Stability theory of differential equations
Bellman, Richard Ernest
1953-01-01
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from
Introduction to complex theory of differential equations
Savin, Anton
2017-01-01
This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each...
Theory of electrophoresis: fate of one equation.
Gas, Bohuslav
2009-06-01
Electrophoresis utilizes a difference in movement of charged species in a separation channel or space for their spatial separation. A basic partial differential equation that results from the balance laws of continuous processes in separation sciences is the nonlinear conservation law or the continuity equation. Attempts at its analytical solution in electrophoresis go back to Kohlrausch's days. The present paper (i) reviews derivation of conservation functions from the conservation law as appeared chronologically, (ii) deals with theory of moving boundary equations and, mainly, (iii) presents the linear theory of eigenmobilities. It shows that a basic solution of the linearized continuity equations is a set of traveling waves. In particular cases the continuity equation can have a resonance solution that leads in practice to schizophrenic dispersion of peaks or a chaotic solution, which causes oscillation of electrolyte solutions.
Handbook of functional equations stability theory
2014-01-01
This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with...
Translation of State Machines from Equational Theories into Rewrite Theories with Tool Support
National Research Council Canada - National Science Library
ZHANG, Min; OGATA, Kazuhiro; NAKAMURA, Masaki
2011-01-01
This paper presents a strategy together with tool support for the translation of state machines from equational theories into rewrite theories, aiming at automatically generating rewrite theory specifications...
Thermodynamic restrictions on the constitutive equations of electromagnetic theory
Coleman, B. D.; Dill, E. H.
1971-01-01
Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences
An introduction to the theory of the Boltzmann equation
Harris, Stewart
2011-01-01
Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes
Theory and applications of fractional differential equations
Kilbas, Anatoly A; Trujillo, Juan J; Van Mill, Jan
2006-01-01
This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of prese
Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras
Put, Marius van der
1999-01-01
The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.
Kurzweil, J
1986-01-01
The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Car
Lectures on the theory of group properties of differential equations
Ovsyannikov, LV
2013-01-01
These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models. Readers
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Theory of a ring laser. [electromagnetic field and wave equations
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.
Master equations and the theory of stochastic path integrals
Weber, Markus F
2016-01-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on methods that are applicable even when stochastic fluctuations are strong. The reviewed methods include the generating function technique and the Poisson representation, as well as novel ways of mapping the forward and backward master equations onto linear partial differential equations (PDEs). Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE obeyed by the generating function. After outlining these methods, we solve the derived PDEs in terms of two path integrals. The path integrals provide distinct exact representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Furthermore, we review a method for the approxima...
Vispoel, Walter P; Morris, Carrie A; Kilinc, Murat
2017-01-23
Although widely recognized as a comprehensive framework for representing score reliability, generalizability theory (G-theory), despite its potential benefits, has been used sparingly in reporting of results for measures of individual differences. In this article, we highlight many valuable ways that G-theory can be used to quantify, evaluate, and improve psychometric properties of scores. Our illustrations encompass assessment of overall reliability, percentages of score variation accounted for by individual sources of measurement error, dependability of cut-scores for decision making, estimation of reliability and dependability for changes made to measurement procedures, disattenuation of validity coefficients for measurement error, and linkages of G-theory with classical test theory and structural equation modeling. We also identify computer packages for performing G-theory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Some functional equations originating from number theory
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations. Keywords. Functional equation; stability; multiplicative function. 1.
Stochastic regulator theory for a class of abstract wave equations
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
DEFF Research Database (Denmark)
Marcussen, Lis; Aasberg-Petersen, K.; Krøll, Annette Elisabeth
2000-01-01
An adsorption isotherm equation for nonideal pure component adsorption based on vacancy solution theory and the Non-Random-Two-Liquid (NRTL) equation is found to be useful for predicting pure component adsorption equilibria at a variety of conditions. The isotherm equation is evaluated successfully...
Methods of qualitative theory of differential equations and related topics
Lerman, L; Shilnikov, L
2000-01-01
Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, b
Galois Theory and Solvable Equations of Prime Degree
Ghatak, Anirban; Tandon, Anshoo
2011-01-01
In this article we review classical and modern Galois theory with historical evolution and prove a criterion of Galois for solvability of an irreducible separable polynomial of prime degree over an arbitrary field k and give many illustrative examples.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples...
Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation
Directory of Open Access Journals (Sweden)
V. O. Vakhnenko
2016-01-01
Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.
Schaum's outline of theory and problems of differential equations
Bronson, Richard
1994-01-01
If you want top grades and thorough understanding of differential equations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 563 accompanying problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, Schaum’s Outlines have sold more than 30 million copies worldwide—and this guide will show you why!
Study of a Model Equation in Detonation Theory
Faria, Luiz
2014-04-24
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation is ut+ 1/2 (u2-uu (0-, t))x=f (x, u (0-, t)), x > 0, t < 0. It describes a detonation shock at x = 0 with the reaction zone in x > 0. We investigate the nature of the steady-state solutions of this nonlocal hyperbolic balance law, the linear stability of these solutions, and the nonlinear dynamics. We establish the existence of instability followed by a cascade of period-doubling bifurcations leading to chaos. © 2014 Society for Industrial and Applied Mathematics.
Equation-of-motion coupled cluster perturbation theory revisited.
Eriksen, Janus J; Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
Some functional equations originating from number theory
Indian Academy of Sciences (India)
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
The frequency-temperature analysis equations of piezoelectric plates with Lee plate theory.
Wang, J
1999-01-01
Frequency-temperature analysis theory of crystal plates based on the incremental field theory (IFT) and the Mindlin plate theory have been widely used in the vibration analysis of crystal resonators subject to temperature change. As one of the two major plate theories for the resonator analysis, the Lee plate theory based on the trigonometric series expansion of displacements has been extensively used for both analytical and numerical analyses of quartz resonators, and efforts have also been made in correcting and perfecting the theory for much broader applications. In this paper, the earlier frequency-temperature analysis equations based on the IFT is further extended to the trigonometric series expansion in a systematic manner. By incorporating the frequency-temperature analysis into the Lee plate theory, the complete analysis of crystal resonators can be made in a consistent way. The thickness-shear and flexural vibration equations have been compared with the Mindlin plate theory to demonstrate the similarity and consistency.
Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama
2017-10-01
Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.
A description of phase equilibria in nonideal systems with the use of integral equation theory
D'Yakonov, S. G.; Klinov, A. V.; D'Yakonov, G. S.
2009-06-01
Integral equation theory for partial distribution functions was used to consider a method for calculations of vapor-liquid phase equilibrium conditions in binary Lennard-Jones systems with substantial deviations from the Berthelot-Lorentz mixing rules. Possible sources of errors in pressure and chemical potential values and methods for refining the results were analyzed. The required accuracy of calculations can be reached using two parameters only, one in the closure to the Ornstein-Zernike equation and the other in the equation for the chemical potential. These parameters are determined independently from two thermodynamic equations.
Oscillation theory for second order dynamic equations
Agarwal, Ravi P; O''Regan, Donal
2003-01-01
The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal. Many books deal exclusively with the oscillation of solutions of differential equations, but most of these books appeal only to researchers who already know the subject. In an effort to bring Oscillation Theory to a new and broader audience, the authors present a compact, but thorough, understanding of Oscillation Theory for second order differential equations. They include several examples throughout the text not only to illustrate the theory, but also to provide new direction.
Perturbation theory and renormalisation group equations
Litim, Daniel F; Litim, Daniel F.; Pawlowski, Jan M.
2002-01-01
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
Thermal Renormalization Group-Equations and the Phase-Transition of Scalar O(N)-Theories
Bergerhoff, Bastian; Reingruber, Juergen
1998-01-01
We discuss the formulation of "thermal renormalization group-equations" and their application to the finite temperature phase-transition of scalar O(N)-theories. Thermal renormalization group-equations allow for a computation of both the universal and the non-universal aspects of the critical behavior directly in terms of the zero-temperature physical couplings. They provide a nonperturbative method for a computation of quantities like real-time correlation functions in a thermal environment,...
Mobile point sensors and actuators in the controllability theory of partial differential equations
Khapalov, Alexander Y
2017-01-01
This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.
On the theory of weak turbulence for the nonlinear Schrödinger equation
Escobedo, M
2015-01-01
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
A Theory of Solvability for Lossless Power Flow Equations -- Part I: Fixed-Point Power Flow
Simpson-Porco, John W.
2017-01-01
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is stated for both meshed and radial networks, and is parameterized by several graph-theoretic matrices -- the power network stiffness matrices -- which quantify the internal coupling strength of the network. The model leads immediately to an explicit approxi...
The Boltzmann equation from quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Drewes, Marco, E-mail: marco.drewes@tum.de [Institut fuer Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, 52056 Aachen (Germany); Physik Department T70, Technische Universitaet Muenchen, James Franck Strasse 1, D-85748 Garching (Germany); Mendizabal, Sebastian [Institut fuer Theoretische Physik, Goethe-Universitaet, 60438 Frankfurt am Main (Germany); Weniger, Christoph [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2013-01-08
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
Hoenders, B.J.
1996-01-01
The geometrical optical concept of rays is generalized for fields generated by any system of coupled non-linear partial differential equations of arbitrary order like the vector wave equations for (non)linear media, the Maxwell equations, the equations of magneto-hydrodynamics, the system of
Directory of Open Access Journals (Sweden)
Zulfiqar Ali
2013-01-01
Full Text Available We find exact solutions of the Generalized Modified Boussinesq (GMB equation, the Kuromoto-Sivashinsky (KS equation the and, Camassa-Holm (CH equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.
The general class of the vacuum spherically symmetric equations of the general relativity theory
Energy Technology Data Exchange (ETDEWEB)
Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N., E-mail: Markov_Victor@mail.ru; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R. [Murmansk State Pedagogical University (Russian Federation)
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
On the Foundational Equations of the Classical Theory of ...
Indian Academy of Sciences (India)
IAS Admin
the type of material media, if any, that might reside at various locations. ... because distant stars and galaxies are not stationary. The ...... r × S(r,t)/c2. The expression of. EM angular momentum density pertains to both spin and orbital angular momenta, as well as to any combination of these two types of angular momentum.
Foundations of the classical theory of partial differential equations
Egorov, Yu V
1998-01-01
From the reviews of the first printing, published as volume 30 of the Encyclopaedia of Mathematical Sciences: "... I think the volume is a great success and an excellent preparation for future volumes in the series. ... the introductory style of Egorov and Shubin is .. attractive. ... a welcome addition to the literature and I am looking forward to the appearance of more volumes of the Encyclopedia in the near future. ..." The Mathematical Intelligencer, 1993 "... According to the authors ... the work was written for nonspecialists and physicists but in my opinion almost every specialist will find something new ... in the text. The style is clear, the notations are chosen luckily. The most characteristic feature of the work is the accurate emphasis on the fundamental notions ..." Acta Scientiarum Mathematicarum, 1993 "... On the whole, a thorough overview on the classical aspects of the topic may be gained from that volume." Monatshefte für Mathematik, 1993 "... It is comparable in scope with the great Coura...
Topological Galois theory solvability and unsolvability of equations in finite terms
Khovanskii, Askold
2014-01-01
This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.
Universal aspects in the equation of state for Yang-Mills theories
Nada, Alessandro
2015-01-01
We present high-precision lattice calculations of the thermodynamics of Yang-Mills theories with different gauge groups. In the confining phase, we show that the equation of state is described remarkably well by a gas of massive, non-interacting glueballs, provided that an effective bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy states. In particular, this model describes very accurately the results for the SU(3) theory reported by Bors\\'anyi et al. in JHEP 07 (2012) 056, as well as a novel set of lattice data for the SU(2) theory. In addition, we also also show that the equation of state in the deconfined phase exhibits a near perfect proportionality to the number of gluon degrees of freedom, including for the Yang-Mills theory based on the exceptional, center-less gauge group $G_2$.
Equilibrium dynamics of the Dean-Kawasaki equation: Mode-coupling theory and its extension
Kim, Bongsoo; Kawasaki, Kyozi; Jacquin, Hugo; van Wijland, Frédéric
2014-01-01
We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004, 10.1088/1742-5468/2008/02/P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-coupling approach.
Stochastic Theories and Deterministic Differential Equations
Directory of Open Access Journals (Sweden)
John F. Moxnes
2010-01-01
Full Text Available We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared.
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)
2005-01-28
Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample
Skorokhod, A. V.
1982-12-01
CONTENTSIntroduction § 1. The finite-dimensional case § 2. Stochastic semigroups in the L2-strong theory § 3. Homogeneous strongly continuous semigroups with the group of the first moments § 4. Stochastic equations of diffusion type with constant coefficients § 5. Continuous homogeneous stochastic semigroups in the presence of two moments References
Standard Error of an Equating by Item Response Theory
1981-11-01
This proceduire adds to the sampling variance of the transformed item parametels and greatly complicates any determination of the sampling variance of...r) a-t a 3 P 03 "_ (r) Ft 2 Pg2 (8 1) .•’. • trg2 2 where P(r) denotes the derivative of P with respect to tgp gp rgp -mom --6-- Similarly, 2 -fl...34 instead of rgp rgP rgpshq a) 2 TI trgpa tshq Y) n+rEz (t - p g r rgp rgp ) rgp r +• E. E z E E (trg - trgp)tsh t )n"i + .. .(9) p q g hr rgp rgp shq shq
Partial Differential Equations and Solitary Waves Theory
Wazwaz, Abdul-Majid
2009-01-01
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...
Energy Technology Data Exchange (ETDEWEB)
Baker, M.
1979-01-01
It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.
Asymptotic Analysis of a System of Algebraic Equations Arising in Dislocation Theory
Hall, Cameron L.
2010-01-01
The system of algebraic equations given by σn j=0, j≠=i sgn(xi-xj )|xi-xj|a = 1, i = 1, 2, ⋯ , n, x0 = 0, appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n→∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment, but, up to corrections of logarithmic order, it also leads to a differential equation. The continuum approximation is valid only for i neither too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem. © 2010 Society for Industrial and Applied Mathematics.
Hagedorn spectrum and equation of state of Yang-Mills theories
Caselle, Michele; Panero, Marco
2015-01-01
We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Difference and differential equations with applications in queueing theory
Haghighi, Aliakbar Montazer
2013-01-01
A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of
Limit cycles of the generalized Li'enard differential equation via averaging theory
Directory of Open Access Journals (Sweden)
Sabrina Badi
2012-05-01
Full Text Available We apply the averaging theory of first and second order to a generalized Lienard differential equation. Our main result shows that for any $n,m geq 1$ there are differential equations $ddot{x}+f(x,dot{x}dot{x}+ g(x=0$, with f and g polynomials of degree n and m respectively, having at most $[n/2]$ and $max{[(n-1/2]+[m/2], [n+(-1^{n+1}/2]}$ limit cycles, where $[cdot]$ denotes the integer part function.
Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory
CERN. Geneva
2015-01-01
The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.
Derivation of Hunt equation for suspension distribution using Shannon entropy theory
Kundu, Snehasis
2017-12-01
In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.
Unified Theory of Wave-Particle Duality and the Schr\\"odinger Equations
Gilson, Greyson
2011-01-01
Individual quantum objects display coexisting wave properties and particle properties. A wave is ordinarily associated with spatial extension while a particle is ordinarily associated with a point-like locality. Coexistence of spatial extension and a point-like locality as properties of a single entity seems paradoxical. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Using this theory, a straightforward derivation of the Schr\\"odinger equations (time-independent and time-dependent) is presented where previously no such derivation was considered to be possible.
Priors on the effective dark energy equation of state in scalar-tensor theories
Raveri, Marco; Bull, Philip; Silvestri, Alessandra; Pogosian, Levon
2017-10-01
Constraining the dark energy (DE) equation of state, wDE, is one of the primary science goals of ongoing and future cosmological surveys. In practice, with imperfect data and incomplete redshift coverage, this requires making assumptions about the evolution of wDE with redshift z . These assumptions can be manifested in a choice of a specific parametric form, which can potentially bias the outcome, or else one can reconstruct wDE(z ) nonparametrically, by specifying a prior covariance matrix that correlates values of wDE at different redshifts. In this work, we derive the theoretical prior covariance for the effective DE equation of state predicted by general scalar-tensor theories with second order equations of motion (Horndeski theories). This is achieved by generating a large ensemble of possible scalar-tensor theories using a Monte Carlo methodology, including the application of physical viability conditions. We also separately consider the special subcase of the minimally coupled scalar field, or quintessence. The prior shows a preference for tracking behaviors in the most general case. Given the covariance matrix, theoretical priors on parameters of any specific parametrization of wDE(z ) can also be readily derived by projection.
Exceptional thermodynamics. The equation of state of G{sub 2} gauge theory
Energy Technology Data Exchange (ETDEWEB)
Bruno, Mattia [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Caselle, Michele [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy); Panero, Marco [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica; Consejo Superior de Investigaciones Cientificas, Madrid (Spain); Pellegrini, Roberto [Swansea Univ. (United Kingdom). Dept. of Physics
2014-10-15
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G{sub 2} gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
Elliptic differential equations theory and numerical treatment
Hackbusch, Wolfgang
2017-01-01
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Relationship of a chaos equation to Piaget's developmental theory and selective attention deficits
Directory of Open Access Journals (Sweden)
Yanagisawa, H.
2016-06-01
Full Text Available Piaget's theory provides a typical example of a relationship between human development and chaos theory. Here, Piaget's developmental theory and selective attention deficits are compared with a chaos equation. Continuous covariation is a necessary condition to equilibrium and the chaos phenomenon, and equilibrium is the converged solution in a chaos equation. Each convergence and non-convergence is a fixed and a chaotic state. In many chaos equations, there are two kinds of variables that change or do not change each site beyond the Feigenbaum point. Two types of developmental disorders are assumed. One is low speed in judging convergence or nonconvergence. The other is low-speed change after a person's own judgment. In the former, a person cannot sense a difference between a converging point and his present state. Because he/she cannot understand others' emotions, he/she will continue with his/her experience with no convergence . Therefore, he/she cannot request help, and it might be thought that he/she can wait. This type is equivalent to Asperger's syndrome. In the latter, a person senses a difference. Because the person strictly feels the difference between a fixed point and his/her present state, he/she cannot wait for convergence. Therefore, he can request help. His present ate might be anger, and this type is equivalent to ADHD. In the former, a wide chaotic state narrows with experience. Piaget's developmental theory might be that humans have the ability to change each state. Chaos theory shows "Selective attention deficits with autism" as two different patterns in non-convergence or convergence.
Assessing the accuracy of integral equation theories for nano-sized hydrophobic solutes in water
Fujita, Takatoshi; Yamamoto, Takeshi
2017-07-01
Integral equation theories provide an efficient route for computing the solvation free energy (SFE) of molecular systems in water. The accuracy of those theories is usually tested against small molecules via comparison of SFE with reference data. However, tests against larger molecules in the nanometer regime are scarce in literature despite recent applications to such systems. Here, we thus study the accuracy and validity of a commonly used integral equation theory, namely, a three-dimensional reference interaction site model (3D-RISM), by considering the following problems: (1) solvation of a small to large Lennard-Jones particle, (2) binding of planar hydrophobic systems with varying size and hydrophobicity, and (3) self-assembly of amphiphilic molecules into a nanocapsule. The energy representation method is also utilized for comparison. The results show that the 3D-RISM method works successfully for small molecules, while the accuracy degrades systematically with system size and hydrophobicity. The size-dependent error in SFE does not cancel adequately between two solute configurations, resulting in a substantial error in the free energy difference. It is also shown that the free energy profiles for hydrophobic association exhibit a fictitious high-energy barrier, suggesting that care must be taken for studying such systems. The numerical difficulties observed above are discussed based on the relation between hypernetted-chain approximation, classical density functional theory with quadratic expansion, and the size-dependent error arising from the cavity region of the system.
Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron
Fujita, Shigeji
2007-01-01
Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron targets scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and material sciences. It is important that the reader have an understanding of dynamics, quantum mechanics, thermodynamics, statistical mechanics, electromagnetism and solid-state physics. Many worked-out problems are included in the book to aid the reader's comprehension of the subject. The Bloch electron (wave packet) moves by following the Newtonian equation of motion. Under an applied magnetic field B the electron circulates around the field B counterclockwise or clockwise depending on the curvature of the Fermi surface. The signs of the Hall coefficient and the Seebeck coefficient are known to give the sign of the major carrier charge. For alkali metals, both are negative, indicating that the carriers are "electrons." These features arise from the Fermi surface difference...
State Selective Equation of Motion Coupled Cluster Theory: Some Preliminary Results
Directory of Open Access Journals (Sweden)
Marcel Nooijen
2002-06-01
Full Text Available Abstract: A multireference variant of coupled cluster theory is described that applies to systems that can qualitatively be described by deleting two electrons from a closed shell determinant, for example biradicals, single bond breaking processes, or valence excited states. The theory can be generalized to arbitrary open-shell systems and takes a form that is akin to equation-of-motion coupled cluster theory, but where all wave function parameters are explicitly optimized for the state of interest. The implementation of the present methods was accomplished in an automated fashion using the recently developed Automatic Program Generator (APG. We present benchmark results for the O2 and F2 molecules and investigate the behaviour of a number of closely related variants within the same general framework.
Three new branched chain equations of state based on Wertheim's perturbation theory
Marshall, Bennett D.; Chapman, Walter G.
2013-05-01
In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.
Difference equations theory, applications and advanced topics
Mickens, Ronald E
2015-01-01
THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...
Lezina, Natalya; Agoshkov, Valery
2017-04-01
Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).
Dynamical systems theory for the Gardner equation
Saha, Aparna; Talukdar, B.; Chatterjee, Supriya
2014-02-01
The Gardner equation ut+auux+bu2ux+μuxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=φ(ξ), ξ =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].
From the GKLS Equation to the Theory of Solar and Fuel Cells
Alicki, R.
The mathematically sound theory of quantum open systems, formulated in the ’70s and highlighted by the discovery of Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation, found a wide range of applications in various branches of physics and chemistry, notably in the field of quantum information and quantum thermodynamics. However, it took 40 years before this formalism has been applied to explain correctly the operation principles of long existing energy transducers like photovoltaic, thermoelectric and fuel cells. This long path is briefly reviewed from the author’s perspective. Finally, the new, fully quantum model of chemical engine based on GKLS equation and applicable to fuel cells or replicators is outlined. The model illustrates the difficulty with an entirely quantum operational definition of work, comparable to the problem of quantum measurement.
Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
Figalli, Alessio
2016-06-23
Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.
Kenji, HAYASHI; Takeshi, SHIRAFUJI; Institute of Physics, University of Tokyo; Physics Department, Saitama University
1980-01-01
We study the equations of motion for test bodies and various limits in Poincare gauge theory with linear and quadratic Lagrangians. The classical equations of motion are derived both for spin-1/2 particles and for macroscopic test bodies. It is also shown that various limits can be taken, including General Relativity and New General Relativity.
Mazur, P.; Nijboer, B.R.A.
1953-01-01
Maxwell's macroscopic field equations are derived from the fundamental microscopic equations of electron theory in a new way. Instead of the usual space-time averaging procedure a statistical ensemble averaging method is applied, which is perhaps more satisfactory both from a physical and from a
Nguyen, Van Minh
In this paper we present a new approach to the spectral theory of non-uniformly continuous functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of C-semigroups, so the obtained results, that extend previous ones, can be applied to large classes of evolution equations and their solutions.
The Theory of Equations and the Birth of Modern Group Theory
Indian Academy of Sciences (India)
. The solutions are simple expressions in the coefficients and involve only the operations of addi- tion, subtraction, multiplication, division and extraction of square roots. This was discovered in Mesopotamia between. 1800 and 1600 Be. For the ...
An introduction to the mathematical theory of the Navier-Stokes equations
Galdi, Giovanni P
1994-01-01
Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbou...
Galaviz, K I; Jauregui-Ulloa, E; Fabrigar, L R; Latimer-Cheung, A; Lopez y Taylor, J; Lévesque, L
2015-03-01
To describe the physical activity (PA) prescribing behaviour of Mexican primary care physicians and determine if the theory of planned behaviour (TPB) explains this behaviour. 633 physicians (56% male, mean age 38 years) from 305 primary care clinics in Jalisco, Mexico self-reported PA prescription behaviour, PA involvement, attitude, subjective norm, perceived behavioural control (PBC) and intention related to PA prescription behaviour. Structural equation modelling (SEM) was employed. 48% of physicians reported they always ask patients about their PA, 33% provide verbal prescriptions, 6% provide written prescriptions, 8% refer patients to PA resources and 4% assess patient fitness. SEM analysis showed that the fit of the TPB model was satisfactory (RMSEA = 0.05, CFI = 0.98, SRMR = 0.05). The model explained 79% of the variance on intention (r(2) = 0.79, p Subjective norm (β = 0.73, p TPB provided useful insight into physician prescription behaviour, although not all the theory tenets were supported. More research testing the TPB and other theories is needed to better understand psychosocial predictors of this behaviour. Strategies aimed at improving physicians' perceived ability to prescribe PA and their own PA involvement seem worthwhile. © 2015 John Wiley & Sons Ltd.
Energy Technology Data Exchange (ETDEWEB)
B. A. Kashiwa; W. B. VanderHeyden
2000-12-01
A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.
Directory of Open Access Journals (Sweden)
Josefa Caballero
2006-05-01
Full Text Available We give an existence theorem for some functional-integral equations which includes many key integral and functional equations that arise in nonlinear analysis and its applications. In particular, we extend the class of characteristic functions appearing in Chandrasekhar's classical integral equation from astrophysics and retain existence of its solutions. Extensive use is made of measures of noncompactness and abstract fixed point theorems such as Darbo's theorem.
Periodic solutions of Lienard differential equations via averaging theory of order two
Directory of Open Access Journals (Sweden)
JAUME LLIBRE
2015-12-01
Full Text Available Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ( x x ′ + n 2 x + g ( x = ε 2 p 1 ( t + ε 3 p 2 ( t , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Energy Technology Data Exchange (ETDEWEB)
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective
Ngu, Bing Hiong; Phan, Huy P.
2016-01-01
The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…
Krylov, N. V.; Rozovskii, B. L.
1982-12-01
CONTENTS § 1. Introduction § 2. Solubility of the direct and inverse Cauchy problems § 3. The direct equation of inverse diffusion. The method of variation of constants § 4. The method of characteristics. First integrals and the Liouville equations for diffusion processes § 5. Inverse filtration equations References
Great moments in kinetic theory: 150 years of Maxwell’s (other) equations
Robson, Robert E.; Mehrling, Timon J.; Osterhoff, Jens
2017-11-01
In 1867, just two years after laying the foundations of electromagnetism, J. Clerk Maxwell presented a fundamental paper on kinetic gas theory, in which he described the evolution of the gas in terms of certain ‘moments’ of its velocity distribution function. This inspired Ludwig Boltzmann to formulate his famous kinetic equation, from which followed the H-theorem and the connection with entropy. On the occasion of the 150th anniversary of publication of Maxwell's paper, we review the Maxwell–Boltzmann formalism and discuss how its generality and adaptability enable it to play a key role in describing the behaviour of a variety of systems of current interest, in both gaseous and condensed matter, and in modern-day physics and technologies which Maxwell and Boltzmann could not possibly have foreseen. In particular, we illustrate the relevance and applicability of Maxwell's formalism to the dynamic field of plasma-wakefield acceleration.
Frank, S A
2012-12-01
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment. © 2012 The Author. Journal of Evolutionary Biology © 2012 European Society For Evolutionary Biology.
Binary fluid mixture of hard ellipses: Integral equation and weighted density functional theory
Moradi, M.; Khordad, R.
2007-10-01
We study a two-dimensional (2D) classical fluid mixture of hard convex shapes. The components of the mixture are two kinds of hard ellipses with different aspect ratios. Two different approaches are used to calculate the direct, pair and total correlation functions of this fluid and results are compared. We first use a formalism based on the weighted density functional theory (WDFT), introduced by Chamoux and Perera [Phys. Rev. E 58 (1998) 1933]. Second, in general the Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations are solved numerically for the 2D fluid mixtures of hard noncircular particles. Explicit results are obtained for the fluid mixtures of hard ellipses and comparisons are made by the two approaches. Also, the results are compared with the recent Monte Carlo simulation for the one-component fluids of hard ellipses. Finally we obtained the equation of state of hard ellipses for the aspect ratio sufficiently close to 1 and compared our results with the simulations of the fluid mixtures of hard disks.
Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory
Zhang, Sanzong
2015-05-26
The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.
Starke, R.; Schober, G. A. H.
2018-03-01
We provide a systematic theoretical, experimental, and historical critique of the standard derivation of Fresnel's equations, which shows in particular that these well-established equations actually contradict the traditional, macroscopic approach to electrodynamics in media. Subsequently, we give a rederivation of Fresnel's equations which is exclusively based on the microscopic Maxwell equations and hence in accordance with modern first-principles materials physics. In particular, as a main outcome of this analysis being of a more general interest, we propose the most general boundary conditions on electric and magnetic fields which are valid on the microscopic level.
VEV of Baxter’s Q-operator in N=2 gauge theory and the BPZ differential equation
Energy Technology Data Exchange (ETDEWEB)
Poghosyan, Gabriel; Poghossian, Rubik [Yerevan Physics Institute,Alikhanian Br. 2, AM-0036 Yerevan (Armenia)
2016-11-09
In this short note using AGT correspondence we express the simplest fully degenerate primary fields of Toda field theory in terms of an analogue of Baxter’s Q-operator naturally emerging on the N=2 gauge theory side. This quantity can be considered as a generating function of certain chiral operators constructed from the scalars of the N=2 vector multiplets. In the special case of Liouville theory, exploring the second order differential equation satisfied by conformal blocks including a primary field which is degenerate at the second level (BPZ equation) we derive a mixed difference-differential relation for Q-operator. Thus we generalize the T-Q difference equation known in Nekrasov-Shatashvili limit of the Ω-background to the generic case.
An ADER-type scheme for a class of equations arising from the water-wave theory
Montecinos G.I.; López-Rios J.C.; Lecaros R.; Ortega J.H.; Toro E.F.
2016-01-01
In this work we propose a numerical strategy to solve a family of partial differential equations arising from the water-wave theory. These problems may contain four terms; a source which is an algebraic function of the solution, a convective part involving first order spatial derivatives of the solution, a diffusive part involving second order spatial derivatives and the transient part. Unlike partial differential equations of hyperbolic or parabolic type, where the transient part is the time...
Polchinski ERG equation and 2D scalar field theory
Kubyshin, Yuri; Neves, Rui; Potting, Robertus
1998-01-01
We investigate a $Z_2$-symmetric scalar field theory in two dimensions using the Polchinski exact renormalization group equation expanded to second order in the derivative expansion. We find preliminary evidence that the Polchinski equation is able to describe the non-perturbative infinite set of fixed points in the theory space, corresponding to the minimal unitary series of 2D conformal field theories. We compute the anomalous scaling dimension $\\eta$ and the correlation l...
Howieson, William B
2008-01-01
In 1996, Professor Robert J House published a reformulated Path-Goal Theory of Work Unit Leadership, based on his earlier 1971 and 1974 theories. Path-goal leadership attempts to explain the impact that leader behaviour has on subordinate motivation, satisfaction and performance. The aim of this context-specific study is to evaluate this reformulated ‘1996 Theory’ via Structural Equation Modelling with engineers from the Royal Air Force as the primary data source. This th...
Equations of State: From the Ideas of van der Waals to Association Theories
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Economou, Ioannis G.
2010-01-01
The ideas of van der Waals have resulted to cubic equations of state like Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) which are widely used in the petroleum and chemical industries. It is often thought that the range of applicability of van der Waals-type models is limited to mixtures...... equations of state are sensitive to the mixing and combining rules used. Moreover, it is shown that previously reported deficiencies for size-asymmetric systems are more related to the van der Waals one fluid mixing rules used rather than the functionality of the cubic equation of state itself. Improved...
Glockner-Rist, Angelika; Hoijtink, Herbert
2003-01-01
Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems…
Maxwell's equations and their consequences elementary electromagnetic theory
Chirgwin, B H; Kilmister, C W 0
2013-01-01
Elementary Electromagnetic Theory Volume 3: Maxwell's Equations and their Consequences is the third of three volumes that intend to cover electromagnetism and its potential theory. The third volume considers the implications of Maxwell's equations, such as electromagnetic radiation in simple cases, and its relation between Maxwell's equation and the Lorenz transformation. Included in this volume are chapters 11-14, which contain an in-depth discussion of the following topics: Electromagnetic Waves The Lorentz Invariance of Maxwell's Equation Radiation Motion of Charged Particles Intended
National Research Council Canada - National Science Library
Asif Ali Laghari
2014-01-01
.... Considering deeply the effect of charge variation in Maxwell's equations for time varying electric and magnetic fields of charges in moving inertial frame, the magnitude of charge particles vary...
An electric-analog simulation of elliptic partial differential equations using finite element theory
Franke, O.L.; Pinder, G.F.; Patten, E.P.
1982-01-01
Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.
"Great expectations" of adoptive parents: theory extension through structural equation modeling.
Foli, Karen J; Lim, Eunjung; South, Susan C; Sands, Laura P
2014-01-01
Most of the 2 million adoptive parents in the United States make the transition to parenting successfully. Adoptive parents who do not make the transition easily may put their children at risk for negative outcomes. The aim of this study was to further refine Foli's midrange theory of postadoption depression, which postulates that fulfillment of expectations is a principal contributor to parental emotional health status, aggravation, and bonding. The linked dataset (National Survey of Children's Health and National Survey of Adoptive Parents) was used for structural equation modeling. The sample consisted of 1,426 parents with adopted children who had been placed in the home more than 2 years before survey completion. Special services and child's behaviors were direct determinants of parental expectations, and parental expectations were direct determinants of parental aggravation and parentalbonding. As anticipated, parental expectations served as a mediator between child-related variables and parental outcomes. A path was also found between child's behaviors and special services and parental emotional health status. Child's past trauma was also associated with parental bonding. Parental expectations showed direct relationships with the latent variables of parental aggravation and bonding. Future research should examine factors associated with early transition when children have been in the adoptive home less than 2 years and include specific expectations held by parents.
Kirsch, Andreas
2015-01-01
This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave propagation problems. The students should have some knowledge on vector analysis (curves, surfaces, divergence theorem) and functional analysis (normed spaces, Hilbert spaces, linear and bounded operators, dual space). Written in an accessible manner, topics are first approached with simpler scale Helmholtz Equations before turning to Maxwell Equations. There are examples and exercises throughout the book. It will be useful for graduate students and researchers in applied mathematics and engineers working in the theoretical ap...
The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.
Lehtonen, Jussi
2018-01-01
A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.
WDVV equations for pure Super-Yang-Mills theory
Hoevenaars, L.K.; Martini, Ruud
2000-01-01
In the literature, there are two proofs that the prepotential of $N=2$ pure Super-Yang-Mills theory satisfies the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. We show that these two methods are in fact equivalent.
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Nath, Sunil
2017-11-01
The vital coupled processes of oxidative phosphorylation and photosynthetic phosphorylation synthesize molecules of adenosine-5'-triphosphate (ATP), the universal biological energy currency, and sustain all life on our planet. The chemiosmotic theory of energy coupling in oxidative and photophosphorylation was proposed by Mitchell >50years ago. It has had a contentious history, with part of the accumulated body of experimental evidence supporting it, and part of it in conflict with the theory. Although the theory was strongly criticized by many prominent scientists, the controversy has never been resolved. Here, the mathematical steps of Mitchell's original derivation leading to the principal equation of the chemiosmotic theory are scrutinized, and a fundamental flaw in them has been identified. Surprisingly, this flaw had not been detected earlier. Discovery of such a defect negates, or at least considerably weakens, the theoretical foundations on which the chemiosmotic theory is based. Ad hoc or simplistic ways to remedy this defect are shown to be scientifically unproductive and sterile. A novel two-ion theory of biological energy coupling salvages the situation by rectifying the fundamental flaw in the chemiosmotic theory, and the governing equations of the new theory have been shown to accurately quantify and predict extensive recent experimental data on ATP synthesis by F1FO-ATP synthase without using adjustable parameters. Some major biological implications arising from the new thinking are discussed. The principles of energy transduction and coupling proposed in the new paradigm are shown to be of a very general and universal nature. It is concluded that the timely availability after a 25-year research struggle of Nath's torsional mechanism of energy transduction and ATP synthesis is a rational alternative that has the power to solve the problems arising from the past, and also meet present and future challenges in this important interdisciplinary field of
Directory of Open Access Journals (Sweden)
S. Sokołowski
2011-03-01
Full Text Available We have studied the structure and thermodynamic properties of isotropic three-dimensional core-softened fluid by using the second-order Ornstein-Zernike integral equations completed by the hypernetted chain and Percus-Yevick closures. The radial distribution functions are compared with those from singlet integral equations and with computer simulation data. The limits of the region of density anomaly resulting from different approximate theories are established. The obtained results show that the second-order hypernetted chain approximation can be used to describe both the structure and the density anomaly of this model fluid. Moreover, we present the results of calculations of the bridge functions.
Diffuse optical tomography through solving a system of quadratic equations: theory and simulations.
Kanmani, B; Vasu, R M
2006-02-21
This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Polchinski ERG Equation in O(N) Scalar Field Theory
Kubyshin, Yuri; Neves, Rui; Potting, Robertus
We investigate the Polchinski ERG equation for d-dimensional O(N) scalar field theory. In the context of the non-pertubative derivative expansion we find families of regular solutions and establish their relation with the physical fixed points of the theory. Special emphasis is given to the limit N=∞ for which many properties can be studied analytically.
Polchinski ERG Equation in O(N) Scalar Field Theory
Kubyshin, Yuri; Neves, Rui; Potting, Robertus
2001-01-01
We investigate the Polchinski ERG equation for d-dimensional O(N) scalar field theory. In the context of the non-perturbative derivative expansion we find families of regular solutions and establish their relation with the physical fixed points of the theory. Special emphasis is given to the large N limit for which many properties can be studied analytically.
Application of perturbation theory to a P-wave eikonal equation in orthorhombic media
Stovas, Alexey
2016-10-12
The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical solutions. To alleviate this complexity, we approximate the solution of this equation by applying a multiparametric perturbation approach. We also investigated the sensitivity of traveltime surfaces inORT mediawith respect to three anelliptic parameters. As a result, a simple and accurate P-wave traveltime approximation valid for ORT media was derived. Two different possible anelliptic parameterizations were compared. One of the parameterizations includes anelliptic parameters defined at zero offset: η1, η2, and ηxy. Another parameterization includes anelliptic parameters defined for all symmetry planes: η1, η2, and η3. The azimuthal behavior of sensitivity coefficients with different parameterizations was used to analyze the crosstalk between anelliptic parameters. © 2016 Society of Exploration Geophysicists.
Tamagawa, Hirohisa; Ikeda, Kota
2017-09-01
Donnan theory and Goldman-Hodgkin-Katz equation (GHK eq.) state that the nonzero membrane potential is generated by the asymmetric ion distribution between two solutions separated by a semipermeable membrane and/or by the continuous ion transport across the semipermeable membrane. However, there have been a number of reports of the membrane potential generation behaviors in conflict with those theories. The authors of this paper performed the experimental and theoretical investigation of membrane potential and found that (1) Donnan theory is valid only when the macroscopic electroneutrality is sufficed and (2) Potential behavior across a certain type of membrane appears to be inexplicable on the concept of GHK eq. Consequently, the authors derived a conclusion that the existing theories have some limitations for predicting the membrane potential behavior and we need to find a theory to overcome those limitations. The authors suggest that the ion adsorption theory named Ling's adsorption theory, which attributes the membrane potential generation to the mobile ion adsorption onto the adsorption sites, could overcome those problems.
Nevanlinna theory, normal families, and algebraic differential equations
Steinmetz, Norbert
2017-01-01
This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers wor...
DEFF Research Database (Denmark)
Queimada, Antonio; Miqueu, C; Marrucho, IM
2005-01-01
and the correct phase equilibrium of water + hydrocarbon systems already obtained from CPA. In this work, preliminary studies involving the vapor-liquid interfacial tensions of some selected associating and non-associating pure components (water, ethanol, n-butane, n-pentane, n-hexane, n-heptane) are presented......With the final purpose of describing the important aqueous + hydrocarbon liquid-liquid interfaces, the gradient theory was combined with the Cubic-Plus-Association equation of state (CPA EOS), taking advantage of the correct representation of interfacial tensions provided by the gradient theory...... and discussed. The good description of equilibrium properties such as vapor pressure and liquid and vapor phase densities is shown in the full range of the vapor-liquid saturation line. For non-associating components, results are compared with those from the Soave-Redlich-Kwong and Peng-Robinson equations...
Spin-dependent semiconductor Bloch equations: Microscopic theory of Bir-Aronov-Pikus spin relaxation
Lechner, C.; Rössler, U.
2005-10-01
Semiconductor Bloch equations, in their extension including the spin degree of freedom of the carriers, are capable to describe spin dynamics on a microscopic level. In the presence of free holes, electron spins can flip simultaneously with hole spins due to electron-hole exchange interaction. This mechanism named after Bir, Aronov, and Pikus is described here by using the extended semiconductor Bloch equations [Phys. Status Solidi B 234, 385 (2002)] and considering carrier-carrier interaction beyond the Hartree-Fock truncation. As a result we derive microscopic expressions for spin-relaxation and spin-dephasing rates.
Modeling Pore-Scale Oil-Gas Systems Using Gradient Theory with Peng-Robinson Equation of State
Fan, Xiaolin
2016-06-01
This research addresses a sequential convex splitting method for numerical simulation of multicomponent two-phase fluids mixture in a single-pore at constant temperature, which is modeled by the gradient theory with Peng-Robinson equation of state. The gradient theory of thermodynamics and variational calculus are utilized to obtain a system of chemical equilibrium equations which are transformed into a transient system as a numerical strategy on which the numerical scheme is based. The proposed numerical algorithm avoids computing Hessian matrix arising from the second-order derivative of homogeneous contribution of free energy; it is also quite robust. This scheme is proved to be unconditionally component-wise energy stable. The Raviart-Thomas mixed finite element method is applied to spatial discretization.
Oscillation theory for a pair of second order dynamic equations with a singular interface
Directory of Open Access Journals (Sweden)
Pallav Kumar Baruah
2008-03-01
Full Text Available In this paper we consider a pair of second order dynamic equations defined on the time scale $I = [a,c]cup [sigma(c,b]$. We impose matching interface conditions at the singular interface $c$. We prove a theorem regarding the relationship between the number of eigenvalues and zeros of the corresponding eigenfunctions.
Energy Technology Data Exchange (ETDEWEB)
Reiss, H.; Casberg, R.V.
1974-08-01
Previous applications of scaled particle theory have been limited to the calculation of thermodynamic properties of fluids rather than structure. In the present paper, the theory is expanded so that it is capable of yielding the radial distribution function. The method is first illustrated by applying it to one-dimensional fluids of hard rods where, as in other theories, the radial distribution function is obtained exactly. It is then applied to a fluid of hard spheres where a closure condition is necessary. This condition is supported by recent work in scaled particle theory dealing with the thermodynamics of boundary layers. It is used to calculate the radial distribution function around a lambda-cule of varying size, including one of the size of a typical hard sphere solvent molecule. (40 refs.)
Kouri, Donald J; Vijay, Amrendra
2003-04-01
The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the frequency. By contrast, it is well known that the Born-Neumann series for the Volterra integral equations in quantum scattering are absolutely convergent, independent of the strength of the coupling characterizing the interaction. The transformation of the Lippmann-Schwinger equation from a Fredholm to a Volterra structure by renormalization has been considered previously for quantum scattering calculations and electromagnetic scattering. In this paper, we employ the renormalization technique to obtain a Volterra equation framework for the inverse acoustic scattering series, proving that this series also converges absolutely in the entire complex plane of coupling constant and frequency values. The present results are for acoustic scattering in one dimension, but the method is general. The approach is illustrated by applications to two simple one-dimensional models for acoustic scattering.
Extension of Golay's plate height equation from laminar to turbulent flow I - Theory.
Gritti, Fabrice
2017-04-07
The reduced plate height (RPH) equation of Golay derived in 1958 for open tubular columns (OTC) is extended from laminar to turbulent-like flow. The mass balance equation is solved under near-equilibrium conditions in the mobile phase for changing shapes of the velocity profile across the OTC diameter. The final expression of the general RPH equation is: [Formula: see text] where ν is the reduced linear velocity, k is the retention factor, D m is the bulk diffusion coefficient in the mobile phase, D a ¯ is the average axial dispersion coefficient, D r ¯ is the average radial dispersion coefficient, D s is the diffusion coefficient of the analyte in the stationary film of thickness d f , D is the OTC inner diameter, and n≥2 is a positive number controlling the shape of the flow profile (polynomial of degree n). The correctness of the derived RPH equation is verified for Poiseuille (n=2), turburlent-like (n=10), and uniformly flat (n→∞) flow profiles. The derived RPH equation is applied to predict the gain in speed-resolution of a 180μm i.d.×20m OTC (d f =2μm) from laminar to turbulent flow in supercritical fluid chromatography. Using pure carbon dioxide as the mobile phase at 297K, k=1, and increasing the Reynolds number from 2000 (laminar) to 4000 (turbulent), the OTC efficiency is expected to increase from 125 to 670 (×5.4) while the hold-up time decreases from 19 to 9s (×0.5). Despite the stronger resistance to mass transfer in the stationary phase, the projected improvement of the column performance in turbulent flow is explained by the quasi-elimination of the resistance to mass transfer in the mobile phase while axial dispersion remains negligible. Copyright © 2017 Elsevier B.V. All rights reserved.
AL-Dossary, Saeed Abdullah
2017-01-01
Cheating on tests is a serious problem in education. The purpose of this study was to test the efficacy of a modified form of the theory of planned behavior (TPB) to predict cheating behavior among a sample of Saudi university students. This study also sought to test the influence of cheating in high school on cheating in college within the…
The Boltzmann Equation in Fluorescent Lamp Theory
Lister, Graeme
Ken Hines was a wonderful mentor in my formative years as a physicist, and a great friend and companion throughout the rest of his life. He introduced me to the Fokker-Planck equation, which formed the basis of my Masters thesis, and showed me how to use it to derive the Boltzmann equation. Many years later, when my research took me into the field of gas discharge lighting, I was to re-discover the Boltzmann equation and apply it to fluorescent lamp modelling. Herein I discuss the important role the electron energy distribution function plays in understanding the physics of fluorescent lamps, and I describe some of the important insights gained from interpreting the Boltzmann equation.
Theory of periodic solutions of the stationary Landau-Lifshitz equation
Energy Technology Data Exchange (ETDEWEB)
Bar' yakhtar, V.G.; Leonov, I.A.; Soboleva, T.K.
1987-04-01
In the phenomenological approach, quasi-one-dimensional structures in a magnet of a definite symmetry are described by solutions of the stationary Landau-Lifshitz equation or, equivalently, by the solutions of a variational problem with Lagrangian L whose actual form is determined by the requirement of invariance with respect to the symmetry group of the paramagnetic phase of the given magnet. In the present note, the methods of the variational calculus in the large are used to estimate the number of possible magnetic phases with periodic superstructure corresponding to a given free energy functional of the magnet.
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.
A New Monotone Iteration Principle in the Theory of Nonlinear Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-08-01
Full Text Available In this paper the author proves the algorithms for the existence as well as approximations of the solutions for the initial value problems of nonlinear fractional diﬀerential equations using the operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid ﬁxed point theorems of Dhage (2014 in a partially ordered normed linear space and the existence and approximations of the solutions of the considered nonlinear fractional diﬀerential equations are obtained under weak mixed partial continuity and partial Lipschitz conditions. Our hypotheses and existence and approximation results are also well illustrated by some numerical examples.
Behavioral Momentum Theory: Equations and Applications
Nevin, John A.; Shahan, Timothy A.
2011-01-01
Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…
Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.
The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,
Testing a theory of aircraft noise annoyance : A structural equation analysis
Kroesen, M.; Molin, E.J.E.; Van Wee, B.
2008-01-01
Previous research has stressed the relevance of nonacoustical factors in the perception of aircraft noise. However, it is largely empirically driven and lacks a sound theoretical basis. In this paper, a theoretical model which explains noise annoyance based on the psychological stress theory is
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making...
Analytic treatment of leading-order parton evolution equations: Theory and tests
Block, Martin M.; Durand, Loyal; McKay, Douglas W.
2009-01-01
We recently derived an explicit expression for the gluon distribution function G(x,Q2)=xg(x,Q2) in terms of the proton structure function F2γp(x,Q2) in leading-order (LO) QCD by solving the LO Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for the Q2 evolution of F2γp(x,Q2) analytically, using a differential-equation method. We showed that accurate experimental knowledge of F2γp(x,Q2) in a region of Bjorken x and virtuality Q2 is all that is needed to determine the gluon distribution in that region. We rederive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function FS(x,Q2) can be determined directly in terms of G from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001 LO analyses to form F2γp(x,Q2), and then solved analytically for G(x,Q2). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q2, while those from CTEQ5L differ significantly from each other for large x values, x≳0.03-0.05, at all Q2. We conclude that the published CTEQ5L distributions are incompatible in this region. Using a nonsinglet evolution equation, we obtain a sensitive test of quark distributions which holds in both LO and next-to-leading order perturbative QCD. We find in either case that the CTEQ5 quark distributions satisfy the tests numerically for small x, but fail the tests for x≳0.03-0.05—their use could potentially lead to significant shifts in predictions of quantities sensitive to large x. We encountered no problems with the MRST2001LO distributions or later CTEQ distributions. We suggest caution in the use of the CTEQ5 distributions.
A theory of solving TAP equations for Ising models with general invariant random matrices
DEFF Research Database (Denmark)
Opper, Manfred; Çakmak, Burak; Winther, Ole
2016-01-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields...... the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida–Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble....
Llibre, Jaume; Spinetti-Rivera, Mario; Colina-Morles, Eliezer
2015-06-01
This paper uses the qualitative theory of differential equations to analyse/design the dynamic behaviour of control systems. In particular, the Poincaré compactification and the Poincaré--Hopf theorem are used for analysing the local dynamics near the finite and infinite equilibrium points. As an application, a large signal characterisation of a Boost type power converter in closed loop, including its equilibrium/bifurcation points and its global dynamics, which depends upon the value of the load resistance, is studied.
The Navier-Stokes Equations Theory and Numerical Methods
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1990-01-01
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
Stability theory for dynamic equations on time scales
Martynyuk, Anatoly A
2016-01-01
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...
Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory
2011-01-01
core, Boltzmann equation, can be found in many text books like Cercignani (1988), Cercignani (2000), Chapman and Cowling (1970) or Vincenti and Kruger...3776–3786. Cercignani , C. (1988). The Boltzmann Equation and its Applications. Applied Mathe- matical Sciences. Springer, New York. RTO-EN-AVT-194 10...45 REFERENCES REFERENCES Cercignani , C. (2000). Rarefied Gas Dynamics: From Basic Concepts to Actual Calcula- tions. Texts in Applied Mathematics
Comments on the symmetry of AdS6 solutions in string/M-theory and Killing spinor equations
Directory of Open Access Journals (Sweden)
Hyojoong Kim
2016-09-01
Full Text Available It was recently pointed out in [1] that AdS6 solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to D=4 internal space leads to a nonlinear sigma model with target SL(3,R/SO(2,1. We continue to study the purely bosonic D=4 effective action, and elucidate how the addition of scalar potential term still allows Killing spinor equations in the absence of gauge fields. In particular, the potential turns out to be a single diagonal component of the coset representative. Furthermore, we perform a general analysis of the integrability conditions of Killing spinor equations and establish that the effective action can be in fact generalized to arbitrary sizes and signatures, e.g. with target SL(n,R/SO(p,n−p and the scalar potential expressible by a single diagonal component of the coset representative. We also comment on a similar construction and its generalizations of effective D=5 purely bosonic non-linear sigma model action related to AdS6 in M-theory.
Elements of partial differential equations
Sneddon, Ian N
2006-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Directory of Open Access Journals (Sweden)
Hrubý Jan
2012-04-01
Full Text Available The study presents some preliminary results of the density gradient theory (GT combined with two different equations of state (EoS: the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT, namely its perturbed-chain (PC modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation or bubbles (boiling, cavitation. However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.
Directory of Open Access Journals (Sweden)
Mi Kyoung Yim
2006-07-01
Full Text Available The passing rate of the Medical Licensing Examination has been variable, which probably originated from the difference in the difficulty of items and/or difference in the ability level of examinees. We tried to explain the origin of the difference using the test equating method based on the item response theory. The number of items and examinees were 500, 3,647 in 2003 and 550, 3,879 in 2004. Common item nonequivalent group design was used for 30 common items. Item and ability parameters were calculated by three parametric logistic models using ICL. Scale transformation and true score equating were executed using ST and PIE. The mean of difficulty index of the year 2003 was ??.957 (SD 2.628 and that of 2004 after equating was ??.456 (SD 3.399. The mean of discrimination index of year 2003 was 0.487 (SD 0.242 and that of 2004 was 0.363 (SD 0.193. The mean of ability parameter of year 2003 was 0.00617 (SD 0.96605 and that of year 2004 was 0.94636 (SD 1.32960. The difference of the equated true score at the same ability level was high at the range of score of 200??50. The reason for the difference in passing rates over two consecutive years was due to the fact that the Examination in 2004 was easier and the abilities of the examinees in 2004 were higher. In addition, the passing rates of examinees with score of 270??94 in 2003, and those with 322??43 in 2004, were affected by the examination year.
Analyses of the Instabilities in the Discretized Diffusion Equations via Information Theory
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Maxence Bigerelle
2016-04-01
Full Text Available In a previous investigation (Bigerelle and Iost, 2004, the authors have proposed a physical interpretation of the instability λ = Δt/Δx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained using integration techniques based on erf functions meaning that no statistical fluctuation was introduced in the mathematical background. In this paper, we showed that the diffusive system can be divided into sub-systems onto which a Brownian motion is applied. Monte Carlo simulations are carried out to reproduce the macroscopic diffusive system. It is shown that the amount of information characterized by the compression ratio of information of the system is pertinent to quantify the entropy of the system according to some concepts introduced by the authors (Bigerelle and Iost, 2007. Thanks to this mesoscopic discretization, it is proved that information on each sub-cell of the diffusion map decreases with time before the unstable equality λ = 1/2 and increases after this threshold involving an increase in negentropy, i.e., a decrease in entropy contrarily to the second principle of thermodynamics.
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Vasiliev Andrey
2017-01-01
Full Text Available A class of dual integral equations is analyzed which arises in solution of a wide range of plane and antiplane contact problems of elasticity theory for a half-plane with functionally graded coating. In particular, a similar equation arises in solution of the contact problem on indentation in the presence of tangential stresses on a surface. The solution of the dual integral equation is sought in the form of a sum of even and odd functions. It makes possible to reduce the problem to independent solution of two dual integral equations over odd and even functions. Kernel transform of these equations is approximated by a product of fractional quadratic functions. The solution of dual integral equations is constructed in approximated analytical form by the bilateral asymptotic method. The expressions obtained are asymptotically exact for small and large values of a characteristic geometrical parameter.
DEFF Research Database (Denmark)
Liang, Xiaodong; Kontogeorgis, Georgios
2015-01-01
resolved the mostly criticized numerical pitfall, that is, the presence of more than three volume roots at real application conditions. Finally, the possibility of using the original PC-SAFT EOS parameters with the new universal constants has been investigated for the phase equilibria of the systems......The Perturbed Chain-Statistical Associating Fluid Theory Equation of State (PC-SAFT EOS) has been successfully applied to model phase behavior of various types of systems, while it is also well-known that the PC-SAFT EOS has difficulties in describing some second-order derivative properties...... roots, have been analyzed. Then, a practical procedure has been proposed to refit the universal constants of the PC-SAFT EOS with the purpose of fixing the numerical pitfalls in the real application ranges and reusing the original parameters. It is shown that the new universal constants have practically...
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Vinš Václav
2013-04-01
Full Text Available In this work, we used the density gradient theory (DGT combined with the cubic equation of state (EoS by Peng and Robinson (PR and the perturbed chain (PC modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.
Planková, Barbora; Hrubý, Jan; Vinš, Václav
2013-04-01
In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.
Wells, Dare A
1967-01-01
The book clearly and concisely explains the basic principles of Lagrangian dynamicsand provides training in the actual physical and mathematical techniques of applying Lagrange's equations, laying the foundation for a later study of topics that bridge the gap between classical and quantum physics, engineering, chemistry and applied mathematics, and for practicing scientists and engineers.
Ding, Y. H.; Hu, S. X.
2017-06-01
Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ˜10% stiffer than the last two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ˜20%. By implementing the FPEOS table into the 1-D radiation-hydrodynamic code LILAC, we studied the EOS effects on beryllium-shell-target implosions. The FPEOS simulation predicts higher neutron yield (˜15%) compared to the simulation using the SESAME 2023 EOS table.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
Giusti, Leonardo
2017-06-10
The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\\epsilon + p )$. The continuum values of the potentials are well represented by Pad\\'e interpolating formulas, which als...
Equation of state of the SU(3) Yang-Mills theory: A precise determination from a moving frame
Giusti, Leonardo; Pepe, Michele
2017-06-01
The equation of state of the SU(3) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to 230Tc with Tc being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few Tc the results exhibit a striking linear behaviour in ln (T /Tc)-1 over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from Ts = (ɛ + p). The continuum values of the potentials are well represented by Padé interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near Tc is analyzed and resolved thanks to the high precision achieved.
Directory of Open Access Journals (Sweden)
Teffera M. Asfaw
2016-01-01
Full Text Available Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X⁎. Let T:X⊇DT→2X⁎ be maximal monotone of type Γdϕ (i.e., there exist d≥0 and a nondecreasing function ϕ:0,∞→0,∞ with ϕ(0=0 such that 〈v⁎,x-y〉≥-dx-ϕy for all x∈DT, v⁎∈Tx, and y∈X,L:X⊃D(L→X⁎ be linear, surjective, and closed such that L-1:X⁎→X is compact, and C:X→X⁎ be a bounded demicontinuous operator. A new degree theory is developed for operators of the type L+T+C. The surjectivity of L can be omitted provided that RL is closed, L is densely defined and self-adjoint, and X=H, a real Hilbert space. The theory improves the degree theory of Berkovits and Mustonen for L+C, where C is bounded demicontinuous pseudomonotone. New existence theorems are provided. In the case when L is monotone, a maximality result is included for L and L+T. The theory is applied to prove existence of weak solutions in X=L20,T;H01Ω of the nonlinear equation given by ∂u/∂t-∑i=1N(∂/∂xiAix,u,∇u+Hλx,u,∇u=fx,t, x,t∈QT; ux,t=0, x,t∈∂QT; and ux,0=ux,T, x∈Ω, where λ>0, QT=Ω×0,T, ∂QT=∂Ω×0,T, Aix,u,∇u=∂/∂xiρx,u,∇u+aix,u,∇u (i=1,2,…,N, Hλx,u,∇u=-λΔu+gx,u,∇u, Ω is a nonempty, bounded, and open subset of RN with smooth boundary, and ρ,ai,g:Ω¯×R×RN→R satisfy suitable growth conditions. In addition, a new existence result is given concerning existence of weak solutions for nonlinear wave equation with nonmonotone nonlinearity.
Gilding, B.H.; Kersner, R.
1996-01-01
A degenerate parabolic partial differential equation with a time derivative and first- and second-order derivatives with respect to one spatial variable is studied. The coefficients in the equation depend nonlinearly on both the unknown and the first spatial derivative of a function of the unknown.
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Mohammad Ali Fariborzi Araghi
2016-02-01
Full Text Available In this paper, a new efficient and applicable method in order to solve the first kind Cauchy integral equation is presented. For this purpose, this integral equation is converted to the second kind, then the homotopy analysis method is applied to solve the obtained integral equation. Also, the convergence of the proposed method is proved. Several applicable examples are presented which are appeared in the theory of airfoils in fluid mechanics. By plotting the $\\hbar$-curves, we show the convergence region of the examples and the tables of absolute errors for different values of $\\hbar$ and $x$ are tabulated.
Zhou, Hongmei; Romero, Stephanie Ballon; Qin, Xiao
2016-10-01
This paper aimed to examine pedestrians' self-reported violating crossing behavior intentions by applying the theory of planned behavior (TPB). We studied the behavior intentions regarding instrumental attitude, subjective norm, perceived behavioral control, the three basic components of TPB, and extended the theory by adding new factors including descriptive norm, perceived risk and conformity tendency to evaluate their respective impacts on pedestrians' behavior intentions. A questionnaire presented with a scenario that pedestrians crossed the road violating the pedestrian lights at an intersection was designed, and the survey was conducted in Dalian, China. Based on the 260 complete and valid responses, reliability and validity of the data for each question was evaluated. The data were then analyzed by using the structural equation modeling (SEM). The results showed that people had a negative attitude toward the behavior of violating road-crossing rules; they perceived social influences from their family and friends; and they believed that this kind of risky behavior would potentially harm them in a traffic accident. The results also showed that instrumental attitude and subjective norm were significant in the basic TPB model. After adding descriptive norm, subjective norm was no more significant. Other models showed that conformity tendency was a strong predictor, indicating that the presence of other pedestrians would influence behavioral intention. The findings could help to design more effective interventions and safety campaigns, such as changing people's attitude toward this violation behavior, correcting the social norms, increasing their safety awareness, etc. in order to reduce pedestrians' road crossing violations. Copyright © 2015 Elsevier Ltd. All rights reserved.
Guo, J L; Wang, T F; Liao, J Y; Huang, C M
2016-02-01
This study assessed the applicability and efficacy of the theory of planned behavior (TPB) in predicting breastfeeding. The TPB assumes a rational approach for engaging in various behaviors, and has been used extensively for explaining health behavior. However, most studies have tested the effectiveness of TPB constructs in predicting how people perform actions for their own benefit rather than performing behaviors that are beneficial to others, such as breastfeeding infants. A meta-analysis approach could help clarify the breastfeeding practice to promote breastfeeding. This study used meta-analytic procedures. We searched for studies to include in our analysis, examining those published between January 1, 1990 and December 31, 2013 in PubMed, Medline, CINAHL, ProQuest, and Mosby's Index. We also reviewed journals with a history of publishing breastfeeding studies and searched reference lists for potential articles to include. Ten studies comprising a total of 2694 participants were selected for analysis. These studies yielded 10 effect sizes from the TPB, which ranged from 0.20 to 0.59. Structural equation model analysis using the pooled correlation matrix enabled us to determine the relative coefficients among TPB constructs. Attitude, subjective norms, and perceived behavioral control were all significant predictors of breastfeeding intention, whereas intention was a strong predictor of breastfeeding behavior. Perceived behavioral control reached a borderline level of significance to breastfeeding behavior. Theoretical and empirical implications are discussed from the perspective of evidence-based practice. Copyright © 2015 Elsevier Inc. All rights reserved.
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
National Research Council Canada - National Science Library
Collamore, Jeffrey F; Vidyashankar, Anand N
2013-01-01
This paper introduces a new approach, based on large deviation theory and nonlinear renewal theory, for analyzing solutions to stochastic fixed point equations of the form V=Df(V), where f(v)=Amax{v,D...
A Study of Tunable Integration and Control Theory for the Analysis of Differential Equation Solvers.
1977-05-01
implementation upon the frequency response of a software package. The results of the studies reported on here- in are onl y a start . The potential promised...this point it should he note° that the final block diagram of the software system is not obtained by simply repla cing each integrator in Figure 11 with...t + - ~) Z ’ ~Z fs i n t 1G (z)~ (4-1) If one disdains algebr a . the frequency response can be determined by actually integrating a sinusoidal
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Scalco, Andrea; Noventa, Stefano; Sartori, Riccardo; Ceschi, Andrea
2017-05-01
During the last decade, the purchase of organic food within a sustainable consumption context has gained momentum. Consequently, the amount of research in the field has increased, leading in some cases to discrepancies regarding both methods and results. The present review examines those works that applied the theory of planned behavior (TPB; Ajzen, 1991) as a theoretical framework in order to understand and predict consumers' motivation to buy organic food. A meta-analysis has been conducted to assess the strength of the relationships between attitude, subjective norms, perceived behavioral control, and intention, as well as between intention and behavior. Results confirm the major role played by individual attitude in shaping buying intention, followed by subjective norms and perceived behavioral control. Intention-behavior shows a large effect size, few studies however explicitly reported such an association. Furthermore, starting from a pooled correlation matrix, a meta-analytic structural equation model has been applied to jointly evaluate the strength of the relationships among the factors of the original model. Results suggest the robustness of the TPB model. In addition, mediation analysis indicates a potential direct effect from subjective norms to individual attitude in the present context. Finally, some issues regarding methodological aspects of the application of the TPB within the context of organic food are discussed for further research developments. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical studies of Einstein's and other relativistic equations/alternative gravity theories
Sorkin, R D
1993-01-01
The topics represented in this workshop spanned a wide range, reﬂecting the diversity of the very large number of abstracts submitted (nearly 100). In View of this breadth, it would be impossible to organize the present report according to subject. Instead I will just summarize the talks of the three sessions individually, pointing out now and then some connections which exist between them.
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
REDUCTION TO CANONICAL-FORMS AND THE STOKES PHENOMENON IN THE THEORY OF LINEAR DIFFERENCE-EQUATIONS
IMMINK, GK
Previous results concerning the existence of right inverses of linear difference operators on Banach Spaces of holomorphic functions are extended. The Stokes phenomenon is analyzed for a class of very singular linear difference equations.
Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito
2017-08-21
A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.
Zhao, Luning; Neuscamman, Eric
2016-08-09
An equation of motion formalism for excited states in variational Monte Carlo is derived, and a pilot implementation for the Jastrow-modified antisymmetric geminal power is tested. In single excitations across a range of small molecules, this combination is shown to be intermediate in accuracy between configuration interaction singles and equation of motion coupled cluster with singles and doubles. For double excitations, energy errors are found to be similar to those for coupled cluster.
Witten, Matthew
1983-01-01
Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq
Correct Linearization of Einstein's Equations
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Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
The Complexity of One-Step Equations
Ngu, Bing
2014-01-01
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Energy Conservation Equations of Motion
Vinokurov, Nikolay A
2015-01-01
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities that is called energy is constant. This paper presents an alternative approach, namely derivation of a general form of equations of motion that keep the system energy, expressed as a function of generalized coordinates and corresponding velocities, constant. These are Lagrange equations with addition of gyroscopic forces. The important fact, that the energy is defined as the function on the tangent bundle of configuration manifold, is used explicitly for the derivation. The Lagrangian is derived from a known energy function. A development of generalized Hamilton and Lagrange equations without the use of variational principles is proposed. The use of new technique is applied to derivation of some equations.
EunYoung Kim, PhD; Inhyo Cho, PhD; Eun Joo Kim, PhD
2017-01-01
Purpose: This study investigated the mediating effects of loneliness and depression on the relationship between adult attachment and smartphone addiction in university students. Methods: A total of 200 university students participated in this study. The data was analysed using descriptive statistics, correlation analysis, and structural equation modeling. Results: There were significant positive relationships between attachment anxiety, loneliness, depression, and smartphone addiction. ...
Teo, Timothy; Tan, Lynde
2012-01-01
This study applies the theory of planned behavior (TPB), a theory that is commonly used in commercial settings, to the educational context to explain pre-service teachers' technology acceptance. It is also interested in examining its validity when used for this purpose. It has found evidence that the TPB is a valid model to explain pre-service…
Poincaré, Henri
2017-01-01
Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. .
Choi, Eunsong; Yethiraj, Arun
2015-07-23
We study the conformational properties of polymers in room temperature ionic liquids using theory and simulations of a coarse-grained model. Atomistic simulations have shown that single poly(ethylene oxide) (PEO) molecules in the ionic liquid 1-butyl 3-methyl imidazolium tetrafluoroborate ([BMIM][BF4]) are expanded at room temperature (i.e., the radius of gyration, Rg), scales with molecular weight, Mw, as Rg ∼ Mw(0.9), instead of the expected self-avoiding walk behavior. The simulations were restricted to fairly short chains, however, which might not be in the true scaling regime. In this work, we investigate a coarse-grained model for the behavior of PEO in [BMIM][BF4]. We use existing force fields for PEO and [BMIM][BF4] and Lorentz–Berthelot mixing rules for the cross interactions. The coarse-grained model predicts that PEO collapses in the ionic liquid. We also present an integral equation theory for the structure of the ionic liquid and the conformation properties of the polymer. The theory is in excellent agreement with the simulation results. We conclude that the properties of polymers in ionic liquids are unusually sensitive to the details of the intermolecular interactions. The integral equation theory is sufficiently accurate to be a useful guide to computational work.
On two functional equations originating from number theory
Indian Academy of Sciences (India)
Lett. 21 (2008) 974–977 to equa- tions in complex variables and quaternions, we find general solutions of the equations. We also obtain the stability of the equations. Keywords. Exponential type functional equation; multiplicative function; quaternion; stability. 2010 Mathematics Subject Classification. 39B82. 1. Introduction.
Random matrix theory and the sixth Painleve equation
Energy Technology Data Exchange (ETDEWEB)
Forrester, P J; Witte, N S [Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia)
2006-09-29
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realized by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be {tau}-functions for Painleve systems, allowing for the former to be characterized as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the {sigma} form of P{sub VI}. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at t = 0, 1, {infinity} of {sigma}P{sub VI} displayed by a generalization of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the {tau}-function of {sigma}P{sub VI} in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to P{sub VI}.
Jordan, Pascual; Ehlers, Jürgen; Sachs, Rainer K.
2013-12-01
This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.
Partial differential equations in action from modelling to theory
Salsa, Sandro
2016-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
Partial differential equations in action from modelling to theory
Salsa, Sandro
2015-01-01
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
Differential equations and stability of competitive economy
Šabata, Marek
2014-01-01
In the thesis, the author will analyse the theory of differential equations and its applications in economic model of price adjustment processes in competitive markets. First of all, the economic model sufficient to study stability of the market is introduced. Next microeconomic theory of competitive markets is presented and theory of differential equations is laid out, including the stability theory. Differences between the general model and the pure exchange model are discussed. Under certa...
Directory of Open Access Journals (Sweden)
Seokbin Lim
2012-01-01
Full Text Available Birkhoff theory exhibits an analytical steady state liner collapse model of shaped charges followed by jetting process. It also provides the fundamental idea in study of shaped charges and has widened its application in many areas, including a configuration where the detonation front strikes the entire liner surface at the same time providing the α = β (liner apex angle α, and the liner collapse point angle β condition in the literature. Upon consideration of the detonation front propagation along the lateral length of the core charge in LSCs (linear shaped charges, a further modification of the Birkhoff theory motivated by the unique geometrical condition of LSCs and the α = β condition is necessary to correctly describe the jetting behavior of LSCs which is different than that of CSCs (conical shaped charges. Based on such unique geometrical properties of LSCs, the original Birkhoff theory was modified and an analytical steady state LSCs model was built. The analytical model was then compared to the numerical simulation results created from Autodyn™ in terms of M/C ratio and apex angles in three different sized LSCs, and it exhibits favorable results in a limited range.
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
Partial differential equations an accessible route through theory and applications
Vasy, András
2015-01-01
This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the fea...
Bochicchio, M.
2009-05-01
We localize the loop equation of large-N YM theory in the anti-self-dual variables on a critical equation for an effective action by means of homological methods as opposed to the cohomological localization of equivariantly closed forms in local field theory. Our localization occurs for some special simple quasi BPS Wilson loops, that have no perimeter divergence and no cusp anomaly for backtracking cusps, in a partial Eguchi-Kawai reduction from four to two dimensions of the non-commutative theory in the limit of infinite non-commutativity and in a lattice regularization in which the anti-self-dual integration variables live at the points of the lattice, thus implying an embedding of parabolic Higgs bundles in the YM functional integral. We find that the beta function of the effective action is saturated by the non-commutative anti-self-dual vortices of the Eguchi-Kawai reduction. An exact canonical beta function of Novikov-Shifman-Vainshtein-Zakharov type, that reproduces the universal first and second perturbative coefficients follows by the localization on vortices. Finally we argue that a scheme can be found in which the canonical coupling coincides with the physical charge between static quark sources in the large-N limit and we compare our theoretical calculation with some numerical lattice result.
Mayhew, Matthew J.; Hubbard, Steven M.; Finelli, Cynthia J.; Harding, Trevor S.; Carpenter, Donald D.
2009-01-01
The purpose of this paper is to validate the use of a modified Theory of Planned Behavior (TPB) for predicting undergraduate student cheating. Specifically, we administered a survey assessing how the TPB relates to cheating along with a measure of moral reasoning (DIT- 2) to 527 undergraduate students across three institutions; and analyzed the…
Korambath, Prakashan P.; Kong, Jing; Furlani, Thomas R.; Head-Gordon, Martin
Solving the coupled-perturbed Hartree-Fock (CPHF) equations is the most time consuming part in the analytical computation of second derivatives of the molecular energy with respect to the nuclei. This paper describes a unique parallelization approach for solving the CPHF equations. The computational load is divided by the nuclear perturbations and distributed evenly among the computing nodes. The parallel algorithm is scalable with respect to the size of the molecule, i.e. the larger the molecule, the greater the parallel speedup. The memory storage requirements are also distributed among the processors, with little communication among the processors. The method is implemented in the Q-Chem software package and its performance is discussed. This work represents the first step in a research project to parallelize analytical frequency calculations at Hartree-Fock and density functional theory levels.
Energy Technology Data Exchange (ETDEWEB)
Habenschuss, Anton {Tony} [ORNL; Tsige, Mesfin [Southern Illinois University; Curro, John G. [Sandia National Laboratories (SNL); Grest, Gary S. [Sandia National Laboratories (SNL); Nath, Shyamal [CULGI Inc, Albuquerque, NM
2007-01-01
Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.
Energy Technology Data Exchange (ETDEWEB)
Habenschuss, Anton {Tony} [ORNL; Tsige, Mesfin [Southern Illinois University; Curro, John G. [Sandia National Laboratories (SNL); Grest, Gary S. [Sandia National Laboratories (SNL); Nath, Shyamal [CULGI Inc, Albuquerque, NM
2007-01-01
Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.
Positive Integer Solutions of Certain Diophantine Equations
Indian Academy of Sciences (India)
29
An important area of number theory is devoted to finding solutions of equations where the solutions are restricted to the set of integers. Diophantine equations get their name from Diophantus of. Alexandria and they are algebraic equations for which rational or integer solutions are sought. Many researchers considered the ...
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Philippos, Coutsikos; Vassilis, Harismiadis
1998-01-01
A novel method for investigating the performance of the repulsive and attractive terms of a cubic equation of state (EoS) along with different combining rules for the cross covolume (b(12)) and cross-energy (a(12)) parameters used with the van der Waals one-fluid theory is presented. The method......(c-fv) values with the experimental ones suggest that the van der Waals (vdW) repulsive term is applicable not only to mixtures with spherical molecules, as originally suggested by van der Waals, but also to very asymmetric ones. On the other hand, the attractive term leads to gamma(res) values that can...
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.
Kim, EunYoung; Cho, Inhyo; Kim, Eun Joo
2017-06-01
This study investigated the mediating effects of loneliness and depression on the relationship between adult attachment and smartphone addiction in university students. A total of 200 university students participated in this study. The data was analysed using descriptive statistics, correlation analysis, and structural equation modeling. There were significant positive relationships between attachment anxiety, loneliness, depression, and smartphone addiction. However, attachment anxiety was not significantly correlated with smartphone addiction. The results also showed that loneliness did not directly mediate between attachment anxiety and smartphone addiction. In addition, loneliness and depression serially mediated between attachment anxiety and smartphone addiction. The results suggest there are mediating effects of loneliness and depression in the relationship between attachment anxiety and smartphone addiction. The hypothesized model was found to be a suitable model for predicting smartphone addiction among university students. Future study is required to find a causal path to prevent smartphone addiction among university students. Copyright © 2017. Published by Elsevier B.V.
DEFF Research Database (Denmark)
Johannesson, Björn
2010-01-01
-Nernst-Planck equations represent a set of diffusion equations for charged species, i.e. dissolved ions. These equations are coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst-Planck equations describing the diffusion of the ionic species and the Gauss’ law in used are...... includes the constituent forms of the quasi-static version of Maxwell’s equations making it suitable for analyzes of the kind addressed in this work. Within the framework of HTM constitutive equations has been derived using the postulate of entropy inequality together with the technique of identifying...
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-04-01
Full Text Available Routinely, Einstein’s equations are be reduced to a wave form (linearly independent of the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel’s symbols. As shown herein, the origin of the problem is the use of the general covariant theory of measurement. Herein the wave form of Einstein’s equations is obtained in terms of Zelmanov’s chronometric invariants (physically observable projections on the observer’s time line and spatial section. The equations so obtained depend solely upon the second derivatives, even for gravitation, the space rotation and Christoffel’s symbols. The correct linearization proves that the Einstein equations are completely compatible with weak waves of the metric.
Theory-guided exploration with structural equation model forests.
Brandmaier, Andreas M; Prindle, John J; McArdle, John J; Lindenberger, Ulman
2016-12-01
Structural equation model (SEM) trees, a combination of SEMs and decision trees, have been proposed as a data-analytic tool for theory-guided exploration of empirical data. With respect to a hypothesized model of multivariate outcomes, such trees recursively find subgroups with similar patterns of observed data. SEM trees allow for the automatic selection of variables that predict differences across individuals in specific theoretical models, for instance, differences in latent factor profiles or developmental trajectories. However, SEM trees are unstable when small variations in the data can result in different trees. As a remedy, SEM forests, which are ensembles of SEM trees based on resamplings of the original dataset, provide increased stability. Because large forests are less suitable for visual inspection and interpretation, aggregate measures provide researchers with hints on how to improve their models: (a) variable importance is based on random permutations of the out-of-bag (OOB) samples of the individual trees and quantifies, for each variable, the average reduction of uncertainty about the model-predicted distribution; and (b) case proximity enables researchers to perform clustering and outlier detection. We provide an overview of SEM forests and illustrate their utility in the context of cross-sectional factor models of intelligence and episodic memory. We discuss benefits and limitations, and provide advice on how and when to use SEM trees and forests in future research. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
A Nonlinear Evolution Equation in an Ordered Space, Arising from Kinetic Theory
Grünfeld, C P
2005-01-01
We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The proof is based on ideas behind a well-known monotonicity method, originally developed within the existence theory of the classical Boltzmann equation in $L^1$. Our application examples concern Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions.
Ambient-temperature passive magnetic bearings: Theory and design equations
Energy Technology Data Exchange (ETDEWEB)
Post, R.F.; Ryutov, D.D.
1997-12-30
Research has been underway at the Lawrence Livermore National Laboratory to build a theoretical and experimental base for the design of ambient-temperature passive magnetic bearings for a variety of possible applications. in the approach taken the limitations imposed by Earnshaw`s theorem with respect to the stability of passive magnetic bearing systems employing axially symmetric permanent-magnet elements are overcome by employing special combinations of elements, as follows: Levitating and restoring forces are provided by combinations of permanent-magnet-excited elements chosen to provide positive stiffnesses (negative force derivatives) for selected displacements (i.e., those involving translations or angular displacement of the axis of rotation). As dictated by Eamshaw`s theorem, any bearing system thus constructed will be statically unstable for at least one of the remaining possible displacements. Stabilization against this displacement is accomplished by using periodic arrays (`Halbach arrays`) of permanent magnets to induce currents in close-packed inductively loaded circuits, thereby producing negative force derivatives stabilizing the system while in rotation. Disengaging mechanical elements stabilize the system when at rest and when below a low critical speed. The paper discusses theory and equations needed for the design of such systems.
The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems
Etingof, Pavel
2005-01-01
The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.
Nayak, B.; Menon, S. V. G.
2017-04-01
A generalized enthalpy-based equation of state, which includes thermal electron excitations and non-equilibrium thermal energies, is formulated for binary solid and porous mixtures. Our approach gives rise to an extra contribution to mixture volume, in addition to those corresponding to average mixture parameters. This excess term involves the difference of thermal enthalpies of the two components, which depend on their individual temperatures. We propose to use the Hugoniot of the components to compute non-equilibrium temperatures in the mixture. These are then compared with the average temperature obtained from the mixture Hugoniot, thereby giving an estimate of non-equilibrium effects. The Birch-Murnaghan model for the zero-temperature isotherm and a linear thermal model are then used for applying the method to several mixtures, including one porous case. Comparison with experimental data on the pressure-volume Hugoniot and shock speed versus particle speed shows good agreement.
Functional renormalisation group equations for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Synatschke-Czerwonka, Franziska
2011-01-11
This work is organised as follows: In chapter 2 the basic facts of quantum field theory are collected and the functional renormalisation group equations are derived. Chapter 3 gives a short introduction to the main concepts of supersymmetry that are used in the subsequent chapters. In chapter 4 the functional RG is employed for a study of supersymmetric quantum mechanics, a supersymmetric model which are studied intensively in the literature. A lot of results have previously been obtained with different methods and we compare these to the ones from the FRG. We investigate the N=1 Wess-Zumino model in two dimensions in chapter 5. This model shows spontaneous supersymmetry breaking and an interesting fixed-point structure. Chapter 6 deals with the three dimensional N=1 Wess-Zumino model. Here we discuss the zero temperature case as well as the behaviour at finite temperature. Moreover, this model shows spontaneous supersymmetry breaking, too. In chapter 7 the two-dimensional N=(2,2) Wess-Zumino model is investigated. For the superpotential a non-renormalisation theorem holds and thus guarantees that the model is finite. This allows for a direct comparison with results from lattice simulations. (orig.)
Modern integral equation techniques for quantum reactive scattering theory
Energy Technology Data Exchange (ETDEWEB)
Auerbach, Scott Michael [Univ. of California, Berkeley, CA (United States)
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H_{2} → H_{2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H_{2} state resolved integral cross sections σ{sub v'j',vj}(E) for the transitions (v = 0,j = 0) to (v'} = 1,j' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
Energy Technology Data Exchange (ETDEWEB)
Sakmann, Kaspar
2010-07-21
In this thesis, the physics of trapped, interacting Bose-Einstein condensates is analyzed by solving the many-body Schroedinger equation. Particular emphasis is put on coherence, fragmentation and reduced density matrices. First, the ground state of a trapped Bose-Einstein condensate and its correlation functions are obtained. Then the dynamics of a bosonic Josephson junction is investigated by solving the time-dependent many-body Schroedinger equation numerically exactly. These are the first exact results in literature in this context. It is shown that the standard approximations of the field, Gross-Pitaevskii theory and the Bose-Hubbard model fail at weak interaction strength and within their range of expected validity. For stronger interactions the dynamics becomes strongly correlated and a new equilibration phenomenon is discovered. By comparison with exact results it is shown that a symmetry of the Bose- Hubbard model between attractive and repulsive interactions must be considered an artefact of the model. A conceptual innovation of this thesis are time-dependent Wannier functions. Equations of motion for time-dependent Wannier functions are derived from the variational principle. By comparison with exact results it is shown that lattice models can be greatly improved at little computational cost by letting the Wannier functions of a lattice model become time-dependent. (orig.)
Perturbation Theory For The Landau-Lifshits-Gilbert Equation
2012-09-01
calculations for the response of a magnetic system to an external magnetic field, using the Landau-Lifshits-Gilbert ( LLG ) equation and a perturbation...convenient to first put this equation in Landau-Lifshits-Gilbert ( LLG ) form (2): if we define the torque vector 2 M H eff and a dimensionless...magnetic field in the LLG equation as follows: mM Mst (3) and h m , H Haeff (4) where 0M Hast and 0 0 0 0 0 0 N N Nz
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...
Korayem, M. H.; Shafei, A. M.
2013-02-01
The goal of this paper is to describe the application of Gibbs-Appell (G-A) formulation and the assumed modes method to the mathematical modeling of N-viscoelastic link manipulators. The paper's focus is on obtaining accurate and complete equations of motion which encompass the most related structural properties of lightweight elastic manipulators. In this study, two important damping mechanisms, namely, the structural viscoelasticity (Kelvin-Voigt) effect (as internal damping) and the viscous air effect (as external damping) have been considered. To include the effects of shear and rotational inertia, the assumption of Timoshenko beam (TB) theory (TBT) has been applied. Gravity, torsion, and longitudinal elongation effects have also been included in the formulations. To systematically derive the equations of motion and improve the computational efficiency, a recursive algorithm has been used in the modeling of the system. In this algorithm, all the mathematical operations are carried out by only 3×3 and 3×1 matrices. Finally, a computational simulation for a manipulator with two elastic links is performed in order to verify the proposed method.
Malkov, M A
1996-01-01
The asymptotic travelling wave solution of the KdV-Burgers equation driven by the long scale periodic driver is constructed. The solution represents a shock-train in which the quasi-periodic sequence of dispersive shocks or soliton chains is interspersed by smoothly varying regions. It is shown that the periodic solution which has the spatial driver period undergoes period doublings as the governing parameter changes. Two types of chaotic behavior are considered. The first type is a weak chaos, where only a small chaotic deviation from the periodic solution occurs. The second type corresponds to the developed chaos where the solution ``ignores'' the driver period and represents a random sequence of uncorrelated shocks. In the case of weak chaos the shock coordinate being repeatedly mapped over the driver period moves on a chaotic attractor, while in the case of developed chaos it moves on a repellor. Both solutions depend on a parameter indicating the reference shock position in the shock-train. The structure...
Chen, Haiwen; Holland, Paul
2009-01-01
In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Quantum theory from a nonlinear perspective Riccati equations in fundamental physics
Schuch, Dieter
2018-01-01
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...
Myeong, Jeon-Ok; Crawley, Frank E.
The theory of reasoned action (Ajzen & Fishbein, 1980; Fishbein & Ajzen, 1975) was used to predict and understand Korean high school students' track choice for college entrance. First-year high school students (N = 665) from four representative regions of Korea participated in the study. The survey instruments were questionnaires developed according to the guidelines of the TRA. The target behavior of interest in this study was Korean students' choice of the science track when they completed the track application forms during the first year of high school. Predictors included TRA model and external variables. Multiple regression and the structural equation modeling with LISREL (Jöreskog & Sörbom, 1986) were used to analyze the data. The TRA was found to be applicable for understanding and predicting track choice, with minor modifications. Subjective norm was found to exert a direct influence on personal beliefs and the target behavior.
Parriault, Marie-Claire; Van Melle, Astrid; Basurko, Célia; Adriouch, Leila; Rogier, Stéphanie; Couppié, Pierre; Nacher, Mathieu
2016-12-01
French Guiana is the French overseas territory that is most affected by HIV. Sex work seems to be an important driver of the epidemic. Although female sex workers are informed by local NGOs, they still have risky behaviours, including not using condoms with their intimate partner despite knowing HIV is highly prevalent. The objective of this study was to find intervention targets on this specific behaviour. For this, a structural equation model (SEM) was built using assumptions from behavioural theories. Behaviour theories attempt to connect research and practice. Within the health belief model framework, perceived threats, perceived benefits, and self-perceived efficacy were tested. Vulnerability was added because of the particular context of French Guiana. The results highlight that female sex workers' perceived self-efficacy was central in condom use with the intimate partner (with a significant correlation coefficient of 0.52 in the SEM). The perceived self-efficacy was strongly influenced by sociodemographic factors, particularly by nationality. Female sex workers from Brazil seemed to be more comfortable about asking their intimate partner to use condoms (OR: 7.81; CI: 1.87-32.63) than sex workers of other nationalities. These results emphasize that prevention interventions for female sex workers should emphasize their empowerment.
Tod, Paul
2013-01-01
I review the equations of Conformal Cyclic Cosmology given by Penrose. I suggest a slight modification to Penrose's prescription and show how this works out for FRW cosmologies and for Class A Bianchi cosmologies.
Skrdla, Peter J
2006-10-12
In recent works, the author has shown the utility of new, semiempirical kinetic model equations for treating dispersive chemical processes ranging from slow (minute/hour time scale) solid-state phase transformations to ultrafast (femtosecond) reactions in the gas phase. These two fundamental models (one for homogeneous/deceleratory sigmoidal conversion kinetics and the other for heterogeneous/acceleratory sigmoidal kinetics; isothermal conditions), based on the assumption of a "Maxwell-Boltzmann-like" distribution of molecular activation energies, provide a novel, quantum-based interpretation of the kinetics. As an extension to previous work, it is shown here that the derivation of these dispersive kinetic equations is supported by classical collision theory (i.e., for gas-phase applications). Furthermore, the successful application of the approach to the kinetic modeling of the solid-state decomposition of a binary system, CO2.C2H2, is demonstrated. Finally, the models derived appear to explain some of the (solid-state) kinetic data collected using isoconversional techniques such as those often reported in the thermal analysis literature.
Partial differential equations of parabolic type
Friedman, Avner
2008-01-01
This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman - Director of the Mathematical Biosciences Institute at The Ohio State University - offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning fundamenta
Th\\'eorie $L^p$ pour l'\\'equation de Cauchy-Riemann
Laurent-Thiébaut, Christine
2013-01-01
In this paper we propose a systematic study of the Cauchy-Riemann operator in the $L^p$-setting in complex manifolds. We first consider $L^p_{loc}$-theory and then we develop an $L^p$ Andreotti-Grauert theory. Finally we consider Serre duality and its applications to the solvability of the Cauchy-Riemann equation with exact support in $L^p$-spaces.
DEFF Research Database (Denmark)
Wæver, Ole
2009-01-01
Kenneth N. Waltz's 1979 book, Theory of International Politics, is the most influential in the history of the discipline. It worked its effects to a large extent through raising the bar for what counted as theoretical work, in effect reshaping not only realism but rivals like liberalism and refle......Kenneth N. Waltz's 1979 book, Theory of International Politics, is the most influential in the history of the discipline. It worked its effects to a large extent through raising the bar for what counted as theoretical work, in effect reshaping not only realism but rivals like liberalism...... and reflectivism. Yet, ironically, there has been little attention to Waltz's very explicit and original arguments about the nature of theory. This article explores and explicates Waltz's theory of theory. Central attention is paid to his definition of theory as ‘a picture, mentally formed' and to the radical anti......-empiricism and anti-positivism of his position. Followers and critics alike have treated Waltzian neorealism as if it was at bottom a formal proposition about cause-effect relations. The extreme case of Waltz being so victorious in the discipline, and yet being consistently mis-interpreted on the question of theory...
Dirac Equation in Gauge and Affine-Metric Gravitation Theories
Giachetta, G.; Sardanashvily, G.
1995-01-01
We show that the covariant derivative of Dirac fermion fields in the presence of a general linear connection on a world manifold is universal for Einstein's, gauge and affine-metric gravitation theories.
Energy Technology Data Exchange (ETDEWEB)
Epple, Mark Dominik
2008-12-03
time, which produces a lineary rising static quark potential. We also obtain a running coupling which shows the correct infrared fixpoint with very high precision. Further numerical studies were made for the fully coupled system without horizon condition. We confirm the analytically predicted result that the system cannot be solved using the horizon condition. But it is a noval result that we can obtain solutions which show for a certain range (but not for arbitrarily large distances) a linearly rising static quark potential. In the last large part of this work we use the newly obtained results to calculate the 't Hoof loop which is a (dis-)order parameter of the confinement phase transition of Yang-Mills theory. We examine analytically and compute numerically a continuum representation for the 't Hooft loop operator that has been given recently. We can show that the 't Hooft loop shows a perimeter law and thus indicates confinement if the relevant renormalization parameter is set to the value representing the minimal vacuum energy. Thus we further reduce the number of renormalization parameters in the Dyson-Schwinger-equations by one. (orig.)
Problems in Hydrodynamics and Partial Differential Equations.
CALCULUS OF VARIATIONS, RESEARCH MANAGEMENT ), NONLINEAR DIFFERENTIAL EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, EQUATIONS, INEQUALITIES, MEASURE THEORY , INTEGRALS, ABSTRACTS
Existence theory for nonlinear volterra integral and differential equations
Directory of Open Access Journals (Sweden)
Sikorska Aneta
2001-01-01
Full Text Available In this paper we prove the existence theorems for the integrodifferential equation where in first part are functions with values in a Banach space and the integral is taken in the sense of Bochner. In second part are weakly–weakly sequentially continuous functions and the integral is the Pettis integral. Additionaly, the functions and satisfy some boundary conditions and conditions expressed in terms of measure of noncompactness or measure of weak noncompactness.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Slavchov, Radomir I
2014-04-28
If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient γ± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally γ±. Comparison with experimental data for γ± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ≈ 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
The solution of the generalized Kepler's equation
López, Rosario; Hautesserres, Denis; San-Juan, Juan Félix
2018-01-01
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produced. During the evaluation of the theory, it is necessary to solve a generalization of the classical Kepler's equation. In this work, the application of a numerical technique and three initial guesses to the generalized Kepler's equation are discussed.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Cheng, Lan; Wang, Fan; Stanton, John F.; Gauss, Jürgen
2018-01-01
A scheme is reported for the perturbative calculation of spin-orbit coupling (SOC) within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e) in combination with the equation-of-motion coupled-cluster singles and doubles method. Benchmark calculations of the spin-orbit splittings in 2Π and 2P radicals show that the accurate inclusion of scalar-relativistic effects using the SFX2C-1e scheme extends the applicability of the perturbative treatment of SOC to molecules that contain heavy elements. The contributions from relaxation of the coupled-cluster amplitudes are shown to be relatively small; significant contributions from correlating the inner-core orbitals are observed in calculations involving third-row and heavier elements. The calculation of term energies for the low-lying electronic states of the PtH radical, which serves to exemplify heavy transition-metal containing systems, further demonstrates the quality that can be achieved with the pragmatic approach presented here.
String, dilaton and divisor equation in symplectic field theory
Fabert, O.; Rossi, P.
2011-01-01
Infinite-dimensional Hamiltonian systems appear naturally in the rich algebraic structure of symplectic field theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an infinite number of symmetries of such systems. As in Gromov-Witten
Directory of Open Access Journals (Sweden)
EunYoung Kim, PhD
2017-06-01
Conclusion: The results suggest there are mediating effects of loneliness and depression in the relationship between attachment anxiety and smartphone addiction. The hypothesized model was found to be a suitable model for predicting smartphone addiction among university students. Future study is required to find a causal path to prevent smartphone addiction among university students.
Tempered fractional Feynman-Kac equation: Theory and examples.
Wu, Xiaochao; Deng, Weihua; Barkai, Eli
2016-03-01
Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.
Stability by fixed point theory for functional differential equations
Burton, T A
2006-01-01
This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicia
Differential equations with Matlab exploration, applications, and theory
McKibben, Mark
2014-01-01
ORDINARY DIFFERENTIAL EQUATIONS Welcome! Introduction This Book Is a Field Guide. What Does That Mean for YOU? Mired in Jargon - A Quick Language Lesson! Introducing MATLAB A First Look at Some Elementary Mathematical Models A Basic Analysis Toolbox Some Basic Mathematical Shorthand Set Algebra Functions The Space (R; j_j) A Closer Look at Sequences in (R; j_j) The Spaces (RN; k_kRN ) and (MN(R); k_kMN(R)Calculus of RN-valued and MN(R)-valued FunctionsSome Elementary ODEs Looking Ahead A First Wave of Mathematical Models Newton's Law of Heating and Cooling-Revisited Pharmocokinetics Uniform Mi
Jagau, Thomas-C
2018-01-14
The impact of residual electron correlation beyond the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) approximation on positions and widths of electronic resonances is investigated. To establish a method that accomplishes this task in an economical manner, several approaches proposed for the approximate treatment of triple excitations are reviewed with respect to their performance in the electron attachment (EA) variant of EOM-CC theory. The recently introduced EOM-CCSD(T)(a)* method [D. A. Matthews and J. F. Stanton, J. Chem. Phys. 145, 124102 (2016)], which includes non-iterative corrections to the reference and the target states, reliably reproduces vertical attachment energies from EOM-EA-CC calculations with single, double, and full triple excitations in contrast to schemes in which non-iterative corrections are applied only to the target states. Applications of EOM-EA-CCSD(T)(a)* augmented by a complex absorbing potential (CAP) to several temporary anions illustrate that shape resonances are well described by EOM-EA-CCSD, but that residual electron correlation often makes a non-negligible impact on their positions and widths. The positions of Feshbach resonances, on the other hand, are significantly improved when going from CAP-EOM-EA-CCSD to CAP-EOM-EA-CCSD(T)(a)*, but the correct energetic order of the relevant electronic states is still not achieved.
Electromagnetic theory and the foundations of electric circuit theory
National Research Council Canada - National Science Library
Carson, John R
1927-01-01
.... The present paper examines the foundation of electric circuit theory from the standpoint of the fundamental equations of electromagnetic theory and a derivation of the former from the latter is made...
SITU, Rong
2005-01-01
Derivation of Ito's formulas, Girsanov's theorems and martingale representation theorem for stochastic DEs with jumpsApplications to population controlReflecting stochastic DE techniqueApplications to the stock market. (Backward stochastic DE approach)Derivation of Black-Scholes formula for market with and without jumpsNon-linear filtering problems with jumps.
Luse, Andy; Rursch, Julie A.; Jacobson, Doug
2014-01-01
In the United States, the number of students entering into and completing degrees in science, technology, engineering, and mathematics (STEM) areas has declined significantly over the past decade. Although modest increases have been shown in enrollments in computer-related majors in the past 4 years, the prediction is that even in 3 to 4 years…
2014-11-19
The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation Maday, Y.a,b,c,e, Mula...interpolant (the Lebesgue constant) by relating it to an inf-sup problem in the case of Hilbert spaces . In the second part of the paper, it will be explained...SUBTITLE The Generalized Empirical Interpolation Method: stability theory on Hilbert spaces with an application to the Stokes equation 5a. CONTRACT
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Giraldi, Filippo [School of Chemistry and Physics, University of KwaZulu-Natal and National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, Westville Campus, Durban 4000, South Africa and Gruppo Nazionale per la Fisica Matematica (GNFM-INdAM), c/o Istituto Nazionale di Alta Matematica Francesco Severi, Città Universitaria, Piazza Aldo Moro 5, 00185 Roma (Italy)
2015-09-15
The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green’s function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.
Directory of Open Access Journals (Sweden)
Aqlan Mohammed H.
2016-01-01
Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_D f(V), where f(v)=Av+g(v) for a random function g(v)=o(v) a.s. as v tends to infinity. Specifically, we provide an explicit characterization of the pair (C,r) in the tail...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...
Brigham, Stephen Scott
2010-01-01
This dissertation concerns factors that influence accounting professors' formal enforcement of academic misconduct rules using the theory of planned behavior ("TPB") as a theoretical framework. The theory posits that intentional behavior, such as enforcement, can be predicted by peoples' perceived behavioral control and…
Liao, David; Tlsty, Thea D
2014-08-06
Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities.
BISON Theory Manual The Equations behind Nuclear Fuel Analysis
Energy Technology Data Exchange (ETDEWEB)
Hales, J. D. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Williamson, R. L. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Novascone, S. R. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Pastore, G. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, B. W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Stafford, D. S. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gamble, K. A. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Perez, D. M. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Liu, W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-09-01
BISON is a finite element-based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO particle fuel, and metallic rod and plate fuel. It solves the fully-coupled equations of thermomechanics and species diffusion, for either 2D axisymmetric or 3D geometries. Fuel models are included to describe temperature and burnup dependent thermal properties, fission product swelling, densification, thermal and irradiation creep, fracture, and fission gas production and release. Plasticity, irradiation growth, and thermal and irradiation creep models are implemented for clad materials. Models are also available to simulate gap heat transfer, mechanical contact, and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition. BISON is based on the MOOSE framework and can therefore efficiently solve problems using standard workstations or very large high-performance computers. This document describes the theoretical and numerical foundations of BISON.
Energy Technology Data Exchange (ETDEWEB)
Miyazaki, Kunimasa; Reichman, David R [Department of Chemistry, Columbia University, 3000 Broadway, New York, NY 10027 (United States)
2005-05-20
In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field-theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove that the derived equations are consistent with the fluctuation-dissipation theorem. We also discuss the generalization of the result given here to real fluids, and the possible description of supercooled fluids in the ageing regime. We demonstrate that the standard idealized mode-coupling theory is not consistent with the FDT in a strict field-theoretic sense. (letter to the editor)
Almost periodic solutions of impulsive differential equations
Stamov, Gani T
2012-01-01
Impulsive differential equations are suitable for the mathematical simulation of evolutionary processes in which the parameters undergo relatively long periods of smooth variation followed by short-term rapid changes (that is, jumps) in their values. Processes of this type are often investigated in various fields of science and technology. The question of the existence and uniqueness of almost periodic solutions of differential equations is an age-old problem of great importance. The qualitative theory of impulsive differential equations is currently undergoing rapid development in relation to the investigation of various processes which are subject to impacts during their evolution, and many findings on the existence and uniqueness of almost periodic solutions of these equations are being made. This book systematically presents findings related to almost periodic solutions of impulsive differential equations and illustrates their potential applications.
Energy Technology Data Exchange (ETDEWEB)
Agassi, D.; Ko, C.M.; Weidenmueller, H.A.
1977-09-06
A random-matrix model is used to describe the transformation of kinetic energy of relative motion into intrinsic excitation energy typical of a deeply inelastic heavy-ion collision. The random-matrix model is based upon statistical assumptions regarding the form factors coupling relative motion with intrinsic excitation of either fragment. Average cross sections are calculated by means of an ensemble average over the random matrix model. Summations over intermediate and final intrinsic spin values are performed. As a result, average cross sections are given by the asymptotic behavior of a probability density which in turn obeys a transport equation. In the transport equation there is no further reference to intrinsic spins. The physical and mathematical properties of this equation are exhibited.
The quantum Fokker-Planck equation of stochastic inflation
Collins, Hael; Holman, Richard; Vardanyan, Tereza
2017-11-01
We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Equation of state for fullerite C60
Rekhviashvili, S. Sh.
2017-04-01
A new equation of state for fullerite C60 is derived in the framework of the quantum-statistical method. This equation includes two Grüneisen parameters responsible for vibration-rotational and intramolecular contributions of fullerene molecules, which are represented in the form of isotropic quantum oscillators. The intramolecular vibrations of carbon atoms are described by the Debye heat capacity theory, and the cold contribution to the free energy is calculated using the Lennard-Jones pair potential for fullerene molecules. The theory is in a very good agreement with the experiment.
Solutions of the coupled Higgs field equations
Talukdar, Benoy; Ghosh, Swapan K.; Saha, Aparna; Pal, Debabrata
2013-07-01
By an appropriate choice for the phase of the complex nucleonic field and going over to the traveling coordinate, we reduce the coupled Higgs equations to the Hamiltonian form and treat the resulting equation using the dynamical system theory. We present a phase-space analysis of its stable points. The results of our study demonstrate that the equation can support both traveling- and standing-wave solutions. The traveling-wave solution appears in the form of a soliton and resides in the midst of doubly periodic standing-wave solutions.
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
The solids-flux theory--confirmation and extension by using partial differential equations.
Diehl, Stefan
2008-12-01
The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.
Holzer, Christof; Klopper, Wim
2017-11-01
A method for calculating intermolecular induction and dispersion energies based on a GW description of the monomers and employing response functions from the Bethe-Salpeter equation is proposed. Calculations on a test set of 10 weakly bound complexes with GW-based symmetry-adapted perturbation theory (GW-SAPT) show an improved performance in comparison with symmetry-adapted perturbation theory based on density-functional theory (DFT-SAPT).
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Galois theory and algorithms for linear differential equations
Put, Marius van der
2005-01-01
This paper is an informal introduction to differential Galois theory. It surveys recent work on differential Galois groups, related algorithms and some applications. (c) 2005 Elsevier Ltd. All rights reserved.
Lie point symmetries of differential-difference equations
Energy Technology Data Exchange (ETDEWEB)
Levi, D [Dipartimento di Ingegneria Elettronica, Universita degli Studi Roma Tre and Sezione INFN, Roma Tre, Via della Vasca Navale 84, 00146 Roma (Italy); Winternitz, P [Centre de recherches mathematiques et, Departement de mathematiques et statistique, Universite de Montreal, C.P. 6128, succ. Centre-ville, H3C 3J7, Montreal, Quebec (Canada); Yamilov, R I, E-mail: levi@roma3.infn.i, E-mail: wintern@crm.umontreal.c, E-mail: RvlYamilov@matem.anrb.r [Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008 (Russian Federation)
2010-07-23
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non-transforming lattices, i.e. equations involving both continuous and discrete-independent variables. The symmetries of a specific integrable discretization of the Krichever-Novikov equation, the Toda lattice and Toda field theory are presented as examples of the general method. (fast track communication)
Canonical structure of evolution equations with non-linear ...
Indian Academy of Sciences (India)
Conditions are derived under which one could construct similar equations which admit a Lagrangian representation. It is shown that the system of equations thus obtained can be Hamiltonized by making use of the Dirac's theory of constraints. The speciﬁc results presented refer to the third- and ﬁfth-order equations of the ...
PyR@TE. Renormalization group equations for general gauge theories
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Partial differential equations and calculus of variations
Leis, Rolf
1988-01-01
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Anisotropic stars obeying Chaplygin equation of state
Indian Academy of Sciences (India)
P Bhar
2017-12-14
Dec 14, 2017 ... change rendering the dark energy star to a wormhole. An interesting proposal regarding dark energy and dark matter is treating them as different manifestations of a single entity. This proposal leads to the Chaplygin gas model in which the equation of state derives from string theory. Various applications of ...
Exact solution of the neutron transport equation in spherical geometry
Energy Technology Data Exchange (ETDEWEB)
Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters
2017-03-15
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.
Analyticity of solutions of singular fractional differential equations
Kangro, Urve
2016-06-01
We study singular fractional differential equations in spaces of analytic functions. We reformulate the equation as a cordial Volterra integral equation of the second kind and use results from the theory of cordial Volterra integral equations. This enables us to obtain conditions under which the equation has a unique analytic solution. Note that the smooth solution in this case is unique without any initial conditions; in fact, giving initial conditions usually results in nonsmooth solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.
Qualitative properties of functional differential equation
Directory of Open Access Journals (Sweden)
Diana Otrocol
2014-10-01
Full Text Available The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence of the fixed point theory for a functional differential equation with an abstract Volterra operator. In the end an application is given.
Kuang, Zhen-Bang
2014-01-01
Theory of Electroelasticity analyzes the stress, strain, electric field and electric displacement in electroelastic structures such as sensors, actuators and other smart materials and structures. This book also describes new theories such as the physical variational principle and the inertial entropy theory. It differs from the traditional method by using the physical variational principle to derive the governing equations of the piezoelectric material, whereas the Maxwell stress is obtained automatically. By using the inertial entropy theory, the temperature wave equation is obtained very easily. The book is intended for scientists, researchers and engineers in the areas of mechanics, physics, smart material and control engineering as well as mechanical, aeronautical and civil engineering, etc. Zhen-Bang Kuang is a professor at Shanghai Jiao Tong University.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Chekhov, Leonid [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom); Eynard, Bertrand [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Ribault, Sylvain [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5 (France)
2013-02-15
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
Communication: An exact bound on the bridge function in integral equation theories
Kast, Stefan M.; Tomazic, Daniel
2012-11-01
We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.
Communication: An exact bound on the bridge function in integral equation theories.
Kast, Stefan M; Tomazic, Daniel
2012-11-07
We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.
Electronic representation of wave equation
Energy Technology Data Exchange (ETDEWEB)
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Xu, Peiliang
2016-01-01
The numerical integration method has been routinely used to produce global standard gravitational models from satellite tracking measurements of CHAMP/GRACE types. It is implemented by solving the differential equations of the partial derivatives of a satellite orbit with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical point of view, satellite gravimetry from satellite tracking is the problem of estimating unknown parameters in t...
Banach, S
1987-01-01
This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.
Pfalzgraff, William C; Kelly, Aaron; Markland, Thomas E
2015-12-03
The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.
Georgiev, Svetlin G
2015-01-01
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
A scattering theory for the wave equation on Kerr black hole exteriors
Dafermos, Mihalis; Shlapentokh-Rothman, Yakov
2014-01-01
We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|
The equation of motion of an electron
Energy Technology Data Exchange (ETDEWEB)
Kim, K. [Argonne National Laboratory, Argonne, Illinois 60439 and The University of Chicago, Chicago, Illinois 60637 (United States); Sessler, A.M. [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
1999-07-01
We review the current status of understanding of the equation of motion of an electron. Classically, a consistent, linearized theory exists for an electron of finite extent, as long as the size of the electron is larger than the classical electron radius. Nonrelativistic quantum mechanics seems to offer a fine theory even in the point particle limit. Although there is as yet no convincing calculation, it is probable that a quantum electrodynamical result will be at least as well-behaved as is the nonrelativistic quantum mechanical results. {copyright} {ital 1999 American Institute of Physics.}
Malheiro, Carine; Mendiboure, Bruno; Plantier, Frédéric; Blas, Felipe J.; Miqueu, Christelle
2014-04-01
As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the "CG" approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the "FMT" extension version gives a good representation solely at low pressures. Hence, the "CG" version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.
Energy Technology Data Exchange (ETDEWEB)
Malheiro, Carine; Mendiboure, Bruno; Plantier, Frédéric; Miqueu, Christelle [Université Pau et Pays Adour, CNRS, TOTAL - UMR 5150 – LFC-R – Laboratoire des Fluides Complexes et leurs Réservoirs, BP 1155 – PAU, F-64013 (France); Blas, Felipe J. [Departamento de Física Aplicada, and Centro de Física Teórica y Matemática FIMAT, Universidad de Huelva, 21071 Huelva (Spain)
2014-04-07
As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the “CG” approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the “FMT” extension version gives a good representation solely at low pressures. Hence, the “CG” version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.
Theory of gravitational interactions
Gasperini, Maurizio
2013-01-01
This reference textbook is an up-to-date and self-contained introduction to the theory of gravitational interactions. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field. A second, advanced part then discusses the deep analogies (and differences) between a geometric theory of gravity and the gauge theories of the other fundamental interactions. This fills a gap which is present in the context of the traditional approach to general relativity, and which usually makes students puzzled about the role of gravity. The necessary notions of differential geometry are reduced to the minimum, leaving more room for those aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational interactions of spinors, and the supersymmetric and higher-dimensional generalization of the Einstein equations. Theory of Gravitational Interactions will be o...
Handbook of differential equations evolutionary equations
Dafermos, CM
2008-01-01
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Advancing towards constitutive equations for the metal industry via the LEDS theory
Kuhlmann-Wilsdorf, Doris
2004-02-01
A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. They are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. While plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newton’s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.
Graphical Solution of Polynomial Equations
Grishin, Anatole
2009-01-01
Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…
Jozsa, Richard
2003-08-01
Pell's equation is x2- dy2=1, where d is a square-free integer and we seek positive integer solutions x, y>0. Let ( x0, y0) be the smallest solution (i.e., having smallest A=x 0+y 0d). Lagrange showed that every solution can easily be constructed from A so given d it suffices to compute A. It is known that A can be exponentially large in d so just to write down A we need exponential time in the input size log d . Hence we introduce the regulator R=ln A and ask for the value of R to n decimal places. The best known classical algorithm has sub-exponential running time O( explog d , poly(n)) . Hallgren's quantum algorithm gives the result in polynomial time O( poly( log d), poly(n)) with probability 1/ poly( log d) . The idea of the algorithm falls into two parts: using the formalism of algebraic number theory we convert the problem of solving Pell's equation into the problem of determining R as the period of a function on the real numbers. Then we generalise the quantum Fourier transform period finding algorithm to work in this situation of an irrational period on the (not finitely generated) abelian group of real numbers. This paper is intended to be accessible to a reader having no prior acquaintance with algebraic number theory; we give a self-contained account of all the necessary concepts and we give elementary proofs of all the results needed. Then we go on to describe Hallgren's generalisation of the quantum period finding algorithm, which provides the efficient computational solution of Pell's equation in the above sense.
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
Evolution equations of von Karman type
Cherrier, Pascal
2015-01-01
In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail. The interested reader will gain a ...
New Numerical Solution of von Karman Equation of Lengthwise Rolling
Rudolf Pernis; Tibor Kvackaj
2015-01-01
The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rol...
Taming the nonlinearity of the Einstein equation.
Harte, Abraham I
2014-12-31
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.
The theory of electromagnetism
Jones, D S
1964-01-01
The Theory of the Electomagnetism covers the behavior of electromagnetic fields and those parts of applied mathematics necessary to discover this behavior. This book is composed of 11 chapters that emphasize the Maxwell's equations. The first chapter is concerned with the general properties of solutions of Maxwell's equations in matter, which has certain macroscopic properties. The succeeding chapters consider specific problems in electromagnetism, including the determination of the field produced by a variable charge, first in isolation and then in the surface distributions of an antenna. The
Bommier, Véronique
2017-11-01
Context. In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). Aims: This paper provides theoretical expressions of the redistribution function for the two-term atom. This redistribution function includes both coherent (RII) and incoherent (RIII) scattering contributions with their branching ratios. Methods: The expressions were derived by applying the formalism outlined above. The statistical equilibrium equation for the atomic density matrix is first formally solved in the case of the two-term atom with unpolarized and infinitely sharp lower levels. Then the redistribution function is derived by substituting this solution for the expression of the emissivity. Results: Expressions are provided for both magnetic and non-magnetic cases. Atomic fine structure is taken into account. Expressions are also separately provided under zero and non-zero hyperfine structure. Conclusions: Redistribution functions are widely used in radiative transfer codes. In our formulation, collisional transitions between Zeeman sublevels within an atomic level (depolarizing collisions effect) are taken into account when possible (I.e., in the non-magnetic case). However, the need for a formal solution of the statistical equilibrium as a preliminary step prevents us from taking into account collisional transfers between the levels of the upper term. Accounting for these collisional transfers could be done via a numerical solution of the statistical equilibrium equation system.
Analysis of solutions of a nonlinear scalar field differential equation
Muhamadiev, E. M.; Naimov, A. N.
2017-10-01
We consider a nonlinear differential equation arising in mathematical models of elementary particle theory. For this equation, we examine questions of the extendability of solutions, the boundedness of solutions at infinity, and the search for new conditions for the existence of a positive particle-like solution.
Review of chiral perturbation theory
Indian Academy of Sciences (India)
the CLEO Collaboration. Other sources could be the decay τ →ππν. In the modern context, a fresh Roy equation analysis with the view of combining dis- persion relations with chiral perturbation theory has been carried out [20]. The evaluation of the inhomogeneous terms, the so-called 'driving terms' for the Roy equations ...
The first-order Euler-Lagrange equations and some of their uses
Energy Technology Data Exchange (ETDEWEB)
Adam, C.; Santamaria, F. [Departamento de Física de Partículas and Instituto Galego de Física de Altas Enerxias (IGFAE),Campus Vida, E-15782 Santiago de Compostela (Spain)
2016-12-13
In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise, further develop and apply one particular method for the order reduction of nonlinear field equations which, despite its systematic and versatile character, is not widely known.
Magnus, Wilhelm
1979-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Observability of discretized partial differential equations
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
The Quest for Equational Axiomatizations of Parallel Composition
DEFF Research Database (Denmark)
Aceto, Luca; Fokkink, Wan
2005-01-01
This essay recounts the story of the quest for equational axiomatizations of parallel composition operators in process description languages, and of similar results in the classic field of formal language theory. Some of the outstanding open problems are also mentioned......This essay recounts the story of the quest for equational axiomatizations of parallel composition operators in process description languages, and of similar results in the classic field of formal language theory. Some of the outstanding open problems are also mentioned...
Energy Technology Data Exchange (ETDEWEB)
Nanda, Kaushik D.; Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)
2015-02-14
The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.
Nanda, Kaushik D; Krylov, Anna I
2015-02-14
The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Sierpinski, Waclaw
1988-01-01
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of
On two functional equations originating from number theory
Indian Academy of Sciences (India)
Author Affiliations. Jaeyoung Chung1 Jeongwook Chang2. Department of Mathematics, Kunsan National University, Kunsan, 573-701, Korea; Department of Mathematics Education, Dankook University, Yongin 448-701, Korea ...
Stability analysis of a class of fractional delay differential equations
Indian Academy of Sciences (India)
[14] A A Kilbas, H M Srivastava and J J Trujillo, Theory and applications of fractional differential equations (Elsevier, Amsterdam, 2006). [15] R L Magin, Fractional calculus in bioengineering (Begll House Publishers, USA, 2006). [16] H Smith, An introduction to delay differential equations with applications to the life sciences.
Mu, Weihua; Li, Xiaoqing; Ou-Yang, Zhongcan
2010-01-01
The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reflect complex chemical reaction systems. ...
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
The use of Structural Equation Modelling (SEM) in Capital Structure ...
African Journals Online (AJOL)
analytic structural equation modelling (SEM) methodology. ... Consistent with the dominant theory, the findings of this study are that non-debt tax shields, business risk and probability of bankruptcy are negatively related to gearing, while tangibility, ...
Rayka, Milad; Goli, Mohammad; Shahbazian, Shant
2018-02-07
An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
Wentzel, Gregor
2003-01-01
A prominent figure in twentieth-century physics, Gregor Wentzel made major contributions to the development of quantum field theory, first in Europe and later at the University of Chicago. His Quantum Theory of Fields offers a knowledgeable view of the original literature of elementary quantum mechanics and helps make these works accessible to interested readers.An introductory volume rather than an all-inclusive account, the text opens with an examination of general principles, without specification of the field equations of the Lagrange function. The following chapters deal with particular
DEFF Research Database (Denmark)
Ferreira, Luisa; Breil, Martin Peter; Pinho, S. P.
2009-01-01
in water, but the correlation for the solubility in pure alcohols was not so satisfactory. The solubility in mixed solvents (ternary systems) was predicted on the basis of the modeling of the solubility in pure solvents, without any additional fitting of the parameters, and the results achieved were......The perturbed-chain statistical associated fluid theory EoS was applied to model the solubilities of glycine, DL-alanine, L-serine, L-threonine, and L-isoleucine in pure water, pure alcohols (ethanol, I-propanol, and 2-propanol) and in mixed solvent systems. Three pure component nonassociating...... parameters for the amino acids were fitted to the densities, activity and osmotic coefficients, vapor pressures, and water activity of their aqueous solutions. The solubilities of amino acids in pure and mixed solvent systems were calculated on the basis of the phase equilibrium conditions for a pure solid...
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Approximative solutions of difference equations
Directory of Open Access Journals (Sweden)
Janusz Migda
2014-03-01
\\Delta^m x_n=a_nf(n,x_{\\sigma(n}+b_n $$ are studied. Using the iterated remainder operator and fixed point theorems we obtain sufficient conditions under which for any solution $y$ of the equation $\\Delta^my=b$ and for any real $s\\leq 0$ there exists a solution $x$ of the above equation such that $\\Delta^kx=\\Delta^ky+\\mathrm{o}(n^{s-k}$ for any nonnegative integer $k\\leq m$. Using a discrete variant of the Bihari lemma and a certain new technique we give also sufficient conditions under which for a given real $s\\leq m-1$ all solutions $x$ of the equation satisfy the condition $x=y+\\mathrm{o}(n^s$ where $y$ is a solution of the equation $\\Delta^my=b$. Moreover, we give sufficient conditions under which for a given natural $k
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Tiec, Alexandre Le
2016-01-01
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein's equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein's quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds a...
Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations
Directory of Open Access Journals (Sweden)
Michael Gil'
2016-01-01
Full Text Available We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.
Poincar wave equations as Fourier transformations of Galilei wave equations
Gomis Torné, Joaquim; Poch Parés, Agustí; Pons Ràfols, Josep Maria
1980-01-01
The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.
LeVeque, William J
1996-01-01
This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha
Differential geometry techniques for sets of nonlinear partial differential equations
Estabrook, Frank B.
1990-01-01
An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.
A modular theory of learning and performance
National Research Council Canada - National Science Library
Guilhardi, Paulo; Yi, Linlin; Church, Russell M
2007-01-01
...). This modular theory is a development of packet theory (Kirkpatrick, 2002; Kirkpatrick & Church, 2003) that adds a distinction between pattern and strength memories, as well as contributing closed-form equations...
Energy Technology Data Exchange (ETDEWEB)
Múnera, Héctor A., E-mail: hmunera@hotmail.com [Centro Internacional de Física (CIF), Apartado Aéreo 4948, Bogotá, Colombia, South America (Colombia); Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America (Colombia)
2016-07-07
It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.
Lyapunov functionals and stability of stochastic functional differential equations
Shaikhet, Leonid
2013-01-01
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for discrete- and continuous-time difference equations. The text begins with a description of the peculiarities of deterministic and stochastic functional differential equations. There follow basic definitions for stability theory of stochastic hereditary systems, and a formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of di...
Mrugalla, Florian; Kast, Stefan M
2016-09-01
Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute-solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute-solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Evolution of basic equations for nearshore wave field
ISOBE, Masahiko
2013-01-01
In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680
A Complete Equation of State for Astrophysical Simulations
Shen, H.
2015-11-01
We construct a complete equation of state (EOS) covering a wide range oftemperature, proton fraction, and baryon density for the use of astrophysical simulations. We employ the relativistic mean-field (RMF) theory to describe nuclear interactions, and adopt the Thomas-Fermi approximation to describe thenonuniform nuclear matter. The uniform matter and nonuniform matter are studied consistently using the same RMF theory.
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Solutions of equations in languages
Hesselink, Wim H.
A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar
Towards a Theory Grounded Theory of Language
Prince, Christopher G.; Mislivec, Eric J.; Kosolapov, Oleksandr V.; Lykken, Troy R.
2002-01-01
In this paper, we build upon the idea of theory grounding and propose one specific form of theory grounding, a theory of language. Theory grounding is the idea that we can imbue our embodied artificially intelligent systems with theories by modeling the way humans, and specifically young children, develop skills with theories. Modeling theory development promises to increase the conceptual and behavioral flexibility of these systems. An example of theory development in children is the social ...
Rajdeep Grewal; Joseph A. Cote; Hans Baumgartner
2004-01-01
The literature on structural equation models is unclear on whether and when multicollinearity may pose problems in theory testing (Type II errors). Two Monte Carlo simulation experiments show that multicollinearity can cause problems under certain conditions, specifically: (1) when multicollinearity is extreme, Type II error rates are generally unacceptably high (over 80%), (2) when multicollinearity is between 0.6 and 0.8, Type II error rates can be substantial (greater than 50% and frequent...
On Reducing a System of Equations to a Single Equation
DEFF Research Database (Denmark)
Frandsen, G.S.; Shparlinski, I.E.
2004-01-01
For a system of polynomial equations over Q;p; we present an efficient construction of a single polynomial of quite small degree whose zero set over Q;p; coincides with the zero set over Q;p; of the original system. We also show that the polynomial has some other attractive features such as low...
Principles and practice of structural equation modeling
Kline, Rex B
2015-01-01
Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex
Hamiltonian methods in the theory of solitons
Faddeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
On solutions of variable-order fractional differential equations
Directory of Open Access Journals (Sweden)
Ali Akgül
2017-01-01
solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhanced numerical methods for fractional differential equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the use of reproducing kernels for the solutions to many problems in the recent years. We give two examples to demonstrate how efficiently our theory can be implemented in practice.
General Reducibility and Solvability of Polynomial Equations ...
African Journals Online (AJOL)
A complete work on general reducibility and solvability of polynomial equations by algebraic meansradicals is developed. These equations called, reanegbèd and vic-emmeous are designed by using simple algebraic principles on how systems of equations and polynomials behave. Reanegbèd equations are capable of ...
CIME course on Control of Partial Differential Equations
Alabau-Boussouira, Fatiha; Glass, Olivier; Le Rousseau, Jérôme; Zuazua, Enrique
2012-01-01
The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010. Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a fri...
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
Mathematical theory of sedimentation analysis
Fujita, Hiroshi; Van Rysselberghe, P
1962-01-01
Mathematical Theory of Sedimentation Analysis presents the flow equations for the ultracentrifuge. This book is organized into two parts encompassing six chapters that evaluate the systems of reacting components, the differential equations for the ultracentrifuge, and the case of negligible diffusion. The first chapters consider the Archibald method for molecular weight determination; pressure-dependent sedimentation; expressions for the refractive index and its gradient; relation between refractive index and concentration; and the analysis of Gaussian distribution. Other chapters deal with th
Optimal control of stochastic difference Volterra equations an introduction
Shaikhet, Leonid
2015-01-01
This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...
Basic methods of soliton theory
Cherednik, I
1996-01-01
In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local cons
Equation of State Project Overview
Energy Technology Data Exchange (ETDEWEB)
Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
Theory of microwave remote sensing
Tsang, L.; Kong, J. A.; Shin, R. T.
1985-01-01
Active and passive microwave remote sensing of earth terrains is studied. Electromagnetic wave scattering and emission from stratified media and rough surfaces are considered with particular application to the remote sensing of soil moisture. Radiative transfer theory for both the random and discrete scatterer models is examined. Vector radiative transfer equations for nonspherical particles are developed for both active and passive remote sensing. Single and multiple scattering solutions are illustrated with applications to remote sensing problems. Analytical wave theory using the Dyson and Bethe-Salpeter equations is employed to treat scattering by random media. The backscattering enhancement effects, strong permittivity fluctuation theory, and modified radiative transfer equations are addressed. The electromagnetic wave scattering from a dense distribution of discrete scatterers is studied. The effective propagation constants and backscattering coefficients are calculated and illustrated for dense media.
Hayes, Bronwyn; Douglas, Clint; Bonner, Ann
2014-12-01
To test an explanatory model of the relationships between the nursing work environment, job satisfaction, job stress and emotional exhaustion for haemodialysis nurses, drawing on Kanter's theory of organizational empowerment. Understanding the organizational predictors of burnout (emotional exhaustion) in haemodialysis nurses is critical for staff retention and improving nurse and patient outcomes. Previous research has demonstrated high levels of emotional exhaustion among haemodialysis nurses, yet the relationships between nurses' work environment, job satisfaction, stress and emotional exhaustion in this population are poorly understood. A cross-sectional online survey. 417 nurses working in haemodialysis units completed an online survey between October 2011-April 2012 using validated measures of the work environment, job satisfaction, job stress and emotional exhaustion. Overall, the structural equation model demonstrated adequate fit and we found partial support for the hypothesized relationships. Nurses' work environment had a direct positive effect on job satisfaction, explaining 88% of the variance. Greater job satisfaction, in turn, predicted lower job stress, explaining 82% of the variance. Job satisfaction also had an indirect effect on emotional exhaustion by mitigating job stress. However, job satisfaction did not have a direct effect on emotional exhaustion. The work environment of haemodialysis nurses is pivotal to the development of job satisfaction. Nurses' job satisfaction also predicts their level of job stress and emotional exhaustion. Our findings suggest staff retention can be improved by creating empowering work environments that promote job satisfaction among haemodialysis nurses. © 2014 John Wiley & Sons Ltd.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Quantization of Equations of Motion
Directory of Open Access Journals (Sweden)
D. Kochan
2007-01-01
Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.
Theory of Optimal Human Motion
Chan, Albert Loongtak
1990-01-01
This thesis presents optimal theories for punching and running. The first is a theory of the optimal karate punch in terms of the duration and the speed of the punch. This theory is solved and compared with experimental data. The theory incorporates the force vs velocity equation (Hill's eq.) and Wilkie's equation for elbow flexation in determining the optimal punch. The time T and the final speed of the punch are dependent on a few physiological parameters for arm muscles. The theoretical punch agrees fairly well with our experiments and other independent experiments. Second, a theory of optimal running is presented, solved and compared with world track records. The theory is similar to Keller's theory for running (1973) except that the power consumed by a runner is assumed to be proportional to the runner's speed v, P = Hv, whereas Keller took P = constant. There are differential equations for velocity and energy, two initial conditions and two constraint inequalities, involving a total of four free parameters. Optimal control techniques are used to solve this problem and minimize the running time T given the race distance D. The resultant predicted times T agree well with the records and the parameter values are consistent with independent physiological measurements.
Irwa Issa; Ulrich Hamm
2017-01-01
Exporting organic fresh fruit and vegetables (FFV) to the European Union could represent a great opportunity for Syrian farmers and exporters. Yet, the organic sector in Syria is comparatively young and only a very small area of FFV is organically managed. To date, little is known about Syrian farmers’ attitudes towards organic FFV production. Therefore, the aim of this study was to explore the intentions and attitudes of Syrian farmers of FFV towards organic farming and how likely they are t...
On the Equational Definition of the Least Prefixed Point
DEFF Research Database (Denmark)
Santocanale, Luigi
2003-01-01
We propose a method to axiomatize by equations the least prefixed point of an order preserving function. We discuss its domain of application and show that the Boolean modal μ-calculus has a complete equational axiomatization. The method relies on the existence of a “closed structure” and its...... relationship to the equational axiomatization of Action Logic is made explicit. The implication operation of a closed structure is not monotonic in one of its variables; we show that the existence of such a term that does not preserve the order is an essential condition for defining by equations the least...... prefixed point. We stress the interplay between closed structures and fixed point operators by showing that the theory of Boolean modal μ-algebras is not a conservative extension of the theory of modal μ-algebras. The latter is shown to lack the finite model property....
Mass, Energy, Space And Time Systemic Theory--MEST--photoelectric conversion equation
Cao, Dayong
2010-03-01
Things have their physical system of the mass, energy, space and time of themselves-MEST. The time is from the frequency of wave, the space is from the amplitude of wave. In the system, the mass-energy is center and the space-time is around. In the general relativity, there is the equation: ma=mg . So get the equation: mar=mv^2=mgr. We use the data of the planets into this equation, and find it is right. (see the figure 1 and table 2) But the kinetic energy's equation is: Ek=mv^2/2mgr. How do explain it? Because the other kinetic energy's equations: Ek=δmc^2 like the wave's energy equation: E'=m'c^2. And things have both of the matter and the wave. So the equation belong to the wave. So the δm can be see like the increased mass of wave of the things. The matter's kinetic energy equal the wave's energy: mv^2/2=δmc^2=δm'c^2. And them give the things the repulsion force together. So the repulsion energy equation is: Er=mv^2=mv^2/2+δm'c^2=mar. The repulsion energy of the planets equal it's potential energy: Er=Ep=GMm/r=mgr. In photoelectron conversion, Not only there is a relationship between the wave and the kinetic energy of the photoelectron, but also there is a relationship between the wave and the mass of the photoelectron. So get the photoelectric conversion equation: m ev^2/2=δm'c^2-E= hν-E, and δm e= h/c λ-m e. The mass of the photoelectron is bigger than the electron's mass.
Mulford, R.; Swift, D. C.; Hamel, S.
2014-05-01
Ammonia and water are critical components of extraterrestrial bodies, determining the density and physical properties of the Outer Planets, their moons, and of extrasolar planets. Ammonia is unusual in having a high heat capacity relative to other molecular species. Equations of state (EOS) are presented for ammonia and for mixtures of ammonia and water. Their properties are discussed in terms of chemical compositions that evolve as pressure and temperature are varied. The NH4OH hydrate of ammonia is known to exist as a separate molecular species at pressures above about 5 GPa, and an effort was made to include reaction between NH3 and H2O in the mixture EOS. The EOS are suitable for calculating structures of icy planets and exoplanets, and of impacts. mass-radius relations which bound the possible interpretations of composition and structure for extraterrestrial bodies of unknown composition, such as exoplanets.
Classical theory of algebraic numbers
Ribenboim, Paulo
2001-01-01
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...
A Note on the Relationship Between Solutions of Einstein, Ramanujan and Chazy Equations
Esmakhanova, Kuralay; Myrzakulov, Yerlan; Nugmanova, Gulgasyl; Myrzakulov, Ratbay
2012-04-01
The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in this simple metric case is sometime a hard job. Therefore, it is useful to construct solutions of the Einstein equation using a known solutions of some other equations which are equivalent or related to the Einstein equation. In this work, we establish the relationship the Einstein equation with two other famous equations namely the Ramanujan equation and the Chazy equation. Both these two equations play an important role in the number theory. Using the known solutions of the Ramanujan and Chazy equations, we find the corresponding solutions of the Einstein equation.
The H sub N method for solving linear transport equation: theory and applications
Tezcan, C; Guelecyuez, M C
2003-01-01
The system of singular integral equations which is obtained from the integro-differential form of the linear transport equation using the Placzek lemma is solved. The exit distributions at the boundaries of the various media and the infinite medium Green's function are used. The process is applied to the half-space and finite slab problems. The neutron angular density in terms of singular eigenfunctions of the method of elementary solutions is also used to derive the same analytical expressions.
Hoffman, Johan; Jansson, Johan; Johnson, Claes
2016-06-01
We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl-Kutta-Zhukovsky formed 100 year ago. The new theory is based on our new resolution of d'Alembert's paradox showing that slightly viscous bluff body flow can be viewed as zero-drag/lift potential flow modified by 3d rotational slip separation arising from a specific separation instability of potential flow, into turbulent flow with nonzero drag/lift. For a wing this separation mechanism maintains the large lift of potential flow generated at the leading edge at the price of small drag, resulting in a lift to drag quotient of size 15-20 for a small propeller plane at cruising speed with Reynolds number {Re≈ 107} and a jumbojet at take-off and landing with {Re≈ 108} , which allows flight at affordable power. The new mathematical theory is supported by computed turbulent solutions of the Navier-Stokes equations with a slip boundary condition as a model of observed small skin friction of a turbulent boundary layer always arising for {Re > 106} , in close accordance with experimental observations over the entire range of angle of attacks including stall using a few millions of mesh points for a full wing-body configuration.
Fourth-order wave equation in Bhabha-Madhavarao spin-3 2 theory
Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.
2017-09-01
Within the framework of the Bhabha-Madhavarao formalism, a consistent approach to the derivation of a system of the fourth-order wave equations for the description of a spin-3 2 particle is suggested. For this purpose an additional algebraic object, the so-called q-commutator (q is a primitive fourth root of unity) and a new set of matrices ημ, instead of the original matrices βμ of the Bhabha-Madhavarao algebra, are introduced. It is shown that in terms of the ημ matrices we have succeeded in reducing a procedure of the construction of fourth root of the fourth-order wave operator to a few simple algebraic transformations and to some operation of the passage to the limit z → q, where z is some (complex) deformation parameter entering into the definition of the η-matrices. In addition, a set of the matrices 𝒫1/2 and 𝒫3/2(±)(q) possessing the properties of projectors is introduced. These operators project the matrices ημ onto the spins 1/2- and 3/2-sectors in the theory under consideration. A corresponding generalization of the obtained results to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out. The application to the problem of construction of the path integral representation in para-superspace for the propagator of a massive spin-3 2 particle in a background gauge field within the Bhabha-Madhavarao approach is discussed.
National Research Council Canada - National Science Library
Lucke, Robert
2002-01-01
.... Design equations are presented to allow quick assessment of the hardware parameters required for a notional system, most notably optical aperture sizes and the laser's power, chirp, and pulse rate capabilities...
On oscillatory solutions of certain difference equations
Directory of Open Access Journals (Sweden)
Grzegorz Grzegorczyk
2006-01-01
Full Text Available Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
General Theories of Regulation
Hertog, J.A. den
1999-01-01
This chapter makes a distinction between three types of theories of regulation: public interest theories, the Chicago theory of regulation and the public choice theories. The Chicago theory is mainly directed at the explanation of economic regulation; public interest theories and public choice
On Approximate Solutions of Functional Equations in Vector Lattices
Directory of Open Access Journals (Sweden)
Bogdan Batko
2014-01-01
Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.
Handbook of differential equations stationary partial differential equations
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.
2017-06-01
A long-standing challenge in the time-dependent density functional theory is to efficiently solve the exact time-dependent optimized effective potential (TDOEP) integral equation derived from orbital-dependent functionals, especially for the study of nonadiabatic dynamics in time-dependent external fields. In this Letter, we formulate a completely equivalent time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham and effective memory orbitals. The time-local formulation is numerically implemented, with the incorporation of exponential memory loss to address the unaccounted for correlation component in the exact-exchange-only functional, to enable the study of the many-electron dynamics of a one-dimensional hydrogen chain. It is shown that the long time behavior of the electric dipole converges correctly and the zero-force theorem is fulfilled in the current implementation.
The numerical solution of the vorticity transport equation
Dennis, S C R
1973-01-01
A method of approximating the two-dimensional vorticity transport equation in which the matrix associated with the difference equations is diagonally dominant and the truncation error is the same as that of the fully central-difference approximation, is discussed. An example from boundary layer theory is given by calculating the viscous stagnation point flow at the nose of a cylinder. Some new solutions of the Navier-Stokes equations are obtained for symmetrical flow past a flat plate of finite length. (16 refs).
Spectral theory and differential equations V. A. Marchenko's 90th anniversary collection
Khruslov, E; Shepelsky, D
2014-01-01
This volume is dedicated to V. A. Marchenko on the occasion of his 90th birthday. It contains refereed original papers and survey articles written by his colleagues and former students of international stature and focuses on the areas to which he made important contributions: spectral theory of differential and difference operators and related topics of mathematical physics, including inverse problems of spectral theory, homogenization theory, and the theory of integrable systems. The papers in the volume provide a comprehensive account of many of the most significant recent developments in th
Lie Symmetry Classification of the Generalized Nonlinear Beam Equation
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Dingjiang Huang
2017-07-01
Full Text Available In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
Analytic, Algebraic and Geometric Aspects of Differential Equations
Haraoka, Yoshishige; Michalik, Sławomir
2017-01-01
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of i...
Some Aspects of Extended Kinetic Equation
Directory of Open Access Journals (Sweden)
Dilip Kumar
2015-09-01
Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.
Global solutions of nonlinear Schrödinger equations
Bourgain, J
1999-01-01
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrödinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research r
Review of Hydroelasticity Theories
DEFF Research Database (Denmark)
Chen, Xu-jun; Wu, You-sheng; Cui, Wei-cheng
2006-01-01
Existing hydroelastic theories are reviewed. The theories are classified into different types: two-dimensional linear theory, two-dimensional nonlinear theory, three-dimensional linear theory and three-dimensional nonlinear theory. Applications to analysis of very large floating structures (VLFS...
Stability analysis of a class of fractional delay differential equations
Indian Academy of Sciences (India)
In this paper we analyse stability of nonlinear fractional order delay differential equations of the form D y ( t ) = a f ( y ( t − ) ) − by ( t ) , where D is a Caputo fractional derivative of order 0 < ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic ...
Feedback stabilization of semilinear heat equations
Directory of Open Access Journals (Sweden)
V. Barbu
2003-01-01
Full Text Available This paper is concerned with the internal and boundary stabilization of the steady-state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.
On the Effective Equation of State of Dark Energy
DEFF Research Database (Denmark)
Sloth, Martin Snoager
2010-01-01
In an effective field theory model with an ultraviolet momentum cutoff, there is a relation between the effective equation of state of dark energy and the ultraviolet cutoff scale. It implies that a measure of the equation of state of dark energy different from minus one, does not rule out vacuum...... energy as dark energy. It also indicates an interesting possibility that precise measurements of the infrared properties of dark energy can be used to probe the ultraviolet cutoff scale of effective quantum field theory coupled to gravity. In a toy model with a vacuum energy dominated universe...... with a Planck scale cutoff, the dark energy effective equation of state is -0.96....
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
Differential equations of my young years
Maz'ya, Vladimir
2014-01-01
Vladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. In this fascinating book he describes the first thirty years of his life in Leningrad (now St. Petersburg). He starts with the story of his family, speaks about his childhood, the high school and university years, and recalls his formative years as a mathematician. Behind the author's personal recollections, with his own joys, sorrows and hopes, one sees a vivid picture of those times in the former Sovjet Union. He speaks warmly about his friends, both outside and inside the world of mathematics, about discovering his passion for mathematics and his early achievements, and about a number of mathematicians who influenced his professional life. The book is written in a highly readable and inviting style, spiced with the occasional touch of humor.
Qualitative mathematical analysis of the Richards equation
Gilding, B.H.
1991-01-01
The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This
Kurasov, Victor
2005-01-01
The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated equation have been established. On the base of these facts taking into account some properties of behavior of solution the uniqueness of the equation appeared in the theory of homogeneous nucleation has been established. The equivalence of aux...
On some properties of the attractor equations
Energy Technology Data Exchange (ETDEWEB)
Bellucci, Stefano [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy)]. E-mail: stefano.bellucci@lnf.infn.it; Ferrara, Sergio [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy) and Physics Department, Theory Unit, CERN, CH-1211 Geneva 23 (Switzerland)]. E-mail: sergio.ferrara@cern.ch; Marrani, Alessio [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy) and Museo Storico della Fisica e Centro Studi e Ricerche ' Enrico Fermi' , Via Panisperna 89A, Compendio Viminale, I-00184 Rome (Italy)]. E-mail: marrani@lnf.infn.it
2006-04-06
We discuss the attractor equations of N=2, d=4 supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS attractor solutions correspond to the vanishing determinant of a (fermionic) gaugino mass matrix. The stability of these solutions is controlled by the data of the underlying special Kahler geometry of the vector multiplets' moduli space. Finally, after analyzing the 1-modulus case more in detail, we briefly comment on the choice of the Kahler gauge and its relevance for the recently discussed entropic functional.
Explicit solutions of the Rand Equation
African Journals Online (AJOL)
user
Keywords: Nonlinear partial differential equations, evolution equations, symmetries, similarity solutions, Rand Equation. PACS-Code: ... Classical symmetry analysis - algebraic group properties ... The result is a well-defined system of eight linear homogeneous PDEs (describing the point symmetries) for the infinitesimals. ),(.
Natroshvili, David; Shargorodsky, Eugene; Wendland, Wolfgang
2017-01-01
This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
Kido, Kentaro; Kasahara, Kento; Yokogawa, Daisuke; Sato, Hirofumi
2015-07-07
In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.
On the Role of Viscosity in the Eyring Equation
Kistemaker, Jos C. M.; Lubbe, Anouk S.; Bloemsma, Erik A.; Feringa, Ben L.
2016-01-01
Transition-state theory allows for the characterization of kinetic processes in terms of enthalpy and entropy of activation by using the Eyring equation. However, for reactions in solution, it fails to take the change of viscosity of solvents with temperature into account. A second-generation
On the specification of structural equation models for ecological systems
Grace, James B.; Anderson, T. Michael; Olff, Han; Scheiner, Samuel M.
The use of structural equation modeling (SEM) is often motivated by its utility for investigating complex networks of relationships, but also because of its promise as a means of representing theoretical Concepts using latent variables. In this paper, we discuss characteristics of ecological theory
On the applicability of the geodesic deviation equation in General Relativity
Philipp, Dennis; Laemmerzahl, Claus
2016-01-01
Within the theory of General Relativity we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. The deviation equation is used to model satellite orbit constellations around the earth. In particular, we reconsider the deviation equation in Newtonian gravity and then determine relativistic effects within the theory of General Relativity. The deviation of nearby orbits, as constructed from exact solutions of the underlying geodesic equation, is compared to the solution of the geodesic deviation equation to assess the accuracy of the latter. Furthermore, we comment on the so-called Shirokov effect in Schwarzschild spacetime.
Application of the simplest equation method to some time-fractional partial differential equations
Directory of Open Access Journals (Sweden)
N. Taghizadeh
2013-12-01
Full Text Available In this paper, we establish exact solutions for some time fractional differential equations. The simplest equation method is used to construct the exact solutions of nonlinear fractional Klein–Gordon equation, Generalized Hirota–Satsuma coupled KdV system of time fractional order and nonlinear fractional Sharma–Tasso–Olever equation. The simplest equation method presents a wide applicability to handling nonlinear wave equations.
On the practical solution of the Thue equation
Tzanakis, N.; de Weger, B.M.M.
1989-01-01
This paper gives in detail a practical general method for the explicit determination of all solutions of any Thue equation. It uses a combination of Baker's theory of linear forms in logarithms and recent computational diophantine approximation techniques. An elaborated example is presented.
Bai, Shirong; Skodje, Rex T
2017-08-17
A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H2 combustion model.
One-dimensional transport equation models for sound energy propagation in long spaces: theory.
Jing, Yun; Larsen, Edward W; Xiang, Ning
2010-04-01
In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency.
Is string theory a theory of strings?
Johnson, Clifford V.; Kaloper, Nemanja; Khuri, Ramzi R.; Myers, Robert C.
1995-01-01
Recently a great deal of evidence has been found indicating that type IIA string theory compactified on K3 is equivalent to heterotic string theory compactified on T^4. Under the transformation which relates the two theories, the roles of fundamental and solitonic string solutions are interchanged. In this letter we show that there exists a solitonic membrane solution of the heterotic string theory which becomes a singular solution of the type IIA theory, and should therefore be interpreted a...
Analysis of the Lev Ginzburg Equation
Bellamy, Michael; Mickens, Ronald
2006-04-01
A second-order differential equation taking the form x=f(x,x,p)(*) was derived by Ginzburg^1. In this ODE, x and x represent the first and second derivatives with respect to time; and p stands for four parameters, p=(p1,p2, p3,p4), where (p1,p2,p3) are non-negative and p4 can be of either sign. The function f is linear in x, but quadratic in x. Ginzburg's main purpose in constructing this equation was to take into consideration the ``inertial behavior of biological populations." However, this ODE can also be used to model a variety of physical dynamical systems.^2 With four parameters, there is a broad range of possible solution behaviors. Our present purpose is to prove that limit-cycle behavior can occur for Eq. (*) under the appropriate conditions on the parameters. We demonstrate this result by means of the Hopf bifurcation theory.^3 References ^1L. Ginzburg and M. Colyvan, Ecological Orbits (Oxford, New York, 2004). ^2S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley; Reading, MA; 1994). ^3E. Beltrami, Mathematics for Dynamic Modeling (Academic Press, Boston, 1987).
Solving the transport equation with quadratic finite elements: Theory and applications
Energy Technology Data Exchange (ETDEWEB)
Ferguson, J.M. [Lawrence Livermore National Lab., CA (United States)
1997-12-31
At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.
Directory of Open Access Journals (Sweden)
Basak Karpuz
2017-03-01
Full Text Available In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1]. We prove some interesting properties of the fractional integrals and derivatives. Based on these properties, the following concepts for the new type fractional differential equations are explored: Existence and uniqueness of solutions; Solutions of autonomous fractional differential equations; Dependence on the initial conditions; Green’s function; Variation of parameters formula.
Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid
Directory of Open Access Journals (Sweden)
Gözde Sarı
2012-01-01
Full Text Available Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
1983-10-01
cofactors 011, D129 .... D33. Let u - Dilo , v D1 2Oi , w D1301 (sum on i, 1= 1,2,3) (10) and substitute these expressions in the three equations in...orthotropic shells. In some publications, even certain terms in equation (14) are neglected. In the following analysis , some of these negligibly small...34 Journal of Composite Materials 1, 1967, pp. 414-423. 5. Calcote, L. R., The Analysis of Laminated Composite Structures, Van Nostrand Reinhold Co., New
Topical Problems and Applications of Creep Theory
Altenbach, H.
2003-06-01
A historical review of achievements in creep theory is given. Primary attention is focused on the phenomenological approach. Different constitutive equations are discussed for primary and secondary creep as well as for creep with damage. New creep problems are examined
On some group properties of heat and mass transfer equations
Stepanova, I. V.
2017-10-01
Heat and mass transfer equations with variable transport coefficients are under study. The forms of unknown thermal conductivity, diffusion and Dufour coefficients are found by means of Lie group theory. It is shown that arbitrary elements have the power-law, logarithmic and exponential dependencies on temperature and concentration.
Cosets of meromorphic CFTs and modular differential equations
Energy Technology Data Exchange (ETDEWEB)
Gaberdiel, Matthias R. [Institut für Theoretische Physik, ETH Zürich,CH-8093 Zürich (Switzerland); Hampapura, Harsha R.; Mukhi, Sunil [Indian Institute of Science Education and Research,Homi Bhabha Rd, Pashan, Pune 411 008 (India)
2016-04-26
Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are constructed. The same method also gives rise to interesting new examples of CFTs with three and four characters.
approximate controllability of a non-autonomous differential equation
Indian Academy of Sciences (India)
53
Abstract. In this paper, we establish the approximate controllability results for a non-autonomous functional differential equation using the theory of linear evolution system, Schauder fixed point theorem, and by making use of resolvent operators. The obtained results in the paper, improve the existing ones in this direction, up ...
Grima, R
2010-07-21
regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.
On the stability of some systems of exponential difference equations
Directory of Open Access Journals (Sweden)
N. Psarros
2018-01-01
Full Text Available In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
Convergence of step-by-step methods for non-linear integro-differential equations.
Mocarsky, W. L.
1971-01-01
The theory of consistent step-by-step methods for solving Volterra integral equations is extended to nonsingular Volterra integro-differential equations. It is shown that standard step-by-step algorithms for these more general equations are convergent. Several numerical examples are included.
New equation of state models for hydrodynamic applications
Young, David A.; Barbee, Troy W.; Rogers, Forrest J.
1998-07-01
Two new theoretical methods for computing the equation of state of hot, dense matter are discussed. The ab initio phonon theory gives a first-principles calculation of lattice frequencies, which can be used to compare theory and experiment for isothermal and shock compression of solids. The ACTEX dense plasma theory has been improved to allow it to be compared directly with ultrahigh pressure shock data on low-Z materials. The comparisons with experiment are good, suggesting that these models will be useful in generating global EOS tables for hydrodynamic simulations.
Galileo and the equations of motion
Boccaletti, Dino
2016-01-01
This book is intended as a historical and critical study on the origin of the equations of motion as established in Newton's Principia. The central question that it aims to answer is whether it is indeed correct to ascribe to Galileo the inertia principle and the law of falling bodies. In order to accomplish this task, the study begins by considering theories on the motion of bodies from classical antiquity, and especially those of Aristotle. The theories developed during the Middle Ages and the Renaissance are then reviewed, with careful analysis of the contributions of, for example, the Merton and Parisian Schools and Galileo’s immediate predecessors, Tartaglia and Benedetti. Finally, Galileo’s work is examined in detail, starting from the early writings. Excerpts from individual works are presented, to allow the texts to speak for themselves, and then commented upon. The book provides historical evidence both for Galileo's dependence on his forerunners and for the major breakthroughs that he achieved...
Hochstadt, Harry
2011-01-01
This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and applicatio
Dmitrenko, A. V.
2017-11-01
New dependences of the coefficients of heat transfer and friction have been presented which are used for calculations in the reactor core at a supercritical water pressure by taking account of the parameters of perturbation in the coolant flow: of the intensity and scale of flow turbulence. These solutions have been obtained based on stochastic systems of equations for the turbulence and the equivalence of measures between deterministic (laminar) and random (turbulent) flows.
About Applications of the Fixed Point Theory
Directory of Open Access Journals (Sweden)
Bucur Amelia
2017-06-01
Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
Mild Solutions of Neutral Stochastic Partial Functional Differential Equations
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T. E. Govindan
2011-01-01
Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.
Nonlinear implicit differential equations of fractional order at resonance
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2016-12-01
Full Text Available In this article, we obtain an existence result for periodic solutions to nonlinear implicit fractional differential equations with Caputo fractional derivatives. Our main tools is coincidence degree theory, which was first introduced by Mawhin. Also we present two examples to show the applicability of our results.
Stability analysis of ecomorphodynamic equations
Bärenbold, F.; Crouzy, B.; Perona, P.
2016-02-01
In order to shed light on the influence of riverbed vegetation on river morphodynamics, we perform a linear stability analysis on a minimal model of vegetation dynamics coupled with classical one- and two-dimensional Saint-Venant-Exner equations of morphodynamics. Vegetation is modeled as a density field of rigid, nonsubmerged cylinders and affects flow via a roughness change. Furthermore, vegetation is assumed to develop following a logistic dependence and may be uprooted by flow. First, we perform the stability analysis of the reduced one-dimensional framework. As a result of the competitive interaction between vegetation growth and removal through uprooting, we find a domain in the parameter space where originally straight rivers are unstable toward periodic longitudinal patterns. For realistic values of the sediment transport parameter, the dominant longitudinal wavelength is determined by the parameters of the vegetation model. Bed topography is found to adjust to the spatial pattern fixed by vegetation. Subsequently, the stability analysis is repeated for the two-dimensional framework, where the system may evolve toward alternate or multiple bars. On a fixed bed, we find instability toward alternate bars due to flow-vegetation interaction, but no multiple bars. Both alternate and multiple bars are present on a movable, vegetated bed. Finally, we find that the addition of vegetation to a previously unvegetated riverbed favors instability toward alternate bars and thus the development of a single course rather than braiding.
Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2004-01-01
The standard Langevin equation is a first order stochastic differential equation where the driving noise term is a Brownian motion. The marginal probability density is a solution to a linear partial differential equation called the Fokker-Planck equation. If the Brownian motion is replaced by so......-called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform......) corresponding to the density function. This equation is frequently called the spectral Fokker-Planck equation. This paper raises doubt about the validity of the spectral Fokker/Planck equation in its standard formulation. The equation can be solved with respect to stationary solutions in the particular case...
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
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Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Coincident Bifurcation of Equilibrium and Periodic Solutions of Evolution Equations.
1979-12-01
of Hoyle [7], involving the center manifold theory. Throughout, we refer to the papers of Crandall and Rabinowitz Ell, [21, for pre- liminary results...bw+ a2 + s2=a)" + b1w q+ p s =0 Solutions of (4.11) lie on secondary branches of solutions of equations (4.1), ponding to secondary branches of...8217. Comm. ’.ath. Ph-Ys., to appear. 6. Henry, D., Geometric theor of serilinear parabolic equations. Vniversity of Kentucky lecture notes, 1974. 7. Hoyle
Boley, Bruno A
1997-01-01
Highly regarded text presents detailed discussion of fundamental aspects of theory, background, problems with detailed solutions. Basics of thermoelasticity, heat transfer theory, thermal stress analysis, more. 1985 edition.
Microscopic tunneling theory of long Josephson junctions
DEFF Research Database (Denmark)
Grønbech-Jensen, N.; Hattel, Søren A.; Samuelsen, Mogens Rugholm
1992-01-01
We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate...
Silicon nitride equation of state
Brown, Robert C.; Swaminathan, Pazhayannur K.
2017-01-01
This report presents the development of a global, multi-phase equation of state (EOS) for the ceramic silicon nitride (Si3N4).1 Structural forms include amorphous silicon nitride normally used as a thin film and three crystalline polymorphs. Crystalline phases include hexagonal α-Si3N4, hexagonal β-Si3N4, and the cubic spinel c-Si3N4. Decomposition at about 1900 °C results in a liquid silicon phase and gas phase products such as molecular nitrogen, atomic nitrogen, and atomic silicon. The silicon nitride EOS was developed using EOSPro which is a new and extended version of the PANDA II code. Both codes are valuable tools and have been used successfully for a variety of material classes. Both PANDA II and EOSPro can generate a tabular EOS that can be used in conjunction with hydrocodes. The paper describes the development efforts for the component solid phases and presents results obtained using the EOSPro phase transition model to investigate the solid-solid phase transitions in relation to the available shock data that have indicated a complex and slow time dependent phase change to the c-Si3N4 phase. Furthermore, the EOSPro mixture model is used to develop a model for the decomposition products; however, the need for a kinetic approach is suggested to combine with the single component solid models to simulate and further investigate the global phase coexistences.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Andrade, F M; Beims, M W; Luz, M G E
2003-01-01
From the poles of a generalized semiclassical Green's function we derive expressions for the eigenvalues of 1D multiple well potentials. In the case of asymmetric and symmetric double wells, we also obtain analytical formulae for, respectively, the shift and splitting of energies. Our results are better than some approximations in the literature because they take more properly into account the tunnelling through the barriers forming the multiple well and depend on energy-dependent Maslov indices. We illustrate the good numerical precision of the method by discussing some case tests on double wells.
Attractors for equations of mathematical physics
Chepyzhov, Vladimir V
2001-01-01
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti
Skeletonized wave equation of surface wave dispersion inversion
Li, Jing
2016-09-06
We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.
Some Aspects of Diffusion Theory
Pignedoli, A
2011-01-01
This title includes: V.C.A. Ferraro: Diffusion of ions in a plasma with applications to the ionosphere; P.C. Kendall: On the diffusion in the atmosphere and ionosphere; F. Henin: Kinetic equations and Brownian motion; T. Kahan: Theorie des reacteurs nucleaires: methodes de resolution perturbationnelles, interactives et variationnelles; C. Cattaneo: Sulla conduzione del calore; C. Agostinelli: Formule di Green per la diffusione del campo magnetico in un fluido elettricamente conduttore; A. Pignedoli: Transformational methods applied to some one-dimensional problems concerning the equations of t
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Solutions of the telegrapher's equation in the presence of traps
Masoliver, Jaume, 1951-; Porrà i Rovira, Josep Maria; Weiss, George H. (George Herbert), 1930-
1992-01-01
Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will ...
Exact solutions of the time-fractional Fisher equation by using modified trial equation method
Tandogan, Yusuf Ali; Bildik, Necdet
2016-06-01
In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
Functional theories of thermoelectric phenomena
Eich, F. G.; Di Ventra, M.; Vignale, G.
2017-02-01
We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the formal structure of thermal density functional theory, a density functional theory with two basic variables—the density and the energy density—and two conjugate fields—the ordinary scalar potential and Luttinger’s thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e. the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttinger’s thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.
Symmetric solutions of evolutionary partial differential equations
Bruell, Gabriele; Ehrnström, Mats; Geyer, Anna; Pei, Long
2017-10-01
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms of three principles, based on the structure of the equations. The first principle covers equations that allow for steady solutions and shows that any spatially symmetric solution is in fact steady with a speed determined by the motion of the axis of symmetry at the initial time. The second principle includes equations that admit breathers and steady waves, and therefore is less strong: it holds that the axes of symmetry are constant in time. The last principle is a mixed case, when the equation contains terms of the kind from both earlier principles, and there may be different outcomes; for a class of such equations one obtains that a spatially symmetric solution must be constant in both time and space. We list and give examples of more than 30 well-known equations and systems in one and several dimensions satisfying these principles; corresponding results for weak formulations of these equations may be attained using the same techniques. Our investigation is a generalisation of a local and one-dimensional version of the first principle from Ehrnström et al (2009 Int. Math. Res. Not. 2009 4578-96) to nonlocal equations, systems and higher dimensions, as well as a study of the standing and mixed cases.
Diffusion in the special theory of relativity.
Herrmann, Joachim
2009-11-01
The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Gauge invariance and equations of motion for closed string modes
Directory of Open Access Journals (Sweden)
B. Sathiapalan
2014-12-01
Full Text Available We continue earlier discussions on loop variables and the exact renormalization group on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motion – this is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space–time curvature of the (arbitrary background is zero. The exact RG equations give quadratic equations of motion for all the modes including the physical graviton. The level (2,2¯ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory.
McDowell, J J; Calvin, Olivia L; Hackett, Ryan; Klapes, Bryan
2017-07-01
Two competing predictions of matching theory and an evolutionary theory of behavior dynamics, and one additional prediction of the evolutionary theory, were tested in a critical experiment in which human participants worked on concurrent schedules for money (Dallery et al., 2005). The three predictions concerned the descriptive adequacy of matching theory equations, and of equations describing emergent equilibria of the evolutionary theory. Tests of the predictions falsified matching theory and supported the evolutionary theory. Copyright © 2017 Elsevier B.V. All rights reserved.
Integrability of conformal fishnet theory
Gromov, Nikolay; Kazakov, Vladimir; Korchemsky, Gregory; Negro, Stefano; Sizov, Grigory
2018-01-01
We study integrability of fishnet-type Feynman graphs arising in planar four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704 as a special double scaling limit of gamma-deformed N = 4 SYM theory. We show that the transfer matrix "building" the fishnet graphs emerges from the R-matrix of non-compact conformal SU(2 , 2) Heisenberg spin chain with spins belonging to principal series representations of the four-dimensional conformal group. We demonstrate explicitly a relationship between this integrable spin chain and the Quantum Spectral Curve (QSC) of N = 4 SYM. Using QSC and spin chain methods, we construct Baxter equation for Q-functions of the conformal spin chain needed for computation of the anomalous dimensions of operators of the type tr( ϕ 1 J ) where ϕ 1 is one of the two scalars of the theory. For J = 3 we derive from QSC a quantization condition that fixes the relevant solution of Baxter equation. The scaling dimensions of the operators only receive contributions from wheel-like graphs. We develop integrability techniques to compute the divergent part of these graphs and use it to present the weak coupling expansion of dimensions to very high orders. Then we apply our exact equations to calculate the anomalous dimensions with J = 3 to practically unlimited precision at any coupling. These equations also describe an infinite tower of local conformal operators all carrying the same charge J = 3. The method should be applicable for any J and, in principle, to any local operators of bi-scalar theory. We show that at strong coupling the scaling dimensions can be derived from semiclassical quantization of finite gap solutions describing an integrable system of noncompact SU(2 , 2) spins. This bears similarities with the classical strings arising in the strongly coupled limit of N = 4 SYM.
Symmetries and first integrals of some differential equations of dynamics
Energy Technology Data Exchange (ETDEWEB)
Eliezer, C.J.
1979-10-01
The theme of this paper is the study of the symmetry properties of some differential equations of dynamics, and of the construction of first integrals. For the time-dependent harmonic oscillator the Lewis invariant provides a quadratic function which is a constant of motion. Different derivatives are considered with a view to assigning some physical meaning to the invariant and to the function rho(t) in terms of which the invariant is expressed. Lie's theory of differential equations, which until recently has been sadly neglected in comparison with his other pioneering works, is applied to consider groups of point transformations which leave invariant the equations of motion. For the time-dependent oscillator, an eight-parameter Lie group is obtained. A five-parameter Noether sub-group leaves also the action function invariant. Some results concerning the symmetries of the Kepler problem are also reported. Dynamical symmetries, not covered by point transformations, are briefly discussed.
Conformal invariance and new exact solutions of the elastostatics equations
Chirkunov, Yu. A.
2017-03-01
We fulfilled a group foliation of the system of n-dimensional (n ≥ 2) Lame equations of the classical static theory of elasticity with respect to the infinite subgroup contained in normal subgroup of main group of this system. It permitted us to move from the Lame equations to the equivalent unification of two first-order systems: automorphic and resolving. We obtained a general solution of the automorphic system. This solution is an n-dimensional analogue of the Kolosov-Muskhelishvili formula. We found the main Lie group of transformations of the resolving system of this group foliation. It turned out that in the two-dimensional and three-dimensional cases, which have a physical meaning, this system is conformally invariant, while the Lame equations admit only a group of similarities of the Euclidean space. This is a big success, since in the method of group foliation, resolving equations usually inherit Lie symmetries subgroup of the full symmetry group that was not used for the foliation. In the three-dimensional case for the solutions of the resolving system, we found the general form of the transformations similar to the Kelvin transformation. These transformations are the consequence of the conformal invariance of the resolving system. In the three-dimensional case with a help of the complex dependent and independent variables, the resolving system is written as a simple complex system. This allowed us to find non-trivial exact solutions of the Lame equations, which direct for the Lame equations practically impossible to obtain. For this complex system, all the essentially distinct invariant solutions of the maximal rank we have found in explicit form, or we reduced the finding of those solutions to the solving of the classical one-dimensional equations of the mathematical physics: the heat equation, the telegraph equation, the Tricomi equation, the generalized Darboux equation, and other equations. For the resolving system, we obtained double wave of a
Some Aspects of Fixed Point Theory!
Indian Academy of Sciences (India)
1999-01-22
Jan 22, 1999 ... mars can be established by an appeal to Tarski's the- orem. This apart, it can be used to prove existence theorems for differential equations. Those who are in- troduced to lattice theory at an early stage, can get glimpses of its connections to other branches of mathe- matics such as topology, set theory and ...
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
The diffusion equation is one of the three great partial differential equations of classical physics. It describes the flow or diffusion of heat in the presence of temperature gradients, fluid flow in porous media in the presence of pressure gradients, and the diffusion of molecules in the presence of chemical gradients. [The other two equations are the wave equation, which describes the propagation of electromagnetic waves (including light), acoustic (sound) waves, and elastic (seismic) waves radiated from earthquakes; and LaPlace’s equation, which describes the behavior of electric, gravitational, and fluid potentials, all part of potential field theory. The diffusion equation reduces to LaPlace’s equation at steady state, when the field of interest does not depend on t. Poisson’s equation is LaPlace’s equation with a source term.
Foundations of Information Theory
Burgin, Mark
2008-01-01
Information is the basic concept of information theory. However, there is no definition of this concept that can encompass all uses of the term information in information theories and beyond. Many question a possibility of such a definition. However, foundations of information theory developed in the context of the general theory of information made it possible to build such a relevant and at the same time, encompassing definition. Foundations of information theory are built in a form of onto...
MACCIA, ELIZABETH S.; AND OTHERS
AN ANNOTATED BIBLIOGRAPHY OF 20 ITEMS AND A DISCUSSION OF ITS SIGNIFICANCE WAS PRESENTED TO DESCRIBE CURRENT UTILIZATION OF SUBJECT THEORIES IN THE CONSTRUCTION OF AN EDUCATIONAL THEORY. ALSO, A THEORY MODEL WAS USED TO DEMONSTRATE CONSTRUCTION OF A SCIENTIFIC EDUCATIONAL THEORY. THE THEORY MODEL INCORPORATED SET THEORY (S), INFORMATION THEORY…
Unification of the Two-Parameter Equation of State and the Principle of Corresponding States
DEFF Research Database (Denmark)
Mollerup, Jørgen
1998-01-01
A two-parameter equation of state is a two-parameter corresponding states model. A two-parameter corresponding states model is composed of two scale factor correlations and a reference fluid equation of state. In a two-parameter equation of state the reference equation of state is the two-paramet...... without refitting any model parameters, and without imposing other restrictions as regards to species and mixing rules as already imposed by the two-parameter equation of state. The theory and procedure is outlined in the paper....
Application of type Timoshenko equations for shock action
Directory of Open Access Journals (Sweden)
Zveryaev Evgeniy
2017-01-01
Full Text Available The generalized Timoshenko type equations are obtained from the plane problem equations of the theory elasticity. They might be applied for quick acting forces or displacements problems as the transversal shock on a beam or quick displacement of beam ends. The quick and slow solutions components аге extracted. The quick ones describe the propagation of the shear wave due to the action of a concentrated force or an explosion; the slow solutions are generated by the common verification of the boundary conditions the slow and quick solutions.
Foundations for a theory of gravitation theories
Thorne, K. S.; Lee, D. L.; Lightman, A. P.
1972-01-01
A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.
Asymptotically periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
Coupling and reduction of the HAWC equations
DEFF Research Database (Denmark)
Nim, E.
2001-01-01
This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...
Oscillations of first order difference equations
Indian Academy of Sciences (India)
Oscillations of first order difference equations. N PARHI. Department of Mathematics, Berhampur University, Berhampur 760 007, India. MS received 10 June 1999; revised 28 December 1999. Abstract. The oscillatory and asymptotic behaviour of solutions of first order diff- erence equations is studied. Keywords. Oscillation ...
't Hooft, Gerardus; Witten, Edward
2005-01-01
In his later years, Einstein sought a unified theory that would extend general relativity and provide an alternative to quantum theory. There is now talk of a "theory of everything"; fifty years after his death, how close are we to such a theory? (3 pages)
A modular theory of learning and performance.
Guilhardi, Paulo; Yi, Linun; Church, Russell M
2007-08-01
We describe a theory to account for the acquisition and extinction of response rate (conditioning) and pattern (timing). This modular theory is a development of packet theory (Kirkpatrick, 2002; Kirkpatrick & Church, 2003) that adds a distinction between pattern and strength memories, as well as contributing closed-form equations. We describe the theory using equations related to a flow diagram and illustrate it by an application to an experiment with repeated acquisitions and extinctions of a multiple-cued-interval procedure using rats. The parameter estimates for the theory were based on a calibration sample from the data, and the predictions for different measures of performance on a validation sample from the same data (cross-validation). The theory's predictions were similar to predictions based on the reliability of the behavior.
Symmetries of nonlinear ordinary differential equations: The ...
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... Lie symmetry analysis is one of the powerful tools to analyse nonlinear ordinary dif- ferential equations. We review the effectiveness of this method in terms of various symmetries. We present the method .... coincides with the linearized equation, then the underlying system is self-adjoint and in this case the ...
An analysis of the nonlinear equation
Indian Academy of Sciences (India)
the nonlinear diffusion equation in which the inhomogeneity is quadratic in ux. The method yields ... Thus, differential equations could be classified in terms of their symmetry groups, thereby identifying the set of ... gives rise to the 'optimal system' of group invariant solutions from which all other solutions can be determined.
On exact solutions of the Bogoyavlenskii equation
Indian Academy of Sciences (India)
Abstract. Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a ...
Ramanujan's modular equations of degree 5
Indian Academy of Sciences (India)
We provide alternative derivations of theta function identities associated with modular equations of degree 5. We then use the identities to derive the corresponding modular equations. Author Affiliations. Nayandeep Deka Baruah1 Jonali Bora2 Kanan Kumari Ojah1. Department of Mathematical Sciences, Tezpur University, ...
equilibrium approach in thederivation of differential equations
African Journals Online (AJOL)
user
In this paper, the differential equations of Mindlin plates are derived from basic principles by simultaneous satisfaction of the differential equations of equilibrium, the stress-strain laws and the strain-displacement relations for isotropic, homogenous linear elastic materials. Equilibrium method was adopted in the derivation.
Energy Technology Data Exchange (ETDEWEB)
Grove, John W. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-08-16
The xRage code supports a variety of hydrodynamic equation of state (EOS) models. In practice these are generally accessed in the executing code via a pressure-temperature based table look up. This document will describe the various models supported by these codes and provide details on the algorithms used to evaluate the equation of state.
High Temperature Equation of State of Metallic Hydrogen
V.T.Shvets
2016-01-01
The equation of state of liquid metallic hydrogen is solved numerically. Investigations are carried out at temperatures, which correspond both to the experimental conditions under which metallic hydrogen is produced on earth and the conditions in the cores of giant planets of the solar system such as Jupiter and Saturn. It is assumed that hydrogen is in an atomic state and all its electrons are collectivized. Perturbation theory in the electron and proton interaction is applied to determine t...
von Davier, Alina A.; Fournier-Zajac, Stephanie; Holland, Paul W.
2007-01-01
In the nonequivalent groups with anchor test (NEAT) design, there are several ways to use the information provided by the anchor in the equating process. One of the NEAT-design equating methods is the linear observed-score Levine method (Kolen & Brennan, 2004). It is based on a classical test theory model of the true scores on the test forms…
Equation for Consciousness in terms of Physics
Kodukula, Siva Prasad
2012-11-01
Based on the concepts 'Double Relativity Effectí. 'Film theory of the Universe ','Heart of the God model of the universeí and'Space time equivalenceí, it is concluded that consciousness is defined in terms of physics as Çthe electromagnetic field containing electromagnetic waves of velocity greater than that of light velocity.? Also it is concluded that because of this high velocity the cell or any living organism will get the perception of events before their happenings. This phenomenon is one of the properties of feeling which is a constituent of consciousness. The degree or strength of consciousness can be measured and defined as the distance of point of generation of conscious wave from the center of space time fluid related to consciousness (d). It can be measured by the equation VCW3.d2= Constant. Where 'VCWí is the velocity of consciousness wave observed. The unit of measurement for degree or strength of consciousness is 'conscious meterí.
New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2015-08-01
Full Text Available In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM and generalized Kudryashov method (GKM are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.
Dynamic density functional theory versus kinetic theory of simple fluids
Energy Technology Data Exchange (ETDEWEB)
Marini Bettolo Marconi, Umberto [Dipartimento di Fisica, Universita di Camerino and Istituto Nazionale di Fisica della Materia, Via Madonna delle Carceri, 62032, Camerino (Italy); Melchionna, Simone, E-mail: umberto.marinibettolo@unicam.i [Institute of Materials, Ecole Polytechnique Federale de Lausanne (EPFL), 1015 Lausanne (Switzerland)
2010-09-15
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as their hydrodynamic behavior. We focus on the evolution of the one-particle phase space distribution, rather than on the evolution of the average particle density which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction where particles are subject to overdamped motion resulting from coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the lattice Boltzmann method.
The Raychaudhuri equations: A brief review
Indian Academy of Sciences (India)
... as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein–Cartan–Sciama–Kibble theory). Finally, we give an overview of some recent applications of these equations in general relativity, quantum field theory, string theory and the theory of relativisitic membranes.
Existence of a coupled system of fractional differential equations
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-10-22
We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.
Multi component equations of state for electrolytes
DEFF Research Database (Denmark)
Lin, Yi; Thomsen, Kaj; de Hemptinne, Jean-Charles
2007-01-01
Four equations of state have been implemented and evaluated for multi component electrolyte solutions at 298.15K and 1 bar. The equations contain terms accounting for short-range and long-range interactions in electrolyte solutions. Short range interactions are described by one of the three...... equations of state, Peng-Robinson, Soave-Redlich-Kwong, or Cubic-Plus-Association (CPA). Long range interactions are described by either the simplified mean spherical approximation (MSA) solution of the Ornstein–Zernicke equation or the simplified Debye-Hückel term. An optional Born term is added...... to these electrostatic terms. The resulting electrolyte equations of state were tested by determining the optimal model parameters for the multi component test system consisting of H2O, Na+, H+, Ca2+, Cl-, OH-, SO42-. In order to describe the thermodynamics of this multi component system, ion specific parameters were...
Multicomponent equations of state for electrolytes
DEFF Research Database (Denmark)
Lin, Yi; Thomsen, Kaj; Hemptinne, Jean-Charles de
2007-01-01
Four equations of state have been implemented and evaluated for multicomponent electrolyte solutions at 298.15 K and 1 bar. The equations contain terms accounting for short-range and long-range interactions in electrolyte solutions. Short range interactions are described by one of the three...... equations of state, Peng-Robinson, Soave-Redlich-Kwong, or Cubic-Plus-Association (CPA). Long-range interactions are described by either the simplified mean spherical approximation (MSA) solution of the Ornstein-Zernicke equation or the simplified Debye-Huchel term. An optional Born term is added...... to these electrostatic terms. The resulting electrolyte equations of state were tested by determining the optimal model parameters for the multicomponent test system consisting of H2O, Na+, H+, Ca2+, Cl-, OH-, SO42-. To describe the thermodynamics of this multicomponent system, ion specific parameters were determined...
Canonical equations of Hamilton with beautiful symmetry
Liang, Guo
2012-01-01
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the first-order differential system is half of that for the second-order differential system. The nonlinear Schr\\"{o}dinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.
Boundary controllability of Maxwell's equations in a spherical region
Kime, Katherine A.
1987-02-01
This paper examines the question of control of electromagnetic fields in a three dimensional spherical region by means of control currents on the boundary of that region. Results of this type are significant in connection with the theory of waveguides, electromagnetic pulse devices, and stealth technology, as well as being of independent mathematical interest. The necessary theory of divergence-free solutions of the vector wave equation is developed. By use of eigenfunctions of the vector Laplacian in appropriate divergence-free domains and moment problem techniques, sufficient conditions for controllability are set forth.
Numerical Solution of a Model Equation of Price Formation
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
On the transformations of the dynamical equations
Levi-Civita, T.
2009-08-01
In this issue we bring to the reader’s attention a translation of Levi-Civita’s work “Sulle trasformazioni delle equazioni dinamiche”. This paper, written by Levi-Civita at the onset of his career, is remarkable in many respects. Both the main result and the method developed in the paper brought the author in line with the greatest mathematicians of his day and seriously influenced the further progress of geometry and the theory of integrable systems. Speaking modern language the main result of his paper is the deduction of the general geodesic equivalence equation in invariant form and local classification of geodesically equivalent Riemannian metrics in the case of arbitrary dimension, i.e., metrics having the same geodesics considered as unparameterized curves (this classification problem was formulated by Beltrami in 1865). Levi-Civita’s work produced a great impact on further development of the theory of geodesically equivalent metrics and geodesic mappings, and still remains one of the most important tools in this area of differential geometry. In this paper the author uses a new method based on the concept of Riemannian connection, which later has been also referred to as the Levi-Civita connection. This paper is truly a pioneering work in the sense that the real power of covariant differentiation techniques in solving a concrete and highly nontrivial problem from the theory of dynamical systems was demonstrated. The author skillfully operates and weaves together many of the most advanced (for that times) algebraic, geometric and analytic methods. Moreover, an attentive reader can also notice several forerunning ideas of the method of moving frames, which was developed a few decades later by E. Cartan. We hope that the reader will appreciate the style of exposition as well. This work, focused on the essence of the problem and free of manipulation with abstract mathematical terms, is a good example of a classical text of the late 19th century. Owing
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
Zygalakis, K. C.
2011-01-01
In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.
Automatic identification of simultaneous equations models
Omtzigt, P.H.
2003-01-01
This paper considers within-equation restrictions in simultaneous equation models. It provides an algorithm, which renders them generically identifying. This algorithm works directly on the the restrictions and renders estimation by means of methods that require identification possible. Using this
Hyperstability of the Drygas Functional Equation
Directory of Open Access Journals (Sweden)
Magdalena Piszczek
2013-01-01
Full Text Available We use the fixed point theorem for functional spaces to obtain the hyperstability result for the Drygas functional equation on a restricted domain. Namely, we show that a function satisfying the Drygas equation approximately must be exactly the solution of it.
Generalized theory of diffusion based on kinetic theory
Schäfer, T.
2016-10-01
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite limit spin hydrodynamics is equivalent to a collisionless Boltzmann treatment of spin propagation. Spin hydrodynamics avoids unphysical effects that arise when the diffusion equation is used to describe to a strongly interacting gas with a dilute corona. We apply spin hydrodynamics to the problem of spin diffusion in a trapped atomic gas. We find that the observed spin relaxation rate in the high-temperature limit [Sommer et al., Nature (London) 472, 201 (2011), 10.1038/nature09989] is consistent with the diffusion constant predicted by kinetic theory.
Equations of motion in relativistic gravity
Lämmerzahl, Claus; Schutz, Bernard
2015-01-01
The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Generalized WDVV equations for F4 pure N=2 Super-Yang-Mills theory
Hoevenaars, L.K.; Kersten, P.H.M.; Martini, Ruud
2000-01-01
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra $F_4$ . Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the
Generalized WDVV equations for F4 pure N=2 Super-Yang-Mills theory
Hoevenaars, L.K.; Kersten, P.H.M.; Martini, Ruud
2001-01-01
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 super-Yang–Mills theory for the Lie algebra F4. Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the
Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV equation
Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu
2016-01-01
Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The ex...
Directory of Open Access Journals (Sweden)
Dhakne Machindra B.
2017-04-01
Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.
Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study
Urbic, Tomaz
2016-01-01
Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures. PMID:27875894
Equations of state for hydrogen and deuterium.
Energy Technology Data Exchange (ETDEWEB)
Kerley, Gerald Irwin (Kerley Technical Services, Appomattox, VA)
2003-12-01
This report describes the complete revision of a deuterium equation of state (EOS) model published in 1972. It uses the same general approach as the 1972 EOS, i.e., the so-called 'chemical model,' but incorporates a number of theoretical advances that have taken place during the past thirty years. Three phases are included: a molecular solid, an atomic solid, and a fluid phase consisting of both molecular and atomic species. Ionization and the insulator-metal transition are also included. The most important improvements are in the liquid perturbation theory, the treatment of molecular vibrations and rotations, and the ionization equilibrium and mixture models. In addition, new experimental data and theoretical calculations are used to calibrate certain model parameters, notably the zero-Kelvin isotherms for the molecular and atomic solids, and the quantum corrections to the liquid phase. The report gives a general overview of the model, followed by detailed discussions of the most important theoretical issues and extensive comparisons with the many experimental data that have been obtained during the last thirty years. Questions about the validity of the chemical model are also considered. Implications for modeling the 'giant planets' are also discussed.
LeVeque, William J
1990-01-01
Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.
Theory of semigroups and applications
Sinha, Kalyan B
2017-01-01
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in...
Wilsonian effective action of superstring theory
Sen, Ashoke
2017-01-01
By integrating out the heavy fields in type II or heterotic string field theory one can construct the effective action for the light fields. This effective theory inherits all the algebraic structures of the parent theory and the effective action automatically satisfies the Batalin-Vilkovisky quantum master equation. This theory is manifestly ultraviolet finite, has only light fields as its explicit degrees of freedom, and the Feynman diagrams of this theory reproduce the exact scattering amplitudes of light states in string theory to any arbitrary order in perturbation theory. Furthermore in this theory the degrees of freedom of light fields above certain energy scale are also implicitly integrated out. This energy scale is determined by a particular parameter labelling a family of equivalent actions, and can be made arbitrarily low, leading to the interpretation of the effective action as the Wilsonian effective action.
On the Role of Viscosity in the Eyring Equation.
Kistemaker, Jos C M; Lubbe, Anouk S; Bloemsma, Erik A; Feringa, Ben L
2016-06-17
Transition-state theory allows for the characterization of kinetic processes in terms of enthalpy and entropy of activation by using the Eyring equation. However, for reactions in solution, it fails to take the change of viscosity of solvents with temperature into account. A second-generation unidirectional rotary molecular motor was used as a probe to study the effects of temperature-dependent viscosity changes upon unimolecular thermal isomerization processes. By combining the free-volume model with transition-state theory, a modified version of the Eyring equation was derived, in which the rate is expressed in terms of both temperature and viscosity. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Potential Theory of Multicomponent Adsorption
DEFF Research Database (Denmark)
Shapiro, Alexander; Stenby, Erling Halfdan
1998-01-01
We developed a theory of multicomponent adsorption on the basis of the potential concept originally suggested by Polanyi. The mixture is considered as a heterogeneous substance segregated in the external field emitted by the adsorbent. The same standard equation of state, with no additional fitting...... parameters, is used for the segregated and for the bulk phases. With this approach, few parameters are needed to correlate pure component adsorption isotherms. These parameters may be used to predict adsorption equilibria of multicomponent mixtures without additional adjustment. A connection between...... the potential theory and the spreading pressure concept is established, and problems of the theory consistency are studied. Numerical algorithms are suggested for evaluation of the segregated state of the mixture in the potential field of adsorption forces. Comparison with experimental data shows good agreement...
A saturating chiral field theory of nuclear matter
Directory of Open Access Journals (Sweden)
J. Boguta
1983-01-01
Full Text Available Catastrophe Theory analysis is used to construct a chiral theory of pions which leads to a saturating nuclear matter equation of state. This is achieved by introducing a vector meson field via the Higgs mechanism. The equation of state and the nuclear optical potential are computed. A metamorphosis of the nuclear force is suggested.
Qualitative and Asymptotic Theory of Detonations
Faria, Luiz
2014-11-09
Shock waves in reactive media possess very rich dynamics: from formation of cells in multiple dimensions to oscillating shock fronts in one-dimension. Because of the extreme complexity of the equations of combustion theory, most of the current understanding of unstable detonation waves relies on extensive numerical simulations of the reactive compressible Euler/Navier-Stokes equations. Attempts at a simplified theory have been made in the past, most of which are very successful in describing steady detonation waves. In this work we focus on obtaining simplified theories capable of capturing not only the steady, but also the unsteady behavior of detonation waves. The first part of this thesis is focused on qualitative theories of detonation, where ad hoc models are proposed and analyzed. We show that equations as simple as a forced Burgers equation can capture most of the complex phenomena observed in detonations. In the second part of this thesis we focus on rational theories, and derive a weakly nonlinear model of multi-dimensional detonations. We also show, by analysis and numerical simulations, that the asymptotic equations provide good quantitative predictions.
Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade
Kaza, K. R. V.; Kvaternik, R. G.
1979-01-01
The second-degree nonlinear aeroelastic equations of motion for a slender, flexible, nonuniform, Darrieus vertical-axis wind turbine blade which is undergoing combined flatwise bending, edgewise bending, torsion, and extension are developed using Hamilton's principle. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional incompressible unsteady airfoil theory. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity and the resulting equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity. These equations are suitable for studying vibrations, static and dynamic aeroelastic instabilities, and dynamic response. Several possible methods of solution of the equations, which have periodic coefficients, are discussed.
The measurement theory of fitness.
Wagner, Günter P
2010-05-01
In this article, an approach to measure fitness is proposed that considers fitness as a measure of competitive ability among phenotypes or genotypes. This approach is based on pairwise competition tests and is related to measures of "utility" in mathematical economics. Extending the results from utility theory it is possible to recover the classical Wrightian fitness measure without reference to models of population growth. A condition, quasi-BTL, similar to the Bradley-Terry-Luce condition of classical utility theory is shown to be necessary for the existence of frequency and context-independent fitness measures. Testing for violations of this quasi-BTL condition can be used to the detect genotype-by-genotype interactions and frequency-dependent fitness. A method for the detection of genotype by environment interactions is proposed that avoids potential scaling artifacts. Furthermore the measurement theoretical approach allows one to derive Wright's selection equation. This shows that classical selection equations are entirely general and exact. It is concluded that measurement theory is able to give definite answers to a number theoretical and practical questions. For instance, this theory identifies the correct scale for measuring gene interaction with respect to fitness and shows that different scales may lead to wrong conclusions.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
ARTICLE Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids
Wang, Xian-zhi; Ma, Hong-ru
2010-12-01
Making use of Weierstrass's theorem and Chebyshev's theorem and referring to the equations of state of the scaled-particle theory and the Percus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.
A Derivation of Maxwell Equations in Quaternion Space
Directory of Open Access Journals (Sweden)
Smarandache F.
2010-04-01
Full Text Available Quaternion space and its respective Quaternion Relativity (it also may be called as Ro- tational Relativity has been defined in a number of papers, and it can be shown that this new theory is capable to describe relativistic motion in elegant and straightforward way. Nonetheless there are subsequent theoretical developments which remains an open question, for instance to derive Maxwell equations in Q-space. Therefore the purpose of the present paper is to derive a consistent description of Maxwell equations in Q-space. First we consider a simplified method similar to the Feynman’s derivation of Maxwell equations from Lorentz force. And then we present another derivation method using Dirac decomposition, introduced by Gersten (1998. Further observation is of course recommended in order to refute or verify some implication of this proposition.
Holographic equation of state in fluid/gravity duality
Directory of Open Access Journals (Sweden)
Andrés Anabalón
2017-07-01
Full Text Available We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulk-dimensions for scalar fields saturating the Breitenlohner–Freedman bound. As a concrete example, we discuss the five dimensional scalar-tensor theories describing dark energy in four dimensions.
Holographic equation of state in fluid/gravity duality
Anabalón, Andrés; Astefanesei, Dumitru; Mann, Robert
2017-07-01
We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulk-dimensions for scalar fields saturating the Breitenlohner-Freedman bound. As a concrete example, we discuss the five dimensional scalar-tensor theories describing dark energy in four dimensions.
Numerical Analysis of Partial Differential Equations
Lui, S H
2011-01-01
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis
Economic theories of dictatorship
Alexandre Debs
2010-01-01
This article reviews recent advances in economic theories of dictatorships and their lessons for the political stability and economic performance of dictatorships. It reflects on the general usefulness of economic theories of dictatorship, with an application to foreign relations.
Michaelis - Menten equation for degradation of insoluble substrate
DEFF Research Database (Denmark)
Andersen, Morten; Kari, Jeppe; Borch, Kim
2017-01-01
. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid...... load of substrate is analyzed and this introduces an extra parameter to the equations. Various experimental setups to practically and reliably estimate all parameters are discussed....
Renormalized asymptotic solutions of the Burgers equation and the Korteweg-de Vries equation
Zakharov, Sergei V.
2015-01-01
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Directory of Open Access Journals (Sweden)
Yumei Zou
2017-01-01
Full Text Available This paper deals with the integral boundary value problems of fractional differential equations at resonance. By Mawhin’s coincidence degree theory, we present some new results on the existence of solutions for a class of differential equations of fractional order with integral boundary conditions at resonance. An example is also included to illustrate the main results.
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstra......This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....