method to solve this equation. Remember to isolate the variable. You will notice here that there are two values on the left. First let’s combine these terms. Now you can use any method to solve the equation. You now should just have to subtract 16 from both sides to isolate the variable. ### Practice Use the models that you have learned to solve for the variables in the following problems. For each of the following models, write a problem involving an equation with a variable on one side of the equation expressed by the model and then solve for the variable. 1. . 1. . 1. . 1. . 1. . ### Vocabulary Language: English constant constant A constant is a value that does not change. In Algebra, this is a number such as 3, 12, 342, etc., as opposed to a variable such as x, y or a. Equation Equation An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs. Numerical Coefficient Numerical Coefficient In mathematical expressions, the numerical coefficients are the numbers associated with the variables. For example, in the expression $4x$, 4 is the numerical coefficient and $x$ is the variable. Variable Variable A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n. Please wait... Please wait...	{"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": 2, "texerror": 0, "math_score": 0.8137242197990417, "perplexity": 617.8040101926317}, "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-2015-48/segments/1448398449258.99/warc/CC-MAIN-20151124205409-00283-ip-10-71-132-137.ec2.internal.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/a-heat-engine-working-between-2800oc-and-4900oc-takes-in-1226107-j-of-heat-and-delivers-27-q3413694	## Maximum efficiency of a gas engine A heat engine working between 280.0oC and 490.0oC, takes in 1.226×107 J of heat and delivers 2.700×106 J of work per cycle. What is its efficiency? What is the maximum possible efficiency of an engine working between these two temperatures?	{"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": 0.8745386600494385, "perplexity": 1559.1182490057804}, "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-2013-20/segments/1368701281163/warc/CC-MAIN-20130516104801-00052-ip-10-60-113-184.ec2.internal.warc.gz"}
http://www.mathdoubts.com/logarithm/identities/change-of-base/division/	# Change of Base Rule of Logarithm in Division form ## Formula $\log_{b} m = \dfrac{\log_{a} m}{\log_{a} b}$ ### Proof $m$ and $a$ are two literals and the logarithm of $m$ to base $a$ is expressed in logarithmic form as $\log_{a} m$. As per the base change rule of the logarithm in product form, the logarithm of $m$ to base $a$ can be expressed in product form by considering another literal number $b$. $\log_{a} m = \log_{b} m \times \log_{a} b$ $\implies \log_{b} m \times \log_{a} b = \log_{a} m$ $\therefore \,\,\,\,\,\, \log_{b} m = \dfrac{\log_{a} m}{\log_{a} b}$ The logarithm of $m$ to base $b$ can be expressed in division form by considering $a$ as a common base to both logarithmic functions. It is called as the change of base law of logarithm in division form. #### Common Logarithmic form The literal $a$ can be any number. So, it can be a number $10$ to express the logarithmic functions as the common logarithms in the ratio. $\implies \log_{b} m = \dfrac{\log_{10} m}{\log_{10} b}$ $\therefore \,\,\,\,\,\, \log_{b} m = \dfrac{\log m}{\log b}$ ##### Verification For example, the logarithm of $27$ to base $3$ is $3$ in logarithmic system. $\log_{3} 27 = 3$ Now, calculate logarithm of $27$ and logarithm of $3$ by taking any number as a common base. In this example, common logarithmic system is used by taking number $10$ as base to both logarithmic terms. $\log_{10} 27 = 1.43236$ $\log_{10} 3 = 0.47712$ Now, calculate the quotient of log of $27$ by log of $3$. $\dfrac{\log_{10} 27}{\log_{10} 3} = \dfrac{1.43236}{0.47712}$ $\implies \dfrac{\log_{10} 27}{\log_{10} 3} = 3$ The quotient of them is $3$. $\therefore \,\,\,\,\,\, \log_{3} 27 = \dfrac{\log_{10} 27}{\log_{10} 3} = 3$ Therefore, the example has successfully verified the change base logarithmic law in division form.	{"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": 0.9700207114219666, "perplexity": 404.2126195213836}, "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-2018-13/segments/1521257647681.81/warc/CC-MAIN-20180321180325-20180321200325-00273.warc.gz"}
https://cse.iith.ac.in/?q=node/579	Invited Talk by Dr. R Inkulu on A polynomial time algorithm for finding an approximate shortest path amid weighted regions Title: A polynomial time algorithm for finding an approximate shortest path amid weighted regions SpeakerDr. R Inkulu, IIT Guwahati Host Faculty: Dr. Subrahmanyam Kalyanasundaram Room No: Room 317 in academic block A. Time: 11:00 Abstract: This talk is on a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated with each triangle, and two points s and t that belong to P are given as the input. The objective is to find a path whose cost is at most (1 + \epsilon)OPT, where OPT is the cost of an optimal path between s and t. The proposed result is about a cubic factor (in n) improvement over the Mitchell and Papadimitriou ’91 result, which is the only known polynomial time algorithm for this problem to date; for these twenty five years, several pseuo-polynomial time algorithms were proposed. Our algorithm progresses a discretized-Dijkstra wavefront in controlled fashion from source s to achieve this improvement. Further, with polynomial time preprocessing of P, a map is computed which allows answering single-source approximate weighted shortest path queries in polynomial time. (This is Dr. Inkulu's joint work with Prof. Sanjiv Kapoor, and is under review.) Speaker's Bio: Dr. Inkulu is an Associate Professor in the department of Computer Science & Engineering at IIT Guwahati. After doing a Masters at IIT Kharagpur, Dr. Inkulu worked for 6+ years in software industry (1.5 years in India and 4.5+ years in USA) prior to joining for PhD at IIT Chicago. After graduating with PhD, he worked as a postdoc at UT-Austin for 2+ years. Thereafter he joined IIT Guwahati. The research interests of Inkulu are in designing (approximation) algorithms to optimization problems in computational geometry. Dates: Monday, December 4, 2017 - 11:00	{"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": 0.8184802532196045, "perplexity": 1970.4495570300903}, "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-2018-17/segments/1524125937440.13/warc/CC-MAIN-20180420100911-20180420120911-00294.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/w-5900-cm-wide-diffraction-grating-200-grooves-used-resolve-two-closely-spaced-lines-doubl-q2433231	A w = 5.900-cm wide diffraction grating with 200 grooves is used to resolve two closely spaced lines (a doublet) in a spectrum. The doublet consists of two wavelengths, λa = 645.7 nm and 645.9 nm. The light illuminates the entire grating at normal incidence. a) Calculate to five significant digits the angle θla and θlb with respect to the normal at which the first-order diffracted beams for the two wavelengths, λa and λb, respectively, will be reflected from the grating. Note that this is not 0°! b) What order of diffraction is required to resolve these two lines using this grating? ### No answer yet. Submit this question to the community. Practice with similar questions University Physics (Standard Version, Chapters 1-35) (2nd Edition) Q: A 5.000-cm-wide diffraction grating with 200 grooves is used to resolve two closely spaced lines (a doublet) in a spectrum. The doublet consists of two wavelengths, λa = 629.8 nm and λb = 630.2 nm. The light illuminates the entire grating at normal incidence. Calculate to four significant digitsthe angles θ1a and θ1b with respect to the normal at which the first-order diffracted beams for the two wavelengths, λa and λb, respectively, will be reflected from the grating. Note that this is not 0°! What order of diffraction is required to resolve these two lines using this grating?	{"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": 0.856074869632721, "perplexity": 2081.138018190996}, "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/1469257826908.63/warc/CC-MAIN-20160723071026-00248-ip-10-185-27-174.ec2.internal.warc.gz"}
https://www.groundai.com/project/icecube-bounds-on-sterile-neutrinos-above-10-ev/	IceCube bounds on sterile neutrinos above 10 eV # IceCube bounds on sterile neutrinos above 10 eV Mattias Blennow Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco E-28049 Madrid, Spain Department of Physics, School of Engineering Sciences, KTH Royal Institute of Technology, AlbaNova University Center, 106 91 Stockholm, Sweden Enrique Fernandez-Martinez Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco E-28049 Madrid, Spain Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco E-28049 Madrid, Spain Julia Gehrlein Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco E-28049 Madrid, Spain Departamento de Física Teórica, Universidad Autónoma de Madrid, Cantoblanco E-28049 Madrid, Spain Josu Hernandez-Garcia SISSA/INFN - Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy Jordi Salvado Institut de Ciències del Cosmos, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain ###### Abstract We study the capabilities of IceCube to search for sterile neutrinos with masses above 10 eV by analyzing its disappearance atmospheric neutrino sample. We find that IceCube is not only sensitive to the mixing of sterile neutrinos to muon neutrinos, but also to the more elusive mixing with tau neutrinos through matter effects. The currently released 1-year data shows a mild (around 2) preference for non-zero sterile mixing, which overlaps with the favoured region for the sterile neutrino interpretation of the ANITA upward shower. Although the null results from CHORUS and NOMAD on to oscillations in vacuum disfavour the hint from the IceCube 1-year data, the relevant oscillation channel and underlying physics are different. At the 99% C.L. an upper bound is obtained instead that improves over the present Super-Kamiokande and DeepCore constraints in some parts of the parameter space. We also investigate the physics reach of the roughly 8 years of data that is already on tape as well as a forecast of 20 years data to probe the present hint or improve upon current constraints. preprint: FTUAM-18-7preprint: IFT-UAM/CSIC-18-023preprint: SISSA 09/2018/FISI ## I Introduction Over the last 20 years neutrino oscillations have been established as the explanation of the experimental evidence for neutrino flavour transitions McDonald:2016ixn (); Kajita:2016cak () with the mixing angles and mass squared differences measured to high accuracy (see Tab. 1 for recent global fit results of the mass and mixing parameters). The simplest extension of the Standard Model accommodating neutrino masses is the addition of sterile (right-handed) neutrinos to its content. The mass of these extra singlets, unlike all other fermions, would not be related to the Higgs mechanism and the electroweak scale due to their singlet nature. Therefore, it is vital to probe their existence experimentally at all possible scales. For instance, short baseline (SBL) experiments like LSND Aguilar:2001ty () and MiniBOONE Aguilar-Arevalo:2012fmn (); AguilarArevalo:2008rc () as well as reactor experiments combined with a recent reevaluation of their expected fluxes Mention:2011rk (); Huber:2011wv () and Gallium source experiments Abdurashitov:2009tn (); Kaether:2010ag (); Giunti:2010zu () have reported oscillation results that are consistent with a mass squared difference with a possible fourth neutrino mass eigenstate of , although this interpretation is in strong tension with other searches Kopp:2013vaa (); Gariazzo:2017fdh (). With an even higher mass, around the keV scale, sterile neutrinos are a viable dark matter candidate Dodelson:1993je (); Shi:1998km () that can be probed via their decay to light neutrinos and X-rays with both stringent constraints Perez:2016tcq () and a possible hint at 3.5 keV Bulbul:2014sua (); Boyarsky:2014jta (), which could come from the decay of such neutrinos. At larger masses, sterile neutrinos would leave their imprint altering the kinematics of beta decays and meson decays and can also be probed for at beam dump and collider experiments Atre:2009rg (); Ruchayskiy:2011aa (). Even when beyond the reach of collider searches, sterile neutrino mixing can be tested indirectly via precision electroweak and flavour observables Shrock:1980vy (); Schechter:1980gr (); Shrock:1980ct (); Shrock:1981wq (); Langacker:1988ur (); Bilenky:1992wv (); Nardi:1994iv (); Tommasini:1995ii (); Antusch:2006vwa (); Antusch:2008tz (); Biggio:2008in (); Alonso:2012ji (); Akhmedov:2013hec (); Antusch:2014woa (); Fernandez-Martinez:2015hxa (); Abada:2015trh (); Abada:2016awd (); Fernandez-Martinez:2016lgt (). Through neutrino oscillation data, MINOS Adamson:2011ku (), IceCube TheIceCube:2016oqi (), SuperKamiokande Abe:2014gda (), MiniBOONE Cheng:2012yy (), and CDHS Dydak:1983zq (), among others, have published limits on the sterile mixing parameters for mass squared differences in the range . These results have been combined to global analyses in refs. Kopp:2013vaa (); Conrad:2012qt (); Esmaili:2013vza (); Collin:2016aqd (); Dentler:2017tkw (). In this study we will consider larger sterile mass squared differences and investigate the sensitivity to the mixing of the sterile neutrinos to the and flavours of the presently released 1 year data, as well as forecasts for 8 years and 20 years, of atmospheric muon neutrino disappearance data at IceCube. In particular, we will study mass squared differences large enough for the sterile-neutrino-driven oscillations to be averaged out at IceCube energies () for atmospheric neutrinos traveling through the Earth ( km). Such mass squared differences are too big to explain the SBL anomalies but are compatible with the sterile neutrino interpretation Cherry:2018rxj () of the upward directed cosmic ray shower observed by ANITA Gorham:2016zah (). These mixings are however ruled out by cosmological constraints Vincent:2014rja () and some non-standard effect suppressing the production of these sterile neutrinos in the early Universe would be necessary to reconcile the results Vecchi:2016lty (). Our results apply for sterile neutrino masses . Note that for sterile masses above 10 MeV stronger bounds on the active-heavy mixing with muon and tau neutrinos are present from laboratory experiments where the sterile neutrino could be detected directly Atre:2009rg ().111Electron neutrino-sterile mixing can be constrained for even smaller mass squared differences via kink searches in spectra of certain isotopes and in neutrinoless double beta decay experiments Atre:2009rg (). SuperKamiokande Abe:2014gda () and DeepCore Aartsen:2017bap () have already published constraints on the sterile mixing parameters in the averaged out regime. It should be noted that the energy threshold of SuperKamiokande is lower than the IceCube one and the averaged out regime for SuperKamiokande therefore starts at smaller mass squared differences (). The same parameter space has also been probed by experiments like CHORUS Eskut:2007rn () and NOMAD Astier:2001yj () although, instead of analyzing the disappearance of atmospheric and the effect of the matter potential from neutral current interactions in presence of steriles, they searched for the appearance of in a beam through vacuum oscillations. We will compare our results to these current experimental bounds. This paper is organized as follows: In Section II we give an overview of the muon neutrino survival probability when the oscillations driven by the new mass eigenvalues are averaged out, in Section III we analyse one year of though-going muon data in IceCube and give forecasts for the 8 years and 20 years sensitivities. Finally, in Section IV we summarise our results and give our concluding remarks. ## Ii Sterile neutrino mixing Upon the addition of several sterile neutrinos, the flavour eigenstates of the weak interactions () are related to the neutrino mass eigenstates , with masses (, 2, 3, 4, 5,…) via the elements of the lepton mixing matrix according to \|να⟩=∑iU∗αi\|νi⟩. (1) In general, the mixing matrix for neutrino flavours can be decomposed as the product of rotations with mixing angles , with physical phases . The usual parametrization is through a series of unitary rotations in the --plane given by U=V3nV2nV1nV3(n−1)V2(n−1)V1(n−1)⋯V34V24V14V23V13V12=U0, (2) with (Vij)ab=⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩cos(θij),a=b∈{i,j}sin(θij)eiδij,a=i, b=j−sin(θij)e−iδij,a=j, b=i1,a=b∉{i,j}0,otherwise, (3) and where has the usual PMNS matrix, , as the upper left block. Note that we have not included rotations in the purely sterile sector, e.g., , as such rotations are unphysical. Written in this fashion, the full mixing matrix takes the block form U=UU0=(1−αΘXY)(Uν001)=((1−α)UνΘXUνY). (4) Here, if the rotations are performed in the order given by Eq. (2), is a lower triangular matrix of the form Xing:2007zj (); Xing:2011ur (); Escrihuela:2015wra (); Li:2015oal (); Blennow:2016jkn () α=⎛⎜⎝αee00αμeαμμ0ατeατματτ⎞⎟⎠, (5) whose components to leading order in the active-heavy mixing elements are given by αβγ≃⎧⎪⎨⎪⎩12∑ni=4\|Uβi\|2,β=γ∑ni=4UβiU∗γi,β>γ0,γ>β. (6) The oscillation probability, , will here be derived and discussed in the case where the active-heavy mixing angles are small, the corresponding mass squared differences are large enough for the oscillations to average out, and where the electron neutrinos do not participate in the oscillations222The oscillation of to at the energies and baselines that characterize the IceCube data are strongly suppressed. Indeed, is small and the solar mass squared difference is too small for the oscillations with to develop. Finally, has been tightly constrained by electron neutrino disappearance experiments Kopp:2013vaa () and would also play a subleading role. (i.e., and ). We do so by considering a basis that is rotated by relative to the flavour basis. In this basis, the neutrino oscillation Hamiltonian in matter takes the form ~H=(H000H1)+VNCU†(1000)U, (7) where is the standard Hamiltonian for - oscillations in vacuum, is a diagonal matrix containing large entries, and (with the upper sign for neutrinos and the lower sign for anti-neutrinos). The upper left block describing the - oscillations (not including the electron neutrino states) can be treated separately, leading to the effective Hamiltonian ~H0 =H0+VNC(1−α†)(1−α)≃H0−VNC(α+α†) (8) where the represents equality up to a matrix proportional to unity and to leading order in . This can be rewritten as ~H0≃Δm2(−cos(2θm)sin(2θm)λ∗sin(2θm)λcos(2θm)), (9) where Δ2m = [Δm2312Ecos(2θ23)+2VNC% (αμμ−αττ)]2+∣∣ ∣∣Δm2312Esin(2θ23)−2VNCατμ∣∣ ∣∣2, sin2(2θm) = 1Δ2m∣∣ ∣∣Δm2312Esin(2θ23)−2VNCατμ∣∣ ∣∣2, (10) and is a phase factor of modulus one. Rotating back to the flavour basis, the muon neutrino survival probability is given by Pμμ=(1−αμμ)4(1−sin2(2θm)sin2(ΔmL2))+n∑i=4\|Uμi\|4, (11) where the last term is a constant leaking term Fong:2016yyh (). Note that, except for the leaking term, all the sterile neutrino effects are encoded in the matrix , in particular in the elements , , and , regardless of how many sterile neutrinos are considered as long as they are all in the averaged out regime Blennow:2016jkn (). However, in our analysis of IceCube data we will allow a free normalization of the events, given the large uncertainties in the atmospheric neutrino fluxes, thus there will be no sensitivity to the normalization factor nor to the leaking term, which does not depend on energy nor baseline. At leading order in , and neglecting whose effect is negligible at the energies of the IceCube data sample, the following probability is obtained Pμμ≃1−V2NC\|ατμ\|2L2, (12) where the overall normalization has also been dropped since we allow a free normalization in the analysis. In order to ease the comparison with existing constraints from SuperKamiokande Abe:2014gda () and DeepCore Aartsen:2017bap () and to make use of the nuSQuIDS software Delgado:2014kpa (); nusquids () for numerical calculations without approximations, we will now particularize these expressions for the addition of a single sterile neutrino. With our given parametrization, we find that Uμ4=s24e−iδ24andUτ4=c24s34, (13) so that αμμ=1−c24≃\|Uμ4\|2/2,αττ=1−c34≃\|Uτ4\|2/2,ατμ=s24s34eiδ24≃Uτ4U∗μ4, (14) and thus Pμμ≃1−V2NC\|Uτ4\|2\|Uμ4\|2L2. (15) Therefore, the bounds will essentially follow a hyperbola in the --plane. Note that, in contrast to IceCube, for the SuperKamiokande and DeepCore energies the atmospheric oscillation driven by is relevant. Thus, the approximate Eq. (15) is not valid and the sensitivity mainly stems from the interference between the standard and sterile oscillations in Eqs. (10). Therefore, the phase of , i.e., in the one extra sterile neutrino scenario, has an impact on the oscillation probability. Specifically, it can change the sign of the interference term between the atmospheric and the sterile terms in the expression for the energy and the mixing angle in matter. As an example of the impact of the phase, in Figure 1 the muon neutrino survival probability as a function of the energy for , km, and two different values of the phase, (solid line) and (dashed line) is shown. As comparison, the muon neutrino disappearance oscillation probability for zero sterile mixing is also shown. These values of the sterile matrix elements are at the border of the C.L. region of SuperKamiokande. The sign of the interference term can also be changed by changing the mass ordering (i.e., the sign of ) or by switching between neutrinos and antineutrinos (i.e., changing the sign of ). However, neither IceCube nor SuperKamiokande or DeepCore can distinguish between neutrinos and antineutrinos so this dependence is diluted in their data. Conversely, experiments such as CHORUS and NOMAD explored the same parameter space but instead exploiting the to appearance channel with negligible matter effects leading to Pμτ≃4\|Uτ4\|2\|Uμ4\|2sin2(Δm241L4E). (16) ## Iii Simulation and results One year of high-energy through-going muons released by the IceCube collaboration TheIceCube:2016oqi () for the last IceCube detector stage with 86 strings will be analyzed. The data sample consists of up-going track events so as to avoid the background from cosmic ray muons giving, after all cuts, a sample purity better than 99.9%. Hence, the distances the signal neutrinos travel are of the order of km. The selected events have reconstructed energies between 400 GeV and 20 TeV and cosine of the reconstructed zenith angle between and . The sensitivity that a full 8-year IceCube sample would have as well as the prospects for an exposure equivalent to 20 years of IceCube data will also be forecasted. For our simulations, the neutrino flux computed with the analytic air shower code Fedynitch:2015zma () using the cosmic ray flux from HondaGaisser model with Gaissser-Hillas H3a correction Gaisser:2013bla () together with the hadronic model QGSJET II-04 Ostapchenko:2010vb () have been adopted. We have also verified that our results do not change significantly under the assumption of different fluxes, such as using the cosmic ray flux from the poly-gonato model TerAntonyan:2000hh (); Hoerandel:2002yg () or the Zatsepin-Sokolskaya Zatsepin:2006ci () model updated with measurements by PAMELA Adriani:2011cu () together with the hadronic model SIBYLL2.3, RC1, point-like Fletcher:1994bd () or QGSJET II-04. The propagation of the neutrinos was simulated using the nuSQuIDS software Delgado:2014kpa (); nusquids (), where the PREM profile Dziewonski:1981xy () is implemented for the Earth matter density. Since we are interested in the averaged out regime our simulations were performed with a sterile mass squared difference of , but we have verified that changing this parameter does not alter the results as long as as expected. Since neutrino and antineutrino interactions cannot be distinguished on an event basis, the signal will contain both and events. After propagating the flux for every value of the sterile neutrino parameter, the Monte Carlo provided with the data releas TheIceCube:2016oqi () has been used to compute the expected number of events in every bin of reconstructed zenith angle. In order to obtain the expected significance of the bounds on the sterile mixing parameters, we adopt a Poisson log-likelihood given by L=−∑i[Nth,i−Nd,i+Nd,ilog(Nd,iNth,i)], (17) where the and are the predicted and observed number of events given a set of parameters in bin , respectively, and the sum is taken over all the reconstructed zenith angle bins . The log-likelihood has been maximized for a number of nuisance parameters to include the effect of possible systematic errors. In particular, the uncertainty in the pion-kaon ratio of the initial flux (), the efficiency of the digital optical modules (DOMs), and the overall flux normalization have been considered. Since the observable is energy independent for large values of the sterile neutrino mass (see Eq. (15)), only one energy bin has been considered and the uncertainty in the energy spectrum slope has been neglected, while 40 bins for the reconstructed zenith angle have been adopted. For the pion-kaon ratio a Gaussian prior with has been adopted and no prior for the DOM efficiency or the overall flux normalization has been assumed. The standard oscillation parameters used in the simulations were set to their respective best-fit values from Tab. 1. To find the confidence regions from the log-likelihood differences we assume that the prerequisites for Wilks’ theorem Wilks:1938dza () holds so that likelihood ratios can be directly converted to a confidence level. In the left panel of Figure 2, the 90% C.L. constraints (for 2 degrees of freedom) obtained for the public 1-year data (pink contours) in the --plane is presented. The existing bounds from SuperKamiokande Abe:2014gda () and DeepCore Aartsen:2017bap () at the same C.L. are also shown for comparison by the hatched gray area. At 90% C.L. present data prefer some degree of sterile mixing and we find that zero sterile mixing is disfavoured at 2.3 (1 degree of freedom333Note that if , the survival oscillation probability is insensitive to .). The preference for non-zero sterile mixing is independent on the atmospheric sterile neutrino flux adopted in the analysis but its significance varies between 1.6 and 3.0 with the different models tested. Given this preference for non-zero sterile mixing, the current constraints from IceCube do not improve upon the combined bounds from SuperKamiokande and DeepCore at 90% C.L. In the right panel, the same information is shown at 99% C.L. In this case, the present 1-year data gives an upper bound that already slightly improves upon the present SuperKamiokande and DeepCore constraints, ruling out the white region in the plot. The physics reach of an 8-year run of IceCube data if the present preference for sterile mixing is maintained is also shown in cyan. In particular, the present best-fit value of , lies in the already disfavoured region by DeepCore and SuperKamiokande. Due to the hyperbola-shaped degeneracy of the oscillation probability in the --plane, there are values of the sterile oscillation parameters that provide an almost equally good fit without being in tension with the other disappearance present data. Remarkably, theses values of are also compatible with the sterile neutrino interpretation Cherry:2018rxj () of the upward directed cosmic ray shower observed by ANITA Gorham:2016zah (). Indeed, the sterile neutrino interpretation of the ANITA results requires that the sterile neutrino mass is between and eV, which would also fall in the averaged out regime for IceCube studied here. However, all the parameter space preferred by IceCube at the 90% C.L. is disfavoured by NOMAD Astier:2001yj () with the same significance. Indeed, the null results in their search translates through Eq. (16) into at the 90% C.L. for eV. Nevertheless, the channel and underlying physics explored to obtain the bounds are very different in the two sets of experiments. While SuperKamiokande, DeepCore and IceCube analyze disappearance and the steriles are probed via their matter effects as shown in Eq. (15), NOMAD and CHORUS searched for appearance essentially in vacuum through Eq. (16). Thus, in presence of non-standard matter effects (also conceivably in the sterile sector) the two results could still be reconciled if a stronger tension should remain upon including more IceCube data. We therefore simulate 8 years of IceCube data assuming , , and as the true oscillation parameters. As can be seen in Figure 2, the expected confidence region region shrinks significantly with the additional statistics, while keeping its shape. In particular, if the values of the sterile neutrino mixing marked by the star were realized in nature, 8-years of IceCube data would disfavour no sterile mixing around the level. The capability of larger IceCube samples to improve the present constraints on sterile mixing in absence of sterile neutrinos have been also studied. In Figure 3, the contours for (left panel) and C.L. (right panel) expected exclusion limits in the --plane together with the existing bounds from SuperKamiokande and DeepCore are presented. The bound on from 8 years of IceCube would improve over present constraints between a factor 1.3 for vanishing values of to around an order of magnitude for close to 0.1. Similarly, for , the constraint on would improve around a factor 5. In particular, the present best fit for non-zero sterile mixing would be excluded at high significance (more than ) and most of the currently preferred parameter space at C.L. (pink area in the left panel of Figure 2) disfavoured. Comparatively, increasing the statistics up to 20-year of IceCube data yields a more modest improvement in sensitivity. Remarkably, not even the 20-year scenario would improve over the present NOMAD limit of at the 90% C.L. Nevertheless, we consider the two constraints complementary given the different physics probed by each of them. The effect of the CP-violating phase is also shown. In particular, the solid lines correspond to and the dashed lines to . As can be seen, IceCube is not very sensitive to the sterile phase as oscillations due to the atmospheric mass squared difference at energies above 100 GeV do not have time to develop. Indeed, from Figure 1 the survival probability is essentially 1 in absence of sterile mixing for GeV. ## Iv Summary and conclusions In this work we have presented the current constraints from the public 1-year IceCube data as well as the expectations of a full 8-year dataset and forecasts for 20 years worth of statistics to the mixing of sterile neutrinos with the and flavours. In particular, we concentrated for the first time on larger masses for the extra neutrinos ( eV) than usually explored so that their oscillations are averaged out at IceCube. We find that the public 1-year IceCube data presents some preference for non-zero sterile mixing in the averaged out regime that would manifest via neutral-current-induced matter effects in the disappearance channel. In particular, values of the squared sterile mixing with the flavour of order and with the between and are favoured at around with respect to no sterile mixing. Interestingly, the large masses assumed in our analysis and the size of the preferred mixing with tau neutrinos correspond to the region of the parameter space that could also explain the upward directed cosmic ray shower observed by ANITA Gorham:2016zah () with sterile neutrinos Cherry:2018rxj (). These mixings are however in strong tension with cosmological constraints Vincent:2014rja () and some non-standard effect suppressing the production of these sterile neutrinos in the early Universe would be necessary to reconcile these results Vecchi:2016lty (). Moreover, these mixings are also in tension with present data from CHORUS Eskut:2007rn () and NOMAD Astier:2001yj () which, however, explore a different channel without matter effects. Thus, in presence of non-standard matter effects the two results could be potentially reconciled. We have also studied the sensitivity that 8 years of IceCube data, close to the data that should be presently available, would have and find that it would be sufficient to either confirm the present preference or exclude it with high significance (more than ) and set stringent constraints improving around an order of magnitude over SuperKamiokande and DeepCore present bounds in some parts of the parameter space. Since sterile neutrinos at some mass scale are a general expectation of many extensions of the SM accounting for neutrino masses, it will be very interesting to explore this part of the parameter space with averaged out sterile neutrino oscillations using the full data sample collected by IceCube. ## Acknowledgments This work is supported in part by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreements 674896-Elusives and 690575-InvisiblesPlus. MB and EFM acknowledge support from the ”Spanish Agencia Estatal de Investigación” (AEI) and the EU ”Fondo Europeo de Desarrollo Regional” (FEDER) through the project FPA2016-78645-P; and the Spanish MINECO through the “Ramón y Cajal” programme and through the Centro de Excelencia Severo Ochoa Program under grant SEV-2012-0249. MB also acknowledges support from the Göran Gustafsson foundation. JS acknowledges support by MINECO grant FPA2016-76005-C2-1-P, Maria de Maetzu program grant MDM-2014-0367 of ICCUB and research grant 2017-SGR-929. JHG warmly thanks IFT of Madrid for its hospitality during part of this work, JG thanks the ITP, University of Heidelberg and EFM thanks the IPMU for its hospitality hosting him during the completion of this work. Finally, we acknowledge the use of the HPC-Hydra cluster at IFT. ## References You are adding the first comment! How to quickly get a good reply: • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made. • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements. • Your comment should inspire ideas to flow and help the author improves the paper. The better we are at sharing our knowledge with each other, the faster we move forward. The feedback must be of minimum 40 characters and the title a minimum of 5 characters	{"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": 0.9261338114738464, "perplexity": 1549.9520020470463}, "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/1593655890092.28/warc/CC-MAIN-20200706011013-20200706041013-00288.warc.gz"}
https://www.physicsforums.com/threads/rise-and-run.50280/	# Rise and Run 1. Oct 29, 2004 undefinedundefined I am in the process of planning my Coursework, I’m investigating rise and run; the time taken for a trolley to slide down a slope with varying distances from the end and with various inclinations, and I’ve hit a wall, a problem... :grumpy: I'm looking for a formula that takes into account all of my variables: Distance, The inclination i.e. the angle, Time, Speed, I have been given the mass of the trolley too, but it's not really a variable. When plotting the graph of the data, I’d like to have a constant that can be got from the gradient or the y- intercept, most likely the gradient thought. 2. Oct 29, 2004 ### Integral Staff Emeritus Perhaps the reason you are not getting any responses, is because it if very difficult to understand what you are doing and what your question is. If you refomulate with a good description of your experiment and a specific question you will get better help. I am moving this to the homework help fourm. 3. Oct 30, 2004 You’re right, hope this explanation is better… My experiment is simple in essence: Its title is, “times for a trolley to roll down slopes of differing lengths and inclinations.” So basically I have a slope and I let a trolley slide down it from differing lengths and inclinations timing how long it takes to get to the bottom of the slope – I have done this with 6 different lengths and of 3 different inclinations, all quite small scale, e.g. having the rise at 0.154m and the run at 1.46m. I have got my results, the experiments outline, the method etc, but alas, as yet I have no aim! Could you help me come up with an aim? I have thought about looking at the speed of the trolley sliding down the slope, but the maths is too simple; I have thought about acceleration, possibly analysing the initial velocity and final velocity, but I think they are all mathematically unchallenging. Does anyone know of a formula linking all my variables together? Or could point me in the right directon? Similar Discussions: Rise and Run	{"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": 0.831276535987854, "perplexity": 580.5280851762586}, "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-2017-43/segments/1508187825308.77/warc/CC-MAIN-20171022150946-20171022170946-00101.warc.gz"}
https://math.stackexchange.com/questions/2714429/find-a-generator-of-the-intersection-of-three-subgroups-of-the-integers	# Find a generator of the intersection of three subgroups of the integers $(\Bbb Z,+)$ is infinite group and cyclic with $a\in(\Bbb Z,+)$. $\langle a \rangle=\langle 24 \rangle\cap \langle 30 \rangle \cap \langle 12 \rangle$. I want to find all of $a$ and I know $$\langle 24\rangle =\{\dots ,-96,-72,-48,-24,0,24,48,72,96,\dots \},$$ $$\langle 30 \rangle =\{\dots,-120,-90,-60,-30,0,30,60,90,120,\dots\},$$ and $$\langle 12\rangle=\{\dots ,-60,-48,-36,-24,-12,0,12,24,36,48,60,\dots\}$$ then $\langle a\rangle=\langle 120\rangle ?$ • $a$ must be the least common multiple of $24,30,12$, which is $120$. – Crostul Mar 30 '18 at 9:43 • @Crostul 1) Why are you answering in a comment? 2) Remember that we may also have $a=-120$. – Arthur Mar 30 '18 at 9:46 @Crostul already wrote but maybe it can be good to show general form. Let $a,b \in \mathbb{Z}$ so we want to show $\langle a\rangle \cap \langle b\rangle = a\mathbb{Z} \cap b\mathbb{Z} = lcm(a,b)\mathbb{Z}.$ Obviously $lcm(a,b) \in a\mathbb{Z} \cap b\mathbb{Z}$ so $lcm(a,b)\mathbb{Z} \subseteq a\mathbb{Z} \cap b\mathbb{Z}.$ To other way, by the definition of $lcm(a,b)$every multiple of a and b must be multiple of $lcm(a,b)$.So $a\mathbb{Z} \cap b\mathbb{Z} \subseteq lcm(a,b)\mathbb{Z}$. (1)$(\forall n \in \mathbb{N})$ $a_{1}\mathbb{Z} \cap ...\cap a_{n}\mathbb{Z} = lcm(a_{1},...,a_{n})\mathbb{Z}.$ (2)$n\mathbb{Z}=m\mathbb{Z}$ iff ($n=m$ or $n=-m$).	{"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": 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": 0.88942950963974, "perplexity": 362.4461401205386}, "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-2019-43/segments/1570987763641.74/warc/CC-MAIN-20191021070341-20191021093841-00288.warc.gz"}
https://indico.cern.ch/event/839985/contributions/3983684/	# LXX International conference "NUCLEUS – 2020. Nuclear physics and elementary particle physics. Nuclear physics technologies" Oct 11 – 17, 2020 Online Europe/Moscow timezone ## Singular background in а model of material plane interacting with Dirac particles Oct 13, 2020, 2:40 PM 25m Online #### Online Oral report Section 4. Relativistic nuclear physics, elementary particle physics and high-energy physics. ### Speaker Prof. Yury Pismak (Department of High Energy and Elementary Particle Physics, State University of Saint-Petersburg) ### Description A method is proposed [1] for constructing a model for the interaction of fields of quantum electrodynamics (QED) with two-dimensional materials in the framework of the Symanzik approach [2]. It is based on the modification of the QED Lagrangian by adding to it an additional contribution (the Lagrangian of the defect) concentrated in a two-dimensional region of space. The requirement to comply with the basic principles of QED (renormalization, locality, gauge invariance) makes significant restrictions on the type of defect Lagrangian. As a result of the modification of QED, a small number of new dimensionless parameters appear in the model which describe the material properties of defect. The Dirac spinor fields in this approach can be used to describe the processes of interaction of spin ½ particles (electrons, protons, neutrons) with two-dimensional objects. The talk presents the results of the study of the scattering of Dirac particles on a homogeneous isotropic plane, as well as properties of bound states arising from the interaction of the spinor field with the plane [3-8]. It is shown that the choice of specific values of the seven dimensionless parameters in the model can achieve significant differences in the quantitative characteristics of the studied physical effects. Theoretical investigations within the framework of the proposed approach may be useful both for improving the methodology of experiments with two-dimensional materials, and for analyzing the possibilities of technical devices created on their basis. References [1] V.N. Markov, Yu.M. Pis'mak, Casimir effect for thin films in QED // Journal of Physics A: Mathematical and General, 2006. --Vol. 39,-- P. 6525-6532; arXiv: hep-th/0505218v3, 2005; D.Yu. Pis'mak, Yu.M. Pis'mak, Modeling the interaction of a material plane with a spinor field in the framework of Symanzik's approach // Theoretical and Mathematical Physics, 2015. --Vol.184,--№ 3.-- P. 505–519. [2] K. Symanzik, Schrödinger representation and Casimir effect in renormalizable quantum field theory//Nucl.Phys. B, 1981-- Vol. 190, P. 1-44. [3] Yu.M. Pismak, O.Yu. Shakhova, Symanzik approach in modeling the interaction of quantum fields with extended objects: scattering of Dirac particles on material plane// Phys. Part. Nucl. Lett., 2019 – Vol. 16, – P. 441-444. [4] Yu.M. Pismak, Modelling of Bound States of Dirac Particles in Singular Background in Framework of Symanzik Approach. // Phys. Part. Nucl. Lett. , 2018— Vol. 15, 4, —P. 380-383. [5] Yu. Pismak, F. Wegner, Dispersion relations and dynamic characteristics of bound states in the model of a Dirac field interacting with a material plane //EPJ Web of Conferences, 2018 —Vol. 191, — P. 06015. [6] Yu.M. Pismak and D.Yu. Shukhobodskaia Symanzik approach in modeling of bound states of Dirac particle in singular background // EPJ Web of Conferences, 2017. — Vol. 158, — P. 07005. [7] Yu.M. Pismak and D.Yu. Shukhobodskaia, Bound states in a model of interaction of Dirac field with material plane // EPJ Web of Conferences, 2016. — Vol. 125, — P. 0522. [8] Yu.M. Pis'mak, D.Yu. Shukhobodskaia, Model of Dirac field interacting with material plane within Symanzik’s approach, // EPJ Web of Conferences, 2016. — Vol. 126, — P. 05012. ### Primary author Prof. Yury Pismak (Department of High Energy and Elementary Particle Physics, State University of Saint-Petersburg)	{"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": 0.8581599593162537, "perplexity": 2398.459323320169}, "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-2023-14/segments/1679296949506.62/warc/CC-MAIN-20230330225648-20230331015648-00202.warc.gz"}
https://curriculum.illustrativemathematics.org/HS/students/2/5/6/index.html	Lesson 6 Scaling Solids • Let’s see how the surface area and volume of solids change when we dilate them. 6.1: Math Talk: Cube Volumes Find the volume of each cube mentally. 6.2: How Do Surface Area and Volume Change with Scaling? 1. Use the applet to build cubes that result from dilating a unit cube by each scale factor shown in the table. Then, complete the table with the surface area and volume of each dilated cube. 2. scale factor surface area in square units volume in cubic units 1 2 3 4 3. Suppose a unit cube is dilated by some scale factor $$k$$. 1. Write an expression for the surface area of the dilated cube. 2. Write an expression for the volume of the dilated cube. 3. Compare and contrast the expression for surface area and the expression for volume. 6.3: Scaling All Solids Clare says, “We know that if we dilate a cube by a factor of $$k$$, the cube’s volume is multiplied by $$k^3$$. It seems like that must apply to all solids, but I’m not sure how to prove it.” Elena says, “Earlier in the unit, we showed that we can cover any two-dimensional shape with rectangles, so the property that area changes by $$k^2$$ when we dilate a figure by $$k$$ applies to all shapes, not just rectangles. Can we do something similar here?” 1. Use Elena’s line of reasoning to argue that for any solid, if it’s dilated by a factor of $$k$$, the volume is multiplied by $$k^3$$. 2. Suppose a triangular prism has surface area 84 square centimeters and volume 36 cubic centimeters. The prism is dilated by scale factor $$k=4$$. Calculate the surface area and volume of the dilated prism. The image shows a figure called Sierpinski’s triangle. It’s formed by starting with an equilateral triangle, then repeatedly removing equilateral triangles created by joining the midpoints of the existing triangle’s sides. The first few stages are shown. If we continue this process of removal forever, we are left with some points that never get removed from the triangle. The remaining points are what we call Sierpinski’s triangle. At any given stage, the triangle at the top of the figure is a scaled copy of the triangle at the previous stage. For the completed Sierpinski’s triangle, though, the top triangle is a scaled copy not of the previous stage, but of the full Sierpinski’s triangle. 1. For the completed figure, what scale factor takes Sierpinski’s triangle to its scaled copy at the top? 2. Based on the scale factor, what fraction of the original shaded region should be contained in the scaled copy at the top? 3. The scaled copy at the top actually contains $$\frac13$$ of the shading of the original. Provide reasoning that shows that this is true. Summary In earlier activities, we saw that if we dilate a two-dimensional shape, the area of the dilated shape is the area of the original shape multiplied by the square of the scale factor. What happens when we dilate three-dimensional solids? Here is a rectangular prism with side lengths 3, 4, and 5 units. When we dilate the prism using a scale factor of 3, the lengths become 9, 12, and 15 units. Since these are three-dimensional shapes, we can look at both volume and surface area. The volume of the original prism is 60 cubic units because $$3 \boldcdot 4 \boldcdot 5=60$$. The volume of the dilated prism is 1,620 cubic units because $$9 \boldcdot 12 \boldcdot 15=1,\!620$$. The volume became 27 times larger! Why? Since the side lengths tripled, when we calculated the volume we were really finding $$(3 \boldcdot 3) \boldcdot (4 \boldcdot 3) \boldcdot (5 \boldcdot 3) = (3 \boldcdot 4 \boldcdot 5)\boldcdot 3^3$$. The volume was multiplied by the cube of the scale factor, or by $$3^3=27$$. Now let’s look at surface area. How do you think the surface area will change when the prism is dilated? In the original prism, 2 faces have area 12 square units, 2 have area 20 square units, and 2 have area 15 square units for a total surface area of 94 square units. The corresponding faces of the dilated prism have areas 108, 180, and 135 square units. The surface area of the new prism totals 846 square units, 9 times that of the original. Just like the area of two-dimensional shapes, the surface area of the prism changed by the square of the scale factor. In general, when you dilate any three-dimensional solid by scale factor $$k$$, the surface area is multiplied by $$k^2$$ and the volume is multiplied by $$k^3$$.	{"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": 0.8227118849754333, "perplexity": 381.91207983352353}, "config": {"markdown_headings": false, "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-2021-39/segments/1631780056890.28/warc/CC-MAIN-20210919125659-20210919155659-00048.warc.gz"}
https://hal-meteofrance.archives-ouvertes.fr/meteo-00340111	# Thermodynamical and radiative impact of the correction of sounding humidity bias in the tropics Abstract : Accurate measurements of atmospheric water vapor are crucial to many aspects of climate research and atmospheric science. This paper discusses some of the meteorological implications of a bias discovered in the measurement of water vapor in widely deployed radiosonde systems. This problem apparently arose in the early 1990s and a correction scheme has been recently developed that intends to remove the bias. The correction scheme also includes improvements in the humidity measurements in the upper troposphere and near the surface. This scheme has been applied to data taken during the Tropical Ocean and Global Atmosphere Coupled OceanAtmosphere Response Experiment (TOGA COARE). The impact of the bias on the general stability of the tropical atmosphere to deep convection, as measured by the convective available potential energy (CAPE) and the convective inhibition (CIN), is quite large. On the basis of the uncorrected data set, one might erroneously conclude that it is difficult to trigger deep convection over the region. When the correction is taken into account, the atmosphere over the tropical western Pacific becomes typically unstable to deep convection, with convective instability similar to that measured from aircraft in the vicinity of active convective sytems. Radiative fluxes are also significantly modified. For clear sky conditions, it is found that, on average, the net surface radiative flux increases by 4 W m-2 due to the humidity correction. Under more realistic cloudy conditions, the differences are weaker, but still significant. Changes in radiative fluxes are explained at first order by the the precipitable water increase. Type de document : Article dans une revue Journal of Climate, American Meteorological Society, 2000, 13, pp.3611-3624 https://hal-meteofrance.archives-ouvertes.fr/meteo-00340111 Contributeur : Francoise Guichard <> Soumis le : mercredi 19 novembre 2008 - 22:58:19 Dernière modification le : mardi 29 mai 2018 - 12:50:49 ### Identifiants • HAL Id : meteo-00340111, version 1 ### Citation Françoise M. Guichard, D. Parsons, E. Miller. Thermodynamical and radiative impact of the correction of sounding humidity bias in the tropics. Journal of Climate, American Meteorological Society, 2000, 13, pp.3611-3624. 〈meteo-00340111〉 ### Métriques Consultations de la notice	{"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": 0.8960093259811401, "perplexity": 2659.065916043511}, "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-2018-34/segments/1534221217354.65/warc/CC-MAIN-20180820215248-20180820235248-00424.warc.gz"}

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