Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
International Nuclear Information System (INIS)
Henderson, D.L.
1987-01-01
Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Integration of Chandrasekhar's integral equation
International Nuclear Information System (INIS)
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
Multidimensional singular integrals and integral equations
Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S
1965-01-01
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...
Goličnik, Marko
2011-01-01
The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.
Completely integrable operator evolutionary equations
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Integral equation for Coulomb problem
International Nuclear Information System (INIS)
Sasakawa, T.
1986-01-01
For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems
Feynman integrals and difference equations
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Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Feynman integrals and difference equations
Energy Technology Data Exchange (ETDEWEB)
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Integration rules for scattering equations
International Nuclear Information System (INIS)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Stochastic integration and differential equations
Protter, Philip E
2003-01-01
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, t...
Linear integral equations and soliton systems
International Nuclear Information System (INIS)
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
Completely integrable operator evolution equations. II
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)
Transformation properties of the integrable evolution equations
International Nuclear Information System (INIS)
Konopelchenko, B.G.
1981-01-01
Group-theoretical properties of partial differential equations integrable by the inverse scattering transform method are discussed. It is shown that nonlinear transformations typical to integrable equations (symmetry groups, Baecklund-transformations) and these equations themselves are contained in a certain universal nonlinear transformation group. (orig.)
An integral transform of the Salpeter equation
International Nuclear Information System (INIS)
Krolikowski, W.
1980-03-01
We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)
Integral equations with contrasting kernels
Directory of Open Access Journals (Sweden)
Theodore Burton
2008-01-01
Full Text Available In this paper we study integral equations of the form $x(t=a(t-\\int^t_0 C(t,sx(sds$ with sharply contrasting kernels typified by $C^*(t,s=\\ln (e+(t-s$ and $D^*(t,s=[1+(t-s]^{-1}$. The kernel assigns a weight to $x(s$ and these kernels have exactly opposite effects of weighting. Each type is well represented in the literature. Our first project is to show that for $a\\in L^2[0,\\infty$, then solutions are largely indistinguishable regardless of which kernel is used. This is a surprise and it leads us to study the essential differences. In fact, those differences become large as the magnitude of $a(t$ increases. The form of the kernel alone projects necessary conditions concerning the magnitude of $a(t$ which could result in bounded solutions. Thus, the next project is to determine how close we can come to proving that the necessary conditions are also sufficient. The third project is to show that solutions will be bounded for given conditions on $C$ regardless of whether $a$ is chosen large or small; this is important in real-world problems since we would like to have $a(t$ as the sum of a bounded, but badly behaved function, and a large well behaved function.
On integrability of the Killing equation
Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori
2018-04-01
Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.
Integrable discretizations of the short pulse equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.
Baecklund transformations for integrable lattice equations
International Nuclear Information System (INIS)
Atkinson, James
2008-01-01
We give new Baecklund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Baecklund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY
Enrique Gonzalo Reyes Garcia
2004-01-01
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Integrable boundary conditions and modified Lax equations
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2008-01-01
We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding 'transfer' matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix
Connecting Related Rates and Differential Equations
Brandt, Keith
2012-01-01
This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.
Counting master integrals. Integration by parts vs. functional equations
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Tarasov, Oleg V.
2016-01-01
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
Scattering integral equations and four nucleon problem
International Nuclear Information System (INIS)
Narodetskii, I.M.
1980-01-01
Existing results from the application of integral equation technique to the four-nucleon bound states and scattering are reviewed. The first numerical calculations of the four-body integral equations have been done ten years ago. Yet, it is still widely believed that these equations are too complicated to solve numerically. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. The presentation is based on the quasiparticle approach. This permits a simple interpretation of the equations in terms of quasiparticle scattering. The mathematical basis for the quasiparticle approach is the Hilbert-Schmidt method of the Fredholm integral equation theory. The first part of this review contains a detailed discussion of the Hilbert-Schmidt expansion as applied to the 2-particle amplitudes and to the kernel of the four-body equations. The second part contains the discussion of the four-body quasiparticle equations and of the resed forullts obtain bound states and scattering
Coupling Integrable Couplings of an Equation Hierarchy
International Nuclear Information System (INIS)
Wang Hui; Xia Tie-Cheng
2013-01-01
Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy. (general)
Integrable peakon equations with cubic nonlinearity
International Nuclear Information System (INIS)
Hone, Andrew N W; Wang, J P
2008-01-01
We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)
On a Volterra Stieltjes integral equation
Directory of Open Access Journals (Sweden)
P. T. Vaz
1990-01-01
Full Text Available The paper deals with a study of linear Volterra integral equations involving Lebesgue-Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed-point principle. An explicit example is also considered.
Non-equilibrium reaction rates in chemical kinetic equations
Gorbachev, Yuriy
2018-05-01
Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.
Adaptive integral equation methods in transport theory
International Nuclear Information System (INIS)
Kelley, C.T.
1992-01-01
In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented
Inequalities for differential and integral equations
Ames, William F
1997-01-01
Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.Key Features* Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations* Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books* Provides a valuable reference to engineers and graduate students
Algorithms For Integrating Nonlinear Differential Equations
Freed, A. D.; Walker, K. P.
1994-01-01
Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.
Abel integral equations analysis and applications
Gorenflo, Rudolf
1991-01-01
In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equatio...
Integral equation hierarchy for continuum percolation
International Nuclear Information System (INIS)
Given, J.A.
1988-01-01
In this thesis a projection operator technique is presented that yields hierarchies of integral equations satisfied exactly by the n-point connectedness functions in a continuum version of the site-bond percolation problem. The n-point connectedness functions carry the same structural information for a percolation problem as then-point correlation functions do for a thermal problem. This method extends the Potts model mapping of Fortuin and Kastelyn to the continuum by exploiting an s-state generalization of the Widom-Rowlinson model, a continuum model for phase separation. The projection operator technique is used to produce an integral equation hierarchy for percolation similar to the Born-Green heirarchy. The Kirkwood superposition approximation (SA) is extended to percolation in order to close this hierarchy and yield a nonlinear integral equation for the two-point connectedness function. The fact that this function, in the SA, is the analytic continuation to negative density of the two-point correlation function in a corresponding thermal problem is discussed. The BGY equation for percolation is solved numerically, both by an expansion in powers of the density, and by an iterative technique due to Kirkwood. It is argued both analytically and numerically, that the BYG equation for percolation, unlike its thermal counterpart, shows non-classical critical behavior, with η = 1 and γ = 0.05 ± .1. Finally a sequence of refinements to the superposition approximations based in the theory of fluids by Rice and Lekner is discussed
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
Complete integrability of the difference evolution equations
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Ivanov, M.I.; Kulish, P.P.
1980-01-01
The class of exactly solvable nonlinear difference evolution equations (DEE) related to the discrete analog of the one-dimensional Dirac problem L is studied. For this starting from L we construct a special linear non-local operator Λ and obtain the expansions of w and σ 3 deltaw over its eigenfunctions, w being the potential in L. This allows us to obtain compact expressions for the integrals of motion and to prove that these DEE are completely integrable Hamiltonian systems. Moreover, it is shown that there exists a hierarchy of Hamiltonian structures, generated by Λ, and the action-angle variables are explicity calculated. As particular cases the difference analog of the non-linear Schroedinger equation and the modified Korteweg-de-Vries equation are considered. The quantization of these Hamiltonian system through the use of the quantum inverse scattering method is briefly discussed [ru
Polynomial solutions of nonlinear integral equations
International Nuclear Information System (INIS)
Dominici, Diego
2009-01-01
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials
Polynomial solutions of nonlinear integral equations
Energy Technology Data Exchange (ETDEWEB)
Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu
2009-05-22
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.
Unconditionally stable integration of Maxwell's equations
Verwer, J.G.; Bochev, Mikhail A.
Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit finite difference
Unconditionally stable integration of Maxwell's equations
J.G. Verwer (Jan); M.A. Botchev
2008-01-01
htmlabstractNumerical integration of Maxwell''s equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction
Unconditionally stable integration of Maxwell's equations
J.G. Verwer (Jan); M.A. Botchev
2009-01-01
textabstractNumerical integration of Maxwell’s equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit –
Lectures on differential equations for Feynman integrals
International Nuclear Information System (INIS)
Henn, Johannes M
2015-01-01
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space–time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE. (topical review)
Nonlinear integral equations for the sausage model
Ahn, Changrim; Balog, Janos; Ravanini, Francesco
2017-08-01
The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.
Darboux invariants of integrable equations with variable spectral parameters
International Nuclear Information System (INIS)
Shin, H J
2008-01-01
The Darboux transformation for integrable equations with variable spectral parameters is introduced. Darboux invariant quantities are calculated, which are used in constructing the Lax pair of integrable equations. This approach serves as a systematic method for constructing inhomogeneous integrable equations and their soliton solutions. The structure functions of variable spectral parameters determine the integrability and nonlinear coupling terms. Three cases of integrable equations are treated as examples of this approach
Bounded solutions for fuzzy differential and integral equations
Energy Technology Data Exchange (ETDEWEB)
Nieto, Juan J. [Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela, 15782 (Spain)] e-mail: amnieto@usc.es; Rodriguez-Lopez, Rosana [Departamento de Analisis Matematico Facultad de Matematicas Universidad de Santiago de Compostela, 15782 (Spain)] e-mail: amrosana@usc.es
2006-03-01
We find sufficient conditions for the boundness of every solution of first-order fuzzy differential equations as well as certain fuzzy integral equations. Our results are based on several theorems concerning crisp differential and integral inequalities.
Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations
Directory of Open Access Journals (Sweden)
Guanfeng Li
2014-01-01
Full Text Available We introduce a class of variational integrals whose Euler equations are nonhomogeneous -harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous -harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.
Recovering an obstacle using integral equations
Rundell, William
2009-05-01
We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.
Integral Equation Methods for Electromagnetic and Elastic Waves
Chew, Weng; Hu, Bin
2008-01-01
Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral eq
An integral equation arising in two group neutron transport theory
International Nuclear Information System (INIS)
Cassell, J S; Williams, M M R
2003-01-01
An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically
Status of rates and rate equations for thermal leptogenesis
Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.
2018-02-01
In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.
Numerov iteration method for second order integral-differential equation
International Nuclear Information System (INIS)
Zeng Fanan; Zhang Jiaju; Zhao Xuan
1987-01-01
In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
Directory of Open Access Journals (Sweden)
Zakieh Avazzadeh
2014-01-01
Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.
Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel
2009-11-01
The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first
Quick and Easy Rate Equations for Multistep Reactions
Savage, Phillip E.
2008-01-01
Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…
Representing Rate Equations for Enzyme-Catalyzed Reactions
Ault, Addison
2011-01-01
Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…
Partially integrable nonlinear equations with one higher symmetry
International Nuclear Information System (INIS)
Mikhailov, A V; Novikov, V S; Wang, J P
2005-01-01
In this letter, we present a family of second order in time nonlinear partial differential equations, which have only one higher symmetry. These equations are not integrable, but have a solution depending on one arbitrary function. (letter to the editor)
Some New Integrable Equations from the Self-Dual Yang-Mills Equations
International Nuclear Information System (INIS)
Ivanova, T.A.; Popov, A.D.
1994-01-01
Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
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
Studies on Microwave Heated Drying-rate Equations of Foods
呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右
1990-01-01
In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...
Theory of nanolaser devices: Rate equation analysis versus microscopic theory
DEFF Research Database (Denmark)
Lorke, Michael; Skovgård, Troels Suhr; Gregersen, Niels
2013-01-01
A rate equation theory for quantum-dot-based nanolaser devices is developed. We show that these rate equations are capable of reproducing results of a microscopic semiconductor theory, making them an appropriate starting point for complex device simulations of nanolasers. The input...
Integral equations for four identical particles in angular momentum representation
International Nuclear Information System (INIS)
Kharchenko, V.F.; Shadchin, S.A.
1975-01-01
In integral equations of motion for a system of four identical spinless particles with central pair interactions, transition is realized from the representation of relative Jacobi momenta to the representation of their moduli and relative angular moments. As a result, the variables associated with the rotation of the system as a whole are separated in the equations. The integral equations of motion for four particles are reduced to the form of an infinite system of three-demensional integral equations. The four-particle kinematic factors contained in integral kernels are expressed in terms of three-particle type kinematic factors. In the case of separable two-particle interaction, the equations of motion for four particles have the form of an infinite system of two-dimensional integral equations
On discrete 2D integrable equations of higher order
International Nuclear Information System (INIS)
Adler, V E; Postnikov, V V
2014-01-01
We study two-dimensional discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund–Darboux transformations for the lattice equations of Bogoyavlensky type. (paper)
Energy preserving integration of bi-Hamiltonian partial differential equations
Karasozen, B.; Simsek, G.
2013-01-01
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the
Fuchs indices and the first integrals of nonlinear differential equations
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method of finding the first integrals of nonlinear differential equations in polynomial form is presented. Basic idea of our approach is to use the scaling of solution of nonlinear differential equation and to find the dimensions of arbitrary constants in the Laurent expansion of the general solution. These dimensions allows us to obtain the scalings of members for the first integrals of nonlinear differential equations. Taking the polynomials with unknown coefficients into account we present the algorithm of finding the first integrals of nonlinear differential equations in the polynomial form. Our method is applied to look for the first integrals of eight nonlinear ordinary differential equations of the fourth order. The general solution of one of the fourth order ordinary differential equations is given
Application of wavelets to singular integral scattering equations
International Nuclear Information System (INIS)
Kessler, B.M.; Payne, G.L.; Polyzou, W.N.
2004-01-01
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms are demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
On monotonic solutions of an integral equation of Abel type
International Nuclear Information System (INIS)
Darwish, Mohamed Abdalla
2007-08-01
We present an existence theorem of monotonic solutions for a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar's integral equation is considered as a special case. The concept of measure of noncompactness and a fi xed point theorem due to Darbo are the main tools in carrying out our proof. (author)
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.
Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan
2017-04-07
In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.
Integrable discretization s of derivative nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tsuchida, Takayuki
2002-01-01
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)
Numerical integration of asymptotic solutions of ordinary differential equations
Thurston, Gaylen A.
1989-01-01
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Equations to Estimate Creatinine Excretion Rate : The CKD Epidemiology Collaboration
Ix, Joachim H.; Wassel, Christina L.; Stevens, Lesley A.; Beck, Gerald J.; Froissart, Marc; Navis, Gerjan; Rodby, Roger; Torres, Vicente E.; Zhang, Yaping (Lucy); Greene, Tom; Levey, Andrew S.
Background and objectives Creatinine excretion rate (CER) indicates timed urine collection accuracy. Although equations to estimate CER exist, their bias and precision are untested and none simultaneously include age, sex, race, and weight. Design, setting, participants, & measurements Participants
Rate equation simulation of temporal characteristics of a pulsed dye ...
Indian Academy of Sciences (India)
-dependent, two-dimensional (in space) rate equation model of a .... fluorescence band of the dye is divided into ten wavelength segments of variable sizes. ... qualitative and reasonably good quantitative agreement with experimental results.
International Nuclear Information System (INIS)
Einzel, D.; Woelfle, P.
1978-01-01
The kinetic equation for Bogoliubov quasiparticles for both the A and B phases of superfluid 3 He is derived from the general matrix kinetic equation. A condensed expression for the exact spin-symmetric collision integral is given. The quasiparticle relaxation rate is calculated for the BW state using the s--p approximation for the quasiparticle scattering amplitude. By using the results for the quasiparticle relaxation rate, the mean free path of Bogoliubov quasiparticles is calculated for all temperatures
Diffusion equations and the time evolution of foreign exchange rates
Energy Technology Data Exchange (ETDEWEB)
Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram
2013-10-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Diffusion equations and the time evolution of foreign exchange rates
International Nuclear Information System (INIS)
Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram
2013-01-01
We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.
Miyake, Y.; Noda, H.
2017-12-01
Earthquake sequences involve many processes in a wide range of time scales, from quasistatic loading to dynamic rupture. At a depth of brittle-plastic transitional and deeper, rock behaves as a viscous fluid in a long timescale, but as an elastic material in a short timescale. Viscoelastic stress relaxation may be important in the interseismic periods at the depth, near the deeper limit of the seismogenic layer or the region of slow slip events (SSEs) [Namiki et al., 2014 and references therein]. In the present study, we implemented the viscoelastic effect (Maxwell material) in fully-dynamic earthquake sequence simulations using a spectral boundary integral equation method (SBIEM) [e.g., Lapusta et al., 2000]. SBIEM is efficient in calculation of convolutional terms for dynamic stress transfer, and the problem size is limited by the amount of memory available. Linear viscoelasticity could be implemented by convolution of slip rate history and Green's function, but this method requires additional memory and thus not suitable for the implementation to the present code. Instead, we integrated the evolution of "effective slip" distribution, which gives static stress distribution when convolved with static elastic Green's function. This method works only for simple viscoelastic property distributions, but such models are suitable for numerical experiments aiming basic understanding of the system behavior because of the virtue of SBIEM, the ability of fine on-fault spatial resolution and efficient computation utilizing the fast Fourier transformation. In the present study, we examined the effect of viscoelasticity on earthquake sequences of a fault with a rate-weakening patch. A series of simulations with various relaxation time tc revealed that as decreasing tc, recurrence intervals of earthquakes increases and seismicity ultimately disappears. As long as studied, this transition to aseismic behavior is NOT associated with SSEs. In a case where the rate-weakening patch
Analytic solution of integral equations for molecular fluids
International Nuclear Information System (INIS)
Cummings, P.T.
1984-01-01
We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
International Nuclear Information System (INIS)
Angilella, G.G.N.; Pucci, R.; March, N.H.
2004-01-01
We give here the derivation of a Gross-Pitaevskii-type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91, 030401 (2003)]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Directory of Open Access Journals (Sweden)
Han Guo
2012-01-01
Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.
The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar
2009-01-01
Roč. 63, č. 21 (2009), s. 227-247 ISSN 0378-620X Institutional research plan: CEZ:AV0Z10190503 Keywords : Poisson equation * Neumann problem * integral equation method Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2009
Tisdell, C. C.
2017-01-01
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
Transmission problem for the Laplace equation and the integral equation method
Czech Academy of Sciences Publication Activity Database
Medková, Dagmar
2012-01-01
Roč. 387, č. 2 (2012), s. 837-843 ISSN 0022-247X Institutional research plan: CEZ:AV0Z10190503 Keywords : transmission problem * Laplace equation * boundary integral equation Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11008985
Sloss, J. M.; Kranzler, S. K.
1972-01-01
The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
A New Algorithm for System of Integral Equations
Directory of Open Access Journals (Sweden)
Abdujabar Rasulov
2014-01-01
Full Text Available We develop a new algorithm to solve the system of integral equations. In this new method no need to use matrix weights. Beacause of it, we reduce computational complexity considerable. Using the new algorithm it is also possible to solve an initial boundary value problem for system of parabolic equations. To verify the efficiency, the results of computational experiments are given.
Feynman path integral related to stochastic schroedinger equation
International Nuclear Information System (INIS)
Belavkin, V.P.; Smolyanov, O.G.
1998-01-01
The derivation of the Schroedinger equation describing the continuous measurement process is presented. The representation of the solution of the stochastic Schroedinger equation for continuous measurements is obtained by means of the Feynman path integral. The connection with the heuristic approach to the description of continuous measurements is considered. The connection with the Senon paradox is established [ru
Multi-component bi-Hamiltonian Dirac integrable equations
Energy Technology Data Exchange (ETDEWEB)
Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu
2009-01-15
A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.
Differential equations for loop integrals in Baikov representation
Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang
2018-05-01
We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.
Monograph - The Numerical Integration of Ordinary Differential Equations.
Hull, T. E.
The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…
Distribution theory for Schrödinger’s integral equation
Lange, R.J.
2015-01-01
Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger's equation. This paper, in contrast, investigates the integral form of Schrödinger's equation. While both forms are known to be equivalent for smooth potentials, this is not true for
Picard-Fuchs equations of dimensionally regulated Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Zayadeh, Raphael
2013-12-15
This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is
Picard-Fuchs equations of dimensionally regulated Feynman integrals
International Nuclear Information System (INIS)
Zayadeh, Raphael
2013-12-01
This thesis is devoted to studying differential equations of Feynman integrals. A Feynman integral depends on a dimension D. For integer values of D it can be written as a projective integral, which is called the Feynman parameter prescription. A major complication arises from the fact that for some values of D the integral can diverge. This problem is solved within dimensional regularization by continuing the integral as a meromorphic function on the complex plane and replacing the ill-defined quantity by a Laurent series in a dimensional regularization parameter. All terms in such a Laurent expansion are periods in the sense of Kontsevich and Zagier. We describe a new method to compute differential equations of Feynman integrals. So far, the standard has been to use integration-by-parts (IBP) identities to obtain coupled systems of linear differential equations for the master integrals. Our method is based on the theory of Picard-Fuchs equations. In the case we are interested in, that of projective and quasiprojective families, a Picard-Fuchs equation can be computed by means of the Griffiths-Dwork reduction. We describe a method that is designed for fixed integer dimension. After a suitable integer shift of dimension we obtain a period of a family of hypersurfaces, hence a Picard-Fuchs equation. This equation is inhomogeneous because the domain of integration has a boundary and we only obtain a relative cycle. As a second step we shift back the dimension using Tarasov's generalized dimensional recurrence relations. Furthermore, we describe a method to directly compute the differential equation for general D without shifting the dimension. This is based on the Griffiths-Dwork reduction. The success of this method depends on the ability to solve large systems of linear equations. We give examples of two and three-loop graphs. Tarasov classifies two-loop two-point functions and we give differential equations for these. For us the most interesting example is the two
Integrability of a system of two nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhukhunashvili, V.Z.
1989-01-01
In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants
Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence
International Nuclear Information System (INIS)
Bloomberg, D.S.; Castelli, V.
1985-01-01
The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor β in the MH approach varies inversely with permeability μ, and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for β 3 , the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on β, degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for βless than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix
On the complete integrability of the discrete Nahm equations
International Nuclear Information System (INIS)
Murray, M.K.
2000-01-01
The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-bundle over the spectral curve, such that the discrete-time DN evolution corresponds to walking in the Jacobian of the spectral curve in a straight line through the line-bundle with steps of a fixed size. Some of the implications for hyperbolic monopoles are also discussed. (orig.)
Integrable semi-discretizations of the reduced Ostrovsky equation
International Nuclear Information System (INIS)
Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro
2015-01-01
Based on our previous work on the reduced Ostrovsky equation (J. Phys. A: Math. Theor. 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one being its original form, the other the differentiated form (the short wave limit of the Degasperis–Procesi equation) two semi-discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified. (paper)
First integrals of the axisymmetric shape equation of lipid membranes
Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun
2018-03-01
The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).
Rebelo, Raphaël; Winternitz, Pavel
2017-01-01
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers...
Differential equations and integrable models: the SU(3) case
International Nuclear Information System (INIS)
Dorey, Patrick; Tateo, Roberto
2000-01-01
We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz
Periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
M. N. Islam
1988-01-01
Full Text Available Consider the system of equationsx(t=f(t+∫−∞tk(t,sx(sds, (1andx(t=f(t+∫−∞tk(t,sg(s,x(sds. (2Existence of continuous periodic solutions of (1 is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1 it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1 and (2 are btained using the contraction mapping principle as the basic tool.
An algorithm of computing inhomogeneous differential equations for definite integrals
Nakayama, Hiromasa; Nishiyama, Kenta
2010-01-01
We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\\"obner basis method in the ring of differential operators.
Canonical algorithms for numerical integration of charged particle motion equations
Efimov, I. N.; Morozov, E. A.; Morozova, A. R.
2017-02-01
A technique for numerically integrating the equation of charged particle motion in a magnetic field is considered. It is based on the canonical transformations of the phase space in Hamiltonian mechanics. The canonical transformations make the integration process stable against counting error accumulation. The integration algorithms contain a minimum possible amount of arithmetics and can be used to design accelerators and devices of electron and ion optics.
Cell membrane temperature rate sensitivity predicted from the Nernst equation.
Barnes, F S
1984-01-01
A hyperpolarized current is predicted from the Nernst equation for conditions of positive temperature derivatives with respect to time. This ion current, coupled with changes in membrane channel conductivities, is expected to contribute to a transient potential shift across the cell membrane for silent cells and to a change in firing rate for pacemaker cells.
Numerical solution of boundary-integral equations for molecular electrostatics.
Bardhan, Jaydeep P
2009-03-07
Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
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Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.
Lax Pairs for Discrete Integrable Equations via Darboux Transformations
International Nuclear Information System (INIS)
Cao Ce-Wen; Zhang Guang-Yao
2012-01-01
A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)
Discrete Painlevé equations: an integrability paradigm
International Nuclear Information System (INIS)
Grammaticos, B; Ramani, A
2014-01-01
In this paper we present a review of results on discrete Painlevé equations. We begin with an introduction which serves as a refresher on the continuous Painlevé equations. Next, in the first, main part of the paper, we introduce the discrete Painlevé equations, the various methods for their derivation, and their properties as well as their classification scheme. Along the way we present a brief summary of the two major discrete integrability detectors and of Quispel–Roberts–Thompson mapping, which plays a primordial role in the derivation of discrete Painlevé equations. The second part of the paper is more technical and focuses on the presentation of new results on what are called asymmetric discrete Painlevé equations. (comment)
Field Method for Integrating the First Order Differential Equation
Institute of Scientific and Technical Information of China (English)
JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu
2007-01-01
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
Modern integral equation techniques for quantum reactive scattering theory
International Nuclear Information System (INIS)
Auerbach, S.M.
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 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
Babenko’s Approach to Abel’s Integral Equations
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Chenkuan Li
2018-03-01
Full Text Available The goal of this paper is to investigate the following Abel’s integral equation of the second kind: y ( t + λ Γ ( α ∫ 0 t ( t − τ α − 1 y ( τ d τ = f ( t , ( t > 0 and its variants by fractional calculus. Applying Babenko’s approach and fractional integrals, we provide a general method for solving Abel’s integral equation and others with a demonstration of different types of examples by showing convergence of series. In particular, we extend this equation to a distributional space for any arbitrary α ∈ R by fractional operations of generalized functions for the first time and obtain several new and interesting results that cannot be realized in the classical sense or by the Laplace transform.
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Lyakhov, Dmitry A.
2017-08-29
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.
2017-01-01
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
Recursive integral equations with positive kernel for lattice calculations
International Nuclear Information System (INIS)
Illuminati, F.; Isopi, M.
1990-11-01
A Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory is derived. The equation is defined in the thermodynamic limit, and its iterative solution is convergent. Moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories. 10 refs
Master equations and the theory of stochastic path integrals
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Integrability of the one dimensional Schrödinger equation
Combot, Thierry
2018-02-01
We present a definition of integrability for the one-dimensional Schrödinger equation, which encompasses all known integrable systems, i.e., systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural of boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.
Numerical treatments for solving nonlinear mixed integral equation
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M.A. Abdou
2016-12-01
Full Text Available We consider a mixed type of nonlinear integral equation (MNLIE of the second kind in the space C[0,T]×L2(Ω,T<1. The Volterra integral terms (VITs are considered in time with continuous kernels, while the Fredholm integral term (FIT is considered in position with singular general kernel. Using the quadratic method and separation of variables method, we obtain a nonlinear system of Fredholm integral equations (NLSFIEs with singular kernel. A Toeplitz matrix method, in each case, is then used to obtain a nonlinear algebraic system. Numerical results are calculated when the kernels take a logarithmic form or Carleman function. Moreover, the error estimates, in each case, are then computed.
Numerical Integration of the Transport Equation For Infinite Homogeneous Media
Energy Technology Data Exchange (ETDEWEB)
Haakansson, Rune
1962-01-15
The transport equation for neutrons in infinite homogeneous media is solved by direct numerical integration. Accounts are taken to the anisotropy and the inelastic scattering. The integration has been performed by means of the trapezoidal rule and the length of the energy intervals are constant in lethargy scale. The machine used is a Ferranti Mercury computer. Results are given for water, heavy water, aluminium water mixture and iron-aluminium-water mixture.
An integrable semi-discretization of the Boussinesq equation
International Nuclear Information System (INIS)
Zhang, Yingnan; Tian, Lixin
2016-01-01
Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.
Minimally coupled N-particle scattering integral equations
International Nuclear Information System (INIS)
Kowalski, K.L.
1977-01-01
A concise formalism is developed which permits the efficient representation and generalization of several known techniques for deriving connected-kernel N-particle scattering integral equations. The methods of Kouri, Levin, and Tobocman and Bencze and Redish which lead to minimally coupled integral equations are of special interest. The introduction of channel coupling arrays is characterized in a general manner and the common base of this technique and that of the so-called channel coupling scheme is clarified. It is found that in the Bencze-Redish formalism a particular coupling array has a crucial function but one different from that of the arrays employed by Kouri, Levin, and Tobocman. The apparent dependence of the proof of the minimality of the Bencze-Redish integral equations upon the form of the inhomogeneous term in these equations is eliminated. This is achieved by an investigation of the full (nonminimal) Bencze-Redish kernel. It is shown that the second power of this operator is connected, a result which is needed for the full applicability of the Bencze-Redish formalism. This is used to establish the relationship between the existence of solutions to the homogeneous form of the minimal equations and eigenvalues of the full Bencze-Redish kernel
An integrable semi-discretization of the Boussinesq equation
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)
2016-10-23
Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.
Numerical Simulation of Antennas with Improved Integral Equation Method
International Nuclear Information System (INIS)
Ma Ji; Fang Guang-You; Lu Wei
2015-01-01
Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object. (paper)
Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste
International Nuclear Information System (INIS)
HU, T.A.
1999-01-01
Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement within a factor of two to three
Integrated vehicle dynamics control using State Dependent Riccati Equations
Bonsen, B.; Mansvelders, R.; Vermeer, E.
2010-01-01
In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this
An approximation method for nonlinear integral equations of Hammerstein type
International Nuclear Information System (INIS)
Chidume, C.E.; Moore, C.
1989-05-01
The solution of a nonlinear integral equation of Hammerstein type in Hilbert spaces is approximated by means of a fixed point iteration method. Explicit error estimates are given and, in some cases, convergence is shown to be at least as fast as a geometric progression. (author). 25 refs
Higher-Order Integral Equation Methods in Computational Electromagnetics
DEFF Research Database (Denmark)
Jørgensen, Erik; Meincke, Peter
Higher-order integral equation methods have been investigated. The study has focused on improving the accuracy and efficiency of the Method of Moments (MoM) applied to electromagnetic problems. A new set of hierarchical Legendre basis functions of arbitrary order is developed. The new basis...
On Fredholm-Stieltjes quadratic integral equation with supremum
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Unconditionally stable integration of Maxwell’s equations
Verwer, J.G.; Botchev, M.A.
2009-01-01
Numerical integration of Maxwell’s equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit - finite
Fringe integral equation method for a truncated grounded dielectric slab
DEFF Research Database (Denmark)
Jørgensen, Erik; Maci, S.; Toccafondi, A.
2001-01-01
The problem of scattering by a semi-infinite grounded dielectric slab illuminated by an arbitrary incident TMz polarized electric field is studied by solving a new set of “fringe” integral equations (F-IEs), whose functional unknowns are physically associated to the wave diffraction processes...
Local first integrals for systems of differential equations
International Nuclear Information System (INIS)
Zhang Xiang
2003-01-01
The main purpose of this paper is to provide some sufficient conditions for a system of differential equations to have local first integrals in a certain neighbourhood of a singularity. Our results generalize those given in Kwek et al (2003 Z. Angew. Math. Phys. 54 26) and Li et al (2003 Z. Angew. Math. Phys. 54 235)
Cut cancellation in the planar integral equation for the Reggeon
International Nuclear Information System (INIS)
Bishari, M.; Veneziano, G.
1975-01-01
Planar unitarity for the Reggeon, analyticity and the multi-Regge assumption with cluster production lead to integral equations of the Chew-Goldberger-Low type with separable self-consistent kernel. Contrary to common prejudice, the authors show the existence of solutions exhibiting moving poles and exact, non-perturbative cancellation of the cut. Previously studied consistency conditions are rederived. (Auth.)
International Nuclear Information System (INIS)
Burde, G.I.
2002-01-01
A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given
Poisson's theorem and integrals of KdV equation
International Nuclear Information System (INIS)
Tasso, H.
1978-01-01
Using Poisson's theorem it is proved that if F = integral sub(-infinity)sup(+infinity) T(u,usub(x),...usub(n,t))dx is an invariant functional of KdV equation, then integral sub(-infinity)sup(+infinity) delta F/delta u dx integral sub(-infinity)sup(+infinity) delta T/delta u dx is also an invariant functional. In the case of a polynomial T, one finds in a simple way the known recursion ΔTr/Δu = Tsub(r-1). This note gives an example of the usefulness of Poisson's theorem. (author)
Integral propagator solvers for Vlasov-Fokker-Planck equations
International Nuclear Information System (INIS)
Donoso, J M; Rio, E del
2007-01-01
We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov-Fokker-Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker-Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step. (fast track communication)
Kwong-Wong-type integral equation on time scales
Directory of Open Access Journals (Sweden)
Baoguo Jia
2011-09-01
Full Text Available Consider the second-order nonlinear dynamic equation $$ [r(tx^Delta(ho(t]^Delta+p(tf(x(t=0, $$ where $p(t$ is the backward jump operator. We obtain a Kwong-Wong-type integral equation, that is: If $x(t$ is a nonoscillatory solution of the above equation on $[T_0,infty$, then the integral equation $$ frac{r^sigma(tx^Delta(t}{f(x^sigma(t} =P^sigma(t+int^infty_{sigma(t}frac{r^sigma(s [int^1_0f'(x_h(sdh][x^Delta(s]^2}{f(x(s f(x^sigma(s}Delta s $$ is satisfied for $tgeq T_0$, where $P^sigma(t=int^infty_{sigma(t}p(sDelta s$, and $x_h(s=x(s+hmu(sx^Delta(s$. As an application, we show that the superlinear dynamic equation $$ [r(tx^{Delta}(ho(t]^Delta+p(tf(x(t=0, $$ is oscillatory, under certain conditions.
Rate equation analysis of hydrogen uptake on Si (100) surfaces
International Nuclear Information System (INIS)
Inanaga, S.; Rahman, F.; Khanom, F.; Namiki, A.
2005-01-01
We have studied the uptake process of H on Si (100) surfaces by means of rate equation analysis. Flowers' quasiequilibrium model for adsorption and desorption of H [M. C. Flowers, N. B. H. Jonathan, A. Morris, and S. Wright, Surf. Sci. 396, 227 (1998)] is extended so that in addition to the H abstraction (ABS) and β 2 -channel thermal desorption (TD) the proposed rate equation further includes the adsorption-induced desorption (AID) and β 1 -TD. The validity of the model is tested by the experiments of ABS and AID rates in the reaction system H+D/Si (100). Consequently, we find it can well reproduce the experimental results, validating the proposed model. We find the AID rate curve as a function of surface temperature T s exhibits a clear anti-correlation with the bulk dangling bond density versus T s curve reported in the plasma-enhanced chemical vapor deposition (CVD) for amorphous Si films. The significance of the H chemistry in plasma-enhanced CVD is discussed
New multidimensional partially integrable generalization of S-integrable N-wave equation
International Nuclear Information System (INIS)
Zenchuk, A. I.
2007-01-01
This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n-1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example
76 FR 48159 - Integrated System Power Rates
2011-08-08
... DEPARTMENT OF ENERGY Southwestern Power Administration Integrated System Power Rates AGENCY... American Electric Reliability Corporation and to cover increased investments and replacements in..., prepared a Current Power Repayment Study using existing system rates. The Study indicates that Southwestern...
Rational first integrals of geodesic equations and generalised hidden symmetries
International Nuclear Information System (INIS)
Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro
2016-01-01
We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson–O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski–Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing–Yano tensors. (paper)
Validation of resting metabolic rate prediction equations for teenagers
Directory of Open Access Journals (Sweden)
Paulo Henrique Santos da Fonseca
2007-09-01
Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991
Lagrangian structures, integrability and chaos for 3D dynamical equations
International Nuclear Information System (INIS)
Bustamante, Miguel D; Hojman, Sergio A
2003-01-01
In this paper, we consider the general setting for constructing action principles for three-dimensional first-order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion
Method of mechanical quadratures for solving singular integral equations of various types
Sahakyan, A. V.; Amirjanyan, H. A.
2018-04-01
The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.
Validation of estimated glomerular filtration rate equations for Japanese children.
Gotoh, Yoshimitsu; Uemura, Osamu; Ishikura, Kenji; Sakai, Tomoyuki; Hamasaki, Yuko; Araki, Yoshinori; Hamda, Riku; Honda, Masataka
2018-01-25
The gold standard for evaluation of kidney function is renal inulin clearance (Cin). However, the methodology for Cin is complicated and difficult, especially for younger children and/or patients with bladder dysfunction. Therefore, we developed a simple and easier method for obtaining the estimated glomerular filtration rate (eGFR) using equations and values for several biomarkers, i.e., serum creatinine (Cr), serum cystatin C (cystC), serum beta-2 microglobulin (β 2 MG), and creatinine clearance (Ccr). The purpose of the present study was to validate these equations with a new data set. To validate each equation, we used data of 140 patients with CKD with clinical need for Cin, using the measured GFR (mGFR). We compared the results for each eGFR equation with the mGFR using mean error (ME), root mean square error (RMSE), P 30 , and Bland-Altman analysis. The ME of Cr, cystC, β 2 MG, and Ccr based on eGFR was 15.8 ± 13.0, 17.2 ± 16.5, 15.4 ± 14.3, and 10.6 ± 13.0 ml/min/1.73 m 2 , respectively. The RMSE was 29.5, 23.8, 20.9, and 16.7, respectively. The P 30 was 79.4, 71.1, 69.5, and 92.9%, respectively. The Bland-Altman bias analysis showed values of 4.0 ± 18.6, 5.3 ± 16.8, 12.7 ± 17.0, and 2.5 ± 17.2 ml/min/1.73 m 2 , respectively, for these parameters. The bias of each eGFR equation was not large. Therefore, each eGFR equation could be used.
Integral equation methods for vesicle electrohydrodynamics in three dimensions
Veerapaneni, Shravan
2016-12-01
In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.
High-precision numerical integration of equations in dynamics
Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.
2018-05-01
An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.
Integrable equation of state for noisy cosmic string
International Nuclear Information System (INIS)
Carter, B.
1990-01-01
It is argued that, independently of the detailed (thermal or more general) noise spectrum of the microscopic extrinsic excitations that can be expected on an ordinary cosmic string, their effect can be taken into account at a macroscopic level by replacing the standard isotropic Goto-Nambu-type string model by the nondegenerate string model characterized by an equation of state of the nondispersive ''fixed determinant'' type, with the effective surface stress-energy tensor satisfying (T ν ν ) 2 -T μ ν T ν μ =2T 0 2 , where T 0 is a constant representing the null-state limit of the string tension T, whose product with the energy density U of the string is thereby held fixed: TU=T 0 2 . It is shown that this equation of state has the special property of giving rise (in a flat background) to explicitly integrable dynamical equations
Integral equations of hadronic correlation functions a functional- bootstrap approach
Manesis, E K
1974-01-01
A reasonable 'microscopic' foundation of the Feynman hadron-liquid analogy is offered, based on a class of models for hadron production. In an external field formalism, the equivalence (complementarity) of the exclusive and inclusive descriptions of hadronic reactions is specifically expressed in a functional-bootstrap form, and integral equations between inclusive and exclusive correlation functions are derived. Using the latest CERN-ISR data on the two-pion inclusive correlation function, and assuming rapidity translational invariance for the exclusive one, the simplest integral equation is solved in the 'central region' and an exclusive correlation length in rapidity predicted. An explanation is also offered for the unexpected similarity observed between pi /sup +/ pi /sup -/ and pi /sup -/ pi /sup -/ inclusive correlations. (31 refs).
Integral equations with difference kernels on finite intervals
Sakhnovich, Lev A
2015-01-01
This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful...
TBA-like integral equations from quantized mirror curves
Energy Technology Data Exchange (ETDEWEB)
Okuyama, Kazumi [Department of Physics, Shinshu University,Matsumoto 390-8621 (Japan); Zakany, Szabolcs [Département de Physique Théorique, Université de Genève,Genève, CH-1211 (Switzerland)
2016-03-15
Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local ℙ{sup 2}. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.
TBA-like integral equations from quantized mirror curves
Okuyama, Kazumi; Zakany, Szabolcs
2016-03-01
Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local P2. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.
Optimum biasing of integral equations in Monte Carlo calculations
International Nuclear Information System (INIS)
Hoogenboom, J.E.
1979-01-01
In solving integral equations and estimating average values with the Monte Carlo method, biasing functions may be used to reduce the variancee of the estimates. A simple derivation was used to prove the existence of a zero-variance collision estimator if a specific biasing function and survival probability are applied. This optimum biasing function is the same as that used for the well known zero-variance last-event estimator
The integral equation method applied to eddy currents
International Nuclear Information System (INIS)
Biddlecombe, C.S.; Collie, C.J.; Simkin, J.; Trowbridge, C.W.
1976-04-01
An algorithm for the numerical solution of eddy current problems is described, based on the direct solution of the integral equation for the potentials. In this method only the conducting and iron regions need to be divided into elements, and there are no boundary conditions. Results from two computer programs using this method for iron free problems for various two-dimensional geometries are presented and compared with analytic solutions. (author)
Deterministic methods to solve the integral transport equation in neutronic
International Nuclear Information System (INIS)
Warin, X.
1993-11-01
We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs
The ICVSIE: A General Purpose Integral Equation Method for Bio-Electromagnetic Analysis.
Gomez, Luis J; Yucel, Abdulkadir C; Michielssen, Eric
2018-03-01
An internally combined volume surface integral equation (ICVSIE) for analyzing electromagnetic (EM) interactions with biological tissue and wide ranging diagnostic, therapeutic, and research applications, is proposed. The ICVSIE is a system of integral equations in terms of volume and surface equivalent currents in biological tissue subject to fields produced by externally or internally positioned devices. The system is created by using equivalence principles and solved numerically; the resulting current values are used to evaluate scattered and total electric fields, specific absorption rates, and related quantities. The validity, applicability, and efficiency of the ICVSIE are demonstrated by EM analysis of transcranial magnetic stimulation, magnetic resonance imaging, and neuromuscular electrical stimulation. Unlike previous integral equations, the ICVSIE is stable regardless of the electric permittivities of the tissue or frequency of operation, providing an application-agnostic computational framework for EM-biomedical analysis. Use of the general purpose and robust ICVSIE permits streamlining the development, deployment, and safety analysis of EM-biomedical technologies.
Introduction to stochastic analysis integrals and differential equations
Mackevicius, Vigirdas
2013-01-01
This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion pro
Functional analysis in the study of differential and integral equations
International Nuclear Information System (INIS)
Sell, G.R.
1976-01-01
This paper illustrates the use of functional analysis in the study of differential equations. Our particular starting point, the theory of flows or dynamical systems, originated with the work of H. Poincare, who is the founder of the qualitative theory of ordinary differential equations. In the qualitative theory one tries to describe the behaviour of a solution, or a collection of solutions, without ''solving'' the differential equation. As a starting point one assumes the existence, and sometimes the uniqueness, of solutions and then one tries to describe the asymptotic behaviour, as time t→+infinity, of these solutions. We compare the notion of a flow with that of a C 0 -group of bounded linear operators on a Banach space. We shall show how the concept C 0 -group, or more generally a C 0 -semigroup, can be used to study the behaviour of solutions of certain differential and integral equations. Our main objective is to show how the concept of a C 0 -group and especially the notion of weak-compactness can be used to prove the existence of an invariant measure for a flow on a compact Hausdorff space. Applications to the theory of ordinary differential equations are included. (author)
A New time Integration Scheme for Cahn-hilliard Equations
Schaefer, R.
2015-06-01
In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.
A New time Integration Scheme for Cahn-hilliard Equations
Schaefer, R.; Smol-ka, M.; Dalcin, L; Paszyn'ski, M.
2015-01-01
In this paper we present a new integration scheme that can be applied to solving difficult non-stationary non-linear problems. It is obtained by a successive linearization of the Crank- Nicolson scheme, that is unconditionally stable, but requires solving non-linear equation at each time step. We applied our linearized scheme for the time integration of the challenging Cahn-Hilliard equation, modeling the phase separation in fluids. At each time step the resulting variational equation is solved using higher-order isogeometric finite element method, with B- spline basis functions. The method was implemented in the PETIGA framework interfaced via the PETSc toolkit. The GMRES iterative solver was utilized for the solution of a resulting linear system at every time step. We also apply a simple adaptivity rule, which increases the time step size when the number of GMRES iterations is lower than 30. We compared our method with a non-linear, two stage predictor-multicorrector scheme, utilizing a sophisticated step length adaptivity. We controlled the stability of our simulations by monitoring the Ginzburg-Landau free energy functional. The proposed integration scheme outperforms the two-stage competitor in terms of the execution time, at the same time having a similar evolution of the free energy functional.
Numerical integration of the Langevin equation: Monte Carlo simulation
International Nuclear Information System (INIS)
Ermak, D.L.; Buckholz, H.
1980-01-01
Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation which uses a memory function in the friction force term. General simulation techniques are derived which are independent of the form of the memory function. A special method requiring less storage space is presented for the case of the exponential memory function
A Generalized Analytic Operator-Valued Function Space Integral and a Related Integral Equation
International Nuclear Information System (INIS)
Chang, K.S.; Kim, B.S.; Park, C.H.; Ryu, K.S.
2003-01-01
We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L p into L p-ci r cumflexprime (1< p ≤ 2) by the analytic continuation of the generalized Wiener integral. We prove the existence of the integral for certain functionals which involve some Borel measures. Also we show that the generalized analytic operator-valued function space integral satisfies an integral equation related to the generalized Schroedinger equation. The resulting theorems extend the theory of operator-valued function space integrals substantially and previous theorems about these integrals are generalized by our results
On solvability of some quadratic functional-integral equation in Banach algebra
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
Using the technique of a suitable measure of non-compactness in Banach algebra, we prove an existence theorem for some functional-integral equations which contain, as particular cases, a lot of integral and functional-integral equations that arise in many branches of nonlinear analysis and its applications. Also, the famous Chandrasekhar's integral equation is considered as a special case. (author)
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
One-way spatial integration of hyperbolic equations
Towne, Aaron; Colonius, Tim
2015-11-01
In this paper, we develop and demonstrate a method for constructing well-posed one-way approximations of linear hyperbolic systems. We use a semi-discrete approach that allows the method to be applied to a wider class of problems than existing methods based on analytical factorization of idealized dispersion relations. After establishing the existence of an exact one-way equation for systems whose coefficients do not vary along the axis of integration, efficient approximations of the one-way operator are constructed by generalizing techniques previously used to create nonreflecting boundary conditions. When physically justified, the method can be applied to systems with slowly varying coefficients in the direction of integration. To demonstrate the accuracy and computational efficiency of the approach, the method is applied to model problems in acoustics and fluid dynamics via the linearized Euler equations; in particular we consider the scattering of sound waves from a vortex and the evolution of hydrodynamic wavepackets in a spatially evolving jet. The latter problem shows the potential of the method to offer a systematic, convergent alternative to ad hoc regularizations such as the parabolized stability equations.
On the Volterra integral equation relating creep and relaxation
International Nuclear Information System (INIS)
Anderssen, R S; De Hoog, F R; Davies, A R
2008-01-01
The evolving stress–strain response of a material to an applied deformation is causal. If the current response depends on the earlier history of the stress–strain dynamics of the material (i.e. the material has memory), then Volterra integral equations become the natural framework within which to model the response. For viscoelastic materials, when the response is linear, the dual linear Boltzmann causal integral equations are the appropriate model. The choice of one rather than the other depends on whether the applied deformation is a stress or a strain, and the associated response is, respectively, a creep or a relaxation. The duality between creep and relaxation is known explicitly and is referred to as the 'interconversion equation'. Rheologically, its importance relates to the fact that it allows the creep to be determined from knowledge of the relaxation and vice versa. Computationally, it has been known for some time that the recovery of the relaxation from the creep is more problematic than the creep from the relaxation. Recent research, using discrete models for the creep and relaxation, has confirmed that this is an essential feature of interconversion. In this paper, the corresponding result is generalized for continuous models of the creep and relaxation
An integrated approach to determine phenomenological equations in metallic systems
Ghamarian, Iman
It is highly desirable to be able to make predictions of properties in metallic materials based upon the composition of the material and the microstructure. Unfortunately, the complexity of real, multi-component, multi-phase engineering alloys makes the provision of constituent-based (i.e., composition or microstructure) phenomenological equations extremely difficult. Due to these difficulties, qualitative predictions are frequently used to study the influence of microstructure or composition on the properties. Neural networks were used as a tool to get a quantitative model from a database. However, the developed model is not a phenomenological model. In this study, a new method based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and monte carlo was proposed. These three methods, when coupled in the manner described in this study, allows for the extraction of phenomenological equations with a concurrent analysis of uncertainty. This approach has been applied to a multi-component, multi-phase microstructure exhibiting phases with varying spatial and morphological distributions. Specifically, this approach has been applied to derive a phenomenological equation for the prediction of yield strength in alpha+beta processed Ti-6-4. The equation is consistent with not only the current dataset but also, where available, the limited information regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium.
Is Yang-Mills equation a totally integrable system. Lecture III
International Nuclear Information System (INIS)
Chau Wang, L.L.
1981-01-01
Topics covered include: loop-space formulation of gauge theory - loop-space chiral equation; two dimensional chiral equation - conservation laws, linear system and integrability; and parallel development for the loop-space chiral equation - subtlety
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
Directory of Open Access Journals (Sweden)
D.X. Horváth
2016-01-01
Full Text Available We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Horváth, D.X., E-mail: esoxluciuslinne@gmail.com [MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, 1111 Budapest (Hungary); Sotiriadis, S., E-mail: sotiriad@sissa.it [SISSA and INFN, Via Bonomea 265, 34136 Trieste (Italy); Takács, G., E-mail: takacsg@eik.bme.hu [MTA-BME “Momentum” Statistical Field Theory Research Group, Budafoki út 8, 1111 Budapest (Hungary); Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, 1111 Budapest (Hungary)
2016-01-15
We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients
Novák, Pavel; Šprlák, Michal
2018-03-01
The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.
Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2
International Nuclear Information System (INIS)
Velarde, G.
1976-01-01
Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)
On integrability conditions of the equations of nonsymmetrical chiral field on SO(4)
International Nuclear Information System (INIS)
Tskhakaya, D.D.
1990-01-01
Possibility of integrating the equations of nonsymmetrical chiral field on SO(4) by means of the inverse scattering method is investigated. Maximal number of the motion integrals is found for the corresponding system of ordinary differential equations
Numerical solution of the potential problem by integral equations without Green's functions
International Nuclear Information System (INIS)
De Mey, G.
1977-01-01
An integral equation technique will be presented to solve Laplace's equation in a two-dimensional area S. The Green's function has been replaced by a particular solution of Laplace equation in order to establish the integral equation. It is shown that accurate results can be obtained provided the pivotal elimination method is used to solve the linear algebraic set
International Nuclear Information System (INIS)
Liu Chunliang; Xie Xi; Chen Yinbao
1991-01-01
The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation
Tokamak plasma shape identification based on the boundary integral equations
International Nuclear Information System (INIS)
Kurihara, Kenichi; Kimura, Toyoaki
1992-05-01
A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)
Integral solution for the spherically symmetric Fokker-Planck equation
International Nuclear Information System (INIS)
Donoso, J.M.; Soler, M.
1993-01-01
We propose an integral method to deal with the spherically symmetric non-linear Fokker-Planck equation appearing in plasma physics. A probability transition expression is obtained, which takes into account the proper domain for the radial velocity component. The analytical and computational results are new, and the time evolution is completely satisfactory. The main achievement of the method is conservation of both the initial norm and energy for unlimited times, which has not been attained in the differential approach to the problem. (orig.)
Explicit solution of Calderon preconditioned time domain integral equations
Ulku, Huseyin Arda
2013-07-01
An explicit marching on-in-time (MOT) scheme for solving Calderon-preconditioned time domain integral equations is proposed. The scheme uses Rao-Wilton-Glisson and Buffa-Christiansen functions to discretize the domain and range of the integral operators and a PE(CE)m type linear multistep to march on in time. Unlike its implicit counterpart, the proposed explicit solver requires the solution of an MOT system with a Gram matrix that is sparse and well-conditioned independent of the time step size. Numerical results demonstrate that the explicit solver maintains its accuracy and stability even when the time step size is chosen as large as that typically used by an implicit solver. © 2013 IEEE.
Geometrical-integrability constraints and equations of motion in four plus extended super spaces
International Nuclear Information System (INIS)
Chau, L.L.
1987-01-01
It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion
Discretization of the induced-charge boundary integral equation.
Bardhan, Jaydeep P; Eisenberg, Robert S; Gillespie, Dirk
2009-07-01
Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.
Crossover integral equation theory for the liquid structure study
International Nuclear Information System (INIS)
Lai, S.K.; Chen, H.C.
1994-08-01
The main purpose of this work is to report on a calculation that describes the role of the long-range bridge function [H. Iyetomi and S. Ichimaru, Phys. Rev. A 25, 2434 (1982)] as applied to the study of structure of simple liquid metals. It was found here that this bridge function accounts pretty well for the major part of long-range interactions but is physically inadequate for describing the short-range part of liquid structure. To improve on the theory we have drawn attention to the crossover integral equation method which, in essence, amounts to adding to the above bridge function a short-range correction of bridge diagrams. The suggested crossover procedure has been tested for the case of liquid metal Cs. Remarkably good agreement with experiment was obtained confirming our conjecture that the crossover integral equation approach as stressed in this work is potentially an appropriate theory for an accurate study of liquid structure possibly for the supercooled liquid regime. (author). 21 refs, 3 figs
Discretization of the induced-charge boundary integral equation.
Energy Technology Data Exchange (ETDEWEB)
Bardhan, J. P.; Eisenberg, R. S.; Gillespie, D.; Rush Univ. Medical Center
2009-07-01
Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.
Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations
International Nuclear Information System (INIS)
Xu Xixiang
2012-01-01
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. (general)
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Kinematic equations for resolved-rate control of an industrial robot arm
Barker, L. K.
1983-01-01
An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.
Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale
Directory of Open Access Journals (Sweden)
Li Jun-Gang
2017-01-01
Full Text Available In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued square integrable martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and set-valued square integrable martingale integral equation. The existence and uniqueness of solution to set-valued stochastic integral equation are proved. The discussion will be useful in optimal control and mathematical finance in psychological factors.
Experiences in integrated leak rate measurements
International Nuclear Information System (INIS)
Shirk, R.E.
1982-01-01
During a hypothetical design basis accident for nuclear power plants, the reactor containment system is relied upon to maintain radioactive exposure limits below acceptable limits. Integrated leak rate testing is a means of verifying that the leakage of radioactivity material from the reactor containment will be below allowable limits. Leakage rate computations are based on the ideal gas law. The absolute method of leakage rate testing utilizing mass point method of data analysis is recommended. Integrated leak rate testing data is obtained from pressure, drybulb temperature, dewpoint temperature, and flow measuring systems. Test data does not support the usual leakage (flow) - pressure square root relationship. The major source of potential leakage from the reactor containment is reactor containment isolation valves
International Nuclear Information System (INIS)
Zhang Yufeng; Fan Engui; Zhang Yongqing
2006-01-01
With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations
Kleinert, H.; Zatloukal, V.
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
The reduced basis method for the electric field integral equation
International Nuclear Information System (INIS)
Fares, M.; Hesthaven, J.S.; Maday, Y.; Stamm, B.
2011-01-01
We introduce the reduced basis method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized electric field integral equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first step consists of a computationally intense assembling of the reduced basis, that needs to be effected only once. In the second step, we compute output functionals of the solution, such as the Radar Cross Section (RCS), independently of the dimension of the discretization space, for many different parameter values in a many-query context at very little cost. Parameters include the wavenumber, the angle of the incident plane wave and its polarization.
Numerical method for solving integral equations of neutron transport. II
International Nuclear Information System (INIS)
Loyalka, S.K.; Tsai, R.W.
1975-01-01
In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)
Integrable equations, addition theorems, and the Riemann-Schottky problem
International Nuclear Information System (INIS)
Buchstaber, Viktor M; Krichever, I M
2006-01-01
The classical Weierstrass theorem claims that, among the analytic functions, the only functions admitting an algebraic addition theorem are the elliptic functions and their degenerations. This survey is devoted to far-reaching generalizations of this result that are motivated by the theory of integrable systems. The authors discovered a strong form of the addition theorem for theta functions of Jacobian varieties, and this form led to new approaches to known problems in the geometry of Abelian varieties. It is shown that strong forms of addition theorems arise naturally in the theory of the so-called trilinear functional equations. Diverse aspects of the approaches suggested here are discussed, and some important open problems are formulated.
Acoustic 3D modeling by the method of integral equations
Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.
2018-02-01
This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, Àngel
2013-12-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
Asymptotics of steady states of a selection–mutation equation for small mutation rate
Calsina, À ngel; Cuadrado, Sí lvia; Desvillettes, Laurent; Raoul, Gaë l
2013-01-01
We consider a selection-mutation equation for the density of individuals with respect to a continuous phenotypic evolutionary trait. We assume that the competition term for an individual with a given trait depends on the traits of all the other individuals, therefore giving an infinite-dimensional nonlinearity. Mutations are modelled by means of an integral operator. We prove existence of steady states and show that, when the mutation rate goes to zero, the asymptotic profile of the population is a Cauchy distribution. © Royal Society of Edinburgh 2013.
Integral leakage rate tests of containments
International Nuclear Information System (INIS)
Engel, M.; Siefart, E.; Walter, R.
1978-01-01
A method is presented for the integral leakage rate tests of containments. This method, used in conjunction with statistical methods, provides reliable information on the tightness of the containment. This method forms the basis of DIN 25436/KTA 3405. (orig.) [de
Reaction Order Ambiguity in Integrated Rate Plots
Lee, Joe
2008-01-01
Integrated rate plots are frequently used in reaction kinetics to determine orders of reactions. It is often emphasised, when using this methodology in practice, that it is necessary to monitor the reaction to a substantial fraction of completion for these plots to yield unambiguous orders. The present article gives a theoretical and statistical…
Directory of Open Access Journals (Sweden)
Totok R. Biyanto
2016-06-01
Full Text Available Safety Instrumented Function (SIF is implemented on the system to prevent hazard in process industry. In general, most of SIF implementation in process industry works in low demand condition. Safety valuation of SIF that works in low demand can be solved by using quantitative method. The quantitative method is a simplified exponential equation form of MacLaurin series, which can be called simplified equation. Simplified equation used in high demand condition will generate a higher Safety Integrity Level (SIL and it will affect the higher safety cost. Therefore, the value of low or high demand rate limit should be determined to prevent it. The result of this research is a first order equation that can fix the error of SIL, which arises from the usage of simplified equation, without looking the demand rate limit for low and high demand. This equation is applied for SIL determination on SIF with 1oo1 vote. The new equation from this research is λ = 0.9428 λMC + 1.062E−04 H/P, with 5% average of error, where λMC is a value of λ from the simplified equation, Hazardous event frequency (H is a probabilistic frequency of hazard event and P is Probability of Failure on Demand (PFD in Independent Protection Layers (IPLs. The equation generated from this research could correct SIL of SIF in various H and P. Therefore, SIL design problem could be solved and it provides an appropriate SIL.
The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations
International Nuclear Information System (INIS)
Chen Jinbing; Qiao Zhijun
2011-01-01
A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.
On the structure of the commutative Z2 graded algebra valued integrable equations
International Nuclear Information System (INIS)
Konopelchenko, B.G.
1980-01-01
Partial differential equations integrable by the linear matrix spectral problem of arbitrary order are considered for the case that the 'potentials' take their values in the commutative infinte-dimensional Z 2 graded algebra (superalgebra). The general form of the integrable equations and their Baecklund transformations are found. The infinite sets of the integrals of the motion are constructed. The hamiltonian character of the integrable equations is proved. (orig.)
Nonlinear Fredholm Integral Equation of the Second Kind with Quadrature Methods
Directory of Open Access Journals (Sweden)
M. Jafari Emamzadeh
2010-06-01
Full Text Available In this paper, a numerical method for solving the nonlinear Fredholm integral equation is presented. We intend to approximate the solution of this equation by quadrature methods and by doing so, we solve the nonlinear Fredholm integral equation more accurately. Several examples are given at the end of this paper
A calderón multiplicative preconditioner for the combined field integral equation
Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric
2009-01-01
A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation
Integrable systems of partial differential equations determined by structure equations and Lax pair
International Nuclear Information System (INIS)
Bracken, Paul
2010-01-01
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.
International Nuclear Information System (INIS)
Edgar, S.B.
1990-01-01
The structures of the N.P. and G.H.P formalisms are reviewed in order to understand and demonstrate the important role played by the commutator equations in the associated integration procedures. Particular attention is focused on how the commutator equations are to be satisfied, or checked for consistency. It is shown that Held's integration method will only guarantee genuine solutions of Einstein's equations when all the commutator equations are correctly and completely satisfied. (authors)
Solution of a modified Lame equation with an integral term
International Nuclear Information System (INIS)
Hagelstein, P.L.
1978-01-01
We consider an equation which occurs in the stability analysis of a passively modelocked laser system in which the pulses overlap. The equation is related to a Lame equation and can be written su(x) =]d 2 /dx 2 -[(2-m)-6dn 2 (x,m)
Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation
International Nuclear Information System (INIS)
Hu, Xing-Biao; Yu, Guo-Fu
2007-01-01
In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented
On integration of the first order differential equations in a finite terms
International Nuclear Information System (INIS)
Malykh, M D
2017-01-01
There are several approaches to the description of the concept called briefly as integration of the first order differential equations in a finite terms or symbolical integration. In the report three of them are considered: 1.) finding of a rational integral (Beaune or Poincaré problem), 2.) integration by quadratures and 3.) integration when the general solution of given differential equation is an algebraical function of a constant (Painlevé problem). Their realizations in Sage are presented. (paper)
Numerical method for solving linear Fredholm fuzzy integral equations of the second kind
Energy Technology Data Exchange (ETDEWEB)
Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)
2007-01-15
In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.
Geometry, heat equation and path integrals on the Poincare upper half-plane
International Nuclear Information System (INIS)
Kubo, Reijiro.
1987-08-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)
Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane
Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University
1988-01-01
Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.
Integrator Performance Analysis In Solving Stiff Differential Equation System
International Nuclear Information System (INIS)
B, Alhadi; Basaruddin, T.
2001-01-01
In this paper we discuss the four-stage index-2 singly diagonally implicit Runge-Kutta method, which is used to solve stiff ordinary differential equations (SODE). Stiff problems require a method where step size is not restricted by the method's stability. We desire SDIRK to be A-stable that has no stability restrictions when solving y'= λy with Reλ>0 and h>0, so by choosing suitable stability function we can determine appropriate constant g) to formulate SDIRK integrator to solve SODE. We select the second stage of the internal stage as embedded method to perform low order estimate for error predictor. The strategy for choosing the step size is adopted from the strategy proposed by Hall(1996:6). And the algorithm that is developed in this paper is implemented using MATLAB 5.3, which is running on Window's 95 environment. Our performance measurement's local truncation error accuracy, and efficiency were evaluated by statistical results of sum of steps, sum of calling functions, average of Newton iterations and elapsed times.As the results, our numerical experiment show that SDIRK is unconditionally stable. By using Hall's step size strategy, the method can be implemented efficiently, provided that suitable parameters are used
Transition flow ion transport via integral Boltzmann equation
International Nuclear Information System (INIS)
Darcie, T.E.
1983-10-01
A new approach is developed to solve the Integral Boltzmann Equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion/neutral mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion beam extractions from high pressure sources. Theoretical predictions are tested through an experiment in which an atmospheric pressure ion source is coupled to a high vacuum energy analyser. Excellent agreement results for configurations in which the radial velocity remains small. Velocity distributions are applied to predicting the efficiency of coupling an atmospheric pressure ion source to a quadrupole mass spectrometer and results clearly indicate the most desirable extracting configuration. A method is devised to calculate ion-molecule hard sphere collision cross sections for easily fragmented organic ions
Accurate and efficient quadrature for volterra integral equations
International Nuclear Information System (INIS)
Knirk, D.L.
1976-01-01
Four quadrature schemes were tested and compared in considerable detail to determine their usefulness in the noniterative integral equation method for single-channel quantum-mechanical calculations. They are two forms of linear approximation (trapezoidal rule) and two forms of quadratic approximation (Simpson's rule). Their implementation in this method is shown, a formal discussion of error propagation is given, and tests are performed to determine actual operating characteristics on various bound and scattering problems in different potentials. The quadratic schemes are generally superior to the linear ones in terms of accuracy and efficiency. The previous implementation of Simpson's rule is shown to possess an inherent instability which requires testing on each problem for which it is used to assure its reliability. The alternative quadratic approximation does not suffer this deficiency, but still enjoys the advantages of higher order. In addition, the new scheme obeys very well an h 4 Richardson extrapolation, whereas the old one does so rather poorly. 6 figures, 11 tables
Dissolution process analysis using model-free Noyes-Whitney integral equation.
Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto
2013-02-01
Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Mesgarani, H; Parmour, P; Aghazadeh, N
2010-01-01
In this paper, we apply Aitken extrapolation and epsilon algorithm as acceleration technique for the solution of a weakly singular nonlinear Volterra integral equation of the second kind. In this paper, based on Tao and Yong (2006 J. Math. Anal. Appl. 324 225-37.) the integral equation is solved by Navot's quadrature formula. Also, Tao and Yong (2006) for the first time applied Richardson extrapolation to accelerating convergence for the weakly singular nonlinear Volterra integral equations of the second kind. To our knowledge, this paper may be the first attempt to apply Aitken extrapolation and epsilon algorithm for the weakly singular nonlinear Volterra integral equations of the second kind.
Zhou, Yajun
This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of
ON ASYMTOTIC APPROXIMATIONS OF FIRST INTEGRALS FOR DIFFERENTIAL AND DIFFERENCE EQUATIONS
Directory of Open Access Journals (Sweden)
W.T. van Horssen
2007-04-01
Full Text Available In this paper the concept of integrating factors for differential equations and the concept of invariance factors for difference equations to obtain first integrals or invariants will be presented. It will be shown that all integrating factors have to satisfya system of partial differential equations, and that all invariance factors have to satisfy a functional equation. In the period 1997-2001 a perturbation method based on integrating vectors was developed to approximate first integrals for systems of ordinary differential equations. This perturbation method will be reviewed shortly. Also in the paper the first results in the development of a perturbation method for difference equations based on invariance factors will be presented.
Derivation and application of hydraulic equation for variable-rate ...
African Journals Online (AJOL)
The variable-rate contour-controlled sprinkler (VRCS) for precision irrigation can throw water on a given shaped area and the flow rate is also varied with the throw distance of the sprinkler for the purpose of high uniformity irrigation. Much of past research work were concentrated on the mechanical availability of ...
International Nuclear Information System (INIS)
Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.
1995-01-01
The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented
Parareal algorithms with local time-integrators for time fractional differential equations
Wu, Shu-Lin; Zhou, Tao
2018-04-01
It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal method to such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions.
Integration of equations of parabolic type by the method of nets
Saul'Yev, V K; Stark, M; Ulam, S
1964-01-01
International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial diff
arXiv Status of rates and rate equations for thermal leptogenesis
Biondini, Simone; Brambilla, Nora; Garny, Mathias; Ghiglieri, Jacopo; Hohenegger, Andreas; Laine, Mikko; Mendizabal, Sebastian; Millington, Peter; Salvio, Alberto; Vairo, Antonio
2018-02-28
In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T \\ll M$. We review recent progresses in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number...
International Nuclear Information System (INIS)
Sanchez, Richard.
1980-11-01
This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr
Stability of negative solitary waves for an integrable modified Camassa-Holm equation
International Nuclear Information System (INIS)
Yin Jiuli; Tian Lixin; Fan Xinghua
2010-01-01
In this paper, we prove that the modified Camassa-Holm equation is Painleve integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation.
International Nuclear Information System (INIS)
Ozgener, B.
1998-01-01
A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation
Analysis and regularization of the thin-wire integral equation with reduced kernel
Beurden, van M.C.; Tijhuis, A.G.
2007-01-01
For the straight wire, modeled as a hollow tube, we establish a conditional equivalence relation between the integral equations with exact and reduced kernel. This relation allows us to examine the existence and uniqueness conditions for the integral equation with reduced kernel, based on a local
An efficient explicit marching on in time solver for magnetic field volume integral equation
Sayed, Sadeed Bin; Ulku, H. Arda; Bagci, Hakan
2015-01-01
An efficient explicit marching on in time (MOT) scheme for solving the magnetic field volume integral equation is proposed. The MOT system is cast in the form of an ordinary differential equation and is integrated in time using a PE(CE)m multistep
Alternative integral equations and perturbation expansions for self-coupled scalar fields
International Nuclear Information System (INIS)
Ford, L.H.
1985-01-01
It is shown that the theory of a self-coupled scalar field may be expressed in terms of a class of integral equations which include the Yang-Feldman equation as a particular case. Other integral equations in this class could be used to generate alternative perturbation expansions which contain a nonanalytic dependence upon the coupling constant and are less ultraviolet divergent than the conventional perturbation expansion. (orig.)
Integration of differential equations by the pseudo-linear (PL) approximation
International Nuclear Information System (INIS)
Bonalumi, Riccardo A.
1998-01-01
A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method
Block-pulse functions approach to numerical solution of Abel’s integral equation
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Monireh Nosrati Sahlan
2015-12-01
Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.
FFTF integrated leak rate computer system
International Nuclear Information System (INIS)
Hubbard, J.A.
1987-01-01
The Fast Flux Test Facility (FFTF) is a liquid-metal-cooled test reactor located on the Hanford site. The FFTF is the only reactor of this type designed and operated to meet the licensing requirements of the Nuclear Regulatory Commission. Unique characteristics of the FFTF that present special challenges related to leak rate testing include thin wall containment vessel construction, cover gas systems that penetrate containment, and a low-pressure design basis accident. The successful completion of the third FFTF integrated leak rate test 5 days ahead of schedule and 10% under budget was a major achievement for the Westinghouse Hanford Company. The success of this operational safety test was due in large part to a special network (LAN) of three IBM PC/XT computers, which monitored the sensor data, calculated the containment vessel leak rate, and displayed test results. The equipment configuration allowed continuous monitoring of the progress of the test independent of the data acquisition and analysis functions, and it also provided overall improved system reliability by permitting immediate switching to backup computers in the event of equipment failure
Irreducibility and co-primeness as an integrability criterion for discrete equations
International Nuclear Information System (INIS)
Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji
2014-01-01
We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)
Application of a mechanism-based rate equation to black liquor gasification rate data
Energy Technology Data Exchange (ETDEWEB)
Overacker, N.L.; Waag, K.J.; Frederick, W.J. [Oregon State University, OR (United States). Dept. of Chemical Engineering; Whitty, K.J.
1995-09-01
There is growing interest worldwide to develop alternate chemical recovery processes for paper mills which are cheaper, safer, more efficient and more environmentally sound than traditional technology. Pressurized gasification of black liquor is the basis for many proposed schemes and offers the possibility to double the amount of electricity generated per unit of dry black liquor solids. Such technology also has capital, safety and environmental advantages. One of the most important considerations regarding this emerging technology is the kinetics of the gasification reaction. This has been studied empirically at Aabo Akademi University for the pressurized gasification with carbon dioxide and steam. For the purposes of reactor modeling and scale-up, however, a thorough understanding of the mechanism behind the reaction is desirable. This report discusses the applicability of a mechanism-based rate equation to gasification of black liquor. The mechanism considered was developed for alkali-catalyzed gasification of carbon and is tested using black liquor gasification data obtained during simultaneous reaction with H{sub 2}O and CO. Equilibrium considerations and the influence of the water-gas shift reaction are also discussed. The work presented here is a cooperative effort between Aabo Akademi University and Oregon State University. The experimental work and some of the data analysis was performed at Aabo Akademi University. Development of the models and consideration of their applicability was performed primarily at Oregon State University
International Nuclear Information System (INIS)
Liao Cui-Cui; Cui Jin-Chao; Liang Jiu-Zhen; Ding Xiao-Hua
2016-01-01
In this paper, we propose a variational integrator for nonlinear Schrödinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrödinger equations with variable coefficients, cubic nonlinear Schrödinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space. (paper)
Numerical integration of the Teukolsky equation in the time domain
International Nuclear Information System (INIS)
Pazos-Avalos, Enrique; Lousto, Carlos O.
2005-01-01
We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code
Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation
International Nuclear Information System (INIS)
Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro
2015-01-01
In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)
Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions
Directory of Open Access Journals (Sweden)
Yeguo Sun
2012-01-01
Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.
Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally
Integral equations for free-molecule ow in MEMS: recent advancements
Directory of Open Access Journals (Sweden)
Fedeli Patrick
2017-03-01
Full Text Available We address a Boundary Integral Equation (BIE approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS. Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented.
Rate equations for tracer studies in recirculating reactors
Energy Technology Data Exchange (ETDEWEB)
Happel, J [Columbia Univ., New York (USA). Dept. of Chemical Engineering
1974-10-01
The employment of isotopic tracers is a useful technique for gaining insight into the rate controlling steps of a complex chemical reaction such as is frequently encountered in heterogeneous catalysis. An effective procedure has been to superpose tracer transfer on a reaction which is occurring under steady state conditions. If tracer transfer is employed in this fashion it is often possible to assess the individual step velocities in an assumed reaction mechanism. If transient transfer of tracer is now introduced it is possible in addition to estimate surface concentrations of chemisorbed species. The purpose of the present paper is to present the mathematical relationships involved when transfer of the tracer is not differential in the investigation. For this purpose a simple example is chosen to illustrate the various possibilities involved.
Rate equations for tracer studies in recirculatinng reactors
International Nuclear Information System (INIS)
Happel, J.
1974-01-01
The employment of isotopic tracers is a useful technique for gaining insight into the rate controlling steps of a complex chemical reaction such as is frequently encountered in heterogeneous catalysis. An effective procedure has been to superpose tracer transfer on a reaction which is occurring under steady state conditions. If tracer transfer is employed in this fashion it is often possible to assess the individual step velocities in an assumed reaction mechanism. If transient transfer of tracer is now introduced it is possible in addition to estimate surface concentrations of chemisorbed species. The purpose of the present paper is to present the mathematical relationships involved when transfer of the tracer is not differential in the investigation. For this purpose a simple example is chosen to illustrate the various possibilities involved. (auth.)
Coupled force-balance and particle-occupation rate equations for high-field electron transport
International Nuclear Information System (INIS)
Lei, X. L.
2008-01-01
It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field
Bifurcations of traveling wave solutions for an integrable equation
International Nuclear Information System (INIS)
Li Jibin; Qiao Zhijun
2010-01-01
This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.
Iterative Solutions of Nonlinear Integral Equations of Hammerstein Type
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Abebe R. Tufa
2015-11-01
Full Text Available Let H be a real Hilbert space. Let F,K : H → H be Lipschitz monotone mappings with Lipschtiz constants L1and L2, respectively. Suppose that the Hammerstein type equation u + KFu = 0 has a solution in H. It is our purpose in this paper to construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein type equation. The results obtained in this paper improve and extend known results in the literature.
Integrability and structural stability of solutions to the Ginzburg-Landau equation
Keefe, Laurence R.
1986-01-01
The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).
Integral equations of the first kind, inverse problems and regularization: a crash course
International Nuclear Information System (INIS)
Groetsch, C W
2007-01-01
This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided
Park, K. C.; Belvin, W. Keith
1990-01-01
A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.
Boundary-integral equation formulation for time-dependent inelastic deformation in metals
Energy Technology Data Exchange (ETDEWEB)
Kumar, V; Mukherjee, S
1977-01-01
The mathematical structure of various constitutive relations proposed in recent years for representing time-dependent inelastic deformation behavior of metals at elevated temperatues has certain features which permit a simple formulation of the three-dimensional inelasticity problem in terms of real time rates. A direct formulation of the boundary-integral equation method in terms of rates is discussed for the analysis of time-dependent inelastic deformation of arbitrarily shaped three-dimensional metallic bodies subjected to arbitrary mechanical and thermal loading histories and obeying constitutive relations of the kind mentioned above. The formulation is based on the assumption of infinitesimal deformations. Several illustrative examples involving creep of thick-walled spheres, long thick-walled cylinders, and rotating discs are discussed. The implementation of the method appears to be far easier than analogous BIE formulations that have been suggested for elastoplastic problems.
An Integrable Discrete Generalized Nonlinear Schrödinger Equation and Its Reductions
International Nuclear Information System (INIS)
Li Hong-Min; Li Yu-Qi; Chen Yong
2014-01-01
An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. (general)
On the integrability of the generalized Fisher-type nonlinear diffusion equations
International Nuclear Information System (INIS)
Wang Dengshan; Zhang Zhifei
2009-01-01
In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2
Oscillatory integrals on Hilbert spaces and Schroedinger equation with magnetic fields
International Nuclear Information System (INIS)
Albeverio, S.; Brzezniak, Z.
1994-01-01
We extend the theory of oscillatory integrals on Hilbert spaces (the mathematical version of ''Feynman path integrals'') to cover more general integrable functions, preserving the property of the integrals to have converging finite dimensional approximations. We give an application to the representation of solutions of the time dependent Schroedinger equation with a scalar and a magnetic potential by oscillatory integrals on Hilbert spaces. A relation with Ramer's functional in the corresponding probabilistic setting is found. (orig.)
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
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Malinowski Marek T.
2015-01-01
Full Text Available We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors. The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect to data of the equation is also presented. We consider equations driven by semimartingale Z and equations driven by processes A;M from decomposition of Z, where A is a process of finite variation and M is a local martingale. These equations are not equivalent. Finally, we show that the analysis of the set-valued stochastic integral equations can be extended to a case of fuzzy stochastic integral equations driven by semimartingales under Osgood type condition. To obtain our results we use the set-valued and fuzzy Maruyama type approximations and Bihari’s inequality.
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Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
International Nuclear Information System (INIS)
LaChapelle, J.
2004-01-01
A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette
Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.
Integration of the three-dimensional Vlasov equation for a magnetized plasma
International Nuclear Information System (INIS)
Cheng, C.Z.
1976-04-01
A second order splitting scheme is developed to integrate the three dimensional Vlasov equation for a plasma in a magnetic field. The integration of the Vlasov equation is divided into a series of intermediate steps and Fourier interpolation and the ASD method with a third order Taylor expansion are used to integrate the fractional equations. Numerical experiments related to cyclotron waves in 2 and 2 1 / 2 D are demonstrated with high accuracy and efficiency. The computer storage requirements are modest; for example, a typical 2D nonlinear electron plasma simulation requires only 4000 ''particles.''
Fibonacci-regularization method for solving Cauchy integral equations of the first kind
Directory of Open Access Journals (Sweden)
Mohammad Ali Fariborzi Araghi
2017-09-01
Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.
Valdé s, Felipe; Andriulli, Francesco P.; Bagci, Hakan; Michielssen, Eric
2011-01-01
A new regularized single source equation for analyzing scattering from homogeneous penetrable objects is presented. The proposed equation is a linear combination of a Calderón-preconditioned single source electric field integral equation and a
[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].
Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin
2012-07-01
Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.
The specification of cross exchange rate equations used to test Purchasing Power Parity
Hunter, J; Simpson, M
2004-01-01
The Article considers the speciÞcation of models used to test Pur- chasing Power Parity when applied to cross exchange rates. SpeciÞcally, conventional dynamic models used to test stationarity of the real exchange rate are likely to be misspeciÞed, except when the parameters of each ex- change rate equation are the same
Integrability of N=3 super Yang-Mills equations
International Nuclear Information System (INIS)
Devchand, C.; Ogievetsky, V.
1993-10-01
We describe the harmonic superspace formulation of the Witten-Manin supertwistor correspondence for N=3 extended super Yang-Mills theories. The essence in that on being sufficiently supersymmetrised (up to the N=3 extension), the Yang-Mills equations of motion can be recast in the form of Cauchy-Riemann-like holomorphicity conditions for a pair of prepotentials in the appropriate harmonic superspace. This formulation makes the explicit construction of solutions a rather more tractable proposition than previous attempts. (orig.)
International Nuclear Information System (INIS)
Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.
1992-01-01
The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented
Nonlinear fluctuation-induced rate equations for linear birth-death processes
International Nuclear Information System (INIS)
Honkonen, J.
2008-01-01
The Fock-space approach to the solution of master equations for the one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov's ecological model and Lanchester's model of modern warfare
Nonlinear fluctuations-induced rate equations for linear birth-death processes
Honkonen, J.
2008-05-01
The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.
On an integrable deformed affinsphären equation. A reciprocal gasdynamic connection
International Nuclear Information System (INIS)
Rogers, C.; Huang, Yehui
2012-01-01
The integrable affinsphären equation originally arose in a geometric context but has an interesting gasdynamic connection. Here, an integrable deformed version of the affinsphären equation is derived in a novel manner via the action of reciprocal transformations on a related anisentropic gasdynamics system. A linear representation for the deformed affinsphären equation is constructed by means of the reciprocal transformations. The latter are then employed to derive a class of exact solutions in parametric form. -- Highlights: ► A deformed affinsphären equation is derived via a reciprocal transformation. ► A linear representation for the deformed affinsphären equation is constructed. ► A class of exact solutions of the deformed affinsphären equation is presented.
Wavelet-like bases for thin-wire integral equations in electromagnetics
Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.
2005-03-01
In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.
International Nuclear Information System (INIS)
Carver, M.B.; Hanley, D.V.; Chaplin, K.R.
1979-02-01
MAKSIMA-CHEMIST was written to compute the kinetics of simultaneous chemical reactions. The ordinary differential equations, which are automatically derived from the stated chemical equations, are difficult to integrate, as they are coupled in a highly nonlinear manner and frequently involve a large range in the magnitude of the reaction rates. They form a classic 'stiff' differential equaton set which can be integrated efficiently only by recently developed advanced techniques. The new program also contains provision for higher order chemical reactions, and has a dynamic storage and decision feature. This permits it to accept any number of chemical reactions and species, and choose an integraton scheme which will perform most efficiently within the available memory. Sparse matrix techniques are used when the size and structure of the equation set is suitable. Finally, a number of post-analysis options are available, including printer and Calcomp plots of transient response of selected species, and graphical representation of the reaction matrix. (auth)
Low-frequency scaling of the standard and mixed magnetic field and Müller integral equations
Bogaert, Ignace; Cools, Kristof; Andriulli, Francesco P.; Bagci, Hakan
2014-01-01
The standard and mixed discretizations for the magnetic field integral equation (MFIE) and the Müller integral equation (MUIE) are investigated in the context of low-frequency (LF) scattering problems involving simply connected scatterers
A calderón multiplicative preconditioner for the combined field integral equation
Bagci, Hakan
2009-10-01
A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation. © 2009 IEEE.
Integrable discretizations for the short-wave model of the Camassa-Holm equation
International Nuclear Information System (INIS)
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.
Integral transform method for solving time fractional systems and fractional heat equation
Directory of Open Access Journals (Sweden)
Arman Aghili
2014-01-01
Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.
Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
Energy Technology Data Exchange (ETDEWEB)
Eden, Burkhard [Institut für Mathematik und Physik, Humboldt-Universität zu Berlin,Zum großen Windkanal 6, 12489 Berlin (Germany); Smirnov, Vladimir A. [Skobeltsyn Institute of Nuclear Physics, Moscow State University,119992 Moscow (Russian Federation)
2016-10-21
We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.
Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations
Eden, Burkhard; Smirnov, Vladimir A.
2016-10-01
We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-01-01
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
A predictor-corrector scheme for solving the Volterra integral equation
Al Jarro, Ahmed; Bagci, Hakan
2011-01-01
The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been
On the mixed discretization of the time domain magnetic field integral equation
Ulku, Huseyin Arda; Bogaert, Ignace; Cools, Kristof; Andriulli, Francesco P.; Bagci, Hakan
2012-01-01
Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed
Vujačić, Ivan; Dattner, Itai
In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.
A new integral method for solving the point reactor neutron kinetics equations
International Nuclear Information System (INIS)
Li Haofeng; Chen Wenzhen; Luo Lei; Zhu Qian
2009-01-01
A numerical integral method that efficiently provides the solution of the point kinetics equations by using the better basis function (BBF) for the approximation of the neutron density in one time step integrations is described and investigated. The approach is based on an exact analytic integration of the neutron density equation, where the stiffness of the equations is overcome by the fully implicit formulation. The procedure is tested by using a variety of reactivity functions, including step reactivity insertion, ramp input and oscillatory reactivity changes. The solution of the better basis function method is compared to other analytical and numerical solutions of the point reactor kinetics equations. The results show that selecting a better basis function can improve the efficiency and accuracy of this integral method. The better basis function method can be used in real time forecasting for power reactors in order to prevent reactivity accidents.
Numerical solution of integral equations, describing mass spectrum of vector mesons
International Nuclear Information System (INIS)
Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.
1988-01-01
The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data
Valdé s, Felipe; Andriulli, Francesco P.; Bagci, Hakan; Michielssen, Eric
2013-01-01
Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
Directory of Open Access Journals (Sweden)
Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
International Nuclear Information System (INIS)
Williams, M.M.R.
2005-01-01
The integral equation derived by Nieuwenhuizen and Luck for transmission of radiation through an optically thick diffusive medium is reconsidered in the light of radiative transfer theory and extended to slabs of arbitrary thickness. (author)
CSIR Research Space (South Africa)
Fedotov, I
2006-07-01
Full Text Available The Combined Helmholtz Integral Equation – Fourier series Formulation (CHIEFF) is based on representation of a velocity potential in terms of Fourier series and finding the Fourier coefficients of this expansion. The solution could be substantially...
International Nuclear Information System (INIS)
Killingbeck, J.
1979-01-01
By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)
Integration of the time-dependent heat equation in the fuel rod performance program IAMBUS
International Nuclear Information System (INIS)
West, G.
1982-01-01
An iterative numerical method for integration of the time-dependent heat equation is described. No presuppositions are made for the dependency of the thermal conductivity and heat capacity on space, time and temperature. (orig.) [de
Stability and square integrability of solutions of nonlinear fourth order differential equations
Directory of Open Access Journals (Sweden)
Moussadek Remili
2016-05-01
Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.
On the initial condition problem of the time domain PMCHWT surface integral equation
Uysal, Ismail Enes; Bagci, Hakan; Ergin, A. Arif; Ulku, H. Arda
2017-01-01
Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced
The Volterra's integral equation theory for accelerator single-freedom nonlinear components
International Nuclear Information System (INIS)
Wang Sheng; Xie Xi
1996-01-01
The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed
RBSDE's with jumps and the related obstacle problems for integral-partial differential equations
Institute of Scientific and Technical Information of China (English)
FAN; Yulian
2006-01-01
The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.
Energy Technology Data Exchange (ETDEWEB)
Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)
2014-06-13
Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.
Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas
International Nuclear Information System (INIS)
Eliezer, S.; Falquina, R.; Minguez, E.
1994-01-01
Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution
Integrable Hierarchy of the Quantum Benjamin-Ono Equation
Directory of Open Access Journals (Sweden)
Maxim Nazarov
2013-12-01
Full Text Available A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables x_1,x_2,…. This construction provides explicit expressions for the Hamiltonians in terms of the power sum symmetric functions p_n=x^n_1+x^n_2+⋯ and is based on our recent results from [Comm. Math. Phys. 324 (2013, 831-849].
Directory of Open Access Journals (Sweden)
Mohammad Almousa
2013-01-01
Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.
The ATOMFT integrator - Using Taylor series to solve ordinary differential equations
Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.
1988-01-01
This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.
The multidensity integral equation approach in the theory of complex liquids
International Nuclear Information System (INIS)
Holovko, M.F.
2001-01-01
Recent development of the multi-density integral equation approach and its application to the statistical mechanical modelling of a different type of association and clusterization in liquids and solutions are reviewed. The effects of dimerization, polymerization and network formation are discussed. The numerical and analytical solutions of the integral equations in the multi-density formalism for pair correlation functions are used for the description of structural and thermodynamical properties of ionic solutions, polymers and network forming fluids
International Nuclear Information System (INIS)
de Jong, G.
1975-01-01
With the aid of a two-dimensional integral equation formulation, the ground wave propagation of electromagnetic waves transmitted by a vertical electric dipole over an inhomogeneous flat earth is investigated. For the configuration in which a ground wave is propagating across an ''island'' on a flat earth, the modulus and argument of the attenuation function have been computed. The results for the two-dimensional treatment are significantly more accurate in detail than the calculations using a one-dimensional integral equation
A review of some basic aspects related to integration of airplane’s equations of motion
Directory of Open Access Journals (Sweden)
Dan TURCANU
2017-09-01
Full Text Available Numerical integration of the airplane’s equations of motion has long been considered among the most fundamental calculations in airplane’s analysis. Numerical algorithms have been implemented and experimentally validated. However, the need for superior speed and accuracy is still very topical, as, nowadays, various optimization algorithms rely heavily on data generated from the integration of the equations of motion and having access to larger amounts of data can increase the quality of the optimization. Now, for a number of decades, engineers have relied heavily on commercial codes based on automatically selected integration steps. However, optimally chosen constant integration steps can save time and allows for larger numbers of integrations to be performed. Yet, the basic papers that presented the fundamentals of numerical integration, as applied to airplane’s equations of motion are nowadays not easy to locate. Consequently, this paper presents a review of basic aspects related to the integration of airplane’s equation of motion. The discussion covers fundamentals of longitudinal and lateral-directional motion as well as the implementation of some numerical integration methods. The relation between numerical integration steps, accuracy, computational resource usage, numerical stability and their relation with the parameters describing the dynamic response of the airplane is considered and suggestions are presented for a faster yet accurate numerical integration.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Integral geometry and inverse problems for hyperbolic equations
Romanov, V G
1974-01-01
There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solutio...
Numerical Integration of the Vlasov Equation of Two Colliding Beams
Zorzano-Mier, M P
2000-01-01
In a circular collider the motion of particles of one beam is strongly perturbed at the interaction points by the electro-magnetic field associated with the counter-rotating beam. For any two arbitrary initial particle distributions the time evolution of the two beams can be known by solving the coupled system of two Vlasov equations. This collective description is mandatory when the two beams have similar strengths, as in the case of LEP or LHC. The coherent modes excited by this beam-beam interaction can be a strong limitation for the operation of LHC. In this work, the coupled Vlasov equations of two colliding flat beams are solved numerically using a finite difference scheme. The results suggest that, for the collision of beams with equal tunes, the tune shift between the $\\sigma$- and $\\pi$- coherent dipole mode depends on the unperturbed tune $q$ because of the deformation that the so-called dynamic beta effect induces on the beam distribution. Only when the unperturbed tune $q\\rightarrow 0.25$ this tun...
Continuous limits for an integrable coupling system of Toda equation hierarchy
International Nuclear Information System (INIS)
Li Li; Yu Fajun
2009-01-01
In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.
The ε-form of the differential equations for Feynman integrals in the elliptic case
Adams, Luise; Weinzierl, Stefan
2018-06-01
Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.
Continuous limits for an integrable coupling system of Toda equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-09-21
In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.
Scattering integral equations and four nucleon problem. Four nucleon bound states and scattering
International Nuclear Information System (INIS)
Narodetskij, I.M.
1981-01-01
Existing results from the application of integral equation technique four-nucleon bound states and scattering are reviewed. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. Developments in the actual numerical solutions of Faddeev-Yakubovsky type equations are such that a detailed comparison can be made with experiment. Bound state calculations indicate that a nonrelativistic description with pairwise nuclear forces does not suffice and additional degrees of freedom are noted [ru
A computational method for direct integration of motion equations of structural systems
International Nuclear Information System (INIS)
Brusa, L.; Ciacci, R.; Creco, A.; Rossi, F.
1975-01-01
The dynamic analysis of structural systems requires the solution of the matrix equations: Md 2 delta/dt(t) + Cddelta/dt(t) + Kdelta(t) = F(t). Many numerical methods are available for direct integration of this equation and their efficiency is due to the fulfillment of the following requirements: A reasonable order of accuracy must be obtained for the approximation of the response relevant to the first modes: the model contributions relevant to the eigenvalues with large real part must be essentially neglected. This paper presents a step-by-step numerical scheme for the integration of this equation which satisfies the requirements previously mentioned. (Auth.)
Iterative solution for nonlinear integral equations of Hammerstein type
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1990-12-01
Let E be a real Banach space with a uniformly convex dual, E*. Suppose N is a nonlinear set-valued accretive map of E into itself with open domain D; K is a linear single-valued accretive map with domain D(K) in E such that Im(N) is contained in D(K); K -1 exists and satisfies -1 x-K -1 y,j(x-y)>≥β||x-y|| 2 for each x, y is an element of Im(K) and some constant β > 0, where j denotes the single-valued normalized duality map on E. Suppose also that for each h is an element Im(K) the equation h is an element x+KNx has a solution x* in D. An iteration method is constructed which converges strongly to x*. Explicit error estimates are also computed. (author). 25 refs
Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication
DEFF Research Database (Denmark)
Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi
2015-01-01
We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser...... characterization and carrier recovery in coherent communication. Two rate equation based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber...
Comment on 'A Forecasting Equation for the Canada-US Dollar Real Exchange Rate'
Kollmann, Robert
1993-01-01
This paper is a comment on the paper 'A Forecasting Equation for the Canada-US Dollar Exchange Rate' (Robert Amano and Simon van Norden, Bank of Canada). The comment was published in: The Exchange Rate and the Economy, Proceedings of 1992 Bank of Canada Conference; Bank of Canada, 1993, Ottawa (ISBN 0-660-15195-2), pp. 266-271.
Validity of predictive equations for basal metabolic rate in Japanese adults.
Miyake, Rieko; Tanaka, Shigeho; Ohkawara, Kazunori; Ishikawa-Takata, Kazuko; Hikihara, Yuki; Taguri, Emiko; Kayashita, Jun; Tabata, Izumi
2011-01-01
Many predictive equations for basal metabolic rate (BMR) based on anthropometric measurements, age, and sex have been developed, mainly for healthy Caucasians. However, it has been reported that many of these equations, used widely, overestimate BMR not only for Asians, but also for Caucasians. The present study examined the accuracy of several predictive equations for BMR in Japanese subjects. In 365 healthy Japanese male and female subjects, aged 18 to 79 y, BMR was measured in the post-absorptive state using a mask and Douglas bag. Six predictive equations were examined. Total error was used as an index of the accuracy of each equation's prediction. Predicted BMR values by Dietary Reference Intakes for Japanese (Japan-DRI), Adjusted Dietary Reference Intakes for Japanese (Adjusted-DRI), and Ganpule equations were not significantly different from the measured BMR in either sex. On the other hand, Harris-Benedict, Schofield, and Food and Agriculture Organization of the United Nations/World Health Organization/United Nations University equations were significantly higher than the measured BMR in both sexes. The prediction error by Japan-DRI, Adjusted-DRI, and Harris-Benedict equations was significantly correlated with body weight in both sexes. Total error using the Ganpule equation was low in both males and females (125 and 99 kcal/d, respectively). In addition, total error using the Adjusted-DRI equation was low in females (95 kcal/d). Thus, the Ganpule equation was the most accurate in predicting BMR in our healthy Japanese subjects, because the difference between the predicted and measured BMR was relatively small, and body weight had no effect on the prediction error.
Directory of Open Access Journals (Sweden)
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
International Nuclear Information System (INIS)
Maccari, A.
1997-01-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio endash temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a open-quotes universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics
On the maximal cut of Feynman integrals and the solution of their differential equations
Directory of Open Access Journals (Sweden)
Amedeo Primo
2017-03-01
Full Text Available The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try to solve them as a Laurent series in ϵ=(4−d/2, where d are the space–time dimensions. The differential equations are, in general, coupled and can be solved using Euler's variation of constants, provided that a set of homogeneous solutions is known. Given an arbitrary differential equation of order higher than one, there exists no general method for finding its homogeneous solutions. In this paper we show that the maximal cut of the integrals under consideration provides one set of homogeneous solutions, simplifying substantially the solution of the differential equations.
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
International Nuclear Information System (INIS)
Matinyan, S.G.; Prokhorenko, E.V.; Savvidy, G.K.
1986-01-01
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. The phase space of this system is shown to have no quasi-periodic motion specific for integrable systems. In particular, the well-known Wu-Yang static solution is unstable, so its vicinity in phase is the stochasticity region
Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation
Directory of Open Access Journals (Sweden)
Berenguer MI
2009-01-01
Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Matinyan, S G; Prokhorenko, E B; Savvidy, G K
1988-03-07
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.
International Nuclear Information System (INIS)
Rezende, J.
1983-01-01
We give a simple proof of Feynman's formula for the Green's function of the n-dimensional harmonic oscillator valid for every time t with Im t<=0. As a consequence the Schroedinger equation for the anharmonic oscillator is integrated and expressed by the Feynman path integral on Hilbert space. (orig.)
Soliton surfaces associated with generalized symmetries of integrable equations
International Nuclear Information System (INIS)
Grundland, A M; Post, S
2011-01-01
In this paper, based on the Fokas et al approach (Fokas and Gel'fand 1996 Commun. Math. Phys. 177 203-20; Fokas et al 2000 Sel. Math. 6 347-75), we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra using the formalism of generalized vector fields, their prolongation structure and links with the Frechet derivatives. We express the necessary and sufficient condition for the existence of such surfaces in terms of the invariance criterion for generalized symmetries and identify additional sufficient conditions which admit an explicit integration of the immersion functions of 2D surfaces in Lie algebras. We discuss in detail the su(N)-valued immersion functions generated by conformal symmetries of the CP N-1 sigma model defined on either the Minkowski or Euclidean space. We further show that the sufficient conditions for explicit integration of such immersion functions impose additional restrictions on the admissible conformal symmetries of the model defined on Minkowski space. On the other hand, the sufficient conditions are identically satisfied for arbitrary conformal symmetries of finite action solutions of the CP N-1 sigma model defined on Euclidean space.
International Nuclear Information System (INIS)
Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.
2008-01-01
We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters
Voytishek, Anton V.; Shipilov, Nikolay M.
2017-11-01
In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.
International Nuclear Information System (INIS)
Jimenez, J.C.
2009-06-01
Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)
Electromagnetic scattering of large structures in layered earths using integral equations
Xiong, Zonghou; Tripp, Alan C.
1995-07-01
An electromagnetic scattering algorithm for large conductivity structures in stratified media has been developed and is based on the method of system iteration and spatial symmetry reduction using volume electric integral equations. The method of system iteration divides a structure into many substructures and solves the resulting matrix equation using a block iterative method. The block submatrices usually need to be stored on disk in order to save computer core memory. However, this requires a large disk for large structures. If the body is discretized into equal-size cells it is possible to use the spatial symmetry relations of the Green's functions to regenerate the scattering impedance matrix in each iteration, thus avoiding expensive disk storage. Numerical tests show that the system iteration converges much faster than the conventional point-wise Gauss-Seidel iterative method. The numbers of cells do not significantly affect the rate of convergency. Thus the algorithm effectively reduces the solution of the scattering problem to an order of O(N2), instead of O(N3) as with direct solvers.
Integrability of the Gross-Pitaevskii equation with Feshbach resonance management
International Nuclear Information System (INIS)
Zhao Dun; Luo Honggang; Chai Huayue
2008-01-01
In this Letter we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98 (2007) 074102]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross-Pitaevskii equation into the well-known standard nonlinear Schroedinger equation. By this transformation, each exact solution of the standard nonlinear Schroedinger equation can be converted into that of the Gross-Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitons and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique
Rate equation modelling of the optically pumped spin-exchange source
International Nuclear Information System (INIS)
Stenger, J.; Rith, K.
1995-01-01
Sources for spin polarized hydrogen or deuterium, polarized via spin-exchange of a laser optically pumped alkali metal, can be modelled by rate equations. The rate equations for this type of source, operated either with hydrogen or deuterium, are given explicitly with the intention of providing a useful tool for further source optimization and understanding. Laser optical pumping of alkali metal, spin-exchange collisions of hydrogen or deuterium atoms with each other and with alkali metal atoms are included, as well as depolarization due to flow and wall collisions. (orig.)
Gumral, Hasan
Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.
International Nuclear Information System (INIS)
Wehner, M.F.
1983-01-01
A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs
Retarded potentials and time domain boundary integral equations a road map
Sayas, Francisco-Javier
2016-01-01
This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...
Splines and their reciprocal-bases in volume-integral equations
International Nuclear Information System (INIS)
Sabbagh, H.A.
1993-01-01
The authors briefly outline the use of higher-order splines and their reciprocal-bases in discretizing the volume-integral equations of electromagnetics. The discretization is carried out by means of the method of moments, in which the expansion functions are the higher-order splines, and the testing functions are the corresponding reciprocal-basis functions. These functions satisfy an orthogonality condition with respect to the spline expansion functions. Thus, the method is not Galerkin, but the structure of the resulting equations is quite regular, nevertheless. The theory is applied to the volume-integral equations for the unknown current density, or unknown electric field, within a scattering body, and to the equations for eddy-current nondestructive evaluation. Numerical techniques for computing the matrix elements are also given
International Nuclear Information System (INIS)
Gunawan, Indra; Sulistyo, Harry; Rochmad
2001-01-01
The numerical analysis of Hooke Jeeves Methods combined with Runge Kutta Methods is used to determine the exact model of reaction rate equation of pyrrole polymerization. Chemical polymerization of pyrrole was conducted with FeCI 3 / pyrrole solution at concentration ratio of 1.62 mole / mole and 2.18 mole / mole with varrying temperature of 28, 40, 50, and 60 o C. FeCl 3 acts as an oxidation agent to form pyrrole cation that will polymerize. The numerical analysis was done to examine the exact model of reaction rate equation which is derived from reaction equation of initiation, propagation, and termination. From its numerical analysis, it is found that the pyrrole polymerization follows third order of pyrrole cation concentration
On a numereeical method for solving the Faddv integral equation without deformation of contour
International Nuclear Information System (INIS)
Belyaev, V.O.; Moller, K.
1976-01-01
A numerical method is proposed for solving the Faddeev equation for separable potentials at positive total energy. The method is based on the fact that after applying a simple interpolation procedure the logarithmic singularities in the kernel of the integral equation can be extracted in the same way as usually the pole singularity is extracted. The method has been applied to calculate the eigenvalues of the Faddeev kernel
A novel hierarchy of differential—integral equations and their generalized bi-Hamiltonian structures
International Nuclear Information System (INIS)
Zhai Yun-Yun; Geng Xian-Guo; He Guo-Liang
2014-01-01
With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 × 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy
Magnetostatic fields computed using an integral equation derived from Green's theorems
International Nuclear Information System (INIS)
Simkin, J.; Trowbridge, C.W.
1976-04-01
A method of computing magnetostatic fields is described that is based on a numerical solution of the integral equation obtained from Green's Theorems. The magnetic scalar potential and its normal derivative on the surfaces of volumes are found by solving a set of linear equations. These are obtained from Green's Second Theorem and the continuity conditions at interfaces between volumes. Results from a two-dimensional computer program are presented and these show the method to be accurate and efficient. (author)
Exact Mathisson-Papapetrou equations in the Schwarzschild metric with integrals of motion
International Nuclear Information System (INIS)
Plyatsko, R.M.; Stefanishin, O.B.
2011-01-01
A new representation for exact Mathisson-Papapetrou equations under the Mathisson-Pirani condition in the Schwarzschild gravitational field, which does not contain third-order derivatives with respect to spinning particle coordinates, has been obtained. For this purpose, the integrals of energy and angular momentum of a spinning particle, as well as a differential relation following from the Mathisson-Papapetrou equations for an arbitrary metric, are used.
78 FR 62616 - Integrated System Power Rates
2013-10-22
.... James K. McDonald, Vice President for Corporate Operations/Chief Operating Office, Southwestern Power...) 595-6690, jim.mcdonald@swpa.gov . SUPPLEMENTARY INFORMATION: Rate Order No. SWPA-66, which has been... final approval by the Federal Energy Regulatory Commission. Available: In the marketing area of...
75 FR 1363 - Integrated System Power Rates
2010-01-11
... increased. Those customers taking transformation service will be affected by an increase in that rate... Regulation Purchased. With factors defined as follows: RPA = The Customer's specific monthly dollar amount of... formulas provided in Customers' contracts indicate an overrun on Hydro Peaking Power, and investigation...
Integrated Monetary and Exchange Rate Frameworks
L. Vinhas de Souza
2002-01-01
textabstractHere the author empirically estimates if the different monetary and exchange rate frameworks observed in the Accession Countries of Central and Eastern Europe and the Baltics do yield different outcomes in terms of level and variance of a set of nominal and real variables. The author
ICM: an Integrated Compartment Method for numerically solving partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.
1981-05-01
An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
International Nuclear Information System (INIS)
Zhang Yu-Feng; Tam, Honwah
2016-01-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A_1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A_1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. (paper)
Solving differential equations for Feynman integrals by expansions near singular points
Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.
2018-03-01
We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.
Integral equation approach to time-dependent kinematic dynamos in finite domains
International Nuclear Information System (INIS)
Xu Mingtian; Stefani, Frank; Gerbeth, Gunter
2004-01-01
The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α 2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples - the α 2 dynamo model with radially varying α and the Bullard-Gellman model - illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α 2 dynamo in rectangular domains
A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates
Directory of Open Access Journals (Sweden)
Shibata Darryl
2010-01-01
Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.
An integral equation-based numerical solver for Taylor states in toroidal geometries
O'Neil, Michael; Cerfon, Antoine J.
2018-04-01
We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.
Integral equation models for image restoration: high accuracy methods and fast algorithms
International Nuclear Information System (INIS)
Lu, Yao; Shen, Lixin; Xu, Yuesheng
2010-01-01
Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of true physical (continuous) models, and hence, inevitably impose bottleneck model errors. We propose to work directly with continuous models for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is conducted in this paper for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images
Thermodynamically self-consistent integral equations and the structure of liquid metals
International Nuclear Information System (INIS)
Pastore, G.; Kahl, G.
1987-01-01
We discuss the application of the new thermodynamically self-consistent integral equations for the determination of the structural properties of liquid metals. We present a detailed comparison of the structure (S(q) and g(r)) for models of liquid alkali metals as obtained from two thermodynamically self-consistent integral equations and some published exact computer simulation results; the range of states extends from the triple point to the expanded metal. The theories which only impose thermodynamic self-consistency without any fitting of external data show an excellent agreement with the simulation results, thus demonstrating that this new type of integral equation is definitely superior to the conventional ones (hypernetted chain, Percus-Yevick, mean spherical approximation, etc). (author)
Nonperturbative time-convolutionless quantum master equation from the path integral approach
International Nuclear Information System (INIS)
Nan Guangjun; Shi Qiang; Shuai Zhigang
2009-01-01
The time-convolutionless quantum master equation is widely used to simulate reduced dynamics of a quantum system coupled to a bath. However, except for several special cases, applications of this equation are based on perturbative calculation of the dissipative tensor, and are limited to the weak system-bath coupling regime. In this paper, we derive an exact time-convolutionless quantum master equation from the path integral approach, which provides a new way to calculate the dissipative tensor nonperturbatively. Application of the new method is demonstrated in the case of an asymmetrical two-level system linearly coupled to a harmonic bath.
On a Painleve test for the complete integrability of Bogomolny's monopole equation
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Chanda, P.K.
1984-09-01
We have made an analysis of the monopole equation of Bogomolny from the stand point of Painleve test. The idea that any non-linear partial differential equation admitting a Lax representation should conform to the criterion of the Painleve analysis seems to hold well in case of Bogomolny equation. We have determined the position for resonances and have proved that at each of these the coefficients in the Forbenius type expansion of the gauge potentials do become arbitrary signalling the complete integrability of the system. (author)
Directory of Open Access Journals (Sweden)
Gemechis File
2012-01-01
Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .
Exponential decay rate of the power spectrum for solutions of the Navier--Stokes equations
International Nuclear Information System (INIS)
Doering, C.R.; Titi, E.S.
1995-01-01
Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier--Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained
Rate equation description of quantum noise in nanolasers with few emitters
DEFF Research Database (Denmark)
Mørk, Jesper; Lippi, G. L.
2018-01-01
Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2...
DEFF Research Database (Denmark)
Riisgård, Hans Ulrik; Larsen, Poul Scheel; Pleissner, Daniel
2014-01-01
rate (F, l h-1), W (g), and L (mm) as described by the equations: FW = aWb and FL = cLd, respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells...
Silberg, Judy L.; And Others
1994-01-01
Applied structural equation modeling to twin data to assess impact of genetic and environmental factors on children's behavioral and emotional functioning. Applied models to maternal ratings of behavior of 515 monozygotic and 749 dizygotic twin pairs. Importance of genetic, shared, and specific environmental factors for explaining variation was…
An estimator for the relative entropy rate of path measures for stochastic differential equations
Energy Technology Data Exchange (ETDEWEB)
Opper, Manfred, E-mail: manfred.opper@tu-berlin.de
2017-02-01
We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.
Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.
2018-05-01
The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.
Comments on the integrability of the loop-space chiral equations
International Nuclear Information System (INIS)
Gu, C.; Wang, L.L.C.
1980-01-01
A demonstration is given how the ordinary space chiral equations provide the existence conditions for the infinite number of conserved currents and how these currents are related to the so-called inverse-scattering equations, whose integrability is provided by the original chiral equations. Loop-space chiral equations are introduced. The integrability conditions of the non-local currents in two possible different situations are discussed. In the first case, the generating functions are functionals of the loop alone. The integrability conditions are not satisfied and higher order conserved non-local currents do not exist. In the second case, the generating functions are functionals of the loop as well as a parameter the integrability conditions at a restricted point of the parameter are satisfied, however there is an infinite fold of arbitrariness. It indicates that additional guiding principles are needed in addition to the original loop-space chiral equation in order to uniquely determine the infinite conserved non-local currents as functionals of the loop and the parameter
On Models with Uncountable Set of Spin Values on a Cayley Tree: Integral Equations
International Nuclear Information System (INIS)
Rozikov, Utkir A.; Eshkobilov, Yusup Kh.
2010-01-01
We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. We reduce the problem of describing the 'splitting Gibbs measures' of the model to the description of the solutions of some nonlinear integral equation. For k = 1 we show that the integral equation has a unique solution. In case k ≥ 2 some models (with the set [0, 1] of spin values) which have a unique splitting Gibbs measure are constructed. Also for the Potts model with uncountable set of spin values it is proven that there is unique splitting Gibbs measure.
A predictor-corrector scheme for solving the Volterra integral equation
Al Jarro, Ahmed
2011-08-01
The occurrence of late time instabilities is a common problem of almost all time marching methods developed for solving time domain integral equations. Implicit marching algorithms are now considered stable with various efforts that have been developed for removing low and high frequency instabilities. On the other hand, literature on stabilizing explicit schemes, which might be considered more efficient since they do not require a matrix inversion at each time step, is practically non-existent. In this work, a stable but still explicit predictor-corrector scheme is proposed for solving the Volterra integral equation and its efficacy is verified numerically. © 2011 IEEE.
Sayed, Sadeed Bin
2016-11-02
An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.
International Nuclear Information System (INIS)
Pujols, Agnes
1991-01-01
We prove that the scattering operator for the wave equation in the exterior of an non-homogeneous obstacle exists. Its distribution kernel is represented by a time-dependent boundary integral equation. A space-time integral variational formulation is developed for determining the current induced by the scattering of an electromagnetic wave by an homogeneous object. The discrete approximation of the variational problem using a finite element method in both space and time leads to stable convergent schemes, giving a numerical code for perfectly conducting cylinders. (author) [fr
Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan
2016-01-01
An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.
On the asymptotic solution to a class of linear integral equations
International Nuclear Information System (INIS)
Gautesen, A.K.
1988-01-01
The authors consider Fredholm integral equations of the first kind whose kernels are a function of the difference between two points times a large parameter. Conditions on the kernel are stated in terms of a function corresponding to a Wiener-Hopf factorization of the Fourier transform of the kernel. They give the complete asymptotic expansions of the solution to the integral equations. As applications of the author's results, the author considers the steady-state, acoustical scattering of a plane wave by both a hard strip and a soft strip. The author's results are uniform with respect to the direction of incidence
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
Directory of Open Access Journals (Sweden)
Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Energy Technology Data Exchange (ETDEWEB)
Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K. [National Research Centre Kurchatov Institute (Russian Federation)
2016-12-15
Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.
International Nuclear Information System (INIS)
Utama, Briandhika; Purqon, Acep
2016-01-01
Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods. (paper)
Valdés, Felipe
2011-06-01
A new regularized single source equation for analyzing scattering from homogeneous penetrable objects is presented. The proposed equation is a linear combination of a Calderón-preconditioned single source electric field integral equation and a single source magnetic field integral equation. The equation is immune to low-frequency and dense-mesh breakdown, and free from spurious resonances. Unlike dual source formulations, this equation involves operator products that cannot be discretized using standard procedures for discretizing standalone electric, magnetic, and combined field operators. Instead, the single source equation proposed here is discretized using a recently developed technique that achieves a well-conditioned mapping from div- to curl-conforming function spaces, thereby fully respecting the space mapping properties of the operators involved, and guaranteeing accuracy and stability. Numerical results show that the proposed equation and discretization technique give rise to rapidly convergent solutions. They also validate the equation\\'s resonant free character. © 2006 IEEE.
Fixation of waste materials in grouts: Part 3, Equation for critical flow rate
International Nuclear Information System (INIS)
Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.
1986-12-01
Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs
On the initial condition problem of the time domain PMCHWT surface integral equation
Uysal, Ismail Enes
2017-05-13
Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Directory of Open Access Journals (Sweden)
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Scholle, M., E-mail: markus.scholle@hs-heilbronn.de; Marner, F., E-mail: florian.marner@hs-heilbronn.de
2016-09-23
In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.
A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations
International Nuclear Information System (INIS)
Scholle, M.; Marner, F.
2016-01-01
In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.
International Nuclear Information System (INIS)
Fujii, Akira; Kluemper, Andreas
1999-01-01
We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation
Sabounchi, N S; Rahmandad, H; Ammerman, A
2013-10-01
Basal metabolic rate (BMR) represents the largest component of total energy expenditure and is a major contributor to energy balance. Therefore, accurately estimating BMR is critical for developing rigorous obesity prevention and control strategies. Over the past several decades, numerous BMR formulas have been developed targeted to different population groups. A comprehensive literature search revealed 248 BMR estimation equations developed using diverse ranges of age, gender, race, fat-free mass, fat mass, height, waist-to-hip ratio, body mass index and weight. A subset of 47 studies included enough detail to allow for development of meta-regression equations. Utilizing these studies, meta-equations were developed targeted to 20 specific population groups. This review provides a comprehensive summary of available BMR equations and an estimate of their accuracy. An accompanying online BMR prediction tool (available at http://www.sdl.ise.vt.edu/tutorials.html) was developed to automatically estimate BMR based on the most appropriate equation after user-entry of individual age, race, gender and weight.
Transforming differential equations of multi-loop Feynman integrals into canonical form
Energy Technology Data Exchange (ETDEWEB)
Meyer, Christoph [Institut für Physik, Humboldt-Universität zu Berlin,12489 Berlin (Germany)
2017-04-03
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Introduction to quantum mechanics Schrödinger equation and path integral
Müller-Kirsten, H J W
2012-01-01
This text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrodinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions. In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introdu...
A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations
International Nuclear Information System (INIS)
Zhang Yufeng; Xu Xixiang
2004-01-01
A subalgebra of loop algebra A-bar 2 is first constructed, which has its own special feature. It follows that a new Liouville integrable hierarchy of evolution equations is obtained, possessing a tri-Hamiltonian structure, which is proved by us in this paper. Especially, three symplectic operators are constructed directly from recurrence relations. The conjugate operator of a recurrence operator is a hereditary symmetry. As reduction cases of the hierarchy presented in this paper, the celebrated MKdV equation and heat-conduction equation are engendered, respectively. Therefore, we call the hierarchy a generalized MKdV-H system. At last, a high-dimension loop algebra G-bar is constructed by making use of a proper scalar transformation. As a result, a type expanding integrable model of the MKdV-H system is given
The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations
Directory of Open Access Journals (Sweden)
Yadong Shang
2012-01-01
Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.
Danwanichakul, Panu; Glandt, Eduardo D
2004-11-15
We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.
Transforming differential equations of multi-loop Feynman integrals into canonical form
Meyer, Christoph
2017-04-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Transforming differential equations of multi-loop Feynman integrals into canonical form
International Nuclear Information System (INIS)
Meyer, Christoph
2017-01-01
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.
Elliptic Euler–Poisson–Darboux equation, critical points and integrable systems
International Nuclear Information System (INIS)
Konopelchenko, B G; Ortenzi, G
2013-01-01
The structure and properties of families of critical points for classes of functions W(z, z-bar ) obeying the elliptic Euler–Poisson–Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(β, β-bar ;1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed. (paper)
Solution of four-nucleon integral equations using the effective UPA
International Nuclear Information System (INIS)
Perne, R.; Sandhas, W.
1978-01-01
In the three-body case it is standard to either solve the (two-dimensional) Faddeev equations directly, or to reduce them first to one-dimensional equations by means of separable approximation (expansion) of the underlying two-body interactions. The basic four-body operator identities are reduced by the latter treatment to effective three-body equations only. These may be handled like their genuine three-body analoga, i.e., by directly solving them, or by expanding the effective interactions ocurring into separable terms. Such a procedure provides us in a second step with one-dimensional integral equations for the four-body problem, too. (orig./WL) [de
Nonlinear integral equations for thermodynamics of the sl(r + 1) Uimin-Sutherland model
International Nuclear Information System (INIS)
Tsuboi, Zengo
2003-01-01
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the those from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIEs). In particular, a subset of these NLIEs forms a system of NLIEs which contains only a finite number of unknown functions. For r=1, this subset of NLIEs reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIEs is clarified. Based on our new NLIEs, we also calculate the high-temperature expansion of the free energy
Stochastic integration of the Bethe-Salpeter equation for two bound fermions
International Nuclear Information System (INIS)
Salomon, M.
1988-09-01
A non-perturbative method using a Monte Carlo algorithm is used to integrate the Bethe-Salpeter equation in momentum space. Solutions for two scalars and two fermions with an arbitrary coupling constant are calculated for bound states in the ladder approximation. The results are compared with other numerical methods. (Author) (13 refs., 2 figs.)
Al Jarro, Ahmed
2011-09-01
A new predictor-corrector scheme for solving the Volterra integral equation to analyze transient electromagnetic wave interactions with arbitrarily shaped inhomogeneous dielectric bodies is considered. Numerical results demonstrating stability and accuracy of the proposed method are presented. © 2011 IEEE.
A surface-integral-equation approach to the propagation of waves in EBG-based devices
Lancellotti, V.; Tijhuis, A.G.
2012-01-01
We combine surface integral equations with domain decomposition to formulate and (numerically) solve the problem of electromagnetic (EM) wave propagation inside finite-sized structures. The approach is of interest for (but not limited to) the analysis of devices based on the phenomenon of
Two hierarchies of multi-component Kaup-Newell equations and theirs integrable couplings
International Nuclear Information System (INIS)
Zhu Fubo; Ji Jie; Zhang Jianbin
2008-01-01
Two hierarchies of multi-component Kaup-Newell equations are derived from an arbitrary order matrix spectral problem, including positive non-isospectral Kaup-Newell hierarchy and negative non-isospectral Kaup-Newell hierarchy. Moreover, new integrable couplings of the resulting Kaup-Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem
Directory of Open Access Journals (Sweden)
A. Anguraj
2014-02-01
Full Text Available We study in this paper,the existence of solutions for fractional integro differential equations with impulsive and integral conditions by using fixed point method. We establish the Sufficient conditions and unique solution for given problem. An Example is also explained to the main results.
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
Directory of Open Access Journals (Sweden)
Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric
2010-01-01
A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well
International Nuclear Information System (INIS)
Biazar, J.; Eslami, M.; Aminikhah, H.
2009-01-01
In this article, an application of He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the first kind. Some non-linear examples are prepared to illustrate the efficiency and simplicity of the method. Applying the method for linear systems is so easily that it does not worth to have any example.
International Nuclear Information System (INIS)
Biazar, J.; Ghazvini, H.
2009-01-01
In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the second kind. Some examples are presented to illustrate the ability of the method for linear and non-linear such systems. The results reveal that the method is very effective and simple.
Korkmaz, Erdal
2017-01-01
In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.
A purely Lagrangian method for the numerical integration of Fokker-Planck equations
International Nuclear Information System (INIS)
Combis, P.; Fronteau, J.
1986-01-01
A new numerical approach to Fokker-Planck equations is presented, in which the integration grid moves according to the solution of a differential system. The method is purely Lagrangian, the mean effect of the diffusion being inserted into the differential system itself
To the complete integrability of long-wave short-wave interaction equations
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Chanda, P.K.
1984-10-01
We show that the non-linear partial differential equations governing the interaction of long and short waves are completely integrable. The methodology we use is that of Ablowitz et al. though in the last section of our paper we have discussed the problem also in the light of the procedure due to Weiss et al. and have obtained a Baecklund transformation. (author)
Spatial symmetry, local integrability and tetrahedron equations in the Baxter-Bazhanov model
International Nuclear Information System (INIS)
Kashaev, R.M.; Mangazeev, V.V.; Stroganov, Yu.G.
1992-01-01
It is shown that the Baxter-Bazhanov model is invariant under the action of the cube symmetry group. The three-dimensional star-star relations, proposed by Baxter and Bazhanov as local integrability conditions, correspond to a particular transformation from this group. Invariant Boltzmann weights, parameterized in terms of the Zamolodchikov's angle variables, apparently satisfy the tetrahedron equations. 12 refs
WKB: an interactive code for solving differential equations using phase integral methods
International Nuclear Information System (INIS)
White, R.B.
1978-01-01
A small code for the analysis of ordinary differential equations interactively through the use of Phase Integral Methods (WKB) has been written for use on the DEC 10. This note is a descriptive manual for those interested in using the code
Directory of Open Access Journals (Sweden)
Erdal Korkmaz
2017-06-01
Full Text Available Abstract In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov’s second method. The results obtained essentially improve, include and complement the results in the literature.
Two-dimensional nonlinear string-type equations and their exact integration
International Nuclear Information System (INIS)
Leznov, A.N.; Saveliev, M.V.
1982-01-01
On the base of group-theoretical formulation for exactly integrable two-dimensional non-linear dynamical systems associated with a local part of an arbitrary graded Lie algebra we study a string-type subclass of the equations. Explicit expressions have been obtained for their general solutions
On the integration of equations of motion for particle-in-cell codes
Czech Academy of Sciences Publication Activity Database
Fuchs, Vladimír; Gunn, J. P.
2006-01-01
Roč. 214, - (2006), s. 299-315 ISSN 0021-9991 R&D Projects: GA ČR GA202/04/0360 Institutional research plan: CEZ:AV0Z20430508 Keywords : Equations of motion * 2nd order integration methods * nonlinear oscillations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.328, year: 2006
M. Denche; A. L. Marhoune
2003-01-01
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
Analysis of Buried Dielectric Objects Using Higher-Order MoM for Volume Integral Equations
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2004-01-01
A higher-order method of moments (MoM) is applied to solve a volume integral equation for dielectric objects in layered media. In comparison to low-order methods, the higher-order MoM, which is based on higher-order hierarchical Legendre vector basis functions and curvilinear hexahedral elements,...
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sarmany, D.; Bochev, Mikhail A.; van der Vegt, Jacobus J.W.
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic
An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.
2005-12-01
We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions of the radial and angular ODEs which arise in the separation of variables. In particular, we prove completeness of the solutions of the separated ODEs.
Energy Technology Data Exchange (ETDEWEB)
Chen, Ke [Univ. of Liverpool (United Kingdom)
1996-12-31
We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.
Directory of Open Access Journals (Sweden)
Liu X
2012-10-01
Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the
Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays
Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.
2018-05-01
Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.
International Nuclear Information System (INIS)
Li Xinyue; Zhao Qiulan
2009-01-01
Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.
Rate concept and retarded master equations for dissipative tight-binding models
International Nuclear Information System (INIS)
Egger, R.; Mak, C.H.; Weiss, U.
1994-01-01
Employing a ''noninteracting-cluster approximation,'' the dynamics of multistate dissipative tight-binding models has been formulated in terms of a set of generalized retarded master equations. The rates for the various pathways are expressed as power series in the intersite couplings. We apply this to the superexchange mechanism, which is relevant for bacterial photosynthesis and bridged electron transfer systems. This approach provides a general and unified description of both incoherent and coherent transport
Characteristics of quantum dash laser under the rate equation model framework
Khan, Mohammed Zahed Mustafa
2010-09-01
The authors present a numerical model to study the carrier dynamics of InAs/InP quantum dash (QDash) lasers. The model is based on single-state rate equations, which incorporates both, the homogeneous and the inhomogeneous broadening of lasing spectra. The numerical technique also considers the unique features of the QDash gain medium. This model has been applied successfully to analyze the laser spectra of QDash laser. ©2010 IEEE.
76 FR 50726 - Integrated System Power Rates: Correction
2011-08-16
... DEPARTMENT OF ENERGY Southwestern Power Administration Integrated System Power Rates: Correction AGENCY: Southwestern Power Administration, DOE. ACTION: Notice of public review and comment; Correction... date listed for the combined Public Information and Comment Forum (Forum) was erroneously listed in the...
Solution of the Stokes system by boundary integral equations and fixed point iterative schemes
International Nuclear Information System (INIS)
Chidume, C.E.; Lubuma, M.S.
1990-01-01
The solution to the exterior three dimensional Stokes problem is sought in the form of a single layer potential of unknown density. This reduces the problem to a boundary integral equation of the first kind whose operator is the velocity component of the single layer potential. It is shown that this component is an isomorphism between two appropriate Sobolev spaces containing the unknown densities and the data respectively. The isomorphism corresponds to a variational problem with coercive bilinear form. The latter property allows us to consider various fixed point iterative schemes that converge to the unique solution of the integral equation. Explicit error estimates are also obtained. The successive approximations are also considered in a more computable form by using the product integration method of Atkinson. (author). 47 refs
International Nuclear Information System (INIS)
Trowbridge, C.W.
1976-06-01
Various integral equation methods are described. For magnetostatic problems three formulations are considered in detail, (a) the direct solution method for the magnetisation distribution in permeable materials, (b) a method based on a scalar potential and (c) the use of an integral equation derived from Green's Theorem, i.e. the so-called Boundary Integral Method (BIM). In the case of (a) results are given for two-and three-dimensional non-linear problems with comparisons against measurement. For methods (b) and (c) which both lead to a more economic use of the computer than (a) some preliminary results are given for simple cases. For eddy current problems various methods are discussed and some results are given from a computer program based on a vector potential formulation. (author)
International Nuclear Information System (INIS)
Xiong, Z.; Tripp, A.C.
1994-01-01
This paper presents an integral equation algorithm for 3D EM modeling at high frequencies for applications in engineering an environmental studies. The integral equation method remains the same for low and high frequencies, but the dominant roles of the displacements currents complicate both numerical treatments and interpretations. With singularity extraction technique they successively extended the application of the Hankel filtering technique to the computation of Hankel integrals occurring in high frequency EM modeling. Time domain results are calculated from frequency domain results via Fourier transforms. While frequency domain data are not obvious for interpretations, time domain data show wave-like pictures that resemble seismograms. Both 1D and 3D numerical results show clearly the layer interfaces
Energy Technology Data Exchange (ETDEWEB)
Trowbridge, C W
1976-06-01
Various integral equation methods are described. For magnetostatic problems three formulations are considered in detail, (a) the direct solution method for the magnetisation distribution in permeable materials, (b) a method based on a scalar potential, and (c) the use of an integral equation derived from Green's Theorem, i.e. the so-called Boundary Integral Method (BIM). In the case of (a) results are given for two-and three-dimensional non-linear problems with comparisons against measurement. For methods (b) and (c), which both lead to a more economical use of the computer than (a), some preliminary results are given for simple cases. For eddy current problems various methods are discussed and some results are given from a computer program based on a vector potential formulation.
A higher order space-time Galerkin scheme for time domain integral equations
Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam
2014-01-01
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.
International Nuclear Information System (INIS)
Dubrovsky, V.G.; Formusatik, I.B.
2003-01-01
The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular
Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral
Hose, R D
2006-01-01
Using the separation of the variables technique, the free particle solutions of the Dirac equation in the momentum space are shown to be actually providing the definition of Delta function for the Schr dinger picture. Further, the said solution is shown to be derivable on the sole strength of geometrical argument that the Dirac equation for free particle is an equation of a plane in momentum space. During the evolution of time in the Schr dinger picture, the normal to the said Dirac equation plane is shown to be constantly changing in direction due to the uncertainty principle and thereby, leading to a zigzag path for the Dirac particle in the momentum space. Further, the time evolution of the said Delta function solutions of the Dirac equation is shown to provide Feynman integral of all such zigzag paths in the momentum space. Towards the end of the paper, Feynman path integral between two fixed spatial points in the co-ordinate space during a certain time interv! al is shown to be composed, in time sequence...
Some thoughts on the pressure integration requirements of the Navier–Stokes equations
International Nuclear Information System (INIS)
Saad, Tony; Majdalani, Joseph
2012-01-01
The Navier–Stokes formulation represents a uniquely challenging system of partial differential equations that continues to influence modern applied science and engineering. In its simplest form, the system can be used to prescribe the motion of a viscous incompressible fluid with constant properties. It consists of four equations in three-dimensional space that account for both the kinematic and dynamic conditions that a fluid element senses. In this work, we investigate the pressure integration rules and restrictions that affect the resolution of the scalar pressure field. We begin our analysis by exploring the integration properties of Euler's equations in two dimensions while making use of Clairaut's theorem on the commutativity of mixed partial derivatives. We then extend our findings to three-dimensional space. This process gives rise to a theorem and four corollaries that help to clarify the conditions needed to obtain exact or asymptotic solutions for the pressure distribution. Consequently, we identify the fundamental conditions under which the Navier–Stokes equations can be properly integrated to arrive at an analytic expression for the pressure field, namely, one that is continuous and twice differentiable. In closing, several configurations are used to test the theorem and showcase its connection with the pressure formulation. These include potential flows for which the pressure can be obtained unconditionally, and inviscid rotational motions of the Taylor–Culick type with and without headwall injection. (paper)
Splitting of the rate matrix as a definition of time reversal in master equation systems
International Nuclear Information System (INIS)
Liu Fei; Le, Hong
2012-01-01
Motivated by recent progress in nonequilibrium fluctuation relations, we present a generalized time reversal for stochastic master equation systems with discrete states, which is defined as a splitting of the rate matrix into irreversible and reversible parts. An immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings. Additionally, we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part, which was previously ignored. (paper)
CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane
2006-10-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. 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, just as 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, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular
Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar
2018-04-01
Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.
Existing creatinine-based equations overestimate glomerular filtration rate in Indians.
Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand
2018-02-01
Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the
Bound states of quarks calculated with stochastic integration of the Bethe-Salpeter equation
International Nuclear Information System (INIS)
Salomon, M.
1992-07-01
We have computed the masses, wave functions and sea quark content of mesons in their ground state by integrating the Bethe-Salpeter equation with a stochastic algorithm. This method allows the inclusion of a large set of diagrams. Inspection of the kernel of the equation shows that q-q-bar pairs with similar constituent masses in a singlet spin state exhibit a high bound state which is not present in other pairs. The pion, kaon and eta belongs to this category. 19 refs., 2 figs., 2 tabs
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe
2013-05-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
The Abel symposium 2008 on differential equations: geometry, symmetries and integrability
Lychagin, Valentin; Straume, Eldar; Abel symposium 2008; Differential equations; Geometry, symmetries and integrability
2008-01-01
The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
High-Order Calderón Preconditioned Time Domain Integral Equation Solvers
Valdes, Felipe; Ghaffari-Miab, Mohsen; Andriulli, Francesco P.; Cools, Kristof; Michielssen,
2013-01-01
Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.
Hamiltonian structures and integrability for a discrete coupled KdV-type equation hierarchy
International Nuclear Information System (INIS)
Zhao Haiqiong; Zhu Zuonong; Zhang Jingli
2011-01-01
Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy. (authors)
Killing spinor equations in dimension 7 and geometry of integrable G2-manifolds
International Nuclear Information System (INIS)
Friedrich, Thomas; Ivanov, Stefan
2001-12-01
We compute the scalar curvature of 7-dimensional G 2 -manifolds admitting a connection with totally skew-symmetric torsion. We prove the formula for the general solution of the Killing spinor equation and express the Riemannian scalar curvature of the solution in terms of the dilation function and the NS 3-form field. In dimension n=7 the dilation function involved in the second fermionic string equation has an interpretation as a conformal change of the underlying integrable G 2 -structure into a cocalibrated one of pure type W 3 . (author)
International Nuclear Information System (INIS)
Belov, V.E.; Rodygin, L.V.; Fil'chenko, S.E.; Yunakovskii, A.D.
1988-01-01
A method is described for calculating the electrodynamic characteristics of periodically corrugated waveguide systems. This method is based on representing the field as the solution of the Helmholtz vector equation in the form of a simple layer potential, transformed with the use of the Floquet conditions. Systems of compound integral equations based on a weighted vector function of the simple layer potential are derived for waveguides with azimuthally symmetric and helical corrugations. A numerical realization of the Fourier method is cited for seeking the dispersion relation of azimuthally symmetric waves of a circular corrugated waveguide
Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines
Directory of Open Access Journals (Sweden)
M. A. Banaja
2015-01-01
Full Text Available The equal width (EW equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW equation is obtained by using the method of lines (MOL based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L2 and L∞ error norms. The results are found in good agreement with exact solution.
On a method for constructing the Lax pairs for nonlinear integrable equations
International Nuclear Information System (INIS)
Habibullin, I T; Poptsova, M N; Khakimova, A R
2016-01-01
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found immediately, coinciding with the linearization of the considered nonlinear equation. The second one is obtained as an invariant manifold to the linearized equation. A surprisingly simple relation between the second operator of the Lax pair and the recursion operator is discussed: the recursion operator can immediately be found from the Lax pair. Examples considered in the article are convincing evidence that the found Lax pairs differ from the classical ones. The examples also show that the suggested objects are true Lax pairs which allow the construction of infinite series of conservation laws and hierarchies of higher symmetries. In the case of the hyperbolic type partial differential equation our algorithm is slightly modified; in order to construct the Lax pairs from the invariant manifolds we use the cutting off conditions for the corresponding infinite Laplace sequence. The efficiency of the method is illustrated by application to some equations given in the Svinolupov–Sokolov classification list for which the Lax pairs and the recursion operators have not been found earlier. (paper)
Asymptotic integration of a linear fourth order differential equation of Poincaré type
Directory of Open Access Journals (Sweden)
Anibal Coronel
2015-11-01
Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.
Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V
2014-05-01
The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.
A Special Variant of the Moment Method for Fredholm Integral Equations of the Second Kind
Directory of Open Access Journals (Sweden)
S. A. Solov’eva
2015-01-01
Full Text Available We consider the linear Fredholm integral equation of the second kind, where the kernel and the free term are smooth functions. We find the unknown function in this class as well.Exact and approximate methods for the solution of linear Fredholm integral equations of the second kind are well developed. However, classical methods do not take into account the structural properties of the kernel and the free term of equation.In this paper we develop and justify a special variant of the moment method to solve this equation, which takes into account the differential properties of initial data. The proposed paper furthers studies of N.S Gabbasov, I.P. Kasakina, and S.A Solov’eva. We use approximation theory, version of the general theory of approximate methods of analysis that Gabdulkhayev B.G suggested, and methods of functional analysis to prove theorems. In addition, we use N.S. Gabbasov’s ideas and methods in papers that are devoted to the Fredholm equations of the first kind, as well as N.S. Gabbasov and S.A Solov’eva’s investigations on the Fredholm equations of the third kind in the space of distributions.The first part of the paper provides a description of the basic function space and elements of the theory of approximation in it.In the second part we propose and theoretically justify a generalized moment method. We have demonstrated that the improvement of differential properties of the initial data improves the approximation accuracy. Since, in practice, the approximate equations are solved, as a rule, only approximately, we prove the stability and causality of the proposed method. The resulting estimate of the paper is in good agreement with the estimate for the ordinary moment method for equations of the second kind in the space of continuous functions.In the final section we have shown that a developed method is optimal in order of accuracy among all polynomial projection methods to solve Fredholm integral equations of the second
Directory of Open Access Journals (Sweden)
Appleby JohnAD
2010-01-01
Full Text Available We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. The result is considered both for a linear Volterra integrodifferential equation as well as for the delay logistic equation from population biology.
Energy Technology Data Exchange (ETDEWEB)
Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica
1978-08-21
The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.
Fu, Wei; Nijhoff, Frank W
2017-07-01
A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.
Validation of predictive equations for glomerular filtration rate in the Saudi population
Directory of Open Access Journals (Sweden)
Al Wakeel Jamal
2009-01-01
Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.
Direct Yaw Control of Vehicle using State Dependent Riccati Equation with Integral Terms
Directory of Open Access Journals (Sweden)
SANDHU, F.
2016-05-01
Full Text Available Direct yaw control of four-wheel vehicles using optimal controllers such as the linear quadratic regulator (LQR and the sliding mode controller (SMC either considers only certain parameters constant in the nonlinear equations of vehicle model or totally neglect their effects to obtain simplified models, resulting in loss of states for the system. In this paper, a modified state-dependent Ricatti equation method obtained by the simplification of the vehicle model is proposed. This method overcomes the problem of the lost states by including state integrals. The results of the proposed system are compared with the sliding mode slip controller and state-dependent Ricatti equation method using high fidelity vehicle model in the vehicle simulation software package, Carsim. Results show 38% reduction in the lateral velocity, 34% reduction in roll and 16% reduction in excessive yaw by only increasing the fuel consumption by 6.07%.
Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.
Chowdury, A; Kedziora, D J; Ankiewicz, A; Akhmediev, N
2014-09-01
We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
A parallel algorithm for solving the integral form of the discrete ordinates equations
International Nuclear Information System (INIS)
Zerr, R. J.; Azmy, Y. Y.
2009-01-01
The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)
47 CFR 64.1801 - Geographic rate averaging and rate integration.
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Geographic rate averaging and rate integration. 64.1801 Section 64.1801 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) MISCELLANEOUS RULES RELATING TO COMMON CARRIERS Geographic Rate Averaging and...
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
Directory of Open Access Journals (Sweden)
Anita Nordenson
2010-09-01
Full Text Available Anita Nordenson2, Anne Marie Grönberg1,2, Lena Hulthén1, Sven Larsson2, Frode Slinde11Department of Clinical Nutrition, Sahlgrenska Academy at University of Gothenburg, Göteborg, Sweden; 2Department of Internal Medicine/Respiratory Medicine and Allergology, Sahlgrenska Academy at University of Gothenburg, SwedenAbstract: Malnutrition is a serious condition in chronic obstructive pulmonary disease (COPD. Successful dietary intervention calls for calculations of resting metabolic rate (RMR. One disease-specific prediction equation for RMR exists based on mainly male patients. To construct a disease-specific equation for RMR based on measurements in underweight or weight-losing women and men with COPD, RMR was measured by indirect calorimetry in 30 women and 11 men with a diagnosis of COPD and body mass index <21 kg/m2. The following variables, possibly influencing RMR were measured: length, weight, middle upper arm circumference, triceps skinfold, body composition by dual energy x-ray absorptiometry and bioelectrical impedance, lung function, and markers of inflammation. Relations between RMR and measured variables were studied using univariate analysis according to Pearson. Gender and variables that were associated with RMR with a P value <0.15 were included in a forward multiple regression analysis. The best-fit multiple regression equation included only fat-free mass (FFM: RMR (kJ/day = 1856 + 76.0 FFM (kg. To conclude, FFM is the dominating factor influencing RMR. The developed equation can be used for prediction of RMR in underweight COPD patients.Keywords: pulmonary disease, chronic obstructive, basal metabolic rate, malnutrition, body composition
Current use of equations for estimating glomerular filtration rate in Spanish laboratories.
Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador
2012-07-17
In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.
International Nuclear Information System (INIS)
Schwenk, G.A. Jr.
1980-01-01
The calculation of neutron-nuclei reaction rates in the lower resolved resonance region (167 eV - 1.855 eV) is considered in this dissertation. Particular emphasis is placed on the calculation of these reaction rates for tight lattices where their accuracy is most important. The results of the continuous energy Monte Carlo code, VIM, are chosen as reference values for this study. The primary objective of this work is to develop a method for calculating resonance reaction rates which agree well with the reference solution, yet is efficient enough to be used by nuclear reactor fuel cycle designers on a production basis. A very efficient multigroup solution of the two spatial region energy dependent integral transport equation is developed. This solution, denoted the Broad Group Integral Method (BGIM), uses escape probabilities to obtain the spatial coupling between regions and uses an analytical flux shape within a multigroup to obtain weighted cross sections which account for the rapidly varying resonance cross sections. The multigroup lethargy widths chosen for the numerical integration of the two region energy-dependent neutron continuity equations can be chosen much wider (a factor of 30 larger) than in the direct numerical integration methods since the analytical flux shape is used to account for fine structure effects. The BGIM solution is made highly efficient through the use of these broad groups. It is estimated that for a 10 step unit cell fuel cycle depletion calculation, the computer running time for a production code such as EPRI-LEOPARD would be increased by only 6% through the use of the more accurate and intricate BGIM method in the lower resonance energy region
Fernandez-Prado, Raul; Castillo-Rodriguez, Esmeralda; Velez-Arribas, Fernando Javier; Gracia-Iguacel, Carolina; Ortiz, Alberto
2016-12-01
Direct oral anticoagulants (DOACs) may require dose reduction or avoidance when glomerular filtration rate is low. However, glomerular filtration rate is not usually measured in routine clinical practice. Rather, equations that incorporate different variables use serum creatinine to estimate either creatinine clearance in mL/min or glomerular filtration rate in mL/min/1.73 m 2 . The Cockcroft-Gault equation estimates creatinine clearance and incorporates weight into the equation. By contrast, the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations estimate glomerular filtration rate and incorporate ethnicity but not weight. As a result, an individual patient may have very different renal function estimates, depending on the equation used. We now highlight these differences and discuss the impact on routine clinical care for anticoagulation to prevent embolization in atrial fibrillation. Pivotal DOAC clinical trials used creatinine clearance as a criterion for patient enrollment, and dose adjustment and Federal Drug Administration recommendations are based on creatinine clearance. However, clinical biochemistry laboratories provide CKD-EPI glomerular filtration rate estimations, resulting in discrepancies between clinical trial and routine use of the drugs. Copyright © 2016 Elsevier Inc. All rights reserved.
Integral-equation formulation for drift eigenmodes in cylindrically symmetric systems
International Nuclear Information System (INIS)
Linsker, R.
1980-12-01
A method for solving the integral eigenmode equation for drift waves in cylindrical (or slab) geometry is presented. A leading-order kinematic effect that has been noted in the past, but incorrectly ignored in recent integral-equation calculations, is incorporated. The present method also allows electrons to be treated with a physical mass ratio (unlike earlier work that is restricted to artificially small m/sub i//m/sub e/ owing to resolution limitations). Results for the universal mode and for the ion-temperature-gradient driven mode are presented. The kinematic effect qualitatively changes the spectrum of the ion mode, and a new second region of instability for k/sub perpendicular to/rho/sub i/greater than or equal to 1 is found
REFLECT: a program to integrate the wave equation through a plane stratified plasma
International Nuclear Information System (INIS)
Greene, J.W.
1975-01-01
A program was developed to integrate the wave equation through a plane stratified plasma with a general density distribution. The reflection and transmission of a plane wave are computed as a function of the angle of incidence. The polarization of the electric vector is assumed to be perpendicular to the plane of incidence. The model for absorption by classical inverse bremsstrahlung avoids the improper extrapolation of underdense formulae that are singular at the plasma critical surface. Surprisingly good agreement with the geometric-optics analysis of a linear layer was found. The system of ordinary differential equations is integrated by the variable-step, variable-order Adams method in the Lawrence Livermore Laboratory Gear package. Parametric studies of the absorption are summarized, and some possibilities for further development of the code are discussed. (auth)
Fuchsia. A tool for reducing differential equations for Feynman master integral to epsilon form
International Nuclear Information System (INIS)
Gituliar, Oleksandr; Magerya, Vitaly
2017-01-01
We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂ x f(x,ε)=A(x,ε)f(x,ε) finds a basis transformation T(x,ε), i.e., f(x,ε)=T(x,ε)g(x,ε), such that the system turns into the epsilon form: ∂ x g(x,ε)=εS(x)g(x,ε), where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ε. That makes the construction of the transformation T(x,ε) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals.
Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Sørensen, John Dalsgaard
Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before...... passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response....... outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first...
An efficient explicit marching on in time solver for magnetic field volume integral equation
Sayed, Sadeed Bin
2015-07-25
An efficient explicit marching on in time (MOT) scheme for solving the magnetic field volume integral equation is proposed. The MOT system is cast in the form of an ordinary differential equation and is integrated in time using a PE(CE)m multistep scheme. At each time step, a system with a Gram matrix is solved for the predicted/corrected field expansion coefficients. Depending on the type of spatial testing scheme Gram matrix is sparse or consists of blocks with only diagonal entries regardless of the time step size. Consequently, the resulting MOT scheme is more efficient than its implicit counterparts, which call for inversion of fuller matrix system at lower frequencies. Numerical results, which demonstrate the efficiency, accuracy, and stability of the proposed MOT scheme, are presented.
Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule
Directory of Open Access Journals (Sweden)
Adem Kılıçman
2012-01-01
Full Text Available The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order O(h4. Numerical examples are given to show abilities of the proposed method for solving linear as well as nonlinear systems. Our results show that the proposed method is simple and effective.
Acidity in DMSO from the embedded cluster integral equation quantum solvation model.
Heil, Jochen; Tomazic, Daniel; Egbers, Simon; Kast, Stefan M
2014-04-01
The embedded cluster reference interaction site model (EC-RISM) is applied to the prediction of acidity constants of organic molecules in dimethyl sulfoxide (DMSO) solution. EC-RISM is based on a self-consistent treatment of the solute's electronic structure and the solvent's structure by coupling quantum-chemical calculations with three-dimensional (3D) RISM integral equation theory. We compare available DMSO force fields with reference calculations obtained using the polarizable continuum model (PCM). The results are evaluated statistically using two different approaches to eliminating the proton contribution: a linear regression model and an analysis of pK(a) shifts for compound pairs. Suitable levels of theory for the integral equation methodology are benchmarked. The results are further analyzed and illustrated by visualizing solvent site distribution functions and comparing them with an aqueous environment.
Properties of linear integral equations related to the six-vertex model with disorder parameter II
International Nuclear Information System (INIS)
Boos, Hermann; Göhmann, Frank
2012-01-01
We study certain functions arising in the context of the calculation of correlation functions of the XXZ spin chain and of integrable field theories related to various scaling limits of the underlying six-vertex model. We show that several of these functions that are related to linear integral equations can be obtained by acting with (deformed) difference operators on a master function Φ. The latter is defined in terms of a functional equation and of its asymptotic behavior. Concentrating on the so-called temperature case, we show that these conditions uniquely determine the high-temperature series expansions of the master function. This provides an efficient calculation scheme for the high-temperature expansions of the derived functions as well. (paper)
Nodal integral method for the neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
The nodal methodology is based on retaining a higher a higher degree of analyticity in the process of deriving the discrete-variable equations compared to conventional numerical methods. As a result, extensive numerical testing of nodal methods developed for a wide variety of partial differential equations and comparison of the results to conventional methods have established the superior accuracy of nodal methods on coarse meshes. Moreover, these tests have shown that nodal methods are more computationally efficient than finite difference and finite-element methods in the sense that they require shorter CPU times to achieve comparable accuracy in the solutions. However, nodal formalisms and the final discrete-variable equations they produce are, in general, more complicated than their conventional counterparts. This, together with anticipated difficulties in applying the transverse-averaging procedure in curvilinear coordinates, has limited the applications of nodal methods, so far, to Cartesian geometry, and with additional approximations to hexagonal geometry. In this paper the authors report recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical r-z geometry. Also, presented are comparisons of numerical solutions to two test problems with those obtained by the Exterminator-2 code, which indicate the superior accuracy of the nodal integral method solutions on much coarser meshes
DEFF Research Database (Denmark)
Kim, Oleksiy S.
2016-01-01
A new technique for estimating the impedance frequency bandwidth of electrically small antennas loaded with magneto-dielectric material from a single-frequency simulation in a surface integral equation solver is presented. The estimate is based on the inverse of the radiation Q computed using newly...... derived expressions for the stored energy and the radiated power of arbitrary coupled electric and magnetic currents in free space....
Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric
2012-01-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Hierarchies of multi-component mKP equations and theirs integrable couplings
International Nuclear Information System (INIS)
Ji Jie; Yao Yuqin; Zhu Fubo; Chen Dengyuan
2008-01-01
First, a new multi-component modified Kadomtsev-Petviashvill (mKP) spectral problem is constructed by k-constraint imposed on a general pseudo-differential operator. Then, two hierarchies of multi-component mKP equations are derived, including positive non-isospectral mKP hierarchy and negative non-isospectral mKP hierarchy. Moreover, new integrable couplings of the resulting mKP soliton hierarchies are constructed by enlarging the associated matrix spectral problem
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2007-01-01
The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume-surface integral equation (VSIE). The method of moments (MoM) based on higher-order hierarchical Legendre basis functions and higher-order curvilinear geometrical elements...... with the analytical Mie series solution. Scattering by more complex metal-dielectric objects are also considered to compare the presented technique with other numerical methods....
Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation
International Nuclear Information System (INIS)
Neyzi, F.; Sheftel, M. B.; Yazici, D.
2007-01-01
We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems
Czech Academy of Sciences Publication Activity Database
Fiala, Zdeněk
2015-01-01
Roč. 226, č. 1 (2015), s. 17-35 ISSN 0001-5970 R&D Projects: GA ČR(CZ) GA103/09/2101 Institutional support: RVO:68378297 Keywords : solid mechanics * finite deformations * evolution equation of Lie-type * time-discrete integration Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.694, year: 2015 http://link.springer.com/article/10.1007%2Fs00707-014-1162-9#page-1
Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations
Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.
2018-04-01
Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.
International Nuclear Information System (INIS)
Adler, A.; Fuchs, B.; Thielheim, K.O.
1977-01-01
The longitudinal development of electromagnetic cascades in air, copper, iron, and lead is studied on the basis of results derived recently by numerical integration of the cascade equations applying rather accurate expressions for the cross-sections involved with the interactions of high energy electrons, positrons, and photons in electromagnetic cascades. Special attention is given to scaling properties of transition curves. It is demonstrated that a good scaling may be achieved by means of the depth of maximum cascade development. (author)
Ulku, Huseyin Arda
2012-09-01
An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.
Fast Near-Field Calculation for Volume Integral Equations for Layered Media
DEFF Research Database (Denmark)
Kim, Oleksiy S.; Meincke, Peter; Breinbjerg, Olav
2005-01-01
. Afterwards, the scattered electric field can be easily computed at a regular rectangular grid on any horizontal plane us-ing a 2-dimensional FFT. This approach provides significant speedup in the near-field calculation in comparison to a straightforward numerical evaluation of the ra-diation integral since......An efficient technique based on the Fast Fourier Transform (FFT) for calculating near-field scattering by dielectric objects in layered media is presented. A higher or-der method of moments technique is employed to solve the volume integral equation for the unknown induced volume current density...
An integrable (2+1)-dimensional Toda equation with two discrete variables
International Nuclear Information System (INIS)
Cao Cewen; Cao Jianli
2007-01-01
An integrable (2+1)-dimensional Toda equation with two discrete variables is presented from the compatible condition of a Lax triad composed of the ZS-AKNS (Zakharov, Shabat; Ablowitz, Kaup, Newell, Segur) eigenvalue problem and two discrete spectral problems. Through the nonlinearization technique, the Lax triad is transformed into a Hamiltonian system and two symplectic maps, respectively, which are integrable in the Liouville sense, sharing the same set of integrals, functionally independent and involutive with each other. In the Jacobi variety of the associated algebraic curve, both the continuous and the discrete flows are straightened out by the Abel-Jacobi coordinates, and are integrated by quadratures. An explicit algebraic-geometric solution in the original variable is obtained by the Riemann-Jacobi inversion
A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver
Liu, Yang
2015-10-26
© 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.
Integral equation models for the inverse problem of biological ion channel distributions
International Nuclear Information System (INIS)
French, D A; Groetsch, C W
2007-01-01
Olfactory cilia are thin hair-like filaments that extend from olfactory receptor neurons into the nasal mucus. Transduction of an odor into an electrical signal is accomplished by a depolarizing influx of ions through cyclic-nucleotide-gated channels in the membrane that forms the lateral surface of the cilium. In an experimental procedure developed by S. Kleene, a cilium is detached at its base and drawn into a recording pipette. The cilium base is then immersed in a bath of a channel activating agent (cAMP) which is allowed to diffuse into the cilium interior, opening channels as it goes and initiating a transmembrane current. The total current is recorded as a function of time and serves as data for a nonlinear integral equation of the first kind modeling the spatial distribution of ion channels along the length of the cilium. We discuss some linear Fredholm integral equations that result from simplifications of this model. A numerical procedure is proposed for a class of integral equations suggested by this simplified model and numerical results using simulated and laboratory data are presented
Three-Axis Attitude Estimation Using Rate-Integrating Gyroscopes
Crassidis, John L.; Markley, F. Landis
2016-01-01
Traditionally, attitude estimation has been performed using a combination of external attitude sensors and internal three-axis gyroscopes. There are many studies of three-axis attitude estimation using gyros that read angular rates. Rate-integrating gyros measure integrated rates or angular displacements, but three-axis attitude estimation using these types of gyros has not been as fully investigated. This paper derives a Kalman filtering framework for attitude estimation using attitude sensors coupled with rate- integrating gyroscopes. In order to account for correlations introduced by using these gyros, the state vector must be augmented, compared with filters using traditional gyros that read angular rates. Two filters are derived in this paper. The first uses an augmented state-vector form that estimates attitude, gyro biases, and gyro angular displacements. The second ignores correlations, leading to a filter that estimates attitude and gyro biases only. Simulation comparisons are shown for both filters. The work presented in this paper focuses only on attitude estimation using rate-integrating gyros, but it can easily be extended to other applications such as inertial navigation, which estimates attitude and position.
On the muon-nucleus integrals entering the neutrinoless μ- → e- conversion rates
International Nuclear Information System (INIS)
Kosmas, T S; Lagaris, I E
2002-01-01
The muon-nucleus integrals which determine the nuclear-structure dependence of the branching ratio R μe , i.e. the rate of the flavour-changing muon-electron conversion divided by the total rate of the ordinary muon capture, are extensively studied. Precise muon wavefunctions are employed which are obtained by solving the Schroedinger and Dirac equations. To this aim a method based on modern neural network techniques is developed which gives the radial muon wavefunctions as a linear combination of sigmoid functions
Utility rate equations of group population dynamics in biological and social systems.
Directory of Open Access Journals (Sweden)
Vyacheslav I Yukalov
Full Text Available We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors and of three groups (cooperators, defectors, and regulators and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K
2013-11-01
This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.
Utility Rate Equations of Group Population Dynamics in Biological and Social Systems
Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier
2013-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163
Chremmos, Ioannis
2010-01-01
The scattering of a surface plasmon polariton (SPP) by a rectangular dielectric channel discontinuity is analyzed through a rigorous magnetic field integral equation method. The scattering phenomenon is formulated by means of the magnetic-type scalar integral equation, which is subsequently treated through an entire-domain Galerkin method of moments (MoM), based on a Fourier-series plane wave expansion of the magnetic field inside the discontinuity. The use of Green's function Fourier transform allows all integrations over the area and along the boundary of the discontinuity to be performed analytically, resulting in a MoM matrix with entries that are expressed as spectral integrals of closed-form expressions. Complex analysis techniques, such as Cauchy's residue theorem and the saddle-point method, are applied to obtain the amplitudes of the transmitted and reflected SPP modes and the radiated field pattern. Through numerical results, we examine the wavelength selectivity of transmission and reflection against the channel dimensions as well as the sensitivity to changes in the refractive index of the discontinuity, which is useful for sensing applications.
Enabling an Integrated Rate-temporal Learning Scheme on Memristor
He, Wei; Huang, Kejie; Ning, Ning; Ramanathan, Kiruthika; Li, Guoqi; Jiang, Yu; Sze, Jiayin; Shi, Luping; Zhao, Rong; Pei, Jing
2014-04-01
Learning scheme is the key to the utilization of spike-based computation and the emulation of neural/synaptic behaviors toward realization of cognition. The biological observations reveal an integrated spike time- and spike rate-dependent plasticity as a function of presynaptic firing frequency. However, this integrated rate-temporal learning scheme has not been realized on any nano devices. In this paper, such scheme is successfully demonstrated on a memristor. Great robustness against the spiking rate fluctuation is achieved by waveform engineering with the aid of good analog properties exhibited by the iron oxide-based memristor. The spike-time-dependence plasticity (STDP) occurs at moderate presynaptic firing frequencies and spike-rate-dependence plasticity (SRDP) dominates other regions. This demonstration provides a novel approach in neural coding implementation, which facilitates the development of bio-inspired computing systems.
Assessment of available integration algorithms for initial value ordinary differential equations
International Nuclear Information System (INIS)
Carver, M.B.; Stewart, D.G.
1979-11-01
There exists an extremely large number of algorithms designed for the ordinary differential equation initial value problem. The integration is normally done by a finite sum at time intervals which are chosen dynamically to satisfy an imposed error tolerance. This report describes the basic logistics of the integration process, identifies common areas of difficulty, and establishes a comprehensive test profile for integration algorithms. A number of algorithms are described, and selected published subroutines are evaluated using the test profile. It concludes that an effective library for general use need have only two such routines. The two selected are versions of the well-known Gear and Runge-Kutta-Fehlberg algorithms. Full documentation and listings are included. (auth)
Ulku, Huseyin Arda
2014-07-06
Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half
Time-Dependent Heat Conduction Problems Solved by an Integral-Equation Approach
International Nuclear Information System (INIS)
Oberaigner, E.R.; Leindl, M.; Antretter, T.
2010-01-01
Full text: A classical task of mathematical physics is the formulation and solution of a time dependent thermoelastic problem. In this work we develop an algorithm for solving the time-dependent heat conduction equation c p ρ∂ t T-kT, ii =0 in an analytical, exact fashion for a two-component domain. By the Green's function approach the formal solution of the problem is obtained. As an intermediate result an integral-equation for the temperature history at the domain interface is formulated which can be solved analytically. This method is applied to a classical engineering problem, i.e. to a special case of a Stefan-Problem. The Green's function approach in conjunction with the integral-equation method is very useful in cases were strong discontinuities or jumps occur. The initial conditions and the system parameters of the investigated problem give rise to two jumps in the temperature field. Purely numerical solutions are obtained by using the FEM (finite element method) and the FDM (finite difference method) and compared with the analytical approach. At the domain boundary the analytical solution and the FEM-solution are in good agreement, but the FDM results show a signicant smearing effect. (author)
Valdés, Felipe
2013-03-01
Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.
Comment on the consistency of truncated nonlinear integral equation based theories of freezing
International Nuclear Information System (INIS)
Cerjan, C.; Bagchi, B.; Rice, S.A.
1985-01-01
We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions
Solution of fractional kinetic equation by a class of integral transform of pathway type
Kumar, Dilip
2013-04-01
Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.
Recent advances in marching-on-in-time schemes for solving time domain volume integral equations
Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan
2015-01-01
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.
Clarke, R.; Lintereur, L.; Bahm, C.
2016-01-01
A desire for more complete documentation of the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC), Edwards, California legacy code used in the core simulation has led to this e ort to fully document the oblate Earth six-degree-of-freedom equations of motion and integration algorithm. The authors of this report have taken much of the earlier work of the simulation engineering group and used it as a jumping-o point for this report. The largest addition this report makes is that each element of the equations of motion is traced back to first principles and at no point is the reader forced to take an equation on faith alone. There are no discoveries of previously unknown principles contained in this report; this report is a collection and presentation of textbook principles. The value of this report is that those textbook principles are herein documented in standard nomenclature that matches the form of the computer code DERIVC. Previous handwritten notes are much of the backbone of this work, however, in almost every area, derivations are explicitly shown to assure the reader that the equations which make up the oblate Earth version of the computer routine, DERIVC, are correct.
Recent advances in marching-on-in-time schemes for solving time domain volume integral equations
Sayed, Sadeed Bin
2015-05-16
Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.
Slew Rate Induced Distortion in Switched-Resistor Integrators
Jiraseree-Amornkun, A.; Jiraseree-amornkun, A.; Worapishet, A.; Klumperink, Eric A.M.; Nauta, Bram; Surakampontorn, W.
2006-01-01
Abstract—OPAMP-RC integrators built with linear resistors and capacitors can achieve very high linearity. By means of a switched resistor, tuning of the RC time-constant is possible via the duty-cycle of the clock controlling the switched resistor. This paper analyzes the effect of OPAMP slew rate
Gainetdinova, A A; Gazizov, R K
2017-01-01
We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
Parallel, explicit, and PWTD-enhanced time domain volume integral equation solver
Liu, Yang
2013-07-01
Time domain volume integral equations (TDVIEs) are useful for analyzing transient scattering from inhomogeneous dielectric objects in applications as varied as photonics, optoelectronics, and bioelectromagnetics. TDVIEs typically are solved by implicit marching-on-in-time (MOT) schemes [N. T. Gres et al., Radio Sci., 36, 379-386, 2001], requiring the solution of a system of equations at each and every time step. To reduce the computational cost associated with such schemes, [A. Al-Jarro et al., IEEE Trans. Antennas Propagat., 60, 5203-5215, 2012] introduced an explicit MOT-TDVIE method that uses a predictor-corrector technique to stably update field values throughout the scatterer. By leveraging memory-efficient nodal spatial discretization and scalable parallelization schemes [A. Al-Jarro et al., in 28th Int. Rev. Progress Appl. Computat. Electromagn., 2012], this solver has been successfully applied to the analysis of scattering phenomena involving 0.5 million spatial unknowns. © 2013 IEEE.
The two-wave X-ray field calculated by means of integral-equation methods
International Nuclear Information System (INIS)
Bremer, J.
1984-01-01
The problem of calculating the two-wave X-ray field on the basis of the Takagi-Taupin equations is discussed for the general case of curved lattice planes. A two-dimensional integral equation which incorporates the nature of the incoming radiation, the form of the crystal/vacuum boundary, and the curvature of the structure, is deduced. Analytical solutions for the symmetrical Laue case with incoming plane waves are obtained directly for perfect crystals by means of iteration. The same method permits a simple derivation of the narrow-wave Laue and Bragg cases. Modulated wave fronts are discussed, and it is shown that a cut-off in the width of an incoming plane wave leads to lateral oscillations which are superimposed on the Pendelloesung fringes. Bragg and Laue shadow fields are obtained. The influence of a non-zero kernel is discussed and a numerical procedure for calculating wave amplitudes in curved crystals is presented. (Auth.)
On the numerical evaluation of algebro-geometric solutions to integrable equations
International Nuclear Information System (INIS)
Kalla, C; Klein, C
2012-01-01
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations