Energy Technology Data Exchange (ETDEWEB)
Sundberg, Kenneth Randall [Iowa State Univ., Ames, IA (United States). Dept. of Electrical and Computer Engineering
1976-01-01
A method is developed to optimize the separated-pair independent particle (SPIP) wave function; it is a special case of the separated-pair theory obtained by using two-term natural expansions of the geminals. The orbitals are optimized by a theory based on the generalized Brillouin theorem and iterative configuration interaction (CI) calculations in the space of the SPIP function and its single excitations. The geminal expansion coefficients are optimized by serial 2 x 2 CI calculations. Formulas are derived for the matrix elements. An algorithm to implement the method is presented, and the work needed to evaluate the molecular integrals is discussed.
Indian Academy of Sciences (India)
Home; Fellowship. Fellow Profile. Elected: 1939 Honorary. Brillouin, Prof. Leon. Date of birth: 7 August 1889. Date of death: 4 October 1969 ... Posted on 21 December 2017. ASTROPHYSICS: An Observational View of the Universe. Math Art and Design: MAD about Math, Math Education and Outreach. Math and Finance ...
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
Heck, Richard G
2011-01-01
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a
Brillouin Spectroscopy Data Base for Biological Threats
National Research Council Canada - National Science Library
Rubel, Glenn
2003-01-01
.... Brillouin scattering from DNA, ovalbumen, the Bacillus spores globigii and thuringiensis were measured to determine the feasibility of biological material discrimination using Brillouin scattering...
Collective stimulated Brillouin scatter
Korotkevich, Alexander O; Rose, Harvey A
2011-01-01
We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. We identify two contributions to BSBS convective instability increment. The first is collective with intensity threshold independent of the laser correlation time and controlled by diffraction. The second is independent of diffraction, it grows with increase of the correlation time and does not have an intensity threshold. The instability threshold is inside the typical parameter region of National Ignition Facility (NIF). We also find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.
Collective stimulated Brillouin backscatter
Lushnikov, Pavel M
2007-01-01
We develop the statistical theory of the stimulated Brillouin backscatter (BSBS) instability of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. Instability is collective because it does not depend on the dynamics of isolated speckles of laser intensity, but rather depends on averaged beam intensity. We identify convective and absolute instability regimes. Well above the incoherent threshold the coherent instability growth rate is recovered. The threshold of convective instability is inside the typical parameter region of National Ignition Facility (NIF) designs although current NIF bandwidth is not large enough to insure dominance of collective instability and suggests lower instability threshold due to speckle contribution. In contrast, we estimate that the bandwidth of KrF-laser-based fusion systems would be larg...
Remer, Itay; Bilenca, Alberto
2017-02-01
Brillouin spectroscopy is a noncontact technique for characterizing the mechanical properties of materials. Typically, Brillouin spectrometers have been realized using scanning Fabry-Perot spectrometers that measure, with long acquisition times, spontaneous Brillouin scattering from the samples. In the last few years, the use of virtually imaged phase array (VIPA) etalons for constructing Brillouin spectrometers has enabled to acquire spontaneous Brillouin spectra times. We will show that this improvement, combined with micrometer-step-size spatial scanning of the sample, provides precise Brillouin profiles of layered liquids at 30-milliseconds pixel-dwell-time, facilitating Brillouin profilometry analysis of materials at high speed.
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
Lecoeuche, V.; Webb, David J.; Pannell, Christopher N.; Jackson, David A.
1998-08-01
Distributed temperature sensors based on Brillouin scattering are attractive because they offer very large sensing length. The intensity of spontaneous Brillouin scattering is directly proportional to the temperature of the fiber, and permits a measurement independent of the strain applied to it. We report on a novel system to detect this signal, incorporating a mode-locked Brillouin fiber ring laser.
Zonas de Brillouin del grafito
A. Velázquez-Arriaga
2009-01-01
La celda unitaria de un cristal de grafito se analiza usando el principio básico de oscilador armónico. Para este propósito, consideramos a los átomos que conforman la celda unitaria hexagonal unidos por pequeños resortes. Se establece la ecuación de movimiento de dicha celda para obtener la frecuencia normal de vibración del sistema (w) en términos del vector de onda (k) y la distancia interatómica. Con estos datos se generan las zonas de Brillouin y se determinan los puntos silla en los con...
Indian Academy of Sciences (India)
Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
Spontaneous Brillouin scattering in a microdroplet
Ching, S. C.; Leung, P. T.; Young, K.
1990-05-01
Spontaneous Brillouin scattering in a micrometer-sized liquid droplet is analyzed from first principles, using the spherical-wave normal-mode basis. Instead of the conservation of linear momentum, this interaction is governed by a selection rule due to the conservation of angular momentum. The Brillouin spectrum is then calculated, both for observation at a given angle and for the sum over all angles, and compared with scattering in a bulk medium. Special attention is paid to the case where the incident and scattered radiation fall on an electromagnetic resonance of the droplet. The analysis lays the foundation for formulating stimulated Brillouin scattering in the same system.
Stimulated Brillouin scattering in metamaterials
Smith, M J A; de Sterke, C Martijn; Wolff, C; Lapine, M; Poulton, C G
2016-01-01
We compute the SBS gain for a metamaterial comprising a cubic lattice of dielectric spheres suspended in a background dielectric material. Theoretical methods are presented to calculate the optical, acoustic, and opto-acoustic parameters that describe the SBS properties of the material at long wavelengths. Using the electromagnetic and strain energy densities we accurately characterise the optical and acoustic properties of the metamaterial. From a combination of energy density methods and perturbation theory, we recover the appropriate terms of the photoelastic tensor for the metamaterial. We demonstrate that electrostriction is not necessarily the dominant mechanism in the enhancement and suppression of the SBS gain coefficient in a metamaterial, and that other parameters, such as the Brillouin linewidth, can dominate instead. Examples are presented that exhibit an order of magnitude enhancement in the SBS gain as well as perfect suppression.
Brillouin Optical Microscopy for Corneal Biomechanics
Scarcelli, Giuliano; Pineda, Roberto
2012-01-01
Purpose. The mechanical properties of corneal tissue are linked to prevalent ocular diseases and therapeutic procedures. Brillouin microscopy is a novel optical technology that enables three-dimensional mechanical imaging. In this study, the feasibility of this noncontact technique was tested for in situ quantitative assessment of the biomechanical properties of the cornea. Methods. Brillouin light-scattering involves a spectral shift proportional to the longitudinal modulus of elasticity of the tissue. A 532-nm single-frequency laser and a custom-developed ultrahigh-resolution spectrometer were used to measure the Brillouin frequency. Confocal scanning was used to perform Brillouin elasticity imaging of the corneas of whole bovine eyes. The longitudinal modulus of the bovine corneas was compared before and after riboflavin corneal collagen photo-cross-linking. The Brillouin measurements were then compared with conventional stress–strain mechanical test results. Results. High-resolution Brillouin images of the cornea were obtained, revealing a striking depth-dependent variation of the elastic modulus across the cornea. Along the central axis, the Brillouin frequency shift varied gradually from 8.2 GHz in the epithelium to 7.5 GHz near the endothelium. The coefficients of the down slope were measured to be approximately 1.09, 0.32, and 2.94 GHz/mm in the anterior, posterior, and innermost stroma, respectively. On riboflavin collagen cross-linking, marked changes in the axial Brillouin profiles (P biomechanical properties of cornea in situ with high spatial resolution. This novel technique has the potential for use in clinical diagnostics and treatment monitoring. PMID:22159012
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
IAS Admin
This article elucidates the important role the no- tion of symmetry has played in physics. It dis- cusses the proof of one of the important theorems of quantum mechanics, viz., Wigner's Symmetry. Representation Theorem. It also shows how the representations of various continuous and dis- crete symmetries follow from the ...
Indian Academy of Sciences (India)
This theorem first appeared in Jordan's Cours d'Analyse. (1887), but his proof was faulty. The first rigorous proof was given by Veblen in 1905. The purpose of this note is tc;> give a elementary (new?) proof of the theorem. Preliminaries. We begin with some definitions. 1. An arc is a space homeomorphic to the unit interval.
Strong moderate deviation theorems
Inglot, Tadeusz; Kallenberg, W.C.M.; Ledwina, Teresa
1992-01-01
Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate
Baralic, Djordje
2013-01-01
We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement formulated by Bradley is given. An open conjecture, established by Bradley, is proved using the theorems of Carnot and Menelaus.
Holevo, A. S.
1998-12-01
ContentsI. IntroductionII. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversionIII. Proof of the direct statement of the coding theorem § 1. Channels with pure signal states § 2. Reliability function § 3. Quantum binary channel § 4. Case of arbitrary states with bounded entropyIV. c-q channels with input constraints § 1. Coding theorem § 2. Gauss channel with one degree of freedom § 3. Classical signal on quantum background noise Bibliography
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Trigonometry, Including Snell's Theorem.
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Interactive Theorem Proving and Verification
Indian Academy of Sciences (India)
Research in the area of automated reasoning is largely concentrated around two major themes – Automated Theorem Proving and Interactive Theorem Proving. The goal of Auto- mated Theorem Proving, as the name suggests, is to try to prove a wide range of mathematical theorems using a computer in an automatic ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
a result is now called the Chinese Remainder. Theorem (CRT). From early times – perhaps, from the 1st century ... The Chinese remainder theorem (CRT) seems to have originated in the work of Sun-Tsu in the 3rd century. AD. ... If Mi denotes the product of all the mj's ex- cepting mi, then the GCD of mi and Mi is 1 for each.
Microcanonical quantum fluctuation theorems.
Talkner, Peter; Hänggi, Peter; Morillo, Manuel
2008-05-01
Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...... singular points nor closed orbits. In this paper, we redefine the standard notion of safety to comply with dynamical systems with multiple singular elements. Hereafter, we prove the converse barrier certificate theorems and highlight the differences between our results and previous work by a number...
DEFF Research Database (Denmark)
Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard
2015-01-01
The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe.......The main result of the present paper is an analogue of Kontsevich formality theorem in the context of the deformation theory of gerbes. We construct an L∞L∞ deformation of the Schouten algebra of multi-vectors which controls the deformation theory of a gerbe....
Converse Barrier Certificate Theorem
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2013-01-01
This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...
Neutron Brillouin scattering in dense fluids
Energy Technology Data Exchange (ETDEWEB)
Verkerk, P. [Technische Univ. Delft (Netherlands); FINGO Collaboration
1997-04-01
Thermal neutron scattering is a typical microscopic probe for investigating dynamics and structure in condensed matter. In contrast, light (Brillouin) scattering with its three orders of magnitude larger wavelength is a typical macroscopic probe. In a series of experiments using the improved small-angle facility of IN5 a significant step forward is made towards reducing the gap between the two. For the first time the transition from the conventional single line in the neutron spectrum scattered by a fluid to the Rayleigh-Brillouin triplet known from light-scattering experiments is clearly and unambiguously observed in the raw neutron data without applying any corrections. Results of these experiments are presented. (author).
A game generalizing Hall's theorem
Rabern, Landon
2012-01-01
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
Weyl's Equidistribution Theorem
Indian Academy of Sciences (India)
groups and matrix representations. It was during his re- search into representation theory that Weyl discovered his theorem on equidistribution. Subsequently a vast amount of literature was devoted to the review of his proof. However, there remain to this day, several unan- swered questions which arose in the aftermath of ...
Indian Academy of Sciences (India)
painting and reading. Unlike most others he dislikes computers. Figure 1. Ritabrata Munshi. Introd uction. In the first part of the article (Resonance, Vol. 4, No.9 ) we proved the Jordan sepa.ration theorem which says that a simple closed curve in E2 separates it into at least two components. In this concluding part after some ...
DEFF Research Database (Denmark)
Thomassen, Carsten
2004-01-01
We present a short proof of the theorem of Tutte that every planar 3-connected graph has a drawing in the plane such that every vertex which is not on the outer cycle is the barycenter of its neighbors. Moreover, this holds for any prescribed representation of the outer cycle. (C) 2004 Wiley Peri...
Kallenberg, W.C.M.; Koning, A.J.; Koning, A.J.
1995-01-01
Wieand's theorem on equivalence of limiting approximate Bahadur efficiency and limiting Pitman efficiency is extended in several ways. Conditions on monotonicity and continuity are obviated, composite null hypotheses are incorporated, and the implications of a weaker form of Wieand's Condition III*
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 8. Cantor's Little Theorem. Arindama Singh. General Article Volume 9 Issue 8 August 2004 pp 8-17 ... Author Affiliations. Arindama Singh1. Department of Mathematics, Indian Institute of Technology, Madras Chennai 600036, India.
Certified Kruskal's Tree Theorem
Directory of Open Access Journals (Sweden)
Christian Sternagel
2014-07-01
Full Text Available This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 3. Multivariable Chinese Remainder Theorem. B Sury. General Article Volume 20 Issue 3 March 2015 pp 206-216 ... Author Affiliations. B Sury1. Stat-Math Unit, Indian Statistical Institute, 8th Mile Road, Bangalore 560 059, India.
Li, Yongqian; An, Qi; Li, Xiaojuan; Zhang, Lixin
2017-05-01
A high-accuracy Brillouin frequency shift (BFS) measurement system for vector Brillouin optical time-domain analysis-based temperature sensor is proposed, in which double sideband modulation is used and the stimulated Brillouin scattering (SBS) gain and loss processes work together to generate a superimposed SBS phase-shift spectrum. The measurement principle is analyzed by mathematical modeling and the proof-of-concept experiment is performed by using a 100-m long standard single-mode fiber. The theoretical and experimental results reveal that the temperature sensitivity of BFS obtained from the measured SBS phase-shift spectrum is 1.059 MHz/°C, and the measurement error of temperature is only half that in traditional single sideband-based system, which indicates that the proposed technique can realize high-accuracy temperature measurement and have huge potential in the field of long-distance and high-accuracy sensing.
Some Generalizations of Rolle's Theorem
Das, J.
2004-01-01
In 1691 Michel Rolle (1652?1719) first published his famous result, now widely known as "Rolle's theorem", in an obscure book on geometry and algebra, named "Methode pour resoudre les egalites." Joseph Louis Lagrange (1736-1813) and Augustin-Louis Cauchy (1789-1857) derived their mean-value theorems easily using Rolle's theorem on suitably chosen…
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Directory of Open Access Journals (Sweden)
Richard F. Patterson
1999-01-01
Full Text Available In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are proved.
Signatures of chaos in the Brillouin zone
Barr, Aaron; Barr, Ariel; Porter, Max D.; Reichl, Linda E.
2017-10-01
When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.
What is next for Brillouin microscopy in biology and medicine?
Yakovlev, Vladislav V.; Ballmann, Charles W.; Coker, Zachary; Meng, Zhaokai; Troyanova-Wood, Maria
2017-02-01
Brillouin microscopy is an emerging technique in biomedical imaging capable of non-invasive assessing viscoelastic properties on a microscopic scale. In this report, we outline the latest developments in Brillouin spectroscopy instrumentation and applications in an attempt to anticipate the future impact areas of this new imaging modality.
BRILLOUIN INSTABILITY IN FIBER LASERS DOPED BY POWER ...
African Journals Online (AJOL)
30 juin 2012 ... dynamic instability arising in a fiber lasers as a consequence of Brillouin effect. The effect of Brillouin back scattering is theoretically analysed by two-coupled modes laser model. We consider the Fabry-Perot fiber ..... pumped high power fiber lasers. Journal of Nonlinear Optical Physics & Materials. 2009 ...
Brillouin Instability in Fiber Lasers Doped By Power | Bouras ...
African Journals Online (AJOL)
With the emergence of rare-earth doped fibers, and especially double-clad fibers, there is a renewed interest in Brillouin effect. First of all, the amplification of a continuous signal in a rare-earth doped fiber amplifier can generate high enough intensities to excite Brillouin effect and then to create a backscattered stokes wave.
Tailorable Stimulated Brillouin Scattering in Nanoscale Silicon Waveguides
Shin, Heedeuk; Jarecki, Robert; Cox, Jonathan A; Olsson, Roy H; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T
2013-01-01
While nanoscale modal confinement radically enhances a variety of nonlinear light-matter interactions within silicon waveguides, traveling-wave stimulated Brillouin scattering nonlinearities have never been observed in silicon nanophotonics. Through a new class of hybrid photonic-phononic waveguides, we demonstrate tailorable traveling-wave forward stimulated Brillouin scattering in nanophotonic silicon waveguides for the first time, yielding 3000 times stronger forward SBS responses than any previous waveguide system. Simulations reveal that a coherent combination of electrostrictive forces and radiation pressures are responsible for greatly enhanced photon-phonon coupling at nano-scales. Highly tailorable Brillouin nonlinearities are produced by engineering the structure of a membrane-suspended waveguide to yield Brillouin resonances from 1 to 18 GHz through high quality-factor (>1000) phonon modes. Such wideband and tailorable stimulated Brillouin scattering in silicon photonics could enable practical real...
Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy.
Scarcelli, Giuliano; Besner, Sebastien; Pineda, Roberto; Yun, Seok Hyun
2014-06-17
Loss of corneal strength is a central feature of keratoconus progression. However, it is currently difficult to measure corneal mechanical changes noninvasively. The objective of this study is to evaluate if Brillouin optical microscopy can differentiate the mechanical properties of keratoconic corneas versus healthy corneas ex vivo. We obtained eight tissue samples from healthy donor corneas used in Descemet's stripping endothelial keratoplasty (DSEK) and 10 advanced keratoconic corneas from patients undergoing deep anterior lamellar keratoplasty (DALK). Within 2 hours after surgery, a confocal Brillouin microscope using a monochromatic laser at 532 nm was used to map the Brillouin frequency shifts of the corneas. The mean Brillouin shift in the anterior 200 μm of the keratoconic corneas at the cone was measured to be 7.99 ± 0.10 GHz, significantly lower than 8.17 ± 0.06 GHz of the healthy corneas (P < 0.001). The Brillouin shift in the keratoconic corneas decreased with depth from the anterior toward posterior regions with a steeper slope than in the healthy corneas (P < 0.001). Within keratoconic corneas, the Brillouin shift in regions away from the apex of the cone was significantly higher than within the cone region (P < 0.001). Brillouin measurements revealed notable differences between healthy and keratoconic corneas. Importantly, Brillouin imaging showed that the mechanical loss is primarily concentrated within the area of the keratoconic cone. Outside the cone, the Brillouin shift was comparable with that of healthy corneas. The results demonstrate the potential of Brillouin microscopy for diagnosis and treatment monitoring of keratoconus. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.
Gmira, Seddik
2015-01-01
The Abel Jacobi theorem is an important result of algebraic geometry. The theory of divisors and the Riemann bilinear relations are fundamental to the developement of this result: if a point O is fixed in a Riemann compact surface X of genus g, the Abel Jaobi map identifies the Picard group: the quotient of divisors of a group of degree zero by the sub-group of divisors associated to meromorphic functions. The Riemann surface of genus g can be embedded in the Jacobian variety via the Abel-Jac...
Directory of Open Access Journals (Sweden)
Narita Keiko
2017-10-01
Full Text Available In this article, we formalize in the Mizar system [1, 4] the F. Riesz theorem. In the first section, we defined Mizar functor ClstoCmp, compact topological spaces as closed interval subset of real numbers. Then using the former definition and referring to the article [10] and the article [5], we defined the normed spaces of continuous functions on closed interval subset of real numbers, and defined the normed spaces of bounded functions on closed interval subset of real numbers. We also proved some related properties.
Legendre's and Kummer's Theorems Again
Indian Academy of Sciences (India)
http://www.ias.ac.in/article/fulltext/reso/015/12/1111-1121. Keywords. Legendre's theorem; Kummer's theorem; binomial coefficient; -adic valuation; base- expansion. Author Affiliations. Dorel Mihet1. West University of Timisoara Faculty of Mathematics and Computer Science Bv. V. Parvan 4, 300223 Timisoara, Romania.
Quantum Correction of Fluctuation Theorem
Monnai, T.; Tasaki, S.
2003-01-01
Quantum analogues of the transient fluctuation theorem(TFT) and steady-state fluctuation theorem(SSFT) are investigated for a harmonic oscillator linearly coupled with a harmonic reservoir. The probability distribution for the work done externally is derived and quantum correction for TFT and SSFT are calculated.
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Optical Sensors Using Stimulated Brillouin Scattering
Christensen, Caleb A (Inventor); Zavriyev, Anton (Inventor)
2017-01-01
A method for enhancing a sensitivity of an optical sensor having an optical cavity counter-propagates beams of pump light within the optical cavity to produce scattered light based on Stimulated Brillouin Scattering (SBS). The properties of the pump light are selected to generate fast-light conditions for the scattered light, such that the scattered light includes counter-propagating beams of fast light. The method prevents the pump light from resonating within the optical cavity, while allowing the scattered light to resonate within the optical cavity. At least portions of the scattered light are interfered outside of the optical cavity to produce a beat note for a measurement of the optical sensor. The disclosed method is particularly applicable to optical gyroscopes.
A Decomposition Theorem for Finite Automata.
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Broad-bandwidth Brillouin slow light in optical fibers
Gonzalez Herraez, M.; Song, Kwang-Yong; Thévenaz, Luc
2006-01-01
We experimentally demonstrate that Brillouin slow light with an arbitrary large bandwidth can be readily obtained in conventional optical fibers using a simple and inexpensive pump spectral broadening technique.
Cascaded forward Brillouin scattering to all Stokes orders
Wolff, Christian; Eggleton, Benjamin J; Steel, Michael J; Poulton, Christopher G
2016-01-01
Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we...
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
Fluctuation theorem: A critical review
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
Visualising higher order Brillouin zones with applications
Andrew, R. C.; Salagaram, T.; Chetty, N.
2017-05-01
A key concept in material science is the relationship between the Bravais lattice, the reciprocal lattice and the resulting Brillouin zones (BZ). These zones are often complicated shapes that are hard to construct and visualise without the use of sophisticated software, even by professional scientists. We have used a simple sorting algorithm to construct BZ of any order for a chosen Bravais lattice that is easy to implement in any scientific programming language. The resulting zones can then be visualised using freely available plotting software. This method has pedagogical value for upper-level undergraduate students since, along with other computational methods, it can be used to illustrate how constant-energy surfaces combine with these zones to create van Hove singularities in the density of states. In this paper we apply our algorithm along with the empirical pseudopotential method and the 2D equivalent of the tetrahedron method to show how they can be used in a simple software project to investigate this interaction for a 2D crystal. This project not only enhances students’ fundamental understanding of the principles involved but also improves transferable coding skills.
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
Cascaded Brillouin lasing in monolithic barium fluoride whispering gallery mode resonators
Lin, Guoping; Saleh, Khaldoun; Martinenghi, Romain; Beugnot, Jean-Charles; Sylvestre, Thibaut; Chembo, Yanne K
2015-01-01
We report the observation of stimulated Brillouin scattering and lasing at 1550~nm in barium fluoride (BaF$_2$) crystal. Brillouin lasing was achieved with ultra-high quality ($Q$) factor monolithic whispering gallery mode (WGM) mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from $8.2$ GHz up to $49$ GHz have been generated through cascaded Brillouin lasing. BaF$_2$ resonator-based Brillouin lasing can find potential applications for high-coherence lasers and microwave photonics.
Lu, Yuangang; Dou, Rongrong; Zhang, Xuping
2008-12-01
Brillouin Optical Time-Domain Reflectometry (BOTDR) is attracting significant attention due to its immense potential applications in temperature or strain monitoring. Conventional BOTDR system based on Spontaneous Brillouin Scattering Spectrum(SBSS) narrow-band detection is not only time-consuming but also controlling complicated. To overcome the drawbacks of the conventional detection method, a new SBSS wideband detection method is proposed in this paper. In the new detection method, the whole SBSS is captured by use of a wideband receiver in a single measurement, and Discrete Fourier Transform (DFT) signal processing algorithm is used to obtain the SBSS. The configuration of a heterodyne detection BOTDR system based on SBSS wideband detection is presented, and the data processing method, the spatial resolution of the system and the measurement time is discussed. The BOTDR system based on SBSS wideband detection has been demonstrated, and a temperature resolution of 3°C and a spatial resolution of 2 m have been achieved. The measurement time is only about one-tenth that of conventional narrow-band detection method.
The Heisenberg Uncertainty Principle and the Nyquist-Shannon Sampling Theorem
Directory of Open Access Journals (Sweden)
Millette P. A.
2013-07-01
Full Text Available The derivation of the Heisenberg Uncertainty Principle (HUP from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on a wave number that exists at the quantum level. It also establishes that the HUP is purely a relationship between the eﬀective widths of Fourier transform pairs of variables (i.e. conjugate variables. We note that the HUP is not a quantum mechanical measurement principle per se. We introduce the Quantum Mechanical equivalent of the Nyquist-Shannon Sampling Theorem of Fourier Transform theory, and show that it is a better principle to describe the measurement limitations of Quantum Mechanics. We show that Brillouin zones in Solid State Physics are a manifestation of the Nyquist-Shannon Sampling Theorem at the quantum level. By comparison with other ﬁelds where Fourier Transform theory is used, we propose that we need todiscern between measurement limitations and inherent limitations when interpreting the impact of the HUP on the nature of the quantum level. We further propose that while measurement limitations result in our perception of indeterminism at the quantum level, there is no evidence that there are any inherent limitations at the quantum level, based on the Nyquist-Shannon Sampling Theorem
On-chip inter-modal Brillouin scattering
Kittlaus, Eric A.; Otterstrom, Nils T.; Rakich, Peter T.
2017-07-01
Brillouin nonlinearities--which result from coupling between photons and acoustic phonons--are exceedingly weak in conventional nanophotonic silicon waveguides. Only recently have Brillouin interactions been transformed into the strongest and most tailorable nonlinear interactions in silicon using a new class of optomechanical waveguides that control both light and sound. In this paper, we use a multi-mode optomechanical waveguide to create stimulated Brillouin scattering between light-fields guided in distinct spatial modes of an integrated waveguide for the first time. This interaction, termed stimulated inter-modal Brillouin scattering, decouples Stokes and anti-Stokes processes to enable single-sideband amplification and dynamics that permit near-unity power conversion. Using integrated mode multiplexers to address separate optical modes, we show that circulators and narrowband filters are not necessary to separate pump and signal waves. We also demonstrate net optical amplification and Brillouin energy transfer as the basis for flexible on-chip light sources, amplifiers, nonreciprocal devices and signal-processing technologies.
Spontaneous Brillouin Scattering Modelling and Measurement in Various Axisymetric Optical Fibres
V. Lanticq; Gabet, R.; AUGUSTE, JL; DELEPINE LESOILLE, S; Fortier, S.; Jaouen, Y.
2007-01-01
We describe a computation method of spontaneous Brillouin scattering process using a simple original acoustic mode analysis. Numerical results have been compared with measured Brillouin spectra for two different commercially available fibres.
Tunable stimulated Brillouin scattering in hybrid polymer-chalcogenide tapered fibers
Beugnot, Jean-Charles; Ahmad, Raja; Rochette, Martin; Laude, Vincent; Maillotte, Hervé; Sylvestre, Thibaut
2014-05-01
We investigate Brillouin scattering in hybrid As2Se3 PMMA tapered fiber and demonstrate that Brillouin frequency shift can be widely tuned over a broad radio-frequency range by varying the core diameter of the optical tapered fiber.
An evaluation based theorem prover
Energy Technology Data Exchange (ETDEWEB)
Degano, P.; Sirovich, F.
1985-01-01
A noninductive method for mechanical theorem proving is presented, which deals with a recursive class of theorems involving iterative functions and predicates. The method is based on the symbolic evaluation of the formula to be proved and requires no inductive step. Induction is avoided since a metatheorem is proved which establishes the conditions on the evaluation of any formula which are sufficient to assure that the formula actually holds. The proof of a supposed theorem consists in evaluating the formula and checking the conditions. The method applies to assertions that involve element-by-element checking of typed homogeneous sequences which are hierarchically constructed out of the primitive type consisting of the truth values. The sequences can be computed by means of iterative and ''accumulator'' functions. The paper includes the definition of a simple typed iterative language in which both predicates and functions are expressed. The language precisely defines the scope of the proof method. The method proves a wide variety of theorems about iterative functions on sequences, including that which states that REVERSE is its own inverse, and that it can be inversely distributed on APPEND, that FLATTEN can be distributed on APPEND and that each element of any sequence is a MEMBER of the sequence itself. Although the method is not complete, it does provide the basis for an extremely efficient tool to be used in a complete mechanical theorem prover.
Nambu-Goldstone theorem and spin-statistics theorem
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Phase-locking in cascaded stimulated Brillouin scattering
Büttner, Thomas F S; Steel, M J; Hudson, Darren D; Eggleton, Benjamin J
2015-01-01
Cascaded stimulated Brillouin scattering (SBS) is a complex nonlinear optical process that results in the generation of several optical waves that are frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM) between these Brillouin shifted optical waves can create an equally spaced optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency comb (BFC). Here, we investigate phase-locking of the spectral components of BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well as from coupling by the acoustic field. Deriving for the first time the coupled-mode equations that include all relevant nonlinear interactions, we examine the contribution of the various nonlinear processes to phase-locking, and show that different regimes can be obtained that depend on the length scale on which the field amplitudes vary.
Recent progress in Brillouin scattering based fiber sensors.
Bao, Xiaoyi; Chen, Liang
2011-01-01
Brillouin scattering in optical fiber describes the interaction of an electro-magnetic field (photon) with a characteristic density variation of the fiber. When the electric field amplitude of an optical beam (so-called pump wave), and another wave is introduced at the downshifted Brillouin frequency (namely Stokes wave), the beating between the pump and Stokes waves creates a modified density change via the electrostriction effect, resulting in so-called the stimulated Brillouin scattering. The density variation is associated with a mechanical acoustic wave; and it may be affected by local temperature, strain, and vibration which induce changes in the fiber effective refractive index and sound velocity. Through the measurement of the static or dynamic changes in Brillouin frequency along the fiber one can realize a distributed fiber sensor for local temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performance parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors can be used in civil structural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the static Bragg grating, one can write a moving Brillouin grating in fibers, with the lifetime of the acoustic wave. The length of the Brillouin grating can be controlled by the writing pulses at any position in fibers. Such gratings can be used to measure changes in birefringence, which is an important parameter in fiber communications. Applications for this kind of sensor can be found in aerospace, material processing and fine structures.
Recent Progress in Brillouin Scattering Based Fiber Sensors
Directory of Open Access Journals (Sweden)
Liang Chen
2011-04-01
Full Text Available Brillouin scattering in optical fiber describes the interaction of an electro-magnetic field (photon with a characteristic density variation of the fiber. When the electric field amplitude of an optical beam (so-called pump wave, and another wave is introduced at the downshifted Brillouin frequency (namely Stokes wave, the beating between the pump and Stokes waves creates a modified density change via the electrostriction effect, resulting in so-called the stimulated Brillouin scattering. The density variation is associated with a mechanical acoustic wave; and it may be affected by local temperature, strain, and vibration which induce changes in the fiber effective refractive index and sound velocity. Through the measurement of the static or dynamic changes in Brillouin frequency along the fiber one can realize a distributed fiber sensor for local temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performance parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors can be used in civil structural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the static Bragg grating, one can write a moving Brillouin grating in fibers, with the lifetime of the acoustic wave. The length of the Brillouin grating can be controlled by the writing pulses at any position in fibers. Such gratings can be used to measure changes in birefringence, which is an important parameter in fiber communications. Applications for this kind of sensor can be found in aerospace, material processing and fine structures.
Fluctuation theorems for quantum processes.
Albash, Tameem; Lidar, Daniel A; Marvian, Milad; Zanardi, Paolo
2013-09-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Fluctuation theorems for quantum processes
Albash, Tameem; Lidar, Daniel A.; Marvian, Milad; Zanardi, Paolo
2013-09-01
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
Multibeam seeded brillouin sidescatter in inertial confinement fusion experiments.
Turnbull, D; Michel, P; Ralph, J E; Divol, L; Ross, J S; Berzak Hopkins, L F; Kritcher, A L; Hinkel, D E; Moody, J D
2015-03-27
We present the first observations of multibeam weakly seeded Brillouin sidescatter in indirect-drive inertial confinement fusion (ICF) experiments. Two seeding mechanisms have been identified and quantified: specular reflections ("glint") from opposite hemisphere beams, and Brillouin backscatter from neighboring beams with a different angle of incidence. Seeded sidescatter can dominate the overall coupling losses, so understanding this process is crucial for proper accounting of energy deposition and drive symmetry. Glint-seeded scattered light could also be used to probe hydrodynamic conditions inside ICF targets.
National Research Council Canada - National Science Library
Noboru Endou
2017-01-01
The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description...
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Directory of Open Access Journals (Sweden)
Pąk Karol
2015-06-01
Full Text Available In this article we prove the Euler’s Partition Theorem which states that the number of integer partitions with odd parts equals the number of partitions with distinct parts. The formalization follows H.S. Wilf’s lecture notes [28] (see also [1].
Angle Defect and Descartes' Theorem
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Bertini and his two fundamental theorems
Kleiman, Steven L.
1997-01-01
After reviewing Bertini's life story, a fascinating drama, we make a critical examination of the old statements and proofs of Bertini's two fundamental theorems, the theorem on variable singular points and the theorem on reducible linear systems. We explain the content of the statements in a way that is accessible to a nonspecialist, and we develop versions of the old proofs that are complete and rigorous by current standards. In particular, we prove a new extension of Bertini's first theorem...
BRILLOUIN INSTABILITY IN FIBER LASERS DOPED BY POWER ...
African Journals Online (AJOL)
30 juin 2012 ... continuous signal in a rare-earth doped fiber amplifier can generate high enough intensities to excite Brillouin ... Such back-reflection is detrimental for amplifier applications and consequently it has been studied .... le paramètre de dichroïsme du pompage. β est le paramètre de saturation croisée.Γ est le.
Rayleigh-Brillouin Scattering in Binary-Gas Mixtures
Gu, Z.; Ubachs, W.M.G.; Marques, W.; van der Water, W.
2015-01-01
Precise measurements are performed on spectral line shapes of spontaneous Rayleigh-Brillouin scattering in mixtures of the noble gases Ar and Kr, with He. Admixture of a light He atomic fraction results in marked changes of the spectra, although in all experiments He is merely a spectator atom: it
A Rayleigh-Brillouin scattering spectrometer for ultraviolet wavelengths
Gu, Z.Y.; Vieitez, M.O.; van Duijn, E.J.; Ubachs, W.M.G.
2012-01-01
A spectrometer for the measurement of spontaneous Rayleigh-Brillouin (RB) scattering line profiles at ultraviolet wavelengths from gas phase molecules has been developed, employing a high-power frequency-stabilized UV-laser with narrow bandwidth (2 MHz). The UV-light from a frequency-doubled
High-speed stimulated Brillouin scattering spectroscopy at 780 nm
Directory of Open Access Journals (Sweden)
Itay Remer
2016-09-01
Full Text Available We demonstrate a high-speed stimulated Brillouin scattering (SBS spectroscopy system that is able to acquire stimulated Brillouin gain point-spectra in water samples and Intralipid tissue phantoms over 2 GHz within 10 ms and 100 ms, respectively, showing a 10-100 fold increase in acquisition rates over current frequency-domain SBS spectrometers. This improvement was accomplished by integrating an ultra-narrowband hot rubidium-85 vapor notch filter in a simplified frequency-domain SBS spectrometer comprising nearly counter-propagating continuous-wave pump-probe light at 780 nm and conventional single-modulation lock-in detection. The optical notch filter significantly suppressed stray pump light, enabling detection of stimulated Brillouin gain spectra with substantially improved acquisition times at adequate signal-to-noise ratios (∼25 dB in water samples and ∼15 dB in tissue phantoms. These results represent an important step towards the use of SBS spectroscopy for high-speed measurements of Brillouin gain resonances in scattering and non-scattering samples.
Electron Gyro-Harmonic Effects on Ionospheric Stimulated Brillouin Scatter
2014-08-21
and piezoelectric semiconductor plasmas, as well as in various biological applications. Due to recent advances , active space experiments using high...27709-2211 Brillouin, SBS, emission lines, pump frequency stepping, cyclotron , EIC, airglow, upper hybrid REPORT DOCUMENTATION PAGE 11. SPONSOR...fiber optics, and piezoelectric semiconductor plasmas, as well as in various biological applications. Due to recent advances , active space experiments
Dilworth's Theorem Revisited, an Algorithmic Proof
W.H.L.M. Pijls (Wim); R. Potharst (Rob)
2011-01-01
textabstractDilworth's theorem establishes a link between a minimal path cover and a maximal antichain in a digraph. A new proof for Dilworth's theorem is given. Moreover an algorithm to find both the path cover and the antichain, as considered in the theorem, is presented.
Investigating the Fundamental Theorem of Calculus
Johnson, Heather L.
2010-01-01
The fundamental theorem of calculus, in its simplified complexity, connects differential and integral calculus. The power of the theorem comes not merely from recognizing it as a mathematical fact but from using it as a systematic tool. As a high school calculus teacher, the author developed and taught lessons on this fundamental theorem that were…
Fluctuation theorems for stochastic dynamics
Harris, R. J.; Schütz, G. M.
2007-07-01
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Fundamental theorem of Wiener calculus
Directory of Open Access Journals (Sweden)
Chull Park
1990-01-01
Full Text Available In this paper we define and develop a theory of differentiation in Wiener space C[0,T]. We then proceed to establish a fundamental theorem of the integral calculus for C[0,T]. First of all, we show that the derivative of the indefinite Wiener integral exists and equals the integrand functional. Secondly, we show that certain functionals defined on C[0,T] are equal to the indefinite integral of their Wiener derivative.
Extreme temperature sensing using brillouin scattering in optical fibers
Fellay, Alexandre
Stimulated Brillouin scattering in silica-based optical fibers may be considered from two different and complementary standpoints. For a physicist, this interaction of light and pressure wave in a material, or equivalently in quantum theory terms between photons and phonons, gives some glimpses of the atomic structure of the solid and of its vibration modes. For an applied engineer, the same phenomenon may be put to good use as a sensing mechanism for distributed measurements, thanks to the dependence of the scattered light on external parameters such as the temperature, the pressure or the strain applied to the fiber. As far as temperature measurements are concerned, Brillouin-based distributed sensors have progressively gained wide recognition as efficient systems, even if their rather high cost still restricts the number of their applications. Yet they are generally used in a relatively narrow temperature range around the usual ambient temperature; in this domain, the frequency of the scattered light incre...
Stimulated Brillouin scattering materials, experimental design and applications: A review
Bai, Zhenxu; Yuan, Hang; Liu, Zhaohong; Xu, Pengbai; Gao, Qilin; Williams, Robert J.; Kitzler, Ondrej; Mildren, Richard P.; Wang, Yulei; Lu, Zhiwei
2018-01-01
Stimulated Brillouin scattering (SBS), as one type of third-order nonlinear optics effect, is extensively exploited and rapidly developed in the field of lasers and optoelectronics. A large number of theoretical and experimental studies on SBS have been carried out in the past decades. Especially, the exploration of new SBS materials and new types of SBS modulation methods have been engaged simultaneously, as the properties of different materials have great influence on the SBS performance such as generation threshold, Brillouin amplification efficiency, frequency shift, breakdown threshold, etc. This article provides a comprehensive review of the characteristics of different types of SBS materials, SBS applications, experimental design methods, as well as the parameter optimization method, which is expected to provide reference and guidance to SBS related experiments.
Stimulated Brillouin scattering of elliptical laser beam in collisionless plasma
Singh, Arvinder; Walia, Keshav
2012-06-01
This paper presents an investigation of self-focusing of elliptical laser beam in collisionless plasma and its effect on stimulated Brillouin scattering. The pump beam interacts with a pre-excited ion-acoustic wave leading to Brillouin back-scattered process. The transverse intensity gradient of a pump beam generates a ponderomotive force, which modifies the background plasma density profile in a direction transverse to pump beam axis. This modification in density effects the incident laser beam, ion-acoustic wave and back-scattered beam. Non-linear differential equations for the beam width parameters of pump laser beam, ion-acoustic wave and back-scattered beam are set up and solved numerically. It is observed from the analysis that the focusing of waves enhances the SBS back-reflectivity.
Stimulated Brillouin scattering revisited: Strong coupling regime and Rabi splitting
Huy, Kien Phan; Tchahame, Joel Cabrel; Sylvestre, Thibaut
2015-01-01
Stimulated Brillouin scattering in optical waveguides is a fundamental interaction between light and acoustic waves mediated by electrostriction and photoelasticity. In this paper, we revisit the usual theory of this inelastic scattering process to get a joint system in which the acoustic wave is strongly coupled to the interference pattern between the optical waves. We show in particular that, when the optoacoustic coupling rate is comparable to the phonon damping rate, the system enters in the strong coupling regime, giving rise to avoided crossing of the dispersion curve and Rabi-like splitting. We further find that optoacoustic Rabi splitting could in principle be observed using backward stimulated Brillouin scattering in sub-wavelength diameter tapered optical fibers with moderate peak pump power.
Stability of Brillouin Flow in Slow-Wave Structures
Simon, David; Lau, Y. Y.; Greening, Geoffrey; Wong, Patrick; Gilgenbach, Ronald; Hoff, Brad
2016-10-01
For the first time, we include a slow-wave structure (SWS) to study the stability of Brillouin flow in the conventional, planar, and inverted magnetron geometry. The resonant interaction of the SWS circuit mode and the corresponding smooth-bore diocotron-like mode is found to be the dominant cause for instability, overwhelming the intrinsic negative (positive) mass property of electrons in the inverted (conventional) magnetron geometry. It severely restricts the wavenumber for instability to the narrow range in which the cold tube frequency of the SWS is within a few percent of the corresponding smooth bore diocotron-like mode in the Brillouin flow. This resonant interaction is absent in a smooth bore magnetron. Work supported by ONR N00014-13-1-0566 and N00014-16-1-2353, AFOSR FA9550-15-1-0097, and L-3 Communications Electron Device Division.
Transformation-optics simulation method for stimulated Brillouin scattering
Zecca, Roberto; Bowen, Patrick T.; Smith, David R.; Larouche, Stéphane
2016-12-01
We develop an approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation-optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.
Phonon-Limited-Linewidth of Brillouin Lasers at Cryogenic Temperatures
Suh, Myoung-Gyun; Yang, Qi-Fan; Vahala, Kerry J.
2017-10-01
Laser linewidth is of central importance in spectroscopy, frequency metrology, and all applications of lasers requiring high coherence. It is also of fundamental importance, because the Schawlow-Townes laser linewidth limit is of quantum origin. Recently, a theory of stimulated Brillouin laser (SBL) linewidth has been reported. While the SBL linewidth formula exhibits power and optical Q factor dependences that are identical to the Schawlow-Townes formula, a source of noise not present in conventional lasers, phonon occupancy of the Brillouin mechanical mode is predicted to be the dominant SBL linewidth contribution. Moreover, the quantum limit of the SBL linewidth is predicted to be twice the Schawlow-Townes limit on account of phonon participation. To help confirm this theory the SBL fundamental linewidth is measured at cryogenic temperatures in a silica microresonator. Its temperature dependence and the SBL linewidth theory are combined to predict the number of thermomechanical quanta at three temperatures. The result agrees with the Bose-Einstein phonon occupancy of the microwave-rate Brillouin mode in support of the SBL linewidth theory prediction.
Brillouin Optical Correlation Domain Analysis in Composite Material Beams
Directory of Open Access Journals (Sweden)
Yonatan Stern
2017-10-01
Full Text Available Structural health monitoring is a critical requirement in many composites. Numerous monitoring strategies rely on measurements of temperature or strain (or both, however these are often restricted to point-sensing or to the coverage of small areas. Spatially-continuous data can be obtained with optical fiber sensors. In this work, we report high-resolution distributed Brillouin sensing over standard fibers that are embedded in composite structures. A phase-coded, Brillouin optical correlation domain analysis (B-OCDA protocol was employed, with spatial resolution of 2 cm and sensitivity of 1 °K or 20 micro-strain. A portable measurement setup was designed and assembled on the premises of a composite structures manufacturer. The setup was successfully utilized in several structural health monitoring scenarios: (a monitoring the production and curing of a composite beam over 60 h; (b estimating the stiffness and Young’s modulus of a composite beam; and (c distributed strain measurements across the surfaces of a model wing of an unmanned aerial vehicle. The measurements are supported by the predictions of structural analysis calculations. The results illustrate the potential added values of high-resolution, distributed Brillouin sensing in the structural health monitoring of composites.
Brillouin Optical Correlation Domain Analysis in Composite Material Beams.
Stern, Yonatan; London, Yosef; Preter, Eyal; Antman, Yair; Diamandi, Hilel Hagai; Silbiger, Maayan; Adler, Gadi; Levenberg, Eyal; Shalev, Doron; Zadok, Avi
2017-10-02
Structural health monitoring is a critical requirement in many composites. Numerous monitoring strategies rely on measurements of temperature or strain (or both), however these are often restricted to point-sensing or to the coverage of small areas. Spatially-continuous data can be obtained with optical fiber sensors. In this work, we report high-resolution distributed Brillouin sensing over standard fibers that are embedded in composite structures. A phase-coded, Brillouin optical correlation domain analysis (B-OCDA) protocol was employed, with spatial resolution of 2 cm and sensitivity of 1 °K or 20 micro-strain. A portable measurement setup was designed and assembled on the premises of a composite structures manufacturer. The setup was successfully utilized in several structural health monitoring scenarios: (a) monitoring the production and curing of a composite beam over 60 h; (b) estimating the stiffness and Young's modulus of a composite beam; and (c) distributed strain measurements across the surfaces of a model wing of an unmanned aerial vehicle. The measurements are supported by the predictions of structural analysis calculations. The results illustrate the potential added values of high-resolution, distributed Brillouin sensing in the structural health monitoring of composites.
High-extinction VIPA-based Brillouin spectroscopy of turbid biological media
Fiore, Antonio; Shao, Peng; Yun, Seok Hyun; Scarcelli, Giuliano
2016-01-01
Brillouin microscopy has recently emerged as powerful technique to characterize the mechanical properties of biological tissue, cell and biomaterials. However, the potential of Brillouin microscopy is currently limited to transparent samples, because Brillouin spectrometers do not have sufficient spectral extinction to reject the predominant non-Brillouin scattered light of turbid media. To overcome this issue, we developed a spectrometer composed of a two VIPA stages and a multi-pass Fabry-Perot interferometer. The Fabry-Perot etalon acts as an ultra-narrow band-pass filter for Brillouin light with high spectral extinction and low loss. We report background-free Brillouin spectra from Intralipid solutions and up to 100 microns deep within chicken muscle tissue.
Expanding the Interaction Equivalency Theorem
Directory of Open Access Journals (Sweden)
Brenda Cecilia Padilla Rodriguez
2015-06-01
Full Text Available Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner is present at a high level. This study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.
Chen, Fuchang; Chen, Bai; Lin, Zunqi
2010-11-01
We design a new system for simultaneous distributed measurement of temperature and strain based on both spontaneous Raman and Brillouin backscattered signals. The Raman signal can determine the temperature. Although the Brillouin frequency shift is dependent on both temperature and strain of fiber, once the temperature is determined from the Raman signal, the strain can then be computed from the frequency measurement of the Brillouin signal.
Temperature and strain dependence of Brillouin scattering in chalcogenide optical microwires
Beugnot, J-C; Jeannin, C; Tchahame, J,; Godet, A; Ndao, A; Sylvestre, T; Ahmad, R; Rochette, M
2016-01-01
International audience; We report the measurement of Brillouin spectrum in polymer-coated chalcogenide microwire as a function of temperature and strain variation. We show a negative variation of Brillouin frequency shift. The coating strongly modify the Brillouin frequency due to temperature. OCIS codes: 060.4370, 190.3270, 190.5890 Chalcogenide-glass fibers offer a unique set of optical properties presenting an excellent platform for development of highly nonlinear optical devices for all-o...
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
A Classification of Viruses through Recursion Theorems
Bonfante, Guillaume; Kaczmarek, Matthieu; Marion, Jean-Yves
2007-01-01
The original publication is available at www.springerlink.com ; ISBN 978-3-540-73000-2 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We study computer virology from an abstract point of view. Viruses and worms are self-replicating programs, whose definitions are based on Kleene's second recursion theorem. We introduce a notion of delayed recursion that we apply to both Kleene's second recursion theorem and Smullyan's double recursion theorem. This leads us to define fou...
On General Summability Factor Theorems
Directory of Open Access Journals (Sweden)
Ekrem Savaş
2007-03-01
Full Text Available The goal of this paper is to obtain sufficient and (different necessary conditions for a series Ã¢ÂˆÂ‘an, which is absolutely summable of order k by a triangular matrix method A, 1
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
Fixed point theorem utilizing operators and functionals
Directory of Open Access Journals (Sweden)
Douglas Anderson
2012-02-01
Full Text Available This paper presents a fixed point theorem utilizing operators and functionals in the spirit of the original Leggett-Williams fixed point theorem which is void of any invariance-like conditions. The underlying sets in the Leggett-Williams fixed point theorem that were defined using the total order of the real numbers are replaced by sets that are defined using an ordering generated by a border-symmetric set, that is, the sets that were defined using functionals in the original Leggett-Williams fixed point theorem are replaced by sets that are defined using operators.
Ou, Zhonghua; Zhang, Lixun; Dai, Zhiyong; Liu, Yongzhi
2008-04-01
A novel method for direct optical detection of spontaneous Brillouin scattering in optical fiber by using a fiber Bragg grating (FBG) Sagnac loop is introduced. The transmission character as an optical filter of FBG Sagnac loop is investigated theoretically. The filter which is based on an asymmetric grating Sagnac loop is manufactured and used in the measurement of spontaneous Brillouin scattering sensing system, and the separation of backscattered spontaneous Brillouin from Rayleigh is achieved effectively. It is demonstrated that the fiber grating Sagnac loop filter can be applied in the distributed sensing system based on spontaneous Brillouin scattering.
Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
Christensen, Sören
2010-01-01
We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers. With the help of error estimates in the renewal theorem we figure out an explicit representation.
Indian Academy of Sciences (India)
On a Theorem of Vito Volterra. V M Sholapurkar. Classroom Volume 12 Issue 1 January 2007 pp 76-79. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/012/01/0076-0079. Keywords. Continuity; discontinuity; rationals; irrationals; nested intervals; Baire category theorem.
A Note on Morley's Triangle Theorem
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
Ehrenfest's Theorem and Nonclassical States of Light
Indian Academy of Sciences (India)
Ehrenfest's Theorem and Nonclassical States of Light - Ehrenfest's Theorem in Quantum Mechanics. Lijo T George C Sudheesh S Lakshmibala V Balakrishnan. General Article Volume 17 Issue 1 January 2012 pp 23-32 ... Keywords. Ehrenfest; expectation values; quantum dynamics; quantum-classical correspondence.
Power-counting theorem for staggered fermions
Giedt, J
2006-01-01
One of the assumptions that is used in Reisz's power-counting theorem does not hold for staggered fermions, as was pointed out long ago by Lüscher. Here, we generalize the power-counting theorem, and the methods of Reisz's proof, such that the dif culties posed by staggered fermions are overcome.
SOME LIMIT-THEOREMS IN LOG DENSITY
BERKES, [No Value; DEHLING, H
Motivated by recent results on pathwise central limit theorems, we study in a systematic way log-average versions of classical limit theorems. For partial sums S(k) of independent r.v.'s we prove under mild technical conditions that (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)I{S(k)/a(k)
A Comment on Holographic Luttinger Theorem
Hashimoto, Koji
2012-01-01
Robustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating theta-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robustness of the theorem is found for strongly correlated fermions coupled with strongly coupled sectors which admit gravity duals. On the other hand, in the deconfined phase, we also show that the deficit appearing in the Luttinger theorem is again universal. It measures a total deficit which measures the charge of the deconfined ("fractionalized") fermions, independent of the deformation parameters.
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Highly sensitive measurement of submicron waveguides based on Brillouin scattering
Godet, Adrien; Ndao, Abdoulaye; Sylvestre, Thibaut; Beugnot, Jean-Charles; Phan Huy, Kien
2017-02-01
Fabrication and characterization of submicron optical waveguides is one of the major challenges in modern photonics, as they find many applications from optical sensors to plasmonic devices. Here we report on a novel technique that allows for a complete and precise characterization of silica optical nanofibers. Our method relies on the Brillouin backscattering spectrum analysis that directly depends on the waveguide geometry. Our method was applied to several fiber tapers with diameter ranging from 500 nm to 3 μm. Results were compared to scanning electron microscopy (SEM) images and numerical simulations with very good agreement and similar sensitivity.
Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides
Smith, M J A; de Sterke, C Martijn; Lapine, M; Kuhlmey, B T; Poulton, C G
2016-01-01
Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for Stimulated Brillouin Scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic applications in on-chip material systems.
Atherosclerotic plaque detection by confocal Brillouin and Raman microscopies
Meng, Zhaokai; Basagaoglu, Berkay; Yakovlev, Vladislav V.
2015-02-01
Atherosclerosis, the development of intraluminal plaque, is a fundamental pathology of cardiovascular system and remains the leading cause of morbidity and mortality worldwide. Biomechanical in nature, plaque rupture occurs when the mechanical properties of the plaque, related to the morphology and viscoelastic properties, are compromised, resulting in intraluminal thrombosis and reduction of coronary blood flow. In this report, we describe the first simultaneous application of confocal Brillouin and Raman microscopies to ex-vivo aortic wall samples. Such a non-invasive, high specific approach allows revealing a direct relationship between the biochemical and mechanical properties of atherosclerotic tissue.
Biomechanics of subcellular structures by non-invasive Brillouin microscopy
Antonacci, Giuseppe; Braakman, Sietse
2016-11-01
Cellular biomechanics play a pivotal role in the pathophysiology of several diseases. Unfortunately, current methods to measure biomechanical properties are invasive and mostly limited to the surface of a cell. As a result, the mechanical behaviour of subcellular structures and organelles remains poorly characterised. Here, we show three-dimensional biomechanical images of single cells obtained with non-invasive, non-destructive Brillouin microscopy with an unprecedented spatial resolution. Our results quantify the longitudinal elastic modulus of subcellular structures. In particular, we found the nucleoli to be stiffer than both the nuclear envelope (p biomechanics and its role in pathophysiology.
Strongly coupled stimulated Brillouin amplification in pump-ionizing plasma
Peng, H.; Wu, Z. H.; Zuo, Y. L.; Zhou, K. N.; Wang, X. D.; Li, Q.; Zhu, H. Y.; Su, J. Q.
2018-02-01
Laser amplification based on strongly coupled stimulated Brillouin scattering in plasma is investigated. The pump and seed are at the same wavelength of 800 nm and the same duration of 3.5 ps, but with a different intensity. The plasma is produced by the front part of the pump via tunnel ionization from hydrogen. The hydrogen is fully ionized to eliminate small-scale density fluctuations in the plasma, so the transmission level of the seed is enhanced to 22%, and a relative amplification factor of 6 is obtained.
New improvements for Brillouin optical time-domain reflectometry
Le Floch, Sébastien; Sauser, Florian
2017-04-01
This paper presents new techniques designed to improve the performances of a BOTDR. The first one introduces a second pump to the sensor, thus doubling the Brillouin signal on the receiver. The second one uses image processing with a two-dimensional Gaussian filter whose parameters are defined. The last technique explores the possibilities offered by colour codes. The benefits of each, in terms of signal-to-noise ratio, is presented by comparing measurements over a distance range of 50km with a spatial resolution of 5m. These techniques can easily be combined and the global improvement is estimated at 10dB, compared to conventional sensors.
Brillouin frequency shift measurement with virtually controlled sensitivity
Tanaka, Yosuke; Ozaki, Yuta
2017-06-01
We propose measuring the change in Brillouin frequency shift (BFS) in an optical fiber with virtually controlled sensitivity based on the Vernier effect using a multimode pump and probe light. We measure BFS from the envelope curve of the spectra for multimode Stokes light without scanning the probe frequency. The sensitivity of BFS is virtually controlled by changing the difference in the mode spacing between the pump and the probe. It is experimentally demonstrated that the virtual sensitivity is controlled from -1.1 to 1.1 GHz/K, the maximum value of which is 1,100 times higher than the standard BFS of 1 MHz/K.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
Energy Technology Data Exchange (ETDEWEB)
Yamada, Tomonori; Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
National Research Council Canada - National Science Library
Yunqi Hao; Qing Ye; Zhengqing Pan; Fei Yang; Haiwen Cai; Ronghui Qu; Qinyuan Zhang; Zhongmin Yang
2012-01-01
...) is larger than 50 dB and the laser linewidth is about 3.1 kHz. Applying the BFL to the BOTDR system, the measured results show that the beat frequency between the spontaneous Brillouin scattering (SBS...
The pointwise Hellmann-Feynman theorem
Directory of Open Access Journals (Sweden)
David Carfì
2010-02-01
Full Text Available In this paper we study from a topological point of view the Hellmann-Feynman theorem of Quantum Mechanics. The goal of the paper is twofold: On one hand we emphasize the role of the strong topology in the classic version of the theorem in Hilbert spaces, for what concerns the kind of convergence required on the space of continuous linear endomorphisms, which contains the space of (continuous observables.On the other hand we state and prove a new pointwise version of the classic Hellmann-Feynman theorem. This new version is not yet present in the literature and follows the idea of A. Bohm concerning the topology which is desiderable to use in Quantum Mechanics. It is indeed out of question that this non-trivial new version of the Hellmann-Feynman theorem is the ideal one - for what concerns the continuous observables on Hilbert spaces, both from a theoretical point of view, since it is the strongest version obtainable in this context - we recall that the pointwise topology is the coarsest one compatible with the linear structure of the space of continuous observables -, and from a practical point of view, because the pointwise topology is the easiest to use among topologies: it brings back the problems to the Hilbert space topology. Moreover, we desire to remark that this basic theorem of Quantum Mechanics, in his most desiderable form, is deeply interlaced with two cornerstones of Functional Analysis: the Banach-Steinhaus theorem and the Baire theorem.
Light beating spectroscopy of Brillouin scattering in gases and solids
Yogi, Takeshi; Sakai, Keiji; Takagi, Kenshiro
2006-07-01
The experimental system of optical beating spectroscopy was improved, and the increased sensitivity and frequency resolution were demonstrated in the Brillouin scattering experiments in solids, crown glass (BK7), and polymethylmetacrylate (PMMA), and also in gases, air, and nitrogen. For their weak light scattering ability, these substances are very tough specimens for Brillouin scattering studies, and the classical spectrometer of Fabry-Pérot étalon has been so far used for the frequency analysis. The phonon peaks were observed with the present light beating system in BK7 at room temperature over the wave number range from k /2π=1.03×104to8.84×104m-1 (corresponding frequency from 61.6to548MHz), and the spectra were fitted with Gaussian curves since a condenser lens in the incident light path caused a large instrumental width that overwhelmed the intrinsic phonon width. The spectra in PMMA were analyzed with Voigt functions. The dispersion relations obtained in these solids were in good agreement with the literature values of ultrasonic velocity. The spectra in air were well fitted with Lorentzian curve representing the phonon lifetime, and the absorption as well as the phase velocity was obtained.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we show how the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....
Fluctuation theorems for quantum master equations.
Esposito, Massimiliano; Mukamel, Shaul
2006-04-01
A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation--i.e., a quantum master equation (QME). Quantum trajectories and their associated entropy, heat, and work appear naturally by transforming the QME to a time-dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady-state fluctuation theorem, and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
of Stokes' theorem for differential forms on manifolds. The main points in the present paper, however, is firstly that this latter fact usually does not get within reach for students in first year calculus courses and secondly that calculus textbooks in general only just hint at the correspondence alluded...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
Security Theorems via Model Theory
Directory of Open Access Journals (Sweden)
Joshua Guttman
2009-11-01
Full Text Available A model-theoretic approach can establish security theorems for cryptographic protocols. Formulas expressing authentication and non-disclosure properties of protocols have a special form. They are quantified implications for all xs . (phi implies for some ys . psi. Models (interpretations for these formulas are *skeletons*, partially ordered structures consisting of a number of local protocol behaviors. *Realized* skeletons contain enough local sessions to explain all the behavior, when combined with some possible adversary behaviors. We show two results. (1 If phi is the antecedent of a security goal, then there is a skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there is a homomorphism from A_phi to B. (2 A protocol enforces for all xs . (phi implies for some ys . psi iff every realized homomorphic image of A_phi satisfies psi. Hence, to verify a security goal, one can use the Cryptographic Protocol Shapes Analyzer CPSA (TACAS, 2007 to identify minimal realized skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in each of these shapes, then the goal holds.
The reciprocity theorem for porous anisotropic media
Directory of Open Access Journals (Sweden)
E. BOSCHI
1972-06-01
Full Text Available In this paper we give a reciprocity theorem for anisotropic
porous media in the quasi-stationary case. The distribution of the
pores is assumed statistically homogeneous.
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Coincidence theorems for some multivalued mappings
Directory of Open Access Journals (Sweden)
B. E. Rhoades
1984-01-01
Full Text Available Two coincidence theorems in a metric space are proved for a multi-valued mapping that commutes with a single-valued mapping and satisfies a general multi-valued contraction type condition.
Exchange fluctuation theorem for correlated quantum systems.
Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio
2015-10-01
We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a "correlation fluctuation theorem". Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem.
Some comments to the quantum fluctuation theorems
Kuzovlev, Yu. E.
2011-01-01
It is demonstrated that today's quantum fluctuation theorems are component part of old quantum fluctuation-dissipation relations [Sov.Phys.-JETP 45, 125 (1977)], and typical misunderstandings in this area are pointed out.
Subleading soft graviton theorem for loop amplitudes
National Research Council Canada - National Science Library
Sen, Ashoke
2017-01-01
... or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton...
The virial theorem for nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo.amore@gmail.com, E-mail: fernande@quimica.unlp.edu.ar
2009-09-15
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular, we consider conservative nonlinear oscillators and obtain the same main result derived earlier from the expansion in Chebyshev polynomials. (letters and comments)
Transformation groups and the virial theorem
Kampen, N.G. van
A generalization of Noether's result for classical mechanics is given, which shows that the virial theorem is related to an invariance property of the Lagrange function. Two examples are discussed in detail.
Sahoo- and Wayment-Type Integral Mean Value Theorems
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
Generalized monotone convergence and Radon-Nikodym theorems
Gudder, S.; Zerbe, J.
1981-11-01
A measure and integration theory is presented in the quantum logic framework. A generalization of the monotone convergence theorem is proved. Counterexamples are used to show that the dominated convergence theorem, Fatou's lemma, Egoroff's theorem, and the additivity of the integral do not hold in this framework. Finally, a generalization of the Radon-Nikodym theorem is proved.
Commentaries on Hilbert's Basis Theorem | Apine | Science World ...
African Journals Online (AJOL)
The famous basis theorem of David Hilbert is an important theorem in commutative algebra. In particular the Hilbert's basis theorem is the most important source of Noetherian rings which are by far the most important class of rings in commutative algebra. In this paper we have used Hilbert's theorem to examine their unique ...
Cauchy-Davenport theorem in group extensions
Karolyi, G
2005-01-01
Let A and B be nonempty subsets of a finite group G in which the order of the smallest nontrivial subgroup is not smaller than d=|A|+|B|-1. Then the product set AB has at least d elements. This extends a classical theorem of Cauchy and Davenport to noncommutative groups. We also generalize Vosper's inverse theorem in the same spirit, giving a complete description of the critical pairs. The proofs depend on the structure of group extensions.
Perelman's collapsing theorem for 3-manifolds
Cao, Jianguo; Ge, Jian
2009-01-01
We will simplify the earlier proofs of Perelman's collapsing theorem of 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's semi-convex analysis of distance functions to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theo...
Noether's first theorem in Hamiltonian mechanics
Sardanashvily, G.
2015-01-01
Non-autonomous non-relativistic mechanics is formulated as Lagrangian and Hamiltonian theory on fibre bundles over the time axis R. Hamiltonian mechanics herewith can be reformulated as particular Lagrangian theory on a momentum phase space. This facts enable one to apply Noether's first theorem both to Lagrangian and Hamiltonian mechanics. By virtue of Noether's first theorem, any symmetry defines a symmetry current which is an integral of motion in Lagrangian and Hamiltonian mechanics. The ...
Levi-Civita's Theorem for Noncommutative Tori
Directory of Open Access Journals (Sweden)
Jonathan Rosenberg
2013-11-01
Full Text Available We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas.
The Serre duality theorem for Reimann surfaces
Directory of Open Access Journals (Sweden)
Ranjan Roy
1984-01-01
Full Text Available Given a Riemann surface S, there exists a finitely generated Fuchsian group G of the first kind acting on the upper half plane U, such that S≅U/G. This isomorphism makes it possible to use Fuchsian group methods to prove theorems about Riemann surfaces. In this note we give a proof of the Serre duality theorem by Fuchsian group methods which is technically simpler than proofs depending on sheaf theoretic methods.
Vieitez, MO; van Duijn; Ubachs, W.; Witschas, B.; Meijer, A.; Wijn, De, JR; Dam, NJ Nico; Water, van de, W Willem
2010-01-01
We study Rayleigh-Brillouin scattering in gases of N2, O2, and SF6 molecules, Kr atoms, and He-Xe and He-CO2 mixtures at pressures ranging from 1 to 3 bar and using two different experimental setups. In one setup, we measure spectra of light scattered by thermal density fluctuations (spontaneous Rayleigh-Brillouin scattering); in the second setup density waves are induced in the overlap region of two counterpropagating laser beams (coherent Rayleigh-Brillouin scattering).We compare measured s...
Alahbabi, M. N.; Cho, Y. T.; Newson, T. P.
2005-06-01
We report on a novel method for simultaneous distributed measurement of temperature and strain based on spatially resolving both spontaneous Raman and Brillouin backscattered anti-Stokes signals. The magnitude of the intensity of the anti-Stokes Raman signal permits the determination of the temperature. The Brillouin frequency shift is dependent on both the temperature and the strain of the fiber; once the temperature has been determined from the Raman signal, the strain can then be computed from the frequency measurement of the Brillouin signal.
Geng, Jihong; Staines, Sean; Blake, Mike; Jiang, Shibin
2007-08-01
A novel technique that enables coherent detection of spontaneous Brillouin scattering in the radio-frequency (<500 MHz) region with excellent long-term stability has been demonstrated for distributed measurements of temperature and strain in long fiber. An actively stabilized single-frequency Brillouin fiber laser with extremely low phase noise and intensity noise is used as a well-defined, frequency-shifted local oscillator for the heterodyne detection, yielding measurements of spontaneous Brillouin scattering with high frequency stability. Based on this approach, a highly stable real-time fiber sensor for distributed measurements of both temperature and strain over long fiber has been developed utilizing advanced digital signal processing techniques.
Analysis of the spontaneous Rayleigh-Brillouin scattering spectra of N2
Wu, Tao; Xia, Ruxiao; He, Xingdao; Zhang, Xinyi; Yu, Huan
2016-10-01
The influence of different pressures, temperatures, scattering angles and incident wavelengths to the relative intensity of the Brillouin peaks to the Rayleigh peak and the Brillouin shift in the spontaneous Rayleigh-Brillouin scattering (SRBS) spectra of N2 is analyzed by using the Tenti S6 model. A system for detecting the SRBS spectra of gas is also introduced in this paper. The SRBS spectra of N2 at different pressures with the incident wavelength of 532nm, the temperature of 300K and the scattering angle of 90° have been measured, the experiment results are well agreed to the simulations.
Multimode Brillouin spectrum in a long tapered birefringent photonic crystal fiber.
Tchahame, Joël Cabrel; Beugnot, Jean-Charles; Kudlinski, Alexandre; Sylvestre, Thibaut
2015-09-15
We investigate the stimulated Brillouin scattering (SBS) in a long tapered birefringent solid-core photonic crystal fiber (PCF) and compare our results with a similar but untapered PCF. It is shown that the taper generates a broadband and multipeaked Brillouin spectrum, while significantly increasing the threshold power. Furthermore, we observe that the strong fiber birefringence gives rise to a frequency shift of the Brillouin spectrum which increases along the fiber. Numerical simulations are also presented to account for the taper effect and the birefringence. Our findings open a new means to control or inhibit the SBS by tapering photonic crystal fibers.
Brillouin light scattering from shear waves in an epoxy resin through the glass transition
Comez, L.; Fioretto, D.; Verdini, L.; Rolla, P. A.
1997-05-01
The temperature dependences of the characteristic frequency and lifetime of hypersonic transverse acoustic waves in the epoxy system EPON 828 have been probed by means of the Brillouin light scattering technique. Evidence has been found of a very broad dispersion region, together with a discontinuity close to the glass transition temperature 0953-8984/9/19/016/img7. For temperatures higher than 0953-8984/9/19/016/img7, the shear loss data obtained from Brillouin spectra are in quantitative agreement with dielectric data for the same system. For lower temperatures, the Brillouin data deviate from the dielectric ones, the former being more sensitive to the secondary relaxation processes.
Brillouin resonance broadening due to structural variations in nanoscale waveguides
Wolff, Christian; Steel, Michael J; Eggleton, Benjamin J; Poulton, Christopher G
2015-01-01
We study the impact of structural variations (that is slowly varying geometry aberrations and internal strain fields) on the resonance width and shape of stimulated Brillouin scattering (SBS) in nanoscale waveguides. We find that they lead to an inhomogeneous resonance broadening through two distinct mechanisms: firstly, the acoustic frequency is directly influenced via mechanical nonlinearities; secondly, the optical wave numbers are influenced via the opto-mechanical nonlinearity leading to an additional acoustic frequency shift via the phase-matching condition. We find that this second mechanism is proportional to the opto-mechanical coupling and, hence, related to the SBS-gain itself. It is absent in intra-mode forward SBS, while it plays a significant role in backward scattering. In backward SBS increasing the opto-acoustic overlap beyond a threshold defined by the fabrication tolerances will therefore no longer yield the expected quadratic increase in overall Stokes amplification. Our results can be tra...
Quantum Rabi model in the Brillouin zone with ultracold atoms
Felicetti, Simone; Rico, Enrique; Sabin, Carlos; Ockenfels, Till; Koch, Johannes; Leder, Martin; Grossert, Christopher; Weitz, Martin; Solano, Enrique
2017-01-01
The quantum Rabi model describes the interaction between a two-level quantum system and a single bosonic mode. We propose a method to perform a quantum simulation of the quantum Rabi model, introducing an implementation of the two-level system provided by the occupation of Bloch bands in the first Brillouin zone by ultracold atoms in tailored optical lattices. The effective qubit interacts with a quantum harmonic oscillator implemented in an optical dipole trap. Our realistic proposal allows one to experimentally investigate the quantum Rabi model for extreme parameter regimes, which are not achievable with natural light-matter interactions. When the simulated wave function exceeds the validity region of the simulation, we identify a generalized version of the quantum Rabi model in a periodic phase space.
Dual-microcavity narrow-linewidth Brillouin laser
Loh, William; Baynes, Frederick; Cole, Daniel; Quinlan, Franklyn; Lee, Hansuek; Vahala, Kerry; Papp, Scott; Diddams, Scott
2014-01-01
Ultralow noise, yet tunable lasers are a revolutionary tool in precision spectroscopy, displacement measurements at the standard quantum limit, and the development of advanced optical atomic clocks. Further applications include LIDAR, coherent communications, frequency synthesis, and precision sensors of strain, motion, and temperature. While all applications benefit from lower frequency noise, many also require a laser that is robust and compact. Here, we introduce a dual-microcavity laser that leverages one chip-integrable silica microresonator to generate tunable 1550 nm laser light via stimulated Brillouin scattering (SBS) and a second microresonator for frequency stabilization of the SBS light. This configuration reduces the fractional frequency noise to $7.8\\times10^{-14} 1/\\sqrt{Hz}$ at 10 Hz offset, which is a new regime of noise performance for a microresonator-based laser. Our system also features terahertz tunability and the potential for chip-level integration. We demonstrate the utility of our du...
High-pressure Brillouin study on methane hydrate
Sasaki, S; Suwa, I; Kume, T; Shimizu, H
2002-01-01
Acoustic velocities and adiabatic elastic constants of structure I of methane hydrate (MH) have been determined as a function of pressure up to 0.6 GPa at 23 deg. C by the high-pressure Brillouin spectroscopy developed for a single molecular crystal. The pressure dependence of the acoustic velocities of MH is very similar to that of ice-Ih except for the longitudinal acoustic (LA) velocity. The value of the LA velocity along the (100) direction of MH at 0.02 GPa is 3.63 km s sup - sup 1 which is about 7% lower than the average of the LA velocities in the ice-Ih phase at -35.5 deg. C and atmospheric pressure.
Nonequilibrium potential and fluctuation theorems for quantum maps.
Manzano, Gonzalo; Horowitz, Jordan M; Parrondo, Juan M R
2015-09-01
We derive a general fluctuation theorem for quantum maps. The theorem applies to a broad class of quantum dynamics, such as unitary evolution, decoherence, thermalization, and other types of evolution for quantum open systems. The theorem reproduces well-known fluctuation theorems in a single and simplified framework and extends the Hatano-Sasa theorem to quantum nonequilibrium processes. Moreover, it helps to elucidate the physical nature of the environment that induces a given dynamics in an open quantum system.
Non-euclidean shadows of classical projective theorems
Vigara, Ruben
2014-01-01
Some translations into non-euclidean geometry of classical theorems of planar projective geometry are explored. The existence of some common triangle centers is dedeuced from theorems of Pascal and Chasles. Desargues' Theorem allows to construct a non-euclidean version of the Euler line and the nine-point circle of a triangle. The whole non-euclidean trigonometry (for triangles and generalizaed triangles) can be deduced from Menelaus' Theorem. A theorem of Carnot about affine triangles implie...
Central limit theorem and almost sure central limit theorem for the ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 2. Central Limit Theorem and almost sure Central Limit Theorem for the Product of some Partial Sums. Yu Miao. Research Articles Volume 118 Issue 2 May 2008 pp 289-294 ...
Central limit theorem and almost sure central limit theorem for the ...
Indian Academy of Sciences (India)
Department of Mathematics and Statistics, Wuhan University, 430072 Hubei, China. E-mail: yumiao728@yahoo.com.cn. MS received 26 January 2007; revised 27 May 2007. Abstract. In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent ...
Zhan, Li; Zhang, Liang; Wang, Tantan; Qin, Minglei; Liu, Jinmei
2015-03-01
Long distance superluminal propagation in optical fibers via cascaded Brillouin lasing oscillation is proposed and experimentally demonstrated. The Gaussian pulses experience negative group-velocity superluminal propagation with the advancement of ~300ns in 20-m single mode fiber.
Alahbabi, M. N.; Cho, Y. T.; Newson, Trevor P.
2004-06-01
We report on a novel method for simultaneous distributed measurement of the temperature and strain in an optical fiber based on spatially resolving the anti-Stokes signals of both the spontaneous Raman and Brillouin backscattered signals.
Analysis of optical pulse coding in spontaneous Brillouin-based distributed temperature sensors
National Research Council Canada - National Science Library
Marcelo A. Soto; Gabriele Bolognini; Fabrizio Di Pasquale
2008-01-01
A theoretical and experimental analysis of optical pulse coding techniques applied to distributed optical fiber temperature sensors based on spontaneous Brillouin scattering using the Landau-Placzek ratio (LPR...
Bi-Directional Brillouin Optical Time Domain Analyzer System for Long Range Distributed Sensing.
Guo, Nan; Wang, Liang; Wang, Jie; Jin, Chao; Tam, Hwa-Yaw; Zhang, A Ping; Lu, Chao
2016-12-16
We propose and experimentally demonstrate a novel scheme of bi-directional Brillouin time domain analyzer (BD-BOTDA) to extend the sensing range. By deploying two pump-probe pairs at two different wavelengths, the Brillouin frequency shift (BFS) distribution over each half of the whole fiber can be obtained with the simultaneous detection of Brillouin signals in both channels. Compared to the conventional unidirectional BOTDA system of the same sensing range, the proposed BD-BOTDA scheme enables distributed sensing with a performance level comparable to the conventional one with half of the sensing range and a spatial resolution of 2 m, while maintaining the Brillouin signal-to-noise ratio (SNR) and the BFS uncertainty. Based on this technique, we have achieved distributed temperature sensing with a measurement range of 81.9 km fiber at a spatial resolution of 2 m and BFS uncertainty of ~0.44 MHz without introducing any complicated components or schemes.
Topological interpretation of the Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-08-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because (i) the Luttinger volume is represented as the winding number of the single-particle Green's function and, thus, (ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for nonmetallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a nonperturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that
Anti-Bell - Refutation of Bell's theorem
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Soto, M A; Bolognini, G.; Di Pasquale, F.
2009-01-01
In this work, we propose the use of optical pulse coding techniques for simultaneous strain and temperature sensing based on spontaneous Brillouin scattering. Optical pulse coding provides a significant receiver signal-to-noise ratio enhancement, allowing for accurate Brillouin intensity and frequency shift measurements at low peak power levels. Due to the cross-sensitivity of these two parameters on both temperature and strain, optical pulse coding improves the temperature and strain resolut...
High-resolution Brillouin analysis in a carbon-fiber-composite unmanned aerial vehicle model wing
Stern, Yonatan; London, Yosef; Preter, Eyal; Antman, Yair; Shlomi, Orel; Silbiger, Maayan; Adler, Gadi; Zadok, Avi
2016-05-01
Standard optical fibers are successfully embedded within a model wing of an unmanned aerial vehicle, constructed of carbon fiber and epoxy, during its production. Time-gated Brillouin optical correlation domain analysis along the embedded optical fibers is performed with a spatial resolution of 4 cm. Tests were carried out using a portable measurement setup prototype. The results represent an important step towards applications of high-resolution Brillouin analysis outside the research laboratory.
First numerical experiences with overlap fermions based on the Brillouin kernel
Durr, Stephan
2016-01-01
Numerical experiences are reported with overlap fermions which employ the Brillouin action as a kernel. After discussing the dispersion relations of both the kernel and the resulting chiral action, some of the physics features are addressed on quenched backgrounds. We find that the overlap with Brillouin kernel is much better localized than the overlap with Wilson kernel. Also a preliminary account is given of the cost of the formulation, in terms of CPU time and memory.
DEFF Research Database (Denmark)
Lorenzen, Michael Rodas; Noordegraaf, Danny; Nielsen, Carsten Vandel
2008-01-01
We demonstrate an increased gain in optical parametric amplier through suppression of stimulated Brillouin scattering by applying a temperature distribution along the fiber resulting in a reduction of the required phase modulation.......We demonstrate an increased gain in optical parametric amplier through suppression of stimulated Brillouin scattering by applying a temperature distribution along the fiber resulting in a reduction of the required phase modulation....
Lindeberg theorem for Gibbs–Markov dynamics
Denker, Manfred; Senti, Samuel; Zhang, Xuan
2017-12-01
A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs–Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs–Markov dynamical systems for convenience.
Energy Technology Data Exchange (ETDEWEB)
A. Burov
2001-05-29
For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping does not have to be rotation-invariant here.
Pauli and the spin-statistics theorem
Duck, Ian M
1997-01-01
This book makes broadly accessible an understandable proof of the infamous spin-statistics theorem. This widely known but little-understood theorem is intended to explain the fact that electrons obey the Pauli exclusion principle. This fact, in turn, explains the periodic table of the elements and their chemical properties. Therefore, this one simply stated fact is responsible for many of the principal features of our universe, from chemistry to solid state physics to nuclear physics to the life cycle of stars.In spite of its fundamental importance, it is only a slight exaggeration to say that
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Morales Claudio H
2004-01-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (17811848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
The aftermath of the intermediate value theorem
Directory of Open Access Journals (Sweden)
Claudio H. Morales
2004-08-01
Full Text Available The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000Ã‚Â–300 B.C.E.. However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano's era (1781Ã‚Â–1848. Indeed, this Czech mathematician or perhaps philosopher has rigorously proven what is known today as the intermediate value theorem, a result that is intimately related to various classical theorems that will be discussed throughout this work.
Spectral mapping theorems a bluffer's guide
Harte, Robin
2014-01-01
Written by an author who was at the forefront of developments in multi-variable spectral theory during the seventies and the eighties, this guide sets out to describe in detail the spectral mapping theorem in one, several and many variables. The basic algebraic systems – semigroups, rings and linear algebras – are summarised, and then topological-algebraic systems, including Banach algebras, to set up the basic language of algebra and analysis. Spectral Mapping Theorems is written in an easy-to-read and engaging manner and will be useful for both the beginner and expert. It will be of great importance to researchers and postgraduates studying spectral theory.
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
Bypassing the bandwidth theorem with PT symmetry
Ramezani, Hamidreza; Ellis, F M; Guenther, Uwe; Kottos, Tsampikos
2012-01-01
The beat time {\\tau}_{fpt} associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound {\\tau}_{fpt}\\sim 1/{\\delta}{\\omega}. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time (PT) symmetry, bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference {\\delta}{\\omega}. Our results foster new design strategies which lead to (stable) pseudo-unitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.
Fluctuation theorems for continuously monitored quantum fluxes.
Campisi, Michele; Talkner, Peter; Hänggi, Peter
2010-10-01
It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the fluctuation theorems are both altered by these measurements, their ratio remains unchanged. This observation allows us to describe the measurement of fluxes through interfaces and, in this way, to bridge the gap between the current theory, based on only two measurements performed at the beginning and end of the protocol, and experiments that are based on continuous monitoring.
Fluctuation theorem for arbitrary open quantum systems.
Campisi, Michele; Talkner, Peter; Hänggi, Peter
2009-05-29
Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force.
Quantum Fluctuation Theorems, Contextuality, and Work Quasiprobabilities
Lostaglio, Matteo
2018-01-01
We discuss the role of contextuality within quantum fluctuation theorems, in the light of a recent no-go result by Perarnau-Llobet et al. We show that any fluctuation theorem reproducing the two-point-measurement scheme for classical states either admits a notion of work quasiprobability or fails to describe protocols exhibiting contextuality. Conversely, we describe a protocol that smoothly interpolates between the two-point-measurement work distribution for projective measurements and Allahverdyan's work quasiprobability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Performance of the distributed Brillouin sensor: Benefits and penalties due to pump depletion
Ravet, Fabien
Disaster prevention in civil infrastructures requires the use of techniques that allow temperature and strain measurements in real time over lengths of a few meters to tens of kilometres. The distributed Brillouin sensor (DBS) technique has the advantage to combine all these characteristics. The sensing mechanism of the DBS involves the interaction of two counter-propagating lightwaves, the Stokes and the pump, in an optical fibre. Spatial information is obtained through time domain analysis. The sensing data are recorded from the measurement of the pump depletion. We explore the benefits and the drawbacks of this approach and show that there is a power range for which the sensing performances are optima. To achieve that goal, Brillouin fibre generator (BFG) and amplifier (BFA) were studied leading to the derivation of a threshold definition for the BFA, which is the configuration of the DBS. Within that context, numerical and analytical models describing the stimulated Brillouin scattering (SBS) interaction are introduced and validated experimentally. Even if pump depletion is carefully controlled, the Brillouin spectrum shape, and hence the sensor performance, still depend on the sensing parameters such as power, pulse and fibre characteristics. We use a signal processing method grounded in the physics of Brillouin scattering. An analytical approximation, valid for the optimum sensing region, reconstructs the Brillouin spectrum distribution from input sensing parameters and measured data. These data are obtained with a spectrum analysis methodology, based on three original tools: the Rayleigh equivalent criterion, the lengthstress diagram, and the spectrum form factors. This methodology has been successfully used on experimental spectra. The DBS and the signal processing approach were then used to monitor the structural changes in steel pipes and in a composite column, all subjected to heavy loads. The DBS measured the strain distribution of those structures
Soto, M A; Bolognini, G.; Di Pasquale, F.
2009-01-01
Proposed and characterised is the use of multi-longitudinal mode Fabry-Perot laser sources, in distributed optical fibre sensors based on spontaneous Brillouin scattering, for simultaneous strain and temperature measurements. Experimental results show that, by using such multi-longitudinal mode lasers, it is possible to measure the Brillouin spectrum, even if the overall laser spectral linewidth is larger than the Brillouin frequency shift. In this case, a suitable receiver scheme, combining ...
Impact of nonlinear loss on Stimulated Brillouin Scattering
Wolff, Christian; Steel, Michael J; Eggleton, Benjamin J; Poulton, Christopher G
2015-01-01
We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of Stimulated Brillouin Scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length and pump power, whereas fifth-order losses lead to a non-monotonic relationship. We define a figure of merit for materials and waveguide designs in the presence of fifth-order losses. From this, we determine the optimal waveguide length for the case of 2PA alone and upper bounds for the total Stokes amplification for the case of 2PA as well as fifth-order losses. The analysis is performed analytically using a small-signal approximation and is compared to numerical solutions of the full nonlinear modal equations.
Acoustic confinement and Stimulated Brillouin Scattering in integrated optical waveguides
Poulton, Christopher G; Eggleton, Benjamin J
2013-01-01
We examine the effect of acoustic mode confinement on Stimulated Brillouin Scattering in optical waveguides that consist of a guiding core embedded in a solid substrate. We find that SBS can arise due to coupling to acoustic modes in three different regimes. First, the acoustic modes may be guided by total internal reflection; in this case the SBS gain depends directly on the degree of confinement of the acoustic mode in the core, which is in turn determined by the acoustic V-parameter. Second, the acoustic modes may be leaky, but may nevertheless have a sufficiently long lifetime to have a large effect on the SBS gain; the lifetime of acoustic modes in this regime depends not only on the contrast in acoustic properties between the core and the cladding, but is also highly dependent on the waveguide dimensions. Finally SBS may occur due to coupling to free modes, which exist even in the absence of acoustic confinement; we find that the cumulative effect of coupling to these non-confined modes results in signi...
Beyond the Brillouin limit with the Penning fusion experiment
Energy Technology Data Exchange (ETDEWEB)
Barnes, D.C.; Mitchell, T.B.; Schauer, M.M.
1996-11-09
Several years ago, it was proposed that a dense nonneutral plasma could be produced in a Penning trap. Nonneutral plasmas have excellent confinement. Thus, such a dense plasma might produce simultaneously high density and good confinement (as needed for fusion). Recently, this theoretical conjecture has been demonstrated in a small (3 mm radius) electron experiment (PFX). Densities up to 35 times the Brillouin density (limiting number density in a static trap) have been inferred from the observed strong (100:1) spherical focussing. Electrons are injected at low energy from a single pole of the sphere. A surprising observation is the self-organization of the system into a spherical state, which occurs precisely when the trap parameters are adjusted to produce a spherical well. This organization is observed by a bootstrapping which produces a hysteresis. Additional observations which confirm the dense spherical focus are energy-scattered electrons and deflections of an electron probe beam by the space charge of the central focus.
A Fubini theorem on a function space and its applications
Chung, Hyun Soo; Choi, Jae Gil; Chang, Seung Jun
2013-01-01
In this paper we establish a Fubini theorem for functionals on a function space. We then establish some relationships as applications of our Fubini theorem. Finally, we present some historical remarks.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 22; Issue 10. On the Hahn--Banach Theorem. S Kesavan ... It has plentyof applications, not only within the subject itself, but alsoin other areas of mathematics like optimization, partial differentialequations, and so on. This article will give a briefoverview of ...
Ehrenfest's Theorem and Nonclassical States of Light
Indian Academy of Sciences (India)
cal and nonclassical states of radiation. 1. Introduction. In the first part1 of this article, we have introduced. Ehrenfest's theorem and discussed its role as a bridge be- tween classical mechanics (CM) and quantum mechanics. (QM). In this second part, we shall use the example of the states of a single-mode electromagnetic ...
Henstock integral and Dini-Riemann theorem
Directory of Open Access Journals (Sweden)
Giuseppe Rao
2009-11-01
Full Text Available In [5] an analogue of the classical Dini-Riemann theorem related to non-absolutely convergent series of real number is obtained for the Lebesgue improper integral. Here we are extending it to the case of the Henstock integral.
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Using Kalai's result, Tay (1995) proved LBT for a bigger class of simplicial complexes (namely, normal pseudomanifolds). In 2008, we (Bagchi & Datta) have presented a self-contained combinatorial proof of LBT for normal pseudomanifolds. Stacked spheres and lower bound theorem. Basudeb Datta.
Trace theorem for quasi-Fuchsian groups
Connes, A.; Sukochev, F. A.; Zanin, D. V.
2017-10-01
We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian groups which was stated and sketched, but not fully proved, on pp. 322–325 of the book Noncommutative geometry of the first author. Bibliography: 34 titles.
Automated theorem proving theory and practice
Newborn, Monty
2001-01-01
As the 21st century begins, the power of our magical new tool and partner, the computer, is increasing at an astonishing rate. Computers that perform billions of operations per second are now commonplace. Multiprocessors with thousands of little computers - relatively little! -can now carry out parallel computations and solve problems in seconds that only a few years ago took days or months. Chess-playing programs are on an even footing with the world's best players. IBM's Deep Blue defeated world champion Garry Kasparov in a match several years ago. Increasingly computers are expected to be more intelligent, to reason, to be able to draw conclusions from given facts, or abstractly, to prove theorems-the subject of this book. Specifically, this book is about two theorem-proving programs, THEO and HERBY. The first four chapters contain introductory material about automated theorem proving and the two programs. This includes material on the language used to express theorems, predicate calculus, and the rules of...
Answering Junior Ant's "Why" for Pythagoras' Theorem
Pask, Colin
2002-01-01
A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…
1/4-pinched contact sphere theorem
DEFF Research Database (Denmark)
Ge, Jian; Huang, Yang
2016-01-01
Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...... results on positively curved contact open 3-manifold are also discussed....
The Embedding Theorems of Whitney and Nash
Indian Academy of Sciences (India)
We begin by briefly motivating the idea of amanifold and then discuss the embedding theorems of Whitney and Nash that allow us toview these objects inside appropriately large Euclidean spaces. Resonance – Journal of Science Education. Current Issue : Vol. 23, Issue 1. Current Issue Volume 23 | Issue 1. January 2018.
Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics
Shivamoggi, B K
2016-01-01
The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.
Pascal's Apartment House and the Multinomial Theorem
Hughes, Barnabas
1977-01-01
The author gives a three dimensional analog of Pascal's Triangle as an exercise in heuristic thinking and an introduction to the multinomial theorem. The analog involves finding the number of shortest routes to various rooms in a cubical apartment house. (MN)
Abel's Theorem Simplifies Reduction of Order
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
LangPro: Natural Language Theorem Prover
Abzianidze, Lasha
2017-01-01
LangPro is an automated theorem prover for natural language (https://github.com/kovvalsky/LangPro). Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic tableau method specially designed for natural logic. The
A composition theorem for decision tree complexity
Montanaro, Ashley
2013-01-01
We completely characterise the complexity in the decision tree model of computing composite relations of the form h = g(f^1,...,f^n), where each relation f^i is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.
Bloch-Messiah theorem at finite temperature
Tanabe, K.; Sugawara-Tanabe, K.
1991-03-01
The Bloch-Messiah theorem is extended to the thermal Hartree-Fock-Bogoliubov (THFB) theory by making use of the thermo field dynamics. This enables us to define the correct order parameter describing the superconducting phase at finite temperature, and demonstrates consistency of the THFB formalism.
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
Four-bubble clusters and Menelaus' theorem
Fischer, Fred
2002-10-01
We discuss a relatively easy way to construct a stable cluster of four soap bubbles using the radii of four selected spherical films out of a total of ten. To this end, we extend Menelaus' theorem, a geometrical relation between a triangle and a straight line in the plane, to three and higher dimensions.
Extension of a theorem due to Ramanujan
Directory of Open Access Journals (Sweden)
Medhat A. Rakha
2014-12-01
Full Text Available The aim of this research paper is to establish an extension of a theorem due to Ramanujan. The result is obtained with the help of two terminating results for the series $_3F_{2}$ very recently obtained by Rakha et al. A few interesting special cases are also given.
Ehrenfest's Theorem and Nonclassical States of Light
Indian Academy of Sciences (India)
Ehrenfest's Theorem and Nonclassical States of Light - Dynamics of Nonclassical States of Light. Lijo T George C Sudheesh S Lakshmibala V Balakrishnan. General Article Volume 17 ... Keywords. Ehrenfest; observables; radiation field; coherent state; non-classical states; photon-added-coherent state; squeezed state.
General Correlation Theorem for Trinion Fourier Transform
Bahri, Mawardi
2017-01-01
- The trinion Fourier transform is an extension of the Fourier transform in the trinion numbers setting. In this work we derive the correlation theorem for the trinion Fourier transform by using the relation between trinion convolution and correlation definitions in the trinion Fourier transform domains.
Ehrenfest's Theorem and Nonclassical States of Light
Indian Academy of Sciences (India)
and its laws left them uneasy, in marked contrast to the familiar terrain of classical physics. It connects the dynamics of the expectation values of operators repre- senting the physical observables of a quantum system to the dynamics of their classical counterparts. The pur- pose of this article is to illustrate this theorem in ...
The Archimedes Principle and Gauss's Divergence Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 11. The Archimedes Principle and Gauss's Divergence Theorem. Subhashis Nag. General Article Volume 3 Issue 11 November 1998 pp 18-29. Fulltext. Click here to view fulltext PDF. Permanent link:
Tennis Rackets and the Parallel Axis Theorem
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Fixed Point Theorems for Asymptotically Contractive Multimappings
Directory of Open Access Journals (Sweden)
M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Central Limit Theorem for Coloured Hard Dimers
Directory of Open Access Journals (Sweden)
Maria Simonetta Bernabei
2010-01-01
Full Text Available We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations.
On the exactness of soft theorems
Guerrieri, Andrea L.; Huang, Yu-tin; Li, Zhizhong; Wen, Congkao
2017-12-01
Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α' expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O({α}^' 6}) . Thus the massless S-matrix of string theory "knows" about the presence of D-branes.
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
Frobenius and His Density Theorem for Primes
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 12. Frobenius and His Density Theorem for Primes. B Sury. General Article Volume 8 Issue 12 December 2003 pp 33-41. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/008/12/0033-0041. Keywords.
Generalizations of the Lax-Milgram Theorem
Directory of Open Access Journals (Sweden)
Dimosthenis Drivaliaris
2007-05-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
Generalizations of the Lax-Milgram Theorem
Directory of Open Access Journals (Sweden)
Yannakakis Nikos
2007-01-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
A stochastic Fubini theorem: BSDE method.
Wang, Yanqing
2017-01-01
In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short) which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.
Fubini theorem for multiparameter stable process
Erraoui, Mohamed; Ouknine, Youssef
2011-01-01
We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet.
Fubini theorem for multiparameter stable process
Directory of Open Access Journals (Sweden)
Mohamed Erraoui
2011-04-01
Full Text Available We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet.
Fubini's Theorem for Vector-Valued Measures
Uglanov, A. V.
1991-02-01
The situation is considered when either the transitional or initial measure is vector-valued (the other is, respectively, scalar-valued; thus the product measure is also vector-valued). The integrable function is vector-valued. In this situation two theorems of Fubini type are proved.
A stochastic Fubini theorem: BSDE method
Directory of Open Access Journals (Sweden)
Yanqing Wang
2017-04-01
Full Text Available Abstract In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition.
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Experimental studies of the transient fluctuation theorem using liquid ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 72; Issue 5. Experimental studies of the transient ... Recently a fluctuation theorem, known as the transient fluctuation theorem (TFT), which generalizes the second law of thermodynamics to small systems has been proposed. This theorem has been tested in small ...
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
The Interpretability of Inconsistency: Feferman's Theorem and Related Results
Visser, Albert
2014-01-01
This paper is an exposition of Feferman's Theorem concerning the interpretability of inconsistency and of further insights directly connected to this result. Feferman's Theorem is a strengthening of the Second Incompleteness Theorem. It says, in metaphorical paraphrase, that it is not just the case
Distributional Wiener-Ikehara theorem and twin primes.
Korevaar, J.
2005-01-01
ABSTRACT. The Wiener-Ikehara theorem was devised to obtain a simple proof of the prime number theorem. It uses no other information about the zeta function zeta (z) than that it is zero-free and analytic for Re z > 1, apart from a simple pole at z = 1 with residue 1. In the Wiener-Ikehara theorem,
Spontaneous and stimulated Brillouin scattering in single-mode silica optical fibers
Yeniay, Aydin
This thesis describes an experimental investigation of Brillouin scattering in silica based single mode optical fibers at IR communication wavelengths (λ = 1550nm). We have investigated the scattering process in spontaneous and stimulated regimes by taking into account of the gain spectrum evolution, stimulated Brillouin scattering (SBS) threshold and polarization properties using laser sources with different spectral lineshapes. We have shown that several acoustic resonance modes, depending on the waveguide properties, exist in the spontaneous regime, but they decay as the process becomes stimulated. In the stimulated regime, only the main Brillouin peak persists with a linewidth approximately 10 times narrower than that in the spontaneous regime. Our results on the linewidth narrowing are in an agreement with the theory, which considers thermal noise fluctuations as the origin of Brillouin scattering in undepleted-pump regime. Moreover, we have found that the lineshape of the SBS light is identical to the input laser lineshape, with a resolution bandwidth that is equal to the SBS linewidth of the medium (7-12 MHz), which makes SBS a practical tool for laser linewidth measurements. In the study of polarization properties of Brillouin scattering, we specifically determined the SBS threshold and Degree of Polarization (DOP) of Brillouin light with respect to the state of polarization (SOP) and DOP of the input laser source. It is found that, for linearly polarized input signal (100% DOP); Rayleigh and Spontaneous Brillouin scattered signals have the DOP of 33%, while the Stimulated Brillouin scattered light has a DOP of 95%. On the other hand, for a depolarized input signal (DOP of 0%); Rayleigh, Spontaneous and Stimulated Brillouin scattered light have the same DOP of 5%. We also found that the depolarized signal yields 1dB higher SBS threshold than the polarized signal as oppose to earlier prediction of 3dB. A possible explanation for the discrepancy is given by
Brillouin scattering, piezobirefringence, and dispersion of photoelastic coefficients of CdS and ZnO
DEFF Research Database (Denmark)
Berkowicz, R.; Skettrup, Torben
1975-01-01
We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position of the i......We have measured the dispersion of the Brillouin scattering from acoustoelectrical domains in CdS and ZnO. These spectra are compared with the birefringence spectra obtained by applying uniaxial stress. The resonant cancellation of the Brillouin scattering occurs at the spectral position...... of the isotropic point of the stress-induced birefringence. From these spectra it is concluded that the Brillouin scattering in CdS and ZnO is determined by elasto-optic effects alone. The spectra of some of the photoelastic coefficients have been determined. A model dielectric constant is derived where both....... It is found that the exchange interaction between the excitons may change the values of the photoelastic coefficients in ZnO about 10%....
Vieitez, M. O.; van Duijn, E. J.; Ubachs, W.; Witschas, B.; Meijer, A.; de Wijn, A. S.; Dam, N. J.; van de Water, W.
2010-10-01
We study Rayleigh-Brillouin scattering in gases of N2, O2, and SF6 molecules, Kr atoms, and He-Xe and He-CO2 mixtures at pressures ranging from 1 to 3 bar and using two different experimental setups. In one setup, we measure spectra of light scattered by thermal density fluctuations (spontaneous Rayleigh-Brillouin scattering); in the second setup density waves are induced in the overlap region of two counterpropagating laser beams (coherent Rayleigh-Brillouin scattering). We compare measured spectra to the Tenti models and to a recent model for mixtures. We find new values of the bulk viscosity, which is a parameter in line-shape models that allows for internal degrees of freedom. Both experiments agree on the value of the bulk viscosity. Our results indicate a need for new line-shape models for mixtures of molecules with internal degrees of freedom.
Investigation of spontaneous Brillouin scattering generation based on non-adiabatic microfibres
Zarei, A.; Jasim, A. A.; Harun, S. W.; Ahmad, H.
2014-12-01
Brillouin Stokes and anti-Stokes generation is successfully demonstrated in backward direction using a non-adiabatic microfibre as the gain medium. The Stokes light wavelength is up-shifted by 0.088 nm (10 GHz) from the BP wavelength as monitored by using an optical spectrum analyzer. The Brillouin scattering can also be enhanced by employing a microfibre based inline Mach-Zehnder interferometer (IMZI) as the gain medium due to its stronger multimode interference effect. It is shown that the microfibre geometry plays an important role in the spontaneous Brillouin scattering generation and gain bandwidth broadening due to its effect on irritation of the acoustic modes inside the microfibre.
Diallo, Souleymane; Aubry, Jean-Pierre; Chembo, Yanne K
2017-11-27
Ultra-high Q whispering-gallery mode resonators pumped by a continuous-wave laser are known to enhance stimulated Brillouin scattering when optimal resonance and phase-matching conditions are met. In crystalline resonators, this process depends critically on the crystal orientation and family, which impose the elastic constants defining the velocity of the acoustic waves. In this article, we investigate the effect of crystalline orientation and family on this velocity which is proportional to the Brillouin frequency down-shift. In particular, the study is based on the development of a model and numerical simulations of acoustic wave velocities that propagate along the periphery of four fluoride crystals, namely calcium, magnesium, lithium and barium fluoride. We find that depending on the crystal and its orientation, the frequency excursion around the Brillouin offset can vary from few tens of kHz to more than a GHz.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Quantum Bochkov-Kuzovlev work fluctuation theorems.
Campisi, Michele; Talkner, Peter; Hänggi, Peter
2011-01-28
The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach, we adopt the 'exclusive' viewpoint, meaning that the coupling to the external work source is not counted as part of the internal energy. The corresponding canonical and microcanonical quantum fluctuation theorems are derived as well, and are compared with the respective theorems obtained within the 'inclusive' approach. The relations between the quantum inclusive work w, the exclusive work w(0) and the dissipated work w(dis), are discussed and clarified. We show by an explicit example that w(0) and w(dis) are distinct stochastic quantities obeying different statistics.
Subleading soft graviton theorem for loop amplitudes
Sen, Ashoke
2017-11-01
Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.
Oseledec multiplicative ergodic theorem for laminations
Nguyên, Viêt-Anh
2017-01-01
Given a n-dimensional lamination endowed with a Riemannian metric, the author introduces the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, the author defines the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. He also proves an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere which is holonomy invariant. Moreover, in the case of differentiable cocycles the author establishes effective integral estimates for the Lyapunov exponents. These results find applications in the geometric and dynamical theory of laminations. They are also applicable to (not necessarily closed) laminations with singularities. Interesting holonomy properties of a generic leaf of a foliation are obtained...
Theorems for asymptotic safety of gauge theories
Bond, Andrew D.; Litim, Daniel F.
2017-06-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Theorem Proving In Higher Order Logics
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Essential criteria for efficient pulse amplification via Raman and Brillouin scattering
Trines, R M G M; Webb, E; Vieira, J; Fiuza, F; Fonseca, R A; Silva, L O; Sadler, J; Ratan, N; Ceurvorst, L; Kasim, M F; Tabak, M; Froula, D; Haberberger, D; Norreys, P A; Cairns, R A; Bingham, R
2016-01-01
Raman and Brillouin amplification are two schemes for amplifying and compressing short laser pulses in plasma. Analytical models have already been derived for both schemes, but the full consequences of these models are little known or used. Here, we present new criteria that govern the evolution of the attractor solution for the seed pulse in Raman and Brillouin amplification, and show how the initial laser pulses need to be shaped to control the properties of the final amplified seed and improve the amplification efficiency.
Temperature sensing in multiple zones based on Brillouin fiber ring laser
Energy Technology Data Exchange (ETDEWEB)
Galindez, C A; Madruga, F J; Ullan, A; Lopez-Higuera, J M [Photonics Engineering Group, Universidad de Cantabria, Av Castros s/n, 39005-Santander (Spain); Lopez-Amo, M, E-mail: galindezca@unican.e [Depto. IngenierIa Electrica y Electronica, Universidad Publica de Navarra, Campus de Arrosadia s/n, 31006 Pamplona (Spain)
2009-07-01
A simple system for sensing temperature in multiple zones based on a multi-wavelength Brillouin fiber laser ring is presented. Optical fiber reels are serially concatenated and divided in zones (one per sensing area). Setting the Brillouin lasing in each spool of fiber generates a characteristic wavelength that depends on the fiber properties and the temperature in the zone. Thus, it is possible to measure temperature independently and accurately through heterodyne detection between two narrow laser signals. The proposed sensor integrates the temperature along the whole spool of fiber in each zone. These real time measurements were successfully checked in our laboratory.
Four theorems on the psychometric function.
Directory of Open Access Journals (Sweden)
Keith A May
Full Text Available In a 2-alternative forced-choice (2AFC discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise x β(Transducer, where β(Noise is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer depends on the transducer. We derive general expressions for β(Noise and β(Transducer, from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx(b, β ≈ β(Noise x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is
Determination of the elastic constants of portlandite by Brillouin spectroscopy
Speziale, S.
2008-10-01
The single crystal elastic constants Cij and the shear and adiabatic bulk modulus of a natural portlandite (Ca(OH)2) crystal were determined by Brillouin spectroscopy at ambient conditions. The elastic constants, expressed in GPa, are: C11 = 102.0(± 2.0), C12 = 32.1(± 1.0), C13 = 8.4(± 0.4), C14 = 4.5(± 0.2), C33 = 33.6(± 0.7), C44 = 12.0(± 0.3), C66 = (C11-C12)/2 = 35.0(± 1.1), where the numbers in parentheses are 1σ standard deviations. The Reuss bounds of the adiabatic bulk and shear moduli are K0S = 26.0(± 0.3) GPa and G0 = 17.5(± 0.4) GPa, respectively, while the Voigt bounds of these moduli are K0S = 37.3(± 0.4) GPa and G0 = 24.4(± 0.3) GPa. The Reuss and Voigt bounds for the aggregate Young\\'s modulus are 42.8(± 1.0) GPa and 60.0(± 0.8) GPa respectively, while the aggregate Poisson\\'s ratio is equal to 0.23(± 0.01). Portlandite exhibits both large compressional elastic anisotropy with C11/C33 = 3.03(± 0.09) equivalent to that of the isostructural hydroxide brucite (Mg(OH)2), and large shear anisotropy with C66/C44 = 2.92(± 0.12) which is 11% larger than brucite. The comparison between the bulk modulus of portlandite and that of lime (CaO) confirms a systematic linear relationship between the bulk moduli of brucite-type simple hydroxides and the corresponding NaCl-type oxides. © 2008 Elsevier Ltd. All rights reserved.
Evaluating and overcoming the impact of second echo in Brillouin echoes distributed sensing.
Yang, Zhisheng; Hong, Xiaobin; Lin, Wenqiao; Wu, Jian
2016-01-25
The detrimental impact of the second echo phenomenon that commonly exists in Brillouin echoes distributed sensing (BEDS) methods is thoroughly investigated by further developing the analytical model of the Brillouin gain on the probe wave. The presented analysis not only points out that the most severe impact imposed by the second echo occurs when the length of the heated/stressed fiber section is exactly equal to the spatial resolution, but also quantifies the systematic error on the estimated Brillouin frequency shift, the maximum of which could reach up to 8.5 MHz. A novel parabolic-amplitude four-section pulse is proposed, which can compensate the impact of the second echo optically, without using extra measurement time and post-processing. The key parameters of the proposed pulse are optimized by combining an upgraded mathematical model and the iterative algorithm. The experimental results show a good agreement with the analysis about the behavior of the second echo, and demonstrate that the proposed technique is capable of providing sub-meter spatial resolution and the natural linewidth of Brillouin gain spectrum simultaneously, while completely eliminating the impact of the second echo.
Brillouin spectroscopy of a novel baria-doped silica glass optical fiber.
Dragic, P; Kucera, C; Furtick, J; Guerrier, J; Hawkins, T; Ballato, J
2013-05-06
Presented here for the first time to the best of our knowledge is a detailed Brillouin spectroscopic study of novel, highly-BaO-doped silica glass optical fibers. The fibers were fabricated utilizing a molten-core method and exhibited baria (BaO) concentrations up to 18.4 mole %. Physical characteristics such as mass density, acoustic velocity, visco-elastic damping, and refractive index are determined for the baria component of the bariosilicate system. It is found that, of each of these parameters, only the acoustic velocity is less than that of pure silica. The effect of temperature and strain on the acoustic velocity also is determined by utilizing estimates of the strain- and thermo-optic coefficients. The dependencies are found to have signs opposite to those of silica, thus suggesting both Brillouin-frequency a-thermal and a-tensic binary compositions. Via the estimate of the strain-optic coefficient and data found in the literature, the Pockels' photoelastic constant p(12) is estimated, and both a calculation and measured estimate of the Brillouin gain versus baria content are presented. Such novel fibers incorporating the unique properties of baria could be of great utility for narrow linewidth fiber lasers, high power passive components (such as couplers and combiners), and Brillouin-based sensor systems.
Wei, Heming; Zhao, Xuefeng; Kong, Xianglong; Zhang, Pinglei; Cui, Yanjun; Sun, Changsen
2013-12-27
The Brillouin optical time-domain analysis (BOTDA)-based optical fiber method has been proposed to measure strain variations caused by corrosion expansion. Spatial resolutions of 1 m can be achieved with this kind of Brillouin sensor for detecting the distributed strain. However, when the sensing fiber is wound around the steel rebar in a number of circles in a range of several meters, this spatial resolution still has limitations for corrosion monitoring. Here, we employed a low-coherent fiber-optic strain sensor (LCFS) to survey the performance of Brillouin sensors based on the fact that the deformation measured by the LCFS equals the integral of the strains obtained from Brillouin sensors. An electrochemical accelerated corrosion experiment was carried out and the corrosion expansion was monitored by both BOTDA and the LCFS. Results demonstrated that the BOTDA can only measure the expansion strain of about 1,000 με, which was generated by the 18 mm steel rebar corrosion, but, the LCFS had high sensitivity from the beginning of corrosion to the destruction of the structure, and no obvious difference in expansion speed was observed during the acceleration stage of the corrosion developed in the reinforced concrete (RC) specimens. These results proved that the BOTDA method could only be employed to monitor the corrosion inside the structure in the early stage.
Spontaneous Rayleigh-Brillouin scattering of ultraviolet light in nitrogen, dry and moist air
Witschas, B.; Vieitez, M.O.; van Duijn, E.-J.; Reitebuch, O.; Van de Water, W.; Ubachs, W.M.G.
2010-01-01
Atmospheric lidar techniques for the measurement of wind, temperature, and optical properties of aerosols rely on the exact knowledge of the spectral line shape of the scattered laser light on molecules. We report on spontaneous Rayleigh-Brillouin scattering measurements in the ultraviolet at a
Statistical properties of the Stokes signal in stimulated Brillouin scattering pulse compressors
Velchev, I.; Ubachs, W.M.G.
2005-01-01
Spontaneous scattering noise is incorporated as a build-up source in a fully transient stimulated Brillouin scattering (SBS) model. This powerful simulation tool is successfully applied for a quantitative investigation of the fluctuations in the output pulse duration of SBS pulse compressors. The
Gu, Z.; Ubachs, W.M.G.
2013-01-01
Values for the bulk viscosity ηb of molecular nitrogen gas (N2) were derived from spontaneous Rayleigh-Brillouin scattering at ultraviolet wavelengths (λ = 366.8 nm) and at a 90° scattering angle. Analysis of the scattering profiles yields values showing a linear increasing trend, ranging from η
Zhou, Hongyan; Zhong, Kun; Zhang, Ru; Lang, Peilin
2011-02-01
Slow light technology will play a key role in future all-optical communication. The slow-light technology based on stimulated Brillouin scattering has become a research highlight because of its additional advantages, such as compatibility of the devices with existing telecommunication systems, room-temperature operation, and tunable at arbitrary wavelengths. According to the propagation of a cw pulse through a Brillouin fiber amplifier, whose frequency is near the Stokes resonance, via three-wave coupling equations, both pump depletion and fiber losses taken into consideration, the principle of how slow-light effect based on stimulated Brillouin scattering produced and the mathematical expression of time delay are strictly deduced. A delay of 8 ns is obtained when the input Stokes pulse is 200ns and the SBS (stimulated Brillouin scattering) gain G is ~18 in our designed experiment of SBS slow-light system. Then the extent of transformation from pump waves to Stokes waves is measured using MATLAB numerical simulation according to the experiment dates, based on the relation between output pump light power and input pump light power and also the relation between output Stokes light power and input pump light power. And the relation between the input light power and propagation distance is discussed as well. Finally the relation between slow light pulse delay and SBS gain is also obtained.
Yu, C.; Chong, Yat C.; Zhou, Hongyi
1990-01-01
Mid IR fiber transmission and exit radiation mode patterns at various incident CO2 laser power levels appear to be effective diagnostic tools for monitoring laser induced stimulated Brillouin scattering in various mid IR fibers. Such processes are deemed to be essential mechanisms for fiber-optic amplifiers and switches as potential replacements of current repeaters and bistable devices.
KrF laser amplifier with phase-conjugate Brillouin retroreflectors.
Gower, M C
1982-09-01
We have demonstrated the use of phase-conjugate stimulated Brillouin scattering mirrors to produce high-quality, short-pulse KrF laser beams from angular multiplexed and regenerative amplifiers. The mirror was also shown to isolate systems optically from amplifier spontaneous emission. Automatic alignment of targets using this mirror as a retroreflector was also demonstrated.
Hayashi, Neisei; Set, Sze Yun; Yamashita, Shinji
2018-02-01
We observed the depolarized guided acoustic-wave Brillouin scattering (GAWBS) spectrum in a highly nonlinear fiber with a partially side-stripped polymer coat. The linewidth of the GAWBS spectral line at 941 MHz was measured to be 6.4 MHz, which was 0.9 times that of a coated fiber.
Study of optical fibers strain-temperature sensitivities using hybrid Brillouin-Rayleigh system
National Research Council Canada - National Science Library
Kishida, Kinzo; Yamauchi, Yoshiaki; Guzik, Artur
.... These requirements are organized and clarified in the paper. It also describes the hybrid Brillouin-Rayleigh system, which exhibits capabilities surpassing those of strain gauges. The principles of the system are illustrated considering the fiber calibration methodology. Formulas required for determining strain, temperature, and hydro-pressure are derived and discussed. Finally, the examples of applications are presented.
Directory of Open Access Journals (Sweden)
Heming Wei
2013-12-01
Full Text Available The Brillouin optical time-domain analysis (BOTDA-based optical fiber method has been proposed to measure strain variations caused by corrosion expansion. Spatial resolutions of 1 m can be achieved with this kind of Brillouin sensor for detecting the distributed strain. However, when the sensing fiber is wound around the steel rebar in a number of circles in a range of several meters, this spatial resolution still has limitations for corrosion monitoring. Here, we employed a low-coherent fiber-optic strain sensor (LCFS to survey the performance of Brillouin sensors based on the fact that the deformation measured by the LCFS equals the integral of the strains obtained from Brillouin sensors. An electrochemical accelerated corrosion experiment was carried out and the corrosion expansion was monitored by both BOTDA and the LCFS. Results demonstrated that the BOTDA can only measure the expansion strain of about 1,000 με, which was generated by the 18 mm steel rebar corrosion, but, the LCFS had high sensitivity from the beginning of corrosion to the destruction of the structure, and no obvious difference in expansion speed was observed during the acceleration stage of the corrosion developed in the reinforced concrete (RC specimens. These results proved that the BOTDA method could only be employed to monitor the corrosion inside the structure in the early stage.
Distributed Brillouin fiber optic strain monitoring applications in advanced composite materials
Bastianini, Filippo; Cargnelutti, Mario; Di Tommaso, Angelo; Toffanin, Massimo
2003-08-01
Composite materials based on glass, carbon and aramid fibers have many advantages such as fast application, lightweight and corrosion resistance, and are widely diffused for manufacturing of tanks, pipings and for restoration, upgrade and seismic retrofit of structures and historical heritage. As several questions regarding long term durability of composite strengthenings remains still unsolved, monitoring of strain and temperature is strongly recommended, respectively to assess proper load transfer and no glass phase transition of the polymeric matrix. In this research work strain and temperature distributed sensing trough Brillouin scattering in single-mode optical fibers was used in different tests in order to understand the influence of different fiber coatings and embedding techniques. Pressure tests were performed on a GFRP piping with inhomogeneous strengthening layout and Brillouin strain data were compared with conventional strain gages. A smart CFRP material has been also developed and evaluated in a seismic retrofit application on an historical building dated 1500 that was seriously damaged in the earthquake of 1997. The developed embedding technique has been demonstrated successful to obtain fiber-optic smart composites with low optical losses, and the data comparison between Brillouin and resistive strain gauges confirms Brillouin technique is very effective for composite monitoring.
Brillouin scattering and diffracted MOKE from arrays of dots and anti-dots.
Energy Technology Data Exchange (ETDEWEB)
Grimsditch, M.; Guedes, I.; Vavassori, P.; Metlushko, V.; Ilic, B.; Neuzil, P.; Kumar, R.
2000-11-01
The magnetic properties of nano-arrays have been investigated using Brillouin scattering, MOKE and Diffracted-MOKE techniques. The anisotropies in negative arrays are found to be due to the shape of the holes and not due to the array itself. The D-MOKE results allow us to extract the domain pattern at remanence.
Rayleigh-Brillouin scattering profiles of air at different temperatures and pressures
Gu, Z.; Witschas, B.; van der Water, W.; Ubachs, W.M.G.
2013-01-01
Rayleigh-Brillouin (RB) scattering profiles for air have been recorded for the temperature range from 255 to 340 K and the pressure range from 640 to 3300 mbar, covering the conditions relevant for the Earth's atmosphere and for planned atmospheric light detection and ranging (LIDAR) missions. The
Short-Pulse Amplification by Strongly-Coupled Stimulated Brillouin Scattering
Edwards, Matthew; Jia, Qing; Mikhailova, Julia; Fisch, Nathaniel
2016-10-01
We examine the feasibility of strongly-coupled stimulated Brillouin scattering as a mechanism for the plasma-based amplification of sub-picosecond pulses. Fluid theory and particle-in-cell calculations are used to compare the relative advantages of Raman and Brillouin amplification over a broad range of parameters, with a focus on determining the maximum amplified pulse intensities and minimum durations that can be achieved. Amplification of short-wavelength pulses is considered in detail, with particular emphasis on the practical development of plasma-based x-ray amplifiers. Our results suggest that Brillouin scattering may allow amplification of shorter wavelength light than Raman scattering, but that at optical frequencies better performance is generally realized with Raman amplification, as strongly-coupled Brillouin scattering has limited capacity for amplifying sub-picosecond pulses. This work was supported by NNSA Grant No. DENA0002948 and AFOSR Grant No. FA9550-15-1-0391. M.R.E. gratefully acknowledges the support of the NSF through a Graduate Research Fellowship.
Geometric fluctuation theorem for a spin-boson system.
Watanabe, Kota L; Hayakawa, Hisao
2017-08-01
We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.
The Surprise Examination Paradox and the Second Incompleteness Theorem
Kritchman, Shira; Raz, Ran
2010-01-01
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the...
Goedel incompleteness theorems and the limits of their applicability. I
Energy Technology Data Exchange (ETDEWEB)
Beklemishev, Lev D [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2011-01-25
This is a survey of results related to the Goedel incompleteness theorems and the limits of their applicability. The first part of the paper discusses Goedel's own formulations along with modern strengthenings of the first incompleteness theorem. Various forms and proofs of this theorem are compared. Incompleteness results related to algorithmic problems and mathematically natural examples of unprovable statements are discussed. Bibliography: 68 titles.
Fatou type theorems for series in Mittag-Leffler functions
Paneva-Konovska, Jordanka
2012-11-01
In studying the behaviour of series, defined by means of the Mittag-Leffler functions, on the boundary of its domain of convergence in the complex plane, we give analogues of the classical theorems for the power series like Cauchy-Hadamard, Abel, as well as Fatou theorems. The asymptotic formulae for the Mittag-Leffler functions in the cases of "large" values of indices that are used in the proofs of the convergence theorems for the considered series are also provided.
Logic for computer science foundations of automatic theorem proving
Gallier, Jean H
2015-01-01
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in fir
A generalization of the Pi-theorem and dimensional analysis.
Sonin, Ain A
2004-06-08
This article introduces a generalization of dimensional analysis and its corollary, the Pi-theorem, to the class of problems in which some of the quantities that define the problem have fixed values in all the cases that are of interest. The procedure can reduce the number of dimensionless similarity variables beyond the prediction of Buckingham's theorem. The generalized Pi-theorem tells when and how large a reduction is attainable.
Nekhoroshev theorem for the periodic Toda lattice.
Henrici, Andreas; Kappeler, Thomas
2009-09-01
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).
Godel's Incompleteness Theorems and Platonic Metaphysics
Mikovic, Aleksandar
2015-01-01
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Applicability constraints of the equivalence theorem
Energy Technology Data Exchange (ETDEWEB)
Dobado, A.; Pelaez, J.R. [Departamento de Fisica Teorica, Universidad Complutense, 28040 Madrid (Spain); Urdiales, M.T. [Departamento de Fisica Teorica, Universidad Autonoma, 28049 Madrid (Spain)
1997-12-01
In this work we study the applicability of the equivalence theorem, either for unitary models or within an effective Lagrangian approach. There are two types of limitations: the existence of a validity energy window and the use of the lowest order in the electroweak constants. For the first kind, we consider some methods, based on dispersion theory or the large N limit, that allow us to extend the applicability. For the second, we obtain numerical estimates of the effect of neglecting higher orders in the perturbative expansion. {copyright} {ital 1997} {ital The American Physical Society}
Interval logic. Proof theory and theorem proving
DEFF Research Database (Denmark)
Rasmussen, Thomas Marthedal
2002-01-01
of a direction of an interval, and present a sound and complete Hilbert proof system for it. Because of its generality, SIL can conveniently act as a general formalism in which other interval logics can be encoded. We develop proof theory for SIL including both a sequent calculus system and a labelled natural...... deduction system. We conduct theoretical investigations of the systems with respect to subformula properties, proof search, etc. The generic theorem proving system Isabelle is used as a framework for encoding both proof theoretical systems. We consider a number of examples/small case-studies and discuss...
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
A Formal Proof Of The Riesz Representation Theorem
Directory of Open Access Journals (Sweden)
Anthony Narkawicz
2011-01-01
Full Text Available This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation. This result follows from the equivalence of the Riemann Stieltjes and Darboux Stieltjes integrals, which would have been a lengthy result to prove in PVS, so a simpler lemma was proved that captures the underlying concept of this integral equivalence. In order to prove the Riesz theorem, the Hahn Banach theorem was proved in the case where the normed linear spaces are the continuous and bounded functions on a closed interval. The proof of the Riesz theorem follows the proof in Haaser and Sullivan's book Real Analysis. The formal proof of this result in PVS revealed an error in textbook's proof. Indeed, the proof of the Riesz representation theorem is constructive, and the function constructed in the textbook does not satisfy a key property. This error illustrates the ability of formal verification to find logical errors. A specific counterexample is given to the proof in the textbook. Finally, a corrected proof of the Riesz representation theorem is presented.
The index theorem and the heat equation method
Yanlin, Yu
2005-01-01
This book provides a self-contained representation of the local version of the Atiyah-Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods. Contents: Preliminaries in Riemannian Geometry; Schrödinger and Heat Operators; MP Parametrix and Applications; Chern-Weil Th
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Energy Technology Data Exchange (ETDEWEB)
Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Birth of a theorem a mathematical adventure
Villani, Cédric
2015-01-01
This man could plainly do for mathematics what Brian Cox has done for physics" (Sunday Times). What goes on inside the mind of a rock-star mathematician? Where does inspiration come from? With a storyteller's gift, Cedric Villani takes us on a mesmerising journey as he wrestles with a new theorem that will win him the most coveted prize in mathematics. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair. We discover how it feels to be obsessed by a theorem during your child's cello practise and throughout your dreams, why appreciating maths is a bit like watching an episode of Columbo, and how sometimes inspiration only comes from locking yourself away in a dark room to think. Blending science with history, biography with myth, Villani conjures up an inimitable cast of characters including the omnipresent Einstein, mad genius Kurt Godel, and Villani's personal hero, John Nash. Bir...
An integral Riemann-Roch theorem for surface bundles
DEFF Research Database (Denmark)
Madsen, Ib Henning
2010-01-01
This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles.......This paper is a response to a conjecture by T. Akita about an integral Riemann–Roch theorem for surface bundles....
Restriction Theorem for Principal bundles in Arbitrary Characteristic
DEFF Research Database (Denmark)
Gurjar, Sudarshan
2015-01-01
The aim of this paper is to prove two basic restriction theorem for principal bundles on smooth projective varieties in arbitrary characteristic generalizing the analogues theorems of Mehta-Ramanathan for vector bundles. More precisely, let G be a reductive algebraic group over an algebraically c...
Discovering Theorems in Abstract Algebra Using the Software "GAP"
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
Conditional and preferential logics proof methods and theorem proving
Pozzato, GL
2010-01-01
Contains a version of the author's PhD dissertation and focuses on proof methods and theorem proving for conditional and preferential logics. This book introduces proof methods (sequent and tableau calculi) for conditional and preferential logics, as well as theorem provers obtained by implementing the proposed calculi.
Leaning on Socrates to Derive the Pythagorean Theorem
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
From Bombieri's Mean Value Theorem to the Riemann Hypothesis
Song, Fu-Gao
2008-01-01
From Bombieri's mean value theorem one can deduce the prime number theorem being equivalent to the Riemann hypothesis and the least prime P(q) satisfying P(q)= O(q^2 [ln q]^32) in any arithmetic progressions with common difference q.
Some fixed point theorems for Hardy-Rogers type mappings
Directory of Open Access Journals (Sweden)
B. E. Rhoades
1984-01-01
Full Text Available The first result establishes a fixed point theorem for three maps of a complete metric space. The contractive definition is a generalization of that of Hardy and Rogers, and the commuting condition of Jungck is replaced by the concept of weakly commuting. The other results are extensions of some theorems of Kannan.
On the Riesz representation theorem and integral operators ...
African Journals Online (AJOL)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces of vector valued extended integrable functions. Keywords: Vector integral, integral operators, operator ...
Common Origin of Quantum Regression and Quantum Fluctuation Dissipation Theorems
Shiktorov, P.; Starikov, E.; Gruzinskis, V.; Reggiani, L.; L. Varani; Vaissiere, J. C.
2000-01-01
It is shown that the quantum fluctuation dissipation theorem can be considered as a mathematical formulation in the spectral representation of Onsager hypothesis on the regression of fluctuations in physical systems. It is shown that the quantum fluctuation dissipation theorem can be generalized to an arbitrary stationary state.
Fixed Point Theorems in Quaternion-Valued Metric Spaces
Directory of Open Access Journals (Sweden)
Ahmed El-Sayed Ahmed
2014-01-01
Full Text Available The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.
A note on the homomorphism theorem for hemirings
Directory of Open Access Journals (Sweden)
D. M. Olson
1978-01-01
Full Text Available The fundamental homomorphism theorem for rings is not generally applicable in hemiring theory. In this paper, we show that for the class of N-homomorphism of hemirings the fundamental theorem is valid. In addition, the concept of N-homomorphism is used to prove that every hereditarily semisubtractive hemiring is of type (K.
Integral theorems for the quaternionic G-monogenic mappings
Shpakivskyi, V. S.; Kuzmenko, T. S.
2014-01-01
In the paper [1] considered a new class of quaternionic mappings, so-called $G$-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for $G$-monogenic mappings.
Generalizing The Morley Trisector and Various Theorems with Realizability Computations
Braude, Eric J.
2016-01-01
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of constraint satisfaction.
Some limit theorems for negatively associated random variables
Indian Academy of Sciences (India)
Abstract. Let {Xn,n ≥ 1} be a sequence of negatively associated random vari- ables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the Lp-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of ...
Generalizations of Karp's theorem to elastic scattering theory
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
The Boundary Crossing Theorem and the Maximal Stability Interval
Directory of Open Access Journals (Sweden)
Jorge-Antonio López-Renteria
2011-01-01
useful tools in the study of the stability of family of polynomials. Although both of these theorem seem intuitively obvious, they can be used for proving important results. In this paper, we give generalizations of these two theorems and we apply such generalizations for finding the maximal stability interval.
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
Shimizu, Kaoru; Horiguchi, Tsuneo; Koyamada, Yahei; Kurashima, Toshio
1993-02-01
Time-domain reflectometry of spontaneous Brillouin scattering in a single-mode optical fiber is performed with a coherent self-heterodyne detection system containing a recently proposed external frequency translator and a single light-wave source. The light wave is divided into probe and reference light waves. The frequency of the probe light wave is upconverted by the translator by an amount approximately equal to the Brillouin frequency shift. The frequency-converted probe is launched into the fiber and spontaneously Brillouin scattered. As the frequency of the scattered probe is downconverted to near that of the reference light wave, coherent self-heterodyne detection of spontaneous Brillouin scattering becomes possible without having to use a fast-speed detector.
National Research Council Canada - National Science Library
Mizuno, Yosuke; Hayashi, Neisei; Tanaka, Hiroki; Nakamura, Kentaro
2014-01-01
.... We then develop a new method of detecting the location of the propagating POF fuse remotely and non visually in real time using Brillouin scattering, which can be clearly observed at such a high power density...
Liu, Xue-Lu; Liu, He-Nan; Wu, Jiang-Bin; Wu, Han-Xu; Zhang, Tao; Zhao, Wei-Qian; Tan, Ping-Heng
2017-05-01
Simultaneous Stokes and anti-Stokes ultralow-frequency (ULF) Raman measurement down to ˜2 cm-1 or 60 GHz is realized by a single-stage spectrometer in combination with volume-Bragg-grating-based notch filters. This system reveals its excellent performance by probing Brillouin signal of acoustic phonons in silicon, germanium, gallium arsenide, and gallium nitride. The deduced sound velocity and elastic constants are in good accordance with previous results determined by various methods. This system can shorten the integration time of the Brillouin signal with a good signal-to-noise ratio by more than 2000-fold compared to a Fabry-Perot interferometer (FPI). This study shows how a filter-based ULF Raman system can be used to reliably achieve Brillouin spectroscopy for condensed materials with high sensitivity and high signal-to-noise ratio, stimulating fast Brillouin spectrum measurements to probe acoustic phonons in semiconductors.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
Steinitz theorems for simple orthogonal polyhedra
Directory of Open Access Journals (Sweden)
David Eppstein
2014-09-01
Full Text Available We define a simple orthogonal polyhedron to be a three-dimensional polyhedron with the topology of a sphere in which three mutually-perpendicular edges meet at each vertex.By analogy to Steinitz's theorem characterizing the graphs of convex polyhedra, we find graph-theoretic characterizations of three classes of simple orthogonal polyhedra: corner polyhedra, which can be drawn by isometric projection in the plane with only one hidden vertex, xyz polyhedra, in which each axis-parallel line through a vertex contains exactly one other vertex, and arbitrary simple orthogonal polyhedra. In particular, the graphs of xyz polyhedra are exactly the bipartite cubic polyhedral graphs, and every bipartite cubic polyhedral graph with a 4-connected dual graph is the graph of a corner polyhedron. Based on our characterizations we find efficient algorithms for constructing orthogonal polyhedra from their graphs.
An Extension of Gregus Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. O. Olaleru
2007-03-01
Full Text Available Let C be a closed convex subset of a complete metrizable topological vector space (X,d and T:CÃ¢Â†Â’C a mapping that satisfies d(Tx,TyÃ¢Â‰Â¤ad(x,y+bd(x,Tx+cd(y,Ty+ed(y,Tx+fd(x,Ty for all x,yÃ¢ÂˆÂˆC, where 0theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of T.
Asset management using an extended Markowitz theorem
Directory of Open Access Journals (Sweden)
Paria Karimi
2014-06-01
Full Text Available Markowitz theorem is one of the most popular techniques for asset management. The method has been widely used to solve many applications, successfully. In this paper, we present a multi objective Markowitz model to determine asset allocation by considering cardinality constraints. The resulted model is an NP-Hard problem and the proposed study uses two metaheuristics, namely genetic algorithm (GA and particle swarm optimization (PSO to find efficient solutions. The proposed study has been applied on some data collected from Tehran Stock Exchange over the period 2009-2011. The study considers four objectives including cash return, 12-month return, 36-month return and Lower Partial Moment (LPM. The results indicate that there was no statistical difference between the implementation of PSO and GA methods.
Probing quantum fluctuation theorems in engineered reservoirs
Elouard, C.; Bernardes, N. K.; Carvalho, A. R. R.; Santos, M. F.; Auffèves, A.
2017-10-01
Fluctuation theorems (FTs) are central in stochastic thermodynamics, as they allow for quantifying the irreversibility of single trajectories. Although they have been experimentally checked in the classical regime, a practical demonstration in the framework of quantum open systems is still to come. Here we propose a realistic platform to probe FTs in the quantum regime. It is based on an effective two-level system coupled to an engineered reservoir, that enables the detection of the photons emitted and absorbed by the system. When the system is coherently driven, a measurable quantum component in the entropy production is evidenced. We quantify the error due to photon detection inefficiency, and show that the missing information can be efficiently corrected, based solely on the detected events. Our findings provide new insights into how the quantum character of a physical system impacts its thermodynamic evolution.
PBR theorem and Einstein's quantum hole argument
Weinstein, Galina
2013-01-01
This note discusses the latest hot topic: Quantum states: ontic or epistemic? and the PBR theorem. Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of the hole argument in his 1914 "Entwurf" general theory of relativity. In their paper, PBR write the following: "an important step towards the derivation of our result is the idea that the quantum state is physical if distinct quantum states correspond to non-overlapping distributions for [the set of possible physical states that a system can be in]", and they then refer to Einstein's argument and views.
Virial Theorem in Nonlocal Newtonian Gravity
Directory of Open Access Journals (Sweden)
Bahram Mashhoon
2016-05-01
Full Text Available Nonlocal gravity is the recent classical nonlocal generalization of Einstein’s theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for “isolated” astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy’s baryonic diameter D 0 —namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time—is predicted to be larger than the effective dark matter fraction f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.
Fluctuation theorem in quantum heat conduction.
Saito, Keiji; Dhar, Abhishek
2007-11-02
We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
If 1+1=2 then the Pythagorean theorem holds, or one more proof of the oldest theorem of mathematics
Directory of Open Access Journals (Sweden)
Alexandru HORVÁTH
2013-06-01
Full Text Available The Pythagorean theorem is one of the oldest theorems of mathematics. It gained during the time a central position and even today it continues to be a source of inspiration. In this note we try to give a proof which is based on a hopefully new approach. Our treatment will be as intuitive as it can be.
Guo, Changlei; Che, Kaijun; Zhang, Pan; Wu, Jinshu; Huang, Yantang; Xu, Huiying; Cai, Zhiping
2015-12-14
We demonstrate the first observation of stimulated Brillouin scattering (SBS) in a high-Q whispering gallery mode tellurite microsphere. Tellurite glass with composition of 70TeO₂-20ZnO-5Na₂O-5La₂O₃ (molar ratio) was prepared in-house using a melt-quenching technique. Moreover, tellurite microspheres with Q in excess of 13 millions at 1550 nm were fabricated by melting tellurite microwires using a CO₂ laser. By pumping the tellurite microspheres with a tunable single frequency laser, SBS is further realized with a threshold as low as 0.58 mW. At last, the beat notes between the pump and the Stokes signals were measured, which indicated the Brillouin frequency shift is at the 8.2 GHz band for our tellurite glass. Our results could propel significant applications utilizing SBS by employing tellurite microspheres.
Raghunathan, Raksha; Zhang, Jitao; Wu, Chen; Rippy, Justin; Singh, Manmohan; Larin, Kirill V.; Scarcelli, Giuliano
2017-08-01
Embryogenesis is regulated by numerous changes in mechanical properties of the cellular microenvironment. Thus, studying embryonic mechanophysiology can provide a more thorough perspective of embryonic development, potentially improving early detection of congenital abnormalities as well as evaluating and developing therapeutic interventions. A number of methods and techniques have been used to study cellular biomechanical properties during embryogenesis. While some of these techniques are invasive or involve the use of external agents, others are compromised in terms of spatial and temporal resolutions. We propose the use of Brillouin microscopy in combination with optical coherence tomography (OCT) to measure stiffness as well as structural changes in a developing embryo. While Brillouin microscopy assesses the changes in stiffness among different organs of the embryo, OCT provides the necessary structural guidance.
Phase-locking in Multi-Frequency Brillouin Oscillator via Four Wave Mixing
Buettner, Thomas F S; Hudson, Darren D; Pant, Ravi; Poulton, Christopher G; Judge, Alexander C; Eggleton, Benjamin J
2014-01-01
Stimulated Brillouin scattering (SBS) and Kerr-nonlinear four wave-mixing (FWM) are among the most important and widely studied nonlinear effects in optical fibres. At high powers SBS can be cascaded producing multiple Stokes waves spaced by the Brillouin frequency shift. Here, we investigate the complex nonlinear interaction of the cascade of Stokes waves, generated in a Fabry-Perot chalcogenide fibre resonator through the combined action of SBS and FWM. We demonstrate the existence of parameter regimes, in which pump and Stokes waves attain a phase-locked steady state. Real-time measurements of 40ps pulses with 8GHz repetition rate are presented, confirming short-and long-term stability. Numerical simulations qualitatively agree with experiments and show the significance of FWM in phase-locking of pump and Stokes waves. Our findings can be applied for the design of novel picosecond pulse sources with GHz repetition rate for optical communication systems.
Veber, A; Cicconi, M R; Reinfelder, H; de Ligny, D
2018-01-15
A new experimental setup combining DSC, Raman and Brillouin spectroscopies was developed. In order to estimate its accuracy and stability a study of silicon and the alpha-beta quartz phase transition were performed. The data obtained demonstrated good agreement with previous studies using these three different techniques. For quartz, the temperature behavior of its 147 cm-1 Raman mode was studied in detail. Using a two-phonon coupling treatment of the Raman band, we show for the first time that its behavior can be well described by Landau theory of first-order phase transitions. The combined DSC-Raman-Brillouin technique is a powerful tool for material science capable of studying thermal, structural and elastic properties simultaneously. Copyright © 2017 Elsevier B.V. All rights reserved.
Coker, Zachary; Meng, Zhaokai; Troyanova-Wood, Maria; Traverso, Andrew; Ballmann, Charles; Petrov, Georgi; Ibey, Bennett L.; Yakovlev, Vladislav
2017-02-01
Burns are thermal injuries that can completely damage or at least compromise the protective function of skin, and affect the ability of tissues to manage moisture. Burn-damaged tissues exhibit lower elasticity than healthy tissues, due to significantly reduced water concentrations and plasma retention. Current methods for determining burn intensity are limited to visual inspection, and potential hospital x-ray examination. We present a unique confocal microscope capable of measuring Raman and Brillouin spectra simultaneously, with concurrent fluorescence investigation from a single spatial location, and demonstrate application by investigating and characterizing the properties of burn-afflicted tissue on chicken skin model. Raman and Brillouin scattering offer complementary information about a material's chemical and mechanical structure, while fluorescence can serve as a useful diagnostic indicator and imaging tool. The developed instrument has the potential for very diverse analytical applications in basic biomedical science and biomedical diagnostics and imaging.
Distributed Brillouin sensing with sub-meter spatial resolution: modeling and processing.
Beugnot, Jean-Charles; Tur, Moshe; Mafang, Stella Foaleng; Thévenaz, Luc
2011-04-11
A general analytic solution for Brillouin distributed sensing in optical fibers with sub-meter spatial resolution is obtained by solving the acoustical-optical coupled wave equations by a perturbation method. The Brillouin interaction of a triad of square pump pulses with a continuous signal is described, covering a wide range of pumping schemes. The model predicts how the acoustic wave, the signal amplitude and the optical gain spectral profile depend upon the pumping scheme. Sub-meter spatial resolution is demonstrated for bright-, dark- and π-shifted interrogating pump pulses, together with disturbing echo effects, and the results compare favorably with experimental data. This analytic solution is an excellent tool not only for optimizing the pumping scheme but also for post-processing the measured data to remove resolution degrading features. © 2011 Optical Society of America
High amplification and low noise achieved by a double-stage non-collinear Brillouin amplifier.
Lu, Zhiwei; Gao, Wei; He, Weiming; Zhang, Zan; Hasi, Wuliji
2009-06-22
We report a double-stage non-collinear Brillouin amplifier structure with high amplification and low noise, achieving an energy amplification of 6 x 10(11) and a signal-to-noise ratio of 10(3) for an input signal of 5.5 x 10(-14)J in the regime above the pump's stimulated Brillouin scattering threshold. The signal of the first-stage amplifier is efficiently amplified and separated from the noise output. The saturation amplification with noise suppressing is implemented in the second stage. The design principles of system parameters such as the intersection angle between the pump and signal beams, the pump energy, and the beam diameter are given.
Chaban, Ievgeniia; Shin, Hyun D.; Klieber, Christoph; Busselez, Rémi; Gusev, Vitalyi E.; Nelson, Keith A.; Pezeril, Thomas
2017-07-01
We present an optical technique based on ultrafast photoacoustics to determine the local temperature distribution profile in liquid samples in contact with a laser heated optical transducer. This ultrafast pump-probe experiment uses time-domain Brillouin scattering (TDBS) to locally determine the light scattering frequency shift. As the temperature influences the Brillouin scattering frequency, the TDBS signal probes the local laser-induced temperature distribution in the liquid. We demonstrate the relevance and the sensitivity of this technique for the measurement of the absolute laser-induced temperature gradient of a glass forming liquid prototype, glycerol, at different laser pump powers—i.e., different steady state background temperatures. Complementarily, our experiments illustrate how this TDBS technique can be applied to measure thermal diffusion in complex multilayer systems in contact with a surrounding liquid.
Zhao, Xuefeng; Gong, Peng; Qiao, Guofu; Lu, Jie; Lv, Xingjun; Ou, Jinping
2011-01-01
In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Energy Technology Data Exchange (ETDEWEB)
Berger, R.L.; Kaiser, T.B.; Lasinski, B.F. [and others
1996-06-01
Using the three-dimensional code (F3D), the authors compute the filamentation and backscattering of laser light. The results show that filamentation can be controlled and stimulated Brillouin backscattering (SBBS) can be reduced by using random phase plates (RPP) and small f-numbers or smoothing by spectral dispersion (SSD) with large bandwidth. An interesting result is that, for uniform plasmas, the SBBS amplification takes place over several laser axial coherence lengths (coherence length = speckle length).
Song, Kwang Yong; Abedin, Kazi S; Hotate, Kazuo
2008-01-07
We demonstrate superluminal propagation of optical pulses with amplification in optical fibers based on stimulated Brillouin scattering. A triple gain peak configuration is used for the generation of narrowband anomalous dispersion in 2 m tellurite glass fiber, where the group index change as much as -1.19 is achieved with 6.9 dB amplification in 34 ns Gaussian pulses, leading to the group index of 0.84.
Steady-State Noise Analysis of Spontaneous and Stimulated Brillouin Scattering in Optical Fibers
Jenkins, R. Brian; Sova, Raymond M.; Joseph, Richard I.
2007-03-01
In this paper, we present a steady-state theoretical and experimental analysis of the noise resulting from spontaneous and stimulated Brillouin scattering in an optical fiber. Wave equations are derived and solved that describe the evolution of the pump and Stokes waves along the fiber. Experiments and numerical results demonstrate the validity of the theory, either when a Stokes wave is launched at the end of the fiber or when the noise in the Stokes wave is spontaneously generated.
Gu, Ziyu; Ubachs, Wim
2013-01-01
Values for the bulk viscosity of molecular nitrogen gas (N2) were derived from spontaneous Rayleigh-Brillouin (RB) scattering at ultraviolet wavelengths (366.8 nm) and at a 90 degree scattering angle. Analysis of the scattering profiles yield values showing a linear increasing trend in the temperature interval from 255 K to 340 K. The present values, pertaining to hypersound acoustics at frequencies in the GHz domain, are found to be in agreement with results from acoustic attenuation experim...
Ni, C. K.; Kung, A. H.
1996-10-01
Backward stimulated Brillouin scattering was used to control the growth of amplified spontaneous emission (ASE), reducing the unwanted emission in a pulse-amplified cw Ti:sapphire laser system from 22% to less than 1 \\times 10-4 in the final output. Suppression of ASE substantially improved the spectral quality of the laser and broadened the range over which the laser is useful. The output duration was compressed, but the pulse remained nearly transform limited.
Cyclic coding for Brillouin optical time-domain analyzers using probe dithering.
Iribas, Haritz; Loayssa, Alayn; Sauser, Florian; Llera, Miguel; Le Floch, Sébastien
2017-04-17
We study the performance limits of mono-color cyclic coding applied to Brillouin optical time-domain analysis (BOTDA) sensors that use probe wave dithering. BOTDA analyzers with dithering of the probe use a dual-probe-sideband setup in which an optical frequency modulation of the probe waves along the fiber is introduced. This avoids non-local effects while keeping the Brillouin threshold at its highest level, thus preventing the spontaneous Brillouin scattering from generating noise in the deployed sensing fiber. In these conditions, it is possible to introduce an unprecedented high probe power into the sensing fiber, which leads to an enhancement of the signal-to-noise ratio (SNR) and consequently to a performance improvement of the analyzer. The addition of cyclic coding in these set-ups can further increase the SNR and accordingly enhance the performance. However, this unprecedented probe power levels that can be employed result in the appearance of detrimental effects in the measurement that had not previously been observed in other BOTDA set-ups. In this work, we analyze the distortion in the decoding process and the errors in the measurement that this distortion causes, due to three factors: the power difference of the successive pulses of a code sequence, the appearance of first-order non-local effects and the non-linear amplification of the probe wave that results when using mono-color cyclic coding of the pump pulses. We apply the results of this study to demonstrate the performance enhancement that can be achieved in a long-range dithered dual-probe BOTDA. A 164-km fiber-loop is measured with 1-m spatial resolution, obtaining 3-MHz Brillouin frequency shift measurement precision at the worst contrast location. To the best of our knowledge, this is the longest sensing distance achieved with a BOTDA sensor using mono-color cyclic coding.
Rayleigh-Brillouin scattering in SF6 in the kinetic regime
Wang, Yuanqing; Yu, Yin; Liang, Kun; Marques, Wilson; van de Water, Willem; Ubachs, Wim
2017-01-01
Rayleigh-Brillouin spectral profiles are measured with a laser-based scatterometry setup for a 90° scattering angle at a high signal-to-noise ratio (r.m.s. noise below 0.15% w.r.t. peak intensity) in sulfur-hexafluoride gas for pressures in the range 0.2–5 bar and for a wavelength of λ=403.0 nm. The
Salwik, Karol; Śliwczyński, Łukasz; Krehlik, Przemysław
2017-08-01
For the dissemination of precise signals from atomic clocks (like e.g. cesium clocks/fountains, H-masers or optical clocks) an optical link operating bi-directionally over the same fiber is essential. In such a link stimulated Brillouin scattering is one of the non-linear effects that may reduce the power of forward optical signal and convert it into the noise that propagates in the backward direction. In the link that uses a number of bi-directional optical amplifiers, the conditions that trigger the Brillouin scattering process may occur relatively easily because of large effective length for the scattering process. Thus in the design phase of the link, checking of the conditions for Brillouin scattering should be a part of optimization procedure (i.e. optimizing bi-directional amplifiers gains). In the paper we consider the mathematical model of the stimulated Brillouin scattering in the long distance, fiber optic links with multiple bidirectional optical amplifiers. The model was implemented in Matlab and consists of the coupled differential equations describing the propagation of pump and scattered signals that develops due to spontaneous scattering. The presence of bi-directional optical amplifiers is modeled as point-like discontinuity of the α parameter that is used to represent the attenuation of the fiber. These discontinuities create an extra level of difficulty when numerically solving the coupled equations (the problem is stiff) so special algorithm is presented that iteratively searches for the solution. The obtained results were compared with the measurements of the real link to confirm the correctness of the solution.
Directory of Open Access Journals (Sweden)
Xingjun Lv
2011-11-01
Full Text Available In this paper, a novel kind of method to monitor corrosion expansion of steel rebars in steel reinforced concrete structures named fiber optic coil winding method is proposed, discussed and tested. It is based on the fiber optical Brillouin sensing technique. Firstly, a strain calibration experiment is designed and conducted to obtain the strain coefficient of single mode fiber optics. Results have shown that there is a good linear relationship between Brillouin frequency and applied strain. Then, three kinds of novel fiber optical Brillouin corrosion expansion sensors with different fiber optic coil winding packaging schemes are designed. Sensors were embedded into concrete specimens to monitor expansion strain caused by steel rebar corrosion, and their performance was studied in a designed electrochemical corrosion acceleration experiment. Experimental results have shown that expansion strain along the fiber optic coil winding area can be detected and measured by the three kinds of sensors with different measurement range during development the corrosion. With the assumption of uniform corrosion, diameters of corrosion steel rebars were obtained using calculated average strains. A maximum expansion strain of 6,738 με was monitored. Furthermore, the uniform corrosion analysis model was established and the evaluation formula to evaluate mass loss rate of steel rebar under a given corrosion rust expansion rate was derived. The research has shown that three kinds of Brillouin sensors can be used to monitor the steel rebar corrosion expansion of reinforced concrete structures with good sensitivity, accuracy and monitoring range, and can be applied to monitor different levels of corrosion. By means of this kind of monitoring technique, quantitative corrosion expansion monitoring can be carried out, with the virtues of long durability, real-time monitoring and quasi-distribution monitoring.
Novel Optical Fiber Materials With Engineered Brillouin Gain Coefficients SSL 1: Novel Fiber Lasers
2015-12-29
Hawkins, C. Ryan, A. D. Yablon, R. Stolen, J. Ballato. Single- and few-moded lithium aluminosilicate optical fiber for athermal Brillouin strain...invited presentations 5 invited journal papers 1 journal cover 1 paper awarded "Spotlight on Optics" by the Optical Society of America 1 paper...Derived Fiber 25 G. Strontium Aluminosilicate Fiber 28 H. Lithium Aluminosilicate Fiber 30 V. Investigations Into Other Compatible
Casas-Bedoya, Alvaro; Pagani, Mattia; Marpaung, David; Eggleton, Benjamin J
2015-01-01
We demonstrate the first functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip SBS gain to create an RF photonic notch filter with 48 dB of suppression, 98 MHz linewidth, and 6 GHz frequency tuning. This device has potential applications in on-chip microwave signal processing and establishes the foundation for the first CMOS-compatible high performance RF photonic filter.
Chunguang, Lan; Liguang, Zhou; Zhiyu, Huo
2017-08-01
Prestress loss is critical to impact the safety of prestressed structures. Unfortunately, up to date, there are no qualified techniques to handle this issue due to the fact that it is too hard for sensors to survive the harsh construction environments and the time-dependent service life of the large-span prestressed structures. This paper proposes a novel technique to monitor prestress loss in prestressed beams using Brillouin optical fiber sensors. A novel smart steel strand based on the sensing technique of full-scale Brillouin optical fiber sensors was introduced. Two kinds of prestressed structure were used to verify the concept of monitoring prestress loss using smart steel strands. The prestress loss data have been taken by Brillouin optical fiber sensors. And the monitoring results agree well with those from the conventional sensors. The monitoring data can reveal both the full-scale distribution and the time history of prestress loss during the construction stage and also in-service phrase.
Brillouin spectroscopy reveals changes in muscular viscoelasticity in Drosophila POMT mutants
Meng, Zhaokai; Baker, Ryan; Panin, Vladislav M.; Yakovlev, Vladislav V.
2015-03-01
Muscular dystrophy (MD) is a group of muscle diseases that induce weakness in skeletal muscle and cause progressive muscle degeneration. The muscular mechanical properties (i.e., viscoelasticity), however, have not been thoroughly examined before and after MD. On the other hand, Brillouin spectroscopy (BS) provides a non-invasive approach to probing the local sound speed within a small volume. Moreover, recent advances in background-free Brillouin spectroscopy enable investigators to imaging not only transparent samples, but also turbid ones. In this study, we investigated the mechanical properties of muscles while employing Drosophila model of dystroglycanopathies, human congenital muscular dystrophies resulting from abnormal glycosylation of alphadystroglycan. Specifically, we analyzed larval abdominal muscles of Drosophila with mutations in protein Omannosyltransferase (POMT) genes. As a comparison, we have also examined muscular tissues dissected from wildtype Drosophila. The Brillouin spectra were obtained by a background free VIPA (virtually imaged phased array) spectrometer described in the previous report. As a reference, the Raman spectra were also acquired for each test. Our current results indicated that POMT defects cause changes in muscle elasticity, which suggests that muscular dystrophy conditions may be also associated with abnormalities in muscle elastic properties.
Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser
Lambin Iezzi, Victor; Büttner, Thomas F. S.; Tehranchi, Amirhossein; Loranger, Sébastien; Kabakova, Irina V.; Eggleton, Benjamin J.; Kashyap, Raman
2016-05-01
This paper provides the first detailed temporal characterization of a multi-wavelength-Brillouin-erbium fiber laser (MWBEFL) by measuring the optical intensity of the individual frequency channels with high temporal resolution. It is found that the power in each channel is highly unstable due to the excitation of several cavity modes for typical conditions of operation. Also provided is the real-time measurements of the MWBEFL output power for two configurations that were previously reported to emit phase-locked picosecond pulse trains, concluded from their autocorrelation measurements. Real-time measurements reveal a high degree of instability without the formation of a stable pulse train. Finally, we model the MWBEFL using coupled wave equations describing the evolution of the Brillouin pump, Stokes and acoustic waves in the presence of stimulated Brillouin scattering, and the optical Kerr effect. A good qualitative consistency between the simulation and experimental results is evident, in which the interference signal at the output shows strong instability as well as the chaotic behavior due to the dynamics of participating pump and Stokes waves.
Directory of Open Access Journals (Sweden)
Sara Mattana
2017-11-01
Full Text Available Amyloidopathy is one of the most prominent hallmarks of Alzheimer’s disease (AD, the leading cause of dementia worldwide, and is characterized by the accumulation of amyloid plaques in the brain parenchyma. The plaques consist of abnormal deposits mainly composed of an aggregation-prone protein fragment, β-amyloid 1-40/1-42, into the extracellular matrix. Brillouin microspectroscopy is an all-optical contactless technique that is based on the interaction between visible light and longitudinal acoustic waves or phonons, giving access to the viscoelasticity of a sample on a subcellular scale. Here, we describe the first application of micromechanical mapping based on Brillouin scattering spectroscopy to probe the stiffness of individual amyloid plaques in the hippocampal part of the brain of a β-amyloid overexpressing transgenic mouse. Correlative analysis based on Brillouin and Raman microspectroscopy showed that amyloid plaques have a complex structure with a rigid core of β-pleated sheet conformation (β-amyloid protein surrounded by a softer ring-shaped region richer in lipids and other protein conformations. These preliminary results give a new insight into the plaque biophysics and biomechanics, and a valuable contrast mechanism for the study and diagnosis of amyloidopathy.
The CAP Theorem Versus Databases with Relaxed ACID properties
DEFF Research Database (Denmark)
Frank, Lars; Ulslev Pedersen, Rasmus; Frank, Christian Havnø
2014-01-01
The CAP theorem combines the three desirable properties C (data consistency), A (data availability), and P (partition-tolerance: tolerance of inconsistencies between data stored in a distributed database where partitions are allowed). The CAP theorem asserts that any distributed system that uses ...... data from different locations can have at most two of the three desirable CAP properties [5]. The NoSQL movement has applied the CAP theorem as an argument against traditional ACID (atomicity, consistency, isolation, and durability) databases, which prioritize consistency and partition...
On Pythagoras Theorem for Products of Spectral Triples
D'Andrea, Francesco; Martinetti, Pierre
2013-05-01
We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.
The direct Flow parametric Proof of Gauss' Divergence Theorem revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
The standard proof of the divergence theorem in undergraduate calculus courses covers the theorem for static domains between two graph surfaces. We show that within first year undergraduate curriculum, the flow proof of the dynamic version of the divergence theorem - which is usually considered...... only much later in more advanced math courses - is comprehensible with only a little extension of the first year curriculum. Moreover, it is more intuitive than the static proof. We support this intuition further by unfolding and visualizing a few examples with increasing complexity. In these examples...
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
The Grothendieck-Riemann-Roch theorem for group scheme actions
Koeck, B.
1998-01-01
Let G be a group or a group scheme. We establish formulas for the equivariant Euler characteristic of locally free G-modules on a projective G-scheme X: We prove an Adams- Riemann-Roch theorem and, under a certain continuity assumption for the push-forward map, a Grothendieck-Riemann- Roch theorem in (higher) equivariant algebraic K-theory. Furthermore, we present the following applications: The Adams-Riemann-Roch theorem specializes to an interchanging rule between Adams operations and induc...
The global Utiyama theorem in Einstein-Cartan theory
Bruzzo, Ugo
1987-09-01
A global formulation of Utiyama's theorem for Einstein-Cartan-type gravitational theories regarded as gauge theories of the group of space-time diffeomorphisms is given. The local conditions for the Lagrangian to be gauge invariant coincide with those found by other authors [A. Pérez-Rendón Collantes, ``Utiyama type theorems,'' in Poincaré Gauge Approach to Gravity. I, Proceedings Journées Relativistes 1984; A. Pérez-Rendón and J. J. Seisdedos, ``Utiyama type theorems in Poincaré gauge approach to gravity. II, '' Preprints de Mathematicas, Universidad de Salamanca, 1986] in Kibble's and Hehl's approaches.
Noether Theorem for Nonholonomic Systems with Time Delay
Directory of Open Access Journals (Sweden)
Shi-Xin Jin
2015-01-01
Full Text Available The paper focuses on studying the Noether theorem for nonholonomic systems with time delay. Firstly, the differential equations of motion for nonholonomic systems with time delay are established, which is based on the Hamilton principle with time delay and the Lagrange multiplier rules. Secondly, based upon the generalized quasi-symmetric transformations for nonconservative systems with time delay, the Noether theorem for corresponding holonomic systems is given. Finally, we obtain the Noether theorem for the nonholonomic nonconservative systems with time delay. At the end of the paper, an example is given to illustrate the application of the results.
Soft pion theorem, asymptotic symmetry and new memory effect
Hamada, Yuta; Sugishita, Sotaro
2017-11-01
It is known that soft photon and graviton theorems can be regarded as the Ward-Takahashi identities of asymptotic symmetries. In this paper, we consider soft theorem for pions, i.e., Nambu-Goldstone bosons associated with a spontaneously broken axial symmetry. The soft pion theorem is written as the Ward-Takahashi identities of the S-matrix under asymptotic transformations. We investigate the asymptotic dynamics, and find that the conservation of charges generating the asymptotic transformations can be interpreted as a pion memory effect.
Quantum fluctuation theorems and power measurements
Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter
2015-07-01
Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.
Inverse halftoning based on the bayesian theorem.
Liu, Yun-Fu; Guo, Jing-Ming; Lee, Jiann-Der
2011-04-01
This study proposes a method which can generate high quality inverse halftone images from halftone images. This method can be employed prior to any signal processing over a halftone image or the inverse halftoning used in JBIG2. The proposed method utilizes the least-mean-square (LMS) algorithm to establish a relationship between the current processing position and its corresponding neighboring positions in each type of halftone image, including direct binary search, error diffusion, dot diffusion, and ordered dithering. After which, a referenced region called a support region (SR) is used to extract features. The SR can be obtained by relabeling the LMS-trained filters with the order of importance. Moreover, the probability of black pixel occurrence is considered as a feature in this work. According to this feature, the probabilities of all possible grayscale values at the current processing position can be obtained by the Bayesian theorem. Consequently, the final output at this position is the grayscale value with the highest probability. Experimental results show that the proposed method offers better visual quality than that of Mese-Vaidyanathan's and Chang et al's methods in terms of human-visual peak signal-to-noise ratio (HPSNR). In addition, the memory consumption is also superior to Mese-Vaidyanathan's method.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Energy Technology Data Exchange (ETDEWEB)
Reichhardt, Charles [Los Alamos National Laboratory; Reichhardt, C J [Los Alamos National Laboratory; Drocco, J A [PRINCETON UNIV.
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
Bayes' theorem: A paradigm research tool in biomedical sciences
African Journals Online (AJOL)
STORAGESEVER
2008-12-29
Dec 29, 2008 ... 1Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria. ... Bayes' theorem in biomedical research using examples. ..... educate prospective mothers aged 20 years or less. The.
A Computer Science Version of Goedel’s Theorem.
1983-08-01
The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)
Analogy to Derive an Extended Pythagorean Theorem to ''N'' Dimensions
Directory of Open Access Journals (Sweden)
Acosta-Robledo J.U.
2012-01-01
Full Text Available This article demonstrates that it is possible to extend the Pythagorean Theorem to ''N'' dimensions. This demonstration is mainly done based on linear algebra, especially in the vector product of ''N'' dimensions.
On the groups satisfying the converse of Schur's theorem
Directory of Open Access Journals (Sweden)
Saeed Kayvanfar
2012-12-01
Full Text Available A famous theorem of Schur states that for a group G finiteness of G/Z(G implies the finiteness of G′. The converse of Schur’s theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur’s theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur’s theorem and at the same time admit the Podoski and Szegedy’s bound as the upper bound for the index of their centers.
Next to subleading soft-graviton theorem in arbitrary dimensions
Energy Technology Data Exchange (ETDEWEB)
Kalousios, Chrysostomos [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, 01140-070, São Paulo, SP (Brazil); Rojas, Francisco [Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, 01140-070, São Paulo, SP (Brazil)
2015-01-21
We study the soft graviton theorem recently proposed by Cachazo and Strominger. We employ the Cachazo, He and Yuan formalism to show that the next to subleading order soft factor for gravity is universal at tree level in arbitrary dimensions.
Chkareuli-Froggatt-Nielsen Theorem and Photon Mass
Siahaan, Haryanto M.
2007-01-01
We analyze there is a relation between fossil charge and the mass of photon based on Chkareuli-Froggatt-Nielsen Theorem and Proca Lagrangian. As generally known, massive photon will lead to Lorentz non-invariance field theory.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
Quantum nonlocality and reality 50 years of Bell's theorem
Gao, Shan
2016-01-01
Description Contents Resources Courses About the Authors Combining twenty-six original essays written by an impressive line-up of distinguished physicists and philosophers of physics, this anthology reflects some of the latest thoughts by leading experts on the influence of Bell's theorem on quantum physics. Essays progress from John Bell's character and background, through studies of his main work, and on to more speculative ideas, addressing the controversies surrounding the theorem, and investigating the theorem's meaning and its deep implications for the nature of physical reality. Combined, they present a powerful comment on the undeniable significance of Bell's theorem for the development of ideas in quantum physics over the past 50 years. Questions surrounding the assumptions and significance of Bell's work still inspire discussion in the field of quantum physics. Adding to this with a theoretical and philosophical perspective, this balanced anthology is an indispensable volume for students and researc...
Generalized -Bernstein-Schurer Operators and Some Approximation Theorems
Directory of Open Access Journals (Sweden)
M. Mursaleen
2013-01-01
Full Text Available We study statistical approximation properties of -Bernstein-Shurer operators and establish some direct theorems. Furthermore, we compute error estimation and show graphically the convergence for a function by operators and give its algorithm.
Limit theorems for unions of random closed sets
Molchanov, Ilya S
1993-01-01
The book concerns limit theorems and laws of large numbers for scaled unionsof independent identically distributed random sets. These results generalizewell-known facts from the theory of extreme values. Limiting distributions (called union-stable) are characterized and found explicitly for many examples of random closed sets. The speed of convergence in the limit theorems for unions is estimated by means of the probability metrics method.It includes the evaluation of distances between distributions of random sets constructed similarly to the well-known distances between distributions of random variables. The techniques include regularly varying functions, topological properties of the space of closed sets, Choquet capacities, convex analysis and multivalued functions. Moreover, the concept of regular variation is elaborated for multivalued (set-valued) functions. Applications of the limit theorems to simulation of random sets, statistical tests, polygonal approximations of compacts, limit theorems for pointw...
A Fresh Look at the Rotten Kid Theorem
Bergstrom, Ted
1989-01-01
Gary Becker's ``Rotten Kid Theorem'' asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. We show by examples that the Rotten Kid theorem is not true without assuming transferable utility. We find a simple condition on utility functions that is necessary and sufficient f...
A simple proof of Perelman's collapsing theorem for 3-manifolds
Cao, Jianguo; Ge, Jian
2010-01-01
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the class...
Fatou's Lemma and Lebesgue's convergence theorem for measures
Directory of Open Access Journals (Sweden)
Onésimo Hernández-Lerma
2000-01-01
Full Text Available Analogues of Fatou's Lemma and Lebesgue's convergence theorems are established for ∫fdμn when {μn} is a sequence of measures. A generalized Dominated Convergence Theorem is also proved for the asymptotic behavior of ∫fndμn and the latter is shown to be a special case of a more general result established in vector lattices and related to the Dunford-Pettis property in Banach spaces.
A short list color proof of Grotzsch's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable.......We give a short proof of the result that every planar graph of girth $5$is $3$-choosable and hence also of Gr\\"{o}tzsch's theorem saying that everyplanar triangle-free graph is $3$-colorable....
Some functional limit theorems for compound Cox processes
Energy Technology Data Exchange (ETDEWEB)
Korolev, Victor Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Institute of Informatics Problems FRC CSC RAS (Russian Federation); Chertok, A. V. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Euphoria Group LLC (Russian Federation); Korchagin, A. Yu. [Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow (Russian Federation); Kossova, E. V. [Higher School of Economics National Research University, Moscow (Russian Federation); Zeifman, Alexander I. [Vologda State University, S.Orlova, 6, Vologda (Russian Federation); Institute of Informatics Problems FRC CSC RAS, ISEDT RAS (Russian Federation)
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Cartan's proof for the Darboux theorem in A -modules | Ntumba ...
African Journals Online (AJOL)
We refer to [4] for a proof of the (affine) Darboux theorem in the category A-ModX of A-modules, defined on a fixed topological space X. Hereby, we present another proof of the same theorem, based on E. Cartan's approach, keeping, as is done in [4], the condition affixed to the coefficient algebra sheaf A, that is, A satisfies ...
Existence Theorems for Generalized Distance on Complete Metric Spaces
Directory of Open Access Journals (Sweden)
Jeong Sheok Ume
2010-01-01
Full Text Available We first introduce the new concept of a distance called u-distance, which generalizes w-distance, Tataru's distance, and τ-distance. Then we prove a new minimization theorem and a new fixed point theorem by using a u-distance on a complete metric space. Our results extend and unify many known results due to Caristi, Ćirić, Ekeland, Kada-Suzuki-Takahashi, Kannan, Ume, and others.
Rigidity theorem for Willmore surfaces in a sphere
Indian Academy of Sciences (India)
compact non-minimal flat Willmore surfaces in S3, and Castro and Urbano [2] constructed many compact non-minimal Willmore surfaces in S4. In [6], Li obtained the following rigidity theorem for Willmore surfaces in a unit sphere. Theorem A. Let M be a compact Willmore surface in S2+p. Then. ∫M ρ2 (2 − 2B ρ2) dv ≤ 0,.
The PBR theorem: Whose side is it on?
Ben-Menahem, Yemima
2017-02-01
This paper examines the implications of the PBR theorem for the debate on the reality of the quantum state. The theorem seeks to undermine epistemic interpretations of the quantum state and support realist interpretations thereof, but there remains ambiguity about the precise nature of epistemic interpretations, and thus ambiguity about the implications of the theorem. The aim of this paper is to examine a radical epistemic interpretation that is not undermined by the theorem and is, arguably, strengthened by it. It is this radical interpretation, rather than the one assumed by the PBR theorem, that many epistemic theorists subscribe to. In order to distinguish the radical epistemic interpretation from alternative interpretations of quantum states-in particular, to distinguish it from instrumentalism-a historical comparison of different approaches to the meaning of quantum probabilities is provided. The comparison highlights, in particular, Schrödinger's work on the nature of quantum probabilities as distinct from probabilities in statistical mechanics, and the implications of this distinction for an epistemic interpretation of probability in the two areas. Schrödinger's work also helps to identify the difficulties in the PBR definition of an epistemic interpretation and is shown to anticipate the radical alternative that is not undermined by the theorem.
Subexponential estimates in Shirshov's theorem on height
Belov, Aleksei Ya; Kharitonov, Mikhail I.
2012-04-01
Suppose that F_{2,m} is a free 2-generated associative ring with the identity x^m=0. In 1993 Zelmanov put the following question: is it true that the nilpotency degree of F_{2,m} has exponential growth? We give the definitive answer to Zelmanov's question by showing that the nilpotency class of an l-generated associative algebra with the identity x^d=0 is smaller than \\Psi(d,d,l), where \\displaystyle \\Psi(n,d,l)=2^{18}l(nd)^{3log_3(nd)+13}d^2. This result is a consequence of the following fact based on combinatorics of words. Let l, n and d\\ge n be positive integers. Then all words over an alphabet of cardinality l whose length is not less than \\Psi(n,d,l) are either n-divisible or contain x^d; a word W is n-divisible if it can be represented in the form W=W_0W_1\\dotsb W_n so that W_1,\\dots,W_n are placed in lexicographically decreasing order. Our proof uses Dilworth's theorem (according to V.N. Latyshev's idea). We show that the set of not n-divisible words over an alphabet of cardinality l has height h<\\Phi(n,l) over the set of words of degree \\le n-1, where \\displaystyle \\Phi(n,l)=2^{87}l\\cdot n^{12log_3n+48}. Bibliography: 40 titles.
Photonic methods of millimeter-wave generation based on Brillouin fiber laser
Al-Dabbagh, R. K.; Al-Raweshidy, H. S.
2016-05-01
In optical communication link, generation and delivering millimeter-wave (mm-waves) in radio over fiber (RoF) systems has limitation due to fiber non-linearity effects. To solve this problem, photonic methods of mm-wave generation based on characterizations of Brillouin fiber laser are proposed in this work for the first time. Three novel photonic approaches for mm-wave generation methods based on Brillouin fiber laser and phase modulator are proposed and demonstrated by simulation. According to our theoretical analysis and simulation, mm-waves with frequency up to 80 GHz and good signal to noise ratio (SNR) up to 90 dB are generated by new and cost effective methods of generation that make them suitable for applications of the fifth generation (5G) networks. The proposed configurations increase the stability and the quality of the mm-wave generation system by using a single laser source as a pump wave and the fiber non-linearity effects are reduced. A key advantage of this research is that proposed a number of very simple generation methods and cost effective which only use standard components of optical telecommunications. Stimulated Brillouin Scattering (SBS) effect that exists in the optical fiber is studied with the characterization of phase modulator. An all optically stable mm-wave carriers are achieved successfully in the three different methods with different frequencies from 20 GHz up to 80 GHz. Simulation results show that all these carriers have low phase noise, good SNR ranging between 60 and 90 dB and tuning capability in comparison with previous methods reported. This makes them suitable for mm-wave transmission in RoF systems to transmit data in the next generation networks.
Stimulated Brillouin scattering in the field of a two-dimensionally localized pumping wave
Energy Technology Data Exchange (ETDEWEB)
Solikhov, D. K., E-mail: davlat56@mail.ru [Tajik National University, Faculty of Physics (Tajikistan); Dvinin, S. A., E-mail: dvinin@phys.msu.ru [Moscow State University, Faculty of Physics (Russian Federation)
2016-06-15
Stimulated Brillouin scattering of electromagnetic waves in the field of a two-dimensionally localized pump wave at arbitrary scattering angles in the regime of forward scattering is analyzed. Spatial variations in the amplitudes of interacting waves are studied for different values of the pump field and different dimensions of the pump wave localization region. The intensity of scattered radiation is determined as a function of the scattering angle and the dimensions of the pump wave localization region. It is shown that the intensity increases with increasing scattering angle.
Surface plasmons at the Brillouin zone boundary of an oblique lattice
Energy Technology Data Exchange (ETDEWEB)
Constant, Thomas J., E-mail: t.j.constant@exeter.ac.uk; Vukusic, Pete; Hibbins, Alastair P.; Sambles, J. Roy [Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, Devon EX4 4QL (United Kingdom)
2015-03-02
In periodic systems of low-symmetry, the Bragg condition for the complete interference of waves along the contour of the Brillouin zone (BZ) boundary is not generally satisfied. As a result, band-gaps do not necessarily occur at this boundary. This letter demonstrates this experimentally by recording the iso-frequency contours for surface plasmon polaritons (SPPs) supported on a diffraction grating with an underlying 2D oblique Bravias lattice. It is shown that these contours do not intersect the BZ boundary perpendicularly, as the symmetry operations of the lattice place no conditions on the surface wave interference at this boundary.
Zhang, Liang; Zhan, Li; Qian, Kai; Liu, Jinmei; Shen, Qishun; Hu, Xiao; Luo, Shouyu
2011-08-26
We report superluminal propagation in optical fibers using Brillouin lasing oscillation in a ring cavity. Negative group velocity propagation through a 10-m single mode fiber has been experimentally demonstrated. An advancement of 221.2 ns was observed before the input signal, which was achieved with a very high slope efficiency of 211.3 ns/dB. This indicates that this way is suitable for long-distance low-loss superluminal propagation via optical fibers. Correspondingly, the group velocity is -0.151c and the group index is -6.636-the highest group velocity ever reported for optical fibers. © 2011 American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Salas, E.; Jimenez-Villacorta, F.; Jimenez Rioboo, R.J.; Prieto, C. [Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientificas, Cantoblanco, 28049 Madrid (Spain); Sanchez-Marcos, J. [Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Cientificas, Cantoblanco, 28049 Madrid (Spain); Departamento de Quimica-Fisica Aplicada, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Munoz-Martin, A.; Prieto, J.E.; Joco, V. [Centro de Microanalisis de Materiales, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)
2013-03-15
Surface acoustic wave (SAW) velocity has been determined by high resolution Brillouin light scattering to study the mechano-elastic properties of boron carbide films prepared by radio frequency (RF) sputtering. The comparison of experimentally observed elastic behaviour with simulations made by considering film composition obtained from elastic recoil detection analysis-time of flight (ERDA-ToF) spectroscopy allows establishing that elastic properties are determined by that of crystalline boron carbide with a lessening of the SAW velocity values due to surface oxidation. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Gu, Ziyu; Ubachs, Wim
2013-04-01
Values for the bulk viscosity of molecular nitrogen gas (N2) were derived from spontaneous Rayleigh-Brillouin (RB) scattering at ultraviolet wavelengths (366.8 nm) and at a 90 degree scattering angle. Analysis of the scattering profiles yield values showing a linear increasing trend in the temperature interval from 255 K to 340 K. The present values, pertaining to hypersound acoustics at frequencies in the GHz domain, are found to be in agreement with results from acoustic attenuation experiments in N2 performed at MHz frequencies.
Alahbabi, Mohamed N.; Cho, Yuh Tat; Newson, Trevor P.; Wait, Peter C.; Hartog, Arthur H.
2004-06-01
The performance of distributed fiber sensors based on spontaneous Brillouin scattering is largely determined by the peak power governed by nonlinear thresholds that can be launched into the sensing fiber. Our investigations show that, in long-range (>20-km) sensors that use a standard single-mode fiber operating at 1.5 μm, modulation instability can limit the acceptable pulse power to below 100 mW. Using a nonzero dispersion-shifted fiber with negative dispersion we can avoid this problem and obtain a ninefold increase in launched power.
Energy Technology Data Exchange (ETDEWEB)
Ni, C.K.; Kung, A.H. [Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 10764 (Taiwan)
1996-10-01
Backward stimulated Brillouin scattering was used to control the growth of amplified spontaneous emission (ASE), reducing the unwanted emission in a pulse-amplified cw Ti:sapphire laser system from 22{percent} to less than 1{times}10{sup {minus}4} in the final output. Suppression of ASE substantially improved the spectral quality of the laser and broadened the range over which the laser is useful. The output duration was compressed, but the pulse remained nearly transform limited. {copyright} {ital 1996 Optical Society of America.}
Ko, Jae-Hyeon; Lee, Kwang-Sei; Ike, Yuji; Kojima, Seiji
2008-11-01
The acoustic waves propagating along the direction perpendicular to the (1 0 0) cleavage plane of aspirin crystal were investigated using micro-Brillouin spectroscopy from which C11, C55 and C66 were obtained. The temperature dependence of the longitudinal acoustic waves could be explained by normal anharmonic lattice models, while the transverse acoustic waves showed an abnormal increase in the hypersonic attenuation at low temperatures indicating their coupling to local remnant dynamics. The sound velocity as well as the attenuation of the longitudinal acoustic waves of glassy aspirin showed a substantial change at ˜235 K confirming a transition from glassy to supercooled liquid state in vitreous aspirin.
Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers
Wolff, C; Poulton, C G
2014-01-01
We derive formal selection rules for Stimulated Brillouin Scattering (SBS) in structured waveguides. Using a group-theoretical approach, we show how the waveguide symmetry determines which optical and acoustic modes interact for both forward and backward SBS. We present a general framework for determining this interaction and give important examples for SBS in waveguides with rectangular, triangular and hexagonal symmetry. The important role played by degeneracy of the optical modes is illustrated. These selection rules are important for SBS-based device design and for a full understanding the physics of SBS in structured waveguides.
Pressure dependence of acoustic anomalies of polydimethylsiloxane studied by Brillouin spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Shin, Seonhyeop [Department of Physics, Hallym University, Chuncheon, Gangwondo 200-702, South Korea (Korea, Republic of); Ko, Jae-Hyeon, E-mail: hwangko@hallym.ac.kr [Department of Physics, Hallym University, Chuncheon, Gangwondo 200-702, South Korea (Korea, Republic of); Park, Jaehoon [Department of Electronic Engineering, Hallym University, Chuncheon, Gangwondo 200-702 (Korea, Republic of); Ko, Young Ho; Kim, Kwang Joo [4-2-2, Agency for Defense Development, P.O. Box 35, Yuseong, Daejeon 305-600 (Korea, Republic of)
2015-06-15
The acoustic properties of polydimethylsiloxane elastomer was investigated as a function of pressure by using a multi-pass Fabry–Perot interferometer and a diamond anvil cell. Pressure dependence of the sound velocity, the Brillouin linewidth, and the refractive index was determined up to ~8.7 GPa. Acoustic properties exhibited a crossover behavior at approximately 1 GPa, which was attributed to the complete collapse of the free volume content in this polymer. The refractive index increased from 1.46 at ambient condition to ~1.63 at 8.67 GPa, which reflected the corresponding increase in density.
Directory of Open Access Journals (Sweden)
Romeo Bernini
2011-01-01
Full Text Available The structural strain measurement of tension and compression in a 4 m long concrete beam was demonstrated with a distributed fiber-optic sensor portable system based on Brillouin scattering. Strain measurements provided by the fiber-optic sensor permitted to detect the formation of a crack in the beam resulting from the external applied load. The sensor system is valuable for structural monitoring applications, enabling the long-term performance and health of structures to be efficiently monitored.
Spatial mapping of correlation profile in Brillouin optical correlation domain analysis
Somepalli, Bhargav; Venkitesh, Deepa; Srinivasan, Balaji
2017-04-01
We report an approach to spatially map the correlation profile along the sensing fiber in Brillouin optical correlation domain analysis by pulsing the pump radiation. Simulations are carried out to demonstrate the influence of frequency modulation parameters of a narrow linewidth source on the width of the correlation profile and its peak position. The simulation results are validated through controlled experiments. The correlation profile is mapped over 1 km long fiber with spatial resolution of 1 m, limited only by the finite lifetime of acoustic phonons in the silica fiber.
Hydrostatic pressure dependence of Brillouin frequency shift in polymer optical fibers
Mizuno, Yosuke; Lee, Heeyoung; Hayashi, Neisei; Nakamura, Kentaro
2018-01-01
We experimentally investigate the pressure dependence of the Brillouin frequency shift (BFS) in a polymer optical fiber. The BFS dependence on pressure shows a hysteresis, but after several cycles of increasing/decreasing pressure, the hysteresis is mitigated. The pressure dependence coefficient at this state is +4.3 MHz/MPa, the absolute value of which is 5.8 times as large as that of bare silica fibers (the sign is opposite). The reason for this unique behavior is discussed. This result indicates that, by using plastic optical fibers instead of silica fibers, distributed pressure sensing with a higher sensitivity is potentially feasible.
Vaughn, Mark D.; Boh Ruffin, A.; Kobyakov, Andrey; Woodfin, Andrew; Mazzali, Claudio; Whitman, Robert; Boskovic, Aleksandra; Wagner, Richard E.; Kozischek, David; Meis, David
2006-01-01
Cost modeling reveals that deployment of fibers with a high stimulated Brillouin scattering threshold in fiber-to-the-home access networks can reduce material and labor expenditures by more than 20%. Theory and measurements of the high stimulated Brillouin scattering fiber are presented to demonstrate its employability.
On local-hidden-variable no-go theorems
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Central limit theorem: the cornerstone of modern statistics.
Kwak, Sang Gyu; Kim, Jong Hae
2017-04-01
According to the central limit theorem, the means of a random sample of size, n , from a population with mean, µ, and variance, σ 2 , distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Formalization of the Integral Calculus in the PVS Theorem Prover
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
[INVITED] State of the art of Brillouin fiber-optic distributed sensing
Motil, Avi; Bergman, Arik; Tur, Moshe
2016-04-01
Fiber-optic distributed sensing, employing the Brillouin effect, is already a commercially available measurement technique for the accurate estimation of the static strain/temperature fields along tens of kilometers with a spatial resolution of the order of a meter. Furthermore, relentless research efforts are paving the way to even much wider usability of the technique through recently achieved enhanced performance in each of its critical dimensions: measurement range has been extended to hundreds of kilometers; spatial resolution is of the order of a centimeter or less, signal to noise ratio has been significantly improved; fast dynamic events can be captured at kHz's sampling rates; and a much better understanding of the underlying physics has been obtained, along with the formulation of figures of merit, and the preparation and early adoption of appropriate standards and guidelines. This paper describes the basics, as well as the state of the art, of the leading Brillouin interrogation methods, with emphasis on the significant progress made in the last 3 years. It also includes a short introduction to coding, which has proven instrumental in many of the recently obtained performance records.
Application of Morlet wavelet in the extraction of Brillouin scattering signal envelope
Wang, Xin; Huang, Cha-xiang; Zhou, Li
2013-08-01
The Brillouin scattering light signal is a wideband signal containing a lot of phase noises and amplitude noises. And the envelope of the Brillouin scattering signal will include some characteristics due to the influences of temperature and strain change on the sensing fiber. In order to obtain the useful temperature and strain change information, the amplitude demodulation of the noise signal should be conducted, and at the same time, it is necessary to effectively suppress the signal noise. In this paper, Morlet wavelet has been used to do the envelope detection since it has band-pass filtering function and signal demodulation function provided by the orthogonal characteristic between real part and imaginary part. Moreover, the Morlet wavelet function has the characteristic of time-frequency analysis, and it can analyze envelope of the signal and extract characteristic of the signal in the whole frequency range by changing the scale factor and translation factor. Meanwhile, it can also suppress the signal noise effectively. The simulation model has been built to verify the validity of envelope demodulation principle by Morlet wavelet algorithm. Theory analysis and experiment show the algorithm is reasonable and efficient.
Stimulated Brillouin scattering suppression in optical fibers by hydrogen-loading technique
Kong, Fanting; Dong, Liang
2013-02-01
Further power scaling of single frequency fiber lasers is of significant interests for many scientific and defense applications. It is currently limited by stimulated Brillouin scattering (SBS). In recent years, a variety of techniques have been investigated for the suppression of SBS in optical fibers. A notable example is to design transverse acoustic properties of optical fibers in order to minimize optical and acoustic mode overlap. It was pointed out recently that SBS suppression from such transverse acoustic tailoring is limited when considering the existence of acoustic leaky modes. We demonstrate, for the first time, a post-processing technique where hydrogen is diffused in to a fiber core and then locally and permanently bonded to core glass by a subsequent UV exposure. Large local acoustic property can be altered this way for significant SBS suppression. It is also possible to use this technique to implement precisely tailored acoustic properties along a fiber for more optimized SBS suppression in a fiber amplifier. Change in Brillouin Stokes frequency of ~320MHz at 1.064μm has been demonstrated using hydrogen, corresponding to a SBS suppression of ~8dB. Much higher SBS suppression is possible at higher hydrogen concentrations.
Generation of high-power few-cycle lasers via Brillouin-based plasma amplification
Zhang, Z. M.; Zhang, B.; Hong, W.; Deng, Z. G.; Teng, J.; He, S. K.; Zhou, W. M.; Gu, Y. Q.
2017-11-01
Strong coupling stimulated Brillouin backscattering (sc-SBS) in plasma is potentially an efficient method of amplifying laser pulses to reach exawatt powers. Here, we report on a new regime of brillouin-based plasma amplification, producing an amplified pulse with a duration of 5 fs and unfocused intensity of 6 × 1017 W/cm2. The results are obtained from 2D particle-in-cell simulations, using two circularly polarized pump and seed pulse with Gaussian transverse profile, both at an intensity of 2.74 × 1016 W/cm2, counter-propagating in a 0.3nc plasma. The significant compression of amplified seed is achieved as a result of sc-SBS amplification as well as additional compression by the interplay between self-phase modulation and negative group delay dispersion. We show that the amplified seed retains high beam qualities since the filamentation can be prevented due to the fast compression. This scheme may pave the way for few-cycle laser pulses to reach exawatt or even zetawatt regime.
Zhang, Yan-jun; Zhang, Shu-guo; Fu, Guang-wei; Li, Da; Liu, Yin; Bi, Wei-hong
2012-04-01
This paper presents a novel algorithm which blends optimize particle swarm optimization (PSO) algorithm and Levenberg-Marquardt (LM) algorithm according to the probability. This novel algorithm can be used for Pseudo-Voigt type of Brillouin scattering spectrum to improve the degree of fitting and precision of shift extraction. This algorithm uses PSO algorithm as the main frame. First, PSO algorithm is used in global search, after a certain number of optimization every time there generates a random probability rand (0, 1). If rand (0, 1) is less than or equal to the predetermined probability P, the optimal solution obtained by PSO algorithm will be used as the initial value of LM algorithm. Then LM algorithm is used in local depth search and the solution of LM algorithm is used to replace the previous PSO algorithm for optimal solutions. Again the PSO algorithm is used for global search. If rand (0, 1) was greater than P, PSO algorithm is still used in search, waiting the next optimization to generate random probability rand (0, 1) to judge. Two kinds of algorithms are alternatively used to obtain ideal global optimal solution. Simulation analysis and experimental results show that the new algorithm overcomes the shortcomings of single algorithm and improves the degree of fitting and precision of frequency shift extraction in Brillouin scattering spectrum, and fully prove that the new method is practical and feasible.
A microrod-resonator Brillouin laser with 240 Hz absolute linewidth
Loh, William; Cole, Daniel C; Coillet, Aurelien; Baynes, Fred N; Papp, Scott B; Diddams, Scott A
2015-01-01
We demonstrate an ultralow-noise microrod-resonator based laser that oscillates on the gain supplied by the stimulated Brillouin scattering optical nonlinearity. Microresonator Brillouin lasers are known to offer an outstanding frequency noise floor, which is limited by fundamental thermal fluctuations. Here, we show experimental evidence that thermal effects also dominate the close-to-carrier frequency fluctuations. The 6-mm diameter microrod resonator used in our experiments has a large optical mode area of ~100 {\\mu}m$^2$, and hence its 10 ms thermal time constant filters the close-to-carrier optical frequency noise. The result is an absolute laser linewidth of 240 Hz with a corresponding white-frequency noise floor of 0.1 Hz$^2$/Hz. We explain the steady-state performance of this laser by measurements of its operation state and of its mode detuning and lineshape. Our results highlight a mechanism for noise that is common to many microresonator devices due to the inherent coupling between intracavity power...
Model Checking Failed Conjectures in Theorem Proving: A Case Study
Pike, Lee; Miner, Paul; Torres-Pomales, Wilfredo
2004-01-01
Interactive mechanical theorem proving can provide high assurance of correct design, but it can also be a slow iterative process. Much time is spent determining why a proof of a conjecture is not forthcoming. In some cases, the conjecture is false and in others, the attempted proof is insufficient. In this case study, we use the SAL family of model checkers to generate a concrete counterexample to an unproven conjecture specified in the mechanical theorem prover, PVS. The focus of our case study is the ROBUS Interactive Consistency Protocol. We combine the use of a mechanical theorem prover and a model checker to expose a subtle flaw in the protocol that occurs under a particular scenario of faults and processor states. Uncovering the flaw allows us to mend the protocol and complete its general verification in PVS.
Towards a Novel no-hair Theorem for Black Holes
Hertog, T
2006-01-01
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Saoithín: A Theorem Prover for UTP
Butterfield, Andrew
Saoithín is a theorem prover developed to support the Unifying Theories of Programming (UTP) framework. Its primary design goal was to support the higher-order logic, alphabets, equational reasoning and "programs as predicates" style that is prevalent in much of the UTP literature, from the seminal work by Hoare & He [HH98] onwards. This paper describes the key features of the theorem prover, with an emphasis on the underlying foundations, and how these affect the design and implementation choices. These key features include: a formalisation of a UTP Theory; support for common proof strategies; sophisticated goal/law matching ; and user-defined language constructs. A simple theory of designs with some proof extracts is used to illustrate the above features. The theorem prover has been used with undergraduate students and we discuss some of those experiences. The paper then concludes with a discussion of current limitations and planned improvements to the tool.
Limit theorems for multi-indexed sums of random variables
Klesov, Oleg
2014-01-01
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who ...
A Macro for Reusing Abstract Functions and Theorems
Directory of Open Access Journals (Sweden)
Sebastiaan J. C. Joosten
2013-04-01
Full Text Available Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of abstract functions and facts proven about them. Defspec is an ACL2 book allowing users to define constrained functions and their associated properties. It contains macros facilitating the definition of such abstract specifications and instances thereof. Currently, lemmas and theorems derived from these abstract functions are not automatically instantiated. This is exactly the purpose of our new macro. instance-of-defspec will not only instantiate functions and theorems within a specification but also many more functions and theorems built on top of the specification. As a working example, we describe various fold functions over monoids, which we gradually built from arbitrary functions.
The Fundamental Theorem of Flood Frequency Analysis
O'Kane, J. P.
The Fundamental Theorem of hazardous events, regarded as a stochastic point pro- cess, says that the return period, or average interval, between events is equal to the reciprocal of their frequency in time. We start with the special cases. There are three ways of defining a discrete time Bernoulli process of hazardous events: by specifying (a) the probability p that an event occurs at a given point in time, (b) the probability that m events occur in an interval of time of duration n - the Bernoulli distribution, or (c) the probability that the return period (recurrence interval) between events is n in- tervals - the geometric distribution. Any one of these implies the other two. It is easily shown that the expected return period between hazardous Bernoulli events in discrete time is the reciprocal of the probability of this event at any point in discrete time. The analogous process in continuous time is a Poisson process which can also be defined in three ways: by specifying (a) the probability r.dt that one and only one event occurs during a small interval of duration dt, (b) the probability that m events occur in an interval of duration t U the Poisson distribution, or (c) the probability that the return period (recurrence interval) between hazardous events is t units of time U the negative exponential distribution. Any one of these implies the other two. Also the expected return period between hazardous Poisson events is the reciprocal of the probability rate, r, of this event per unit of continuous time. A (2x2) transition matrix P describes a correlated discrete-time Markov process of hazardous events. The Bernoulli process is a special case. Since P is ergodic it has a limiting probability vector (p1, p2) of the unconditional probabilities of a hazardous event occurring, p1, or of not occurring, p2, at a randomly chosen point in time. The return period between hazardous Markov events can be shown to be 1/p1 in agreement with the Bernoulli process. Now it is
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E
2015-01-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.
A Simple Proof of a Folklore Theorem about Delimited Control
DEFF Research Database (Denmark)
Biernacki, Dariusz; Danvy, Olivier
2006-01-01
We formalize and prove the folklore theorem that the static delimited-control operators shift and reset can be simulated in terms of the dynamic delimited-control operators control and prompt. The proof is based on small-step operational semantics.......We formalize and prove the folklore theorem that the static delimited-control operators shift and reset can be simulated in terms of the dynamic delimited-control operators control and prompt. The proof is based on small-step operational semantics....
A nonsmooth Morse-Sard theorem for subanalytic functions
Bolte, Jerome; Daniilidis, Aris; Lewis, Adrian
2006-09-01
According to the Morse-Sard theorem, any sufficiently smooth function on a Euclidean space remains constant along any arc of critical points. We prove here a theorem of Morse-Sard type suitable as a tool in variational analysis: we broaden the definition of a critical point to the standard notion in nonsmooth optimization, while we restrict the functions under consideration to be semialgebraic or subanalytic. We make no assumption of subdifferential regularity. Lojasiewicz-type inequalities for nonsmooth functions follow quickly from tools of the kind we develop, leading to convergence theory for subgradient dynamical systems.
Wiener Tauberian theorems for vector-valued functions
Directory of Open Access Journals (Sweden)
K. Parthasarathy
1994-01-01
Full Text Available Different versions of Wiener's Tauberian theorem are discussed for the generalized group algebra L1(G,A (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A using A-valued Fourier transforms. A weak form of Wiener's Tauberian property is introduced and it is proved that L1(G,A is weakly Tauberian if and only if A is. The vector analogue of Wiener's L2-span of translates theorem is examined.
Addition theorems for spin spherical harmonics: II. Results
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
Based on the results of part I (2011 J. Phys. A: Math. Theor. 44 165301), we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-s' and one spin-s spherical harmonics with s', s = 1/2, 1, 3/2, and |s' - s| = 0, 1. We also obtain a fully general addition theorem for one scalar and one tensor spherical harmonic of arbitrary rank. A variety of bilocal sums of ordinary and spin spherical harmonics are given in explicit form, including a general explicit expression for bilocal spherical harmonics.
Addition theorems for spin spherical harmonics: I. Preliminaries
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@mda.cinvestav.mx [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo. Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2011-04-22
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin degrees of freedom in certain products of Clebsch-Gordan coefficients, and obtain general explicit results for the matrix elements in configuration space of tensor products of arbitrary rank of the position and angular-momentum operators. These results are the basis of the addition theorems for spin spherical harmonics obtained in part II (2011 J. Phys. A: Math. Theor. 44 165302).
Generalization of Carey's equality and a theorem on stationary population.
Srinivasa Rao, Arni S R; Carey, James R
2015-09-01
Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.
Towards a Reverse Newman's Theorem in Interactive Information Complexity
DEFF Research Database (Denmark)
Brody, Joshua Eric; Buhrman, Harry; Koucký, Michal
2016-01-01
that uses private randomness and convert it into one that only uses public randomness while preserving the information revealed to each player? We prove that the answer is yes, at least for protocols that use a bounded number of rounds. As an application, we prove new direct sum theorems through......Newman’s theorem states that we can take any public-coin communication protocol and convert it into one that uses only private randomness with only a little increase in communication complexity. We consider a reversed scenario in the context of information complexity: can we take a protocol...
Asymptotic symmetries of gravity and soft theorems for massive particles
Energy Technology Data Exchange (ETDEWEB)
Campiglia, Miguel [Instituto de Física, Facultad de Ciencias, Universidad de la República,Iguá 4225, Montevideo (Uruguay); Laddha, Alok [Chennai Mathematical Institute,SIPCOT IT Park, Siruseri 603103 (India)
2015-12-15
The existing equivalence between (generalized) BMS Ward identities with leading and subleading soft graviton theorems is extended to the case where the scattering particles are massive scalars. By extending the action of generalized BMS group off null infinity at late times, we show that there is a natural action of such group not only on the radiative data at null infinity but also on the scattering data of the massive scalar field. This leads to a formulation of Ward identities associated to the generalized BMS group when the scattering states are massive scalars or massless gravitons and we show that these Ward identities are equivalent to the leading and subleading soft graviton theorems.
The unknown sister of Noether's theorem
Energy Technology Data Exchange (ETDEWEB)
Smilga, Walter
2016-07-01
Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to strong conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem is another law that has an opposite effect: it requires the exchange of momentum between two particles that are described by an irreducible two-particle representation of the Poincare group. Exchange of momentum determines an interaction. On closer inspection, this interaction is uniquely identified as the electromagnetic interaction. This finding sheds new light on the phenomenon of particle interaction in general and, in particular, on the perturbation algorithm of quantum electrodynamics.
A vizing-type theorem for matching forests
Keijsper, J.C.M.
2000-01-01
A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this Theorem for directed graphs was proved by Frank. It states that one can colour the arcs of a digraph by $\\Delta +\\alpha$ colours, such that arcs of the same colour form a branching. For a digraph, $\\...
Decomposing Borel functions using the Shore-Slaman join theorem
Kihara, Takayuki
2013-01-01
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\\sigma$ set under it is again $F_\\sigma$. Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rog...
General self-tuning solutions and no-go theorem
Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min
2013-03-01
We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodox Lagrangians.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
2017-03-16
seed can be made to follow a triangular waveform in time, spanning up to 100 nm, larger than the entire Yb gain spectrum.Error! Bookmark not defined...due to a temperature variation is well known.Error! Bookmark not defined. The large difference between the spatial variation of Brillouin frequency
Excitons at the center of the Brillouin zone in CuB{sub 2}O{sub 4} magnetoelectric
Energy Technology Data Exchange (ETDEWEB)
Menshenin, V. V., E-mail: menshenin@imp.uran.ru [Russian Academy of Sciences, Mikheev Institute of Metal Physics, Ural Branch (Russian Federation)
2017-02-15
The possibility of exciton excitation in CuB{sub 2}O{sub 4} magnetoelectric at point Γ(0, 0, 0) of the Brillouin zone has been analyzed using group theory. All possible orientations of the electric and magnetic fields that permit the excitation of these excitons have been determined.
Alahbabi, M. N.; Cho, Y. T.; Newson, T. P.
2005-05-01
Brillouin intensity and frequency measurements achieved temperature and strain to be unambiguously resolved with resolutions of 3.5°C and 85 μɛ at 50km. Frequency only measurements, achieved temperature or strain resolution of 1.7°C and 35 μɛ at 100km.
DEFF Research Database (Denmark)
Lorenzen, Michael Rodas; Noordegraaf, Danny; Nielsen, Carsten Vandel
2009-01-01
An increased gain in a fibre-optical parametric amplifier through suppression of stimulated Brillouin scattering is demonstrated by applying a temperature distribution along the fibre for a fixed phase modulation of the pump. The temperature distribution slightly impacts the gain spectrum....
Weber, Isabell; Yun, Seok-Hyun; Scarcelli, Guillano; Franze, Kristian
2017-04-13
Cells in the central nervous system (CNS) respond to the stiffness of their environment. CNS tissue is mechanically highly heterogeneous, thus providing motile cells with region-specific mechanical signals. While CNS mechanics has been measured with a variety of techniques, reported values of tissue stiffness vary greatly, and the morphological structures underlying spatial changes in tissue stiffness remain poorly understood. We here exploited two complementary techniques, contact-based atomic force microscopy and contact-free Brillouin microscopy, to determine the mechanical properties of ruminant retinae, which are built up by different tissue layers. As in all vertebrate retinae, layers of high cell body densities ('nuclear layers') alternate with layers of low cell body densities ('plexiform layers'). Different tissue layers varied significantly in their mechanical properties, with the photoreceptor layer being the stiffest region of the retina, and the inner plexiform layer belonging to the softest regions. As both techniques yielded similar results, our measurements allowed us to calibrate the Brillouin microscopy measurements and convert the Brillouin shift into a quantitative assessment of elastic tissue stiffness with optical resolution. Similar as in the mouse spinal cord and the developing Xenopus brain, we found a strong correlation between nuclear densities and tissue stiffness. Hence, the cellular composition of retinae appears to strongly contribute to local tissue stiffness, and Brillouin microscopy shows a great potential for the application in vivo to measure the mechanical properties of transparent tissues. © 2017 IOP Publishing Ltd.
Hayashi, Neisei; Suzuki, Kohei; Set, Sze Yun; Yamashita, Shinji
2017-09-01
We measured the temperature dependence of the polarized guided acoustic-wave Brillouin scattering (GAWBS) spectrum using a highly nonlinear fiber. The temperature coefficient is 168 kHz/K, which is 1.7 times larger than that of small-core photonic crystal fibers. This result indicates that highly temperature-sensitive GAWBS-based sensing is feasible.
Weber, Isabell P.; Yun, Seok Hyun; Scarcelli, Giuliano; Franze, Kristian
2017-12-01
Cells in the central nervous system (CNS) respond to the stiffness of their environment. CNS tissue is mechanically highly heterogeneous, thus providing motile cells with region-specific mechanical signals. While CNS mechanics has been measured with a variety of techniques, reported values of tissue stiffness vary greatly, and the morphological structures underlying spatial changes in tissue stiffness remain poorly understood. We here exploited two complementary techniques, contact-based atomic force microscopy and contact-free Brillouin microscopy, to determine the mechanical properties of ruminant retinae, which are built up by different tissue layers. As in all vertebrate retinae, layers of high cell body densities (‘nuclear layers’) alternate with layers of low cell body densities (‘plexiform layers’). Different tissue layers varied significantly in their mechanical properties, with the photoreceptor layer being the stiffest region of the retina, and the inner plexiform layer belonging to the softest regions. As both techniques yielded similar results, our measurements allowed us to calibrate the Brillouin microscopy measurements and convert the Brillouin shift into a quantitative assessment of elastic tissue stiffness with optical resolution. Similar as in the mouse spinal cord and the developing Xenopus brain, we found a strong correlation between nuclear densities and tissue stiffness. Hence, the cellular composition of retinae appears to strongly contribute to local tissue stiffness, and Brillouin microscopy shows a great potential for the application in vivo to measure the mechanical properties of transparent tissues.
The design of an electron gun switchable between immersed and Brillouin flow.
Becker, R; Kester, O
2012-02-01
An electron gun, which can be switched from immersed flow to Brillouin flow during operation, may have advantages for charge breeders as well as for electron beam ion sources and traps (EBISTs). For EBISTs this allows to change the current density according to the repetition frequency and charge state, for charge breeders and EBISTs a lower current density in immersed flow provides higher acceptance for injected ions, while the higher current density in Brillouin flow results in shorter breeding times and a lower emittance for the extracted beam. Therefore, we have designed such a gun for an EBIS with 5 T central magnetic field and without the use of iron and moving the gun. The gun was placed in the axial fringing field of the 5 T solenoid in such a position that a gate valve can be placed between the gun and the cryostat to allow for simple maintenance. The field at the cathode surface turned out to be only 0.05 T, which is not enough to focus 50 A∕cm(2) at a few kV. However, if a small normal conducting solenoid is placed over the vacuum tube in position of the gun, a field of 0.1 T may be obtained. With this the use of LaB(6) as cathode material results in a magnetic compression of 44 and therewith in a focused current density in the trap region of more than 2000 A∕cm(2). By reversing the current in the gun solenoid the cathode field can easily compensated to zero. By proper design of the electrodes and the compression region, the gun will be able to deliver a beam in Brillouin flow. While this is interesting by itself--remember the "super-compression" reported on CRYEBIS-I--any magnetic field between zero and the value for immersed flow will result in an electron beam with a wide range of adjustable high current densities. The design tools used have been INTMAG(C) for the calculation of magnetic fields, EGN2(C) for the simulation of the gun and ANALYSE(C) for detailed analysis of the results (for more information see www.egun-igun.com).
A systematic study of Rayleigh-Brillouin scattering in air, N₂, and O₂ gases.
Gu, Ziyu; Ubachs, Wim
2014-09-14
Spontaneous Rayleigh-Brillouin scattering experiments in air, N2, and O2 have been performed for a wide range of temperatures and pressures at a wavelength of 403 nm and at a 90° scattering angle. Measurements of the Rayleigh-Brillouin spectral scattering profile were conducted at high signal-to-noise ratio for all three species, yielding high-quality spectra unambiguously showing the small differences between scattering in air, and its constituents N2 and O2. Comparison of the experimental spectra with calculations using the Tenti S6 model, developed in the 1970s based on linearized kinetic equations for molecular gases, demonstrates that this model is valid to high accuracy for N2 and O2, as well as for air. After previous measurements performed at 366 nm, the Tenti S6 model is here verified for a second wavelength of 403 nm, and for the pressure-temperature parameter space covered in the present study (250-340 K and 0.6-3 bars). In the application of the Tenti S6 model, based on the transport coefficients of the gases, such as thermal conductivity κ, internal specific heat capacity c(int) and shear viscosity η, as well as their temperature dependencies taken as inputs, values for the more elusive bulk viscosity η(b) for the gases are derived by optimizing the model to the measurements. It is verified that the bulk viscosity parameters obtained from previous experiments at 366 nm are valid for wavelengths of 403 nm. Also for air, which is treated as a single-component gas with effective gas transport coefficients, the Tenti S6 treatment is validated for 403 nm as for the previously used wavelength of 366 nm, yielding an accurate model description of the scattering profiles for a range of temperatures and pressures, including those of relevance for atmospheric studies. It is concluded that the Tenti S6 model, further verified in the present study, is applicable to LIDAR applications for exploring the wind velocity and the temperature profile distributions of
On Common Coupled Fixed Point Theorems for Comparable Mappings in Ordered Partially Metric Spaces
Ali Mutlu; Nermin Yolcu; Berrin Mutlu; Necdet Bildik
2013-01-01
Common coupled fixed point theorems are examined in this paper for comparable mappings ensuring nonlinear contraction in ordered partial metric spaces. Given theorems enlarge and universalize some conclusions of Gnana Bhaskar and Lakshmikantham (2006).
On a Fixed Point Theorem for a Cyclical Kannan-type Mapping
Chakraborty, Mitropam; Samanta, S. K.
2013-01-01
This paper deals with an extension of a recent result by the authors generalizing Kannan's fixed point theorem based on a theorem of Vittorino Pata. The generalization takes place via a cyclical condition.
Common fixed point theorems for a weak distance in complete metric spaces
Directory of Open Access Journals (Sweden)
Jeong Sheok Ume
2002-01-01
Full Text Available Using the concept of a w-distance, we obtain common fixed point theorems on complete metric spaces. Our results generalize the corresponding theorems of Jungck, Fisher, Dien, and Liu.
Asymptotic representation theorems for poverty indices | Lo | Afrika ...
African Journals Online (AJOL)
Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty ...
Closed graph and open mapping theorems for normed cones
Indian Academy of Sciences (India)
A quasi-normed cone is a pair (, ) such that is a (not necessarily cancellative) cone and is a quasi-norm on . The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that ...
A sparse flat extension theorem for moment matrices
M. Laurent (Monique); B. Mourrain
2008-01-01
htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free
A generalized flat extension theorem for moment matrices
M. Laurent (Monique); B. Mourrain
2009-01-01
htmlabstractIn this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free
A simple proof of the density Hales-Jewett theorem
Dodos, Pandelis; Kanellopoulos, Vassilis; Tyros, Konstantinos
2012-01-01
We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform measure.
The Unforgettable Experience of a Workshop on Pythagoras Theorem
Arwani, Salima Shahzad
2011-01-01
The author conducted a workshop with colleagues in which awareness of Pythagoras' theorem was raised. This workshop was an unforgettable event in the author's life because it was the first time that she had interacted with teachers from a different school system, and it allowed her to develop presentation skills and confidence in her own…
On Nieuwenhuizen's Treatment of Contextuality in Bell's Theorem
Lambare, Justo Pastor
2017-12-01
A discussion of Nieuwenhuizen's description for the hidden variables of the detectors in the derivation of Bell's theorem is presented. This description prevents Bell's inequalities from being effected. However it will be argued, on mathematical and physical bases, that the flaws attributed by Nieuwenhuizen to Bell's probability distribution function are unjustified.
Critical types of Krasnoselskii fixed point theorems in weak topologies
African Journals Online (AJOL)
In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.
Decomposition Theorems for Various Kinds of Languages Parallel in Nature
DEFF Research Database (Denmark)
Skyum, Sven
1976-01-01
In this paper we give a method for decomposing subclasses of different families of languages, parallel in nature, into other families. These decomposition theorems can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family....
A Fixed Point Theorem for Multifunctions in Partial Metric spaces
Directory of Open Access Journals (Sweden)
Priscilla S. Macansantos
2013-08-01
Full Text Available Fixed Point theorems on partial metric spaces have been the subject of recent work, with the interest generated in partial metric spaces (as a suitable structure for studies in theoretical computer science. Several approaches to fixed point theory for point-valued functions on complete metric spaces have been generalized to partial metric spaces (see, for instance, Alghamdi [1]. On the other hand, it appears that substantial work may still be done to generalize the theory (in the partial metric space context to set-valued functions. Recently, Damjanovic et al [3] looked into pairs of multi-valued and single-valued maps in complete metric spaces, and used coincidence and common fixed points, to establish a theorem on fixed points for pairs of multivalued functions. In this paper we take off from Damjanovic and proceed to establish the same result in the setting of partial metric spaces. As a consequence of our generalization, we are able to include as special cases the theorem of Aydi et al [2] and our [9] generalization of [4]. Further, Reich's result is also generalized to multivalued functions in partial metric spaces. Special cases include the partial metric space version of Kannan's theorem, as well as that due to Hardy and Rogers.
A Neutrosophic Binomial Factorial Theorem with their Refrains
Khalid, Huda; Smarandache, Florentin; Essa, Ahmed
2016-01-01
The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.
Equivalent moduli of continuity, Bloch's theorem for pluriharmonic ...
Indian Academy of Sciences (India)
where C is a positive constant which depends only on f (see [13]). Dyakonov [8] characterized the holomorphic functions in ω in terms of their modulus. Later in Theorems A and B of [22], Pavlovic came up with a relatively simple proof of the results of Dyakonov. Recently, many authors considered this topic and generalized.
A Basic Elementary Extension of the Duchet-Meyniel Theorem
DEFF Research Database (Denmark)
Pedersen, Anders Sune; Toft, Bjarne
2010-01-01
$ by $2\\alpha - 2$ when $\\alpha$ is at least 3. In this paper a basic elementary extension of the Theorem of Duchet and Meyniel is presented. This may be of help to avoid dealing with basic cases when looking for more substantial improvements. The main unsolved problem (due to Seymour) is to improve, even...
Atomic electric dipole moments : The Schiff theorem and its corrections
Liu, C. -P.; Ramsey-Musolf, M. J.; Haxton, W. C.; Timmermans, R. G. E.; Dieperink, A. E. L.
Searches for the permanent electric dipole moments (EDMs) of diamagnetic atoms provide powerful probes of CP-violating hadronic and semileptonic interactions. The theoretical interpretation of such experiments, however, requires careful implementation of a well-known theorem by Schiff that implies a
An analogous of Jouanolou's Theorem in positive characteristic
Vitório Pereira, Jorge
2000-01-01
We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This contrast with Jouanolou's Theorem that shows that in characteristic zero the situation is completely opposite. That is a generic vector field in the complex plane does not admit any invariant algebraic curve.
Bounding the number of remarkable values via Jouanolou's theorem
Chèze, Guillaume
2015-01-01
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.
Bounding the number of remarkable values via Jouanolou's theorem
Chèze, Guillaume
2015-05-01
In this article we bound the number of remarkable values of a polynomial vector field. The proof is short and based on Jouanolou's theorem about rational first integrals of planar polynomial derivations. Our bound is given in term of the size of a Newton polygon associated to the vector field. We prove that this bound is almost reached.
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we ...
Cowling–Price theorem and characterization of heat kernel on ...
Indian Academy of Sciences (India)
We extend the uncertainty principle, the Cowling–Price theorem, on non-compact Riemannian symmetric spaces . We establish a characterization of the heat kernel of the Laplace–Beltrami operator on from integral estimates of the Cowling–Price type.
An Experiment on a Physical Pendulum and Steiner's Theorem
Russeva, G. B.; Tsutsumanova, G. G.; Russev, S. C.
2010-01-01
Introductory physics laboratory curricula usually include experiments on the moment of inertia, the centre of gravity, the harmonic motion of a physical pendulum, and Steiner's theorem. We present a simple experiment using very low cost equipment for investigating these subjects in the general case of an asymmetrical test body. (Contains 3 figures…
A Summability Factor Theorem for Quasi-Power-Increasing Sequences
Directory of Open Access Journals (Sweden)
Savaş E
2010-01-01
Full Text Available We establish a summability factor theorem for summability , where is lower triangular matrix with nonnegative entries satisfying certain conditions. This paper is an extension of the main result of the work by Rhoades and Savaş (2006 by using quasi -increasing sequences.
A Classroom Simulation of the Central Limit Theorem.
McLean, James E.
This simple method for simulating the Central Limit Theorem with students in a beginning nonmajor statistics class requires students to use dice to simulate drawing samples from a discrete uniform distribution. On a chalkboard, the distribution of sample means is superimposed on a graph of the discrete uniform distribution to provide visual…
Understanding the Sampling Distribution and the Central Limit Theorem.
Lewis, Charla P.
The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…
A note on the Fuglede–Putnam theorem
Indian Academy of Sciences (India)
We prove the following generalization of the Fuglede–Puntam theorem. Let N be an unbounded normal operator in the Hilbert space, and let A be an unbounded self-adjoint operator such that D(N) ⊆ D(A). Then, AN ⊆ N∗ A ⇒ AN∗ ⊆ N A. Keywords. Unbounded normal operator; abelian von Neumann algebra; bounding.
Common Fixed Point Theorems in a New Fuzzy Metric Space
Directory of Open Access Journals (Sweden)
Weiquan Zhang
2012-01-01
metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, under ϕ-contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.
An Elementary Proof of a Converse Mean-Value Theorem
Almeida, Ricardo
2008-01-01
We present a new converse mean value theorem, with a rather elementary proof. [The work was supported by Centre for Research on Optimization and Control (CEOC) from the "Fundacaopara a Ciencia e a Tecnologia" FCT, co-financed by the European Community Fund FEDER/POCTI.
Razumikhin Stability Theorem for Fractional Systems with Delay
Directory of Open Access Journals (Sweden)
D. Baleanu
2010-01-01
Full Text Available Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems.
Can we make the second incompleteness theorem coordinate free?
Visser, A.
2008-01-01
Is it possible to give a coordinate free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence, (ii) consistency
Reflections on the PBR Theorem: Reality Criteria & Preparation Independence
Directory of Open Access Journals (Sweden)
Shane Mansfield
2014-12-01
Full Text Available This paper contains initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves dualising a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the Pusey-Barrett-Rudolph theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a new characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to a precise analogy with the kind of locality prohibited by Bell's theorem. Motivated by this, we propose a weakening of the assumption to something analogous to no-signalling. This amounts to allowing global or non-local correlations in the joint ontic state, which nevertheless do not allow for superluminal signalling. This is, at least, consistent with the Bell and Kochen-Specker theorems. We find a counter-example to the PBR argument, which violates preparation independence, but does satisfy this physically motivated assumption. The question of whether the PBR result can be strengthened to hold under the relaxed assumption is therefore posed.
A Six-Point Ceva-Menelaus Theorem
McConnell, B. D. S. "Blue"
2014-01-01
We provide a companion to the recent Benyi-Curgus generalization of the well-known theorems of Ceva and Menelaus, so as to characterize both the collinearity of points and the concurrence of lines determined by six points on the edges of a triangle. A companion for the generalized area formula of Routh appears, as well.
FUNCTIONS TO THE EDREI-FUCHS ELLIPSE THEOREM
African Journals Online (AJOL)
ABSTRACT: In this paper we study the asymptotic behaviour of functions extremal for the well known inequality introduced by Edrei-Fuchs (called the Ellipse Theorem) by considering a normal family of 6-subharmonic functions. This approach allows us to describe precisely the prototype of all functions extremal for the ...
Nagaoka's Theorem in the Holstein-Hubbard Model
Miyao, Tadahiro
2017-09-01
Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.
Common fixed point theorems of contractive-type mappings
Directory of Open Access Journals (Sweden)
Hee Soo Park
2004-01-01
Full Text Available Using the concept of D-metric we prove some common fixed point theorems for generalized contractive mappings on a complete D-metric space. Our results extend, improve, and unify results of Fisher and Ćirić.
Sturm-Picone type theorems for nonlinear differential systems
Directory of Open Access Journals (Sweden)
Aydin Tiryaki
2015-06-01
Full Text Available In this article, we establish a Picone-type inequality for a pair of first-order nonlinear differential systems. By using this inequality, we give Sturm-Picone type comparison theorems for these systems and a special class of second-order half-linear equations with damping term.
Poincaré-Birkhoff theorem in quantum mechanics.
Wisniacki, D A; Saraceno, M; Arranz, F J; Benito, R M; Borondo, F
2011-08-01
Quantum manifestations of the dynamics around resonant tori in perturbed hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.
A Converse to the Cayley-Hamilton Theorem
Indian Academy of Sciences (India)
Hamilton theorem. GENERAL I ARTICLE. Recall that .,\\ E K is called an eigenvalue of A E Mn (K), if A v =.,\\ v for some 0 f v E Kn. Note that any ..... [6] L H Rowen, Ring theory II, Academic Press, 1988. [7] E Formanek, Polynomial identities and ...
Beurling algebra analogues of the classical theorems of Wiener and ...
Indian Academy of Sciences (India)
absolutely convergent for some weight on the set of integers Z . If is nowhere vanishing on , then there exists a weight on Z such that 1/ had -absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary ...
Limit Theorems For the Grover Walk Without Memory
Ampadu, Clement
2011-01-01
We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak limit theorem
Babylonian Pythagoras' Theorem, the Early History of Zero and a ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 1. Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science. Rahul Roy. General Article Volume 8 Issue 1 January 2003 pp 30-40 ...
Transient state work fluctuation theorem for a classical harmonic ...
Indian Academy of Sciences (India)
theorem for a classical harmonic oscillator coupled linearly to a harmonic bath. Because of the coupling to the bath, the system becomes dissipative. We start from a Hamiltonian description for the system plus the harmonic heat bath and then the system is driven by an external agent for a time period of τ for a series. 666.
Lyapunov convexity type theorems for non-atomic vector measures ...
African Journals Online (AJOL)
atomic, and σ-additive X-valued measure has a convex closure. We give a survey of Lyapunov convexity type theorems pertaining to this problem. We also give a necessary and sufficient condition that will insure the convexity of the closure of the ...
Sobolev Embedding Theorems for a Class of Anisotropic Irregular Domains
Trushin, B. V.
Sufficient conditions for the embedding of a Sobolev space in Lebesgue spaces on a domain depend on the integrability and smoothness parameters of the spaces and on the geometric features of the domain. In the present paper, Sobolev embedding theorems are obtained for a class of domains with
A Gauss-Kusmin theorem for optimal continued fractions
Dajani, K.; Kraaikamp, C.
1996-01-01
One of the first and still one of the most important results in the metrical theory of continued fractions is the so-called Gauss-Kusmin theorem. Let and let be the regular continued fraction (RCF) expansion of then it was observed by Gauss in 1800 that -
Gauss-Bonnet's Theorem and Closed Frenet Frames
DEFF Research Database (Denmark)
Røgen, Peter
1997-01-01
curves are found using Gauss-Bonnet's Theorem after cutting the curve into simple closed sub-curves. At this point an error in the litterature is corrected. If the spherecal curve is the tangent indicatrix of a space-curve we obtain a new short proof of a formula for integrated torsion presented...
Stochastic functionals and fluctuation theorem for multikangaroo processes.
Van den Broeck, C; Toral, R
2014-06-01
We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.
Fluctuation theorems and orbital magnetism in nonequilibrium state
Indian Academy of Sciences (India)
We study Langevin dynamics of a driven charged particle in the presence as well as in the absence of magnetic field. We discuss the validity of various work fluctuation theorems using different model potentials and external drives. We also show that one can generate an orbital magnetic moment in a nonequilibrium state ...
Instability of Nagaoka's Theorem within The Hubbard Model ...
African Journals Online (AJOL)
Hence the t – J model is a better model for studying magnetism than the t – U model. Investigation also revealed that the inclusion of the on-site Coulomb interaction term U, in the t – J model enhances ferromagnetic tendencies in the systems studied. In this work, Nagaoka's theorem on ferromagnetism has been extended ...
A vizing-type theorem for matching forests
Keijsper, J.C.M.
2000-01-01
A well known Theorem of Vizing states that one can colour the edges of a graph by $\\Delta +\\alpha$ colours, such that edges of the same colour form a matching. Here, $\\Delta$ denotes the maximum degree of a vertex, and $\\alpha$ the maximum multiplicity of an edge in the graph. An analogue of this
Negating Four Color Theorem with Neutrosophy and Quadstage Method
Directory of Open Access Journals (Sweden)
Fu Yuhua
2015-03-01
Full Text Available With the help of Neutrosophy and Quad-stage Method, the proof for negation of “the four color theorem” is given. In which the key issue is to consider the color of the boundary, thus “the two color theorem” and “the five color theorem” are derived to replace "the four color theorem".
The Nielsen-Ninomiya theorem, \\renewcommand{\\P}{{{ P}}} \
Chernodub, M. N.
2017-09-01
The Nielsen-Ninomiya theorem implies that any local, Hermitian and translationally invariant lattice action in even-dimensional spacetime possesses an equal number of left- and right-handed chiral fermions. We argue that if one sacrifices the property of Hermiticity while keeping the locality and translation invariance, and imposing invariance of the action under the space-time ( \\renewcommand{\\P}{{{ P}}} \
Nagaoka's theorem in the Holstein-Hubbard model
Miyao, Tadahiro
2016-01-01
Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.
Confinement, average forces, and the Ehrenfest theorem for a one ...
Indian Academy of Sciences (India)
The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: A free particle moving on the entire real line, which is then permanently confined to a line segment or `a box' (this situation is achieved by taking the limit V 0 → ∞ in ...
Fermat's last theorem and Catalan's conjecture in weak exponential arithmetics
Czech Academy of Sciences Publication Activity Database
Glivický, Petr; Kala, V.
2017-01-01
Roč. 63, 3-4 (2017), s. 162-174 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : Fermat's last theorem * Catalan's conjecture Subject RIV: BA - General Mathematics Impact factor: 0.250, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/malq.201500069/full
A stochastic Ergodic Theorem in Von-Neumann algebras | Tijani ...
African Journals Online (AJOL)
In this paper we introduce the notion of stochastic convergence of τ- measurable operators and prove a noncommutative extension of pointwise ergodic theorem of G. D. Birkhoff by means of it by using the techniques developed by Petz in [12] Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp.
Ehrenfest theorem, Galilean invariance and nonlinear Schroedinger equations
Energy Technology Data Exchange (ETDEWEB)
Kaelbermann, G [Soil and Water Department, Faculty of Agriculture, Rehovot 76100 (Israel)
2004-02-25
We prove that Galilean invariant Schroedinger equations derived from Lagrangian densities necessarily obey the Ehrenfest theorem for velocity-independent potentials. The conclusion holds as well for Lagrangians describing nonlinear self-interactions. An example of Doebner and Goldin motivates the result.
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Soft Cone Metric Spaces and Some Fixed Point Theorems
Altıntaş, İsmet; Taşköprü, Kemal
2016-01-01
This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric spaces.
The Archimedes Principle and Gauss's Divergence Theorem -18 ...
Indian Academy of Sciences (India)
of Mathematical Sciences,. Chennai. His research interests centre around complex analytic geometry and its intimate relation with mathematical physics via 'string theory'. Subhashis Nag. This article explores the connection between the Ar- chimedes principle in physics and Gauss's divergence theorem in mathematics.
Testing the No-Hair Theorem with Sgr A*
Directory of Open Access Journals (Sweden)
Tim Johannsen
2012-01-01
Full Text Available The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI. The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
Euler characteristics, Fubini's theorem, and the Riemann-Hurwitz formula
Morrow, Matthew
2009-01-01
We relate Fubini's theorem for Euler characteristics to Riemann-Hurwtiz formulae, and reprove a classical result of Iversen. The techniques used include algebraic geometry, complex geometry, and model theory. Possible applications to the study of wild ramification in finite characteristic are discussed.
The generation-recombination theorem and noise in photoconductors
Cook, J.G.; Blok, J.; Kampen, N.G. van
1967-01-01
The validity of the well-known generation-recombination (g-ν) theorem is examined for the case of noise in photoconductors. A master equation for the conditional probability of the level occupancies is set up in which the generation and recombination rates are functions of the incident light
Teng, Lei; Dong, Yongkang; Zhou, Dengwang; Bao, Xiaoyi; Chen, Liang
2017-04-01
A distributed hydrostatic pressure sensor based on Brillouin dynamic gratings (BDGs) was proposed and demonstrated for the first time to the best of our knowledge. Through measuring the pressure-induced birefringence changes through exciting and probing the BDGs, the hydrostatic pressure sensing is realized. The thin-diameter PM-PCF is used as the fiber under test. The temperature can be compensated by measuring the temperature-induced Brillouin frequency shift (BFS) through differential pulse-width pair Brillouin optical time-domain analysis (DPP-BOTDA). A distributed measurement is reported with a 20-cm spatial resolution and measurement accuracy as high as 0.025 MPa.
Tchahame, J.C.; Beugnot, J-C; Brilland, L; Méchin, D; Troles, J; Maillotte, H; Sylvestre, T
2014-01-01
International audience; Dans ce document, nous présentons les résultats de caractérisation de la rétrodiffusion Brillouin dans une fibre optique microstructurée (FOM) en verre de chalcogénure As 42 S 58 . Les résultats obtenus montrent que cette fibre optique serait appropriée pour des applications en optique non-linéaire basées sur l'effet Brillouin. MOTS-CLEFS : Effet Brillouin ; verres chalcogénures ; fibres optiques microstructurées.
Brillouin spectroscopy of fluid inclusions proposed as a paleothermometer for subsurface rocks.
El Mekki-Azouzi, Mouna; Tripathi, Chandra Shekhar Pati; Pallares, Gaël; Gardien, Véronique; Caupin, Frédéric
2015-08-28
As widespread, continuous instrumental Earth surface air temperature records are available only for the last hundred fifty years, indirect reconstructions of past temperatures are obtained by analyzing "proxies". Fluid inclusions (FIs) present in virtually all rock minerals including exogenous rocks are routinely used to constrain formation temperature of crystals. The method relies on the presence of a vapour bubble in the FI. However, measurements are sometimes biased by surface tension effects. They are even impossible when the bubble is absent (monophasic FI) for kinetic or thermodynamic reasons. These limitations are common for surface or subsurface rocks. Here we use FIs in hydrothermal or geodic quartz crystals to demonstrate the potential of Brillouin spectroscopy in determining the formation temperature of monophasic FIs without the need for a bubble. Hence, this novel method offers a promising way to overcome the above limitations.
Impact Wave Monitoring in Soil Using a Dynamic Fiber Sensor Based on Stimulated Brillouin Scattering
Directory of Open Access Journals (Sweden)
Qingsong Cui
2015-04-01
Full Text Available The impact wave response of soil due to a ball drop is monitored on a 30.5 cm by 30.5 cm square soil box using a fiber sensor with dynamic strain sensing capability. The experiments are conducted in real time using a simple one-laser one-modulator configuration with stimulated Brillouin scattering. The embedded BOTDA sensor grid successfully monitored the distribution and evolution of the inner strains of a sand bed during a mass impact on its surface. The measurement of the distributed dynamic strains was possible in several milliseconds and with 1 cm actual location resolution. This paper presents a time-domain signal analysis utilized for determining the dynamic strains in embedded fiber sensor. The results demonstrate the method to be a promising one for detection of subsurface vibration and movement in geotechnical Structure Health Monitoring (SHM.
Light scattering by a nematic liquid crystal droplet: Wentzel–Kramers–Brillouin approximation
Energy Technology Data Exchange (ETDEWEB)
Loiko, V. A., E-mail: loiko@dragon.bas-net.by; Konkolovich, A. V.; Miskevich, A. A. [National Academy of Science of Belarus, Stepanov Institute of Physics (Belarus)
2016-01-15
Light scattering by an optically anisotropic liquid crystal (LC) droplet of a nematic in an isotropic polymer matrix is considered in the Wentzel–Kramers–Brillouin (WKB) approximation. General relations are obtained for elements of the amplitude matrix of light scattering by a droplet of arbitrary shape and for the structure of the director field. Analytic expressions for the amplitude matrices are derived for spherical LC droplets with a uniformly oriented structure of local optical axes for strictly forward and strictly backward scattering. The efficiency factors of extinction and backward scattering for a spherical nonabsorbing LC droplet depending on the LC optical anisotropy, refractive index of the polymer, illumination conditions, and orientation of the optical axis of the droplet are analyzed. Verification of the obtained solutions has been performed.