New constitutive equations to describe infinitesimal elastic-plastic deformations

International Nuclear Information System (INIS)

Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.

1983-01-01

A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)

A stable computational scheme for stiff time-dependent constitutive equations

International Nuclear Information System (INIS)

Shih, C.F.; Delorenzi, H.G.; Miller, A.K.

1977-01-01

Viscoplasticity and creep type constitutive equations are increasingly being employed in finite element codes for evaluating the deformation of high temperature structural members. These constitutive equations frequently exhibit stiff regimes which makes an analytical assessment of the structure very costly. A computational scheme for handling deformation in stiff regimes is proposed in this paper. By the finite element discretization, the governing partial differential equations in the spatial (x) and time (t) variables are reduced to a system of nonlinear ordinary differential equations in the independent variable t. The constitutive equations are expanded in a Taylor's series about selected values of t. The resulting system of differential equations are then integrated by an implicit scheme which employs a predictor technique to initiate the Newton-Raphson procedure. To examine the stability and accuracy of the computational scheme, a series of calculations were carried out for uniaxial specimens and thick wall tubes subjected to mechanical and thermal loading. (Auth.)

Linear determining equations for differential constraints

International Nuclear Information System (INIS)

Kaptsov, O V

1998-01-01

A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed

Structure and Calibration of Constitutive Equations for Granular Soils

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Sawicki Andrzej

2015-02-01

Full Text Available The form of incremental constitutive equations for granular soils is discussed for the triaxial configuration. The classical elasto-plastic approach and the semi-empirical model are discussed on the basis of constitutive relations determined directly from experimental data. First, the general structure of elasto-plastic constitutive equations is presented. Then, the structure of semiempirical constitutive equations is described, and a method of calibrating the model is presented. This calibration method is based on a single experiment, performed in the triaxial apparatus, which also involves a partial verification of the model, on an atypical stress path. The model is shown to give reasonable predictions. An important feature of the semi-empirical incremental model is the definition of loading and unloading, which is different from that assumed in elasto-plasticity. This definition distinguishes between spherical and deviatoric loading/unloading. The definition of deviatoric loading/unloading has been subject to some criticism. It was therefore discussed and clarified in this paper on the basis of the experiment presented.

Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

International Nuclear Information System (INIS)

Theodorakis, Stavros

2003-01-01

We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

Study on the creep constitutive equation of Hastelloy X, (1)

International Nuclear Information System (INIS)

Suzuki, Kazuhiko; Mutoh, Yasushi

1983-01-01

In order to carry out the structural design of high temperature pipings, intermediate heat exchangers and isolating valves for a multipurpose high temperature gas-cooled reactor, in which coolant temperature reaches 1000 deg C, the creep characteristics of Hastelloy X used as the heat resistant material must be clarified. In addition to usual creep rupture life and the time to reach a specified creep strain, the dependence of creep strain curves on time, temperature and stress must be determined and expressed with equations. Therefore, using the creep data of Hastelloy X given in the literatures, the creep constitutive equation was made. Since the creep strain curves under the same test condition were different according to heats, the sensitivity analysis of the creep constitutive equation was performed. The form of the creep constitutive equation was determined to be Garofalo type. The result of the sensitivity analysis is reported. (Kako, I.)

Development of constitutive equations for nuclear reactor core materials

International Nuclear Information System (INIS)

Lee, D.; Zaverl, F. Jr.; Plaza-Meyer, E.

1980-01-01

A set of strain rate dependent constitutive equations has been described which is capable of predicting deformation behavior of anisotropic metals under complex loading conditions with or without the presence of a neutron flux. The important feature of the constitutive equations is that they describe history dependent plastic deformation behavior of anisotropic metals under three-dimensional stress states. Since the analytical model accounts for the effect of prior deformation history at all times, it is capable of handling consecutive or simultaneous loading histories, such as post-irradiation loading, in-pile loading, etc. It is demonstrated that the general form of the constitutive relations is consistent with experimental observations made for Zircaloys under both unirradiated and irradiated conditions. (orig.)

Extended irreversible thermodynamics and the Jeffreys type constitutive equations

International Nuclear Information System (INIS)

Serdyukov, S.I.

2003-01-01

A postulate of extended irreversible thermodynamics is considered, according to which the entropy density is a function of the internal energy, the specific volume, and their material time derivatives. On the basis of this postulate, entropy balance equations and phenomenological equations are obtained, which directly lead to the Jeffreys type constitutive equations

Application of viscoplastic constitutive equations in finite element programs

International Nuclear Information System (INIS)

Hornberger, K.; Stamm, H.

1987-04-01

The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de

Isomorphism of Intransitive Linear Lie Equations

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Jose Miguel Martins Veloso

2009-11-01

Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

Materials with memory initial-boundary value problems for constitutive equations with internal variables

CERN Document Server

Alber, Hans-Dieter

1998-01-01

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

Students’ difficulties in solving linear equation problems

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Computing with linear equations and matrices

International Nuclear Information System (INIS)

Churchhouse, R.F.

1983-01-01

Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)

Correct Linearization of Einstein's Equations

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Rabounski D.

2006-06-01

Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage

International Nuclear Information System (INIS)

Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu

2007-01-01

Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material

Lie algebras and linear differential equations.

Science.gov (United States)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

A strategy of implementation of the improved constitutive equations for the advanced subchannel code

International Nuclear Information System (INIS)

Shirai, Hiroshi; Hotta, Akitoshi; Ninokata, Hisashi

2004-01-01

To develop the advanced subchannel analysis code, the dominant factors that influence the boiling transitional process must be taken into account in the mechanistic constitutive equations based on the flow geometries and the fluid properties. The dominant factors that influence the boiling transitional processes are (1) the gas-liquid re-distribution by cross flow, (2) the liquid film dryout, (3) the two-phase flow regime transition, (4) the droplet deposition, and (5) the spacer-droplet interaction. At first, we indicated the strategy for the development of the constitutive equations for the five dominant factors based on the experimental database by the latest measurement technique and the latest computational fluid dynamics method. Then, the problems of the present constitutive equations and the improvement plan of the constitutive equations were indicated. Finally, the layered structure for the two-phase/three-field subchannel code including the new constitutive equations was designed. (author)

Linear q-nonuniform difference equations

International Nuclear Information System (INIS)

Bangerezako, Gaspard

2010-01-01

We introduce basic concepts of q-nonuniform differentiation and integration and study linear q-nonuniform difference equations and systems, as well as their application in q-nonuniform difference linear control systems. (author)

MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

International Nuclear Information System (INIS)

Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

1991-05-01

MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

Schwarz maps of algebraic linear ordinary differential equations

Science.gov (United States)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Basic linear partial differential equations

CERN Document Server

Treves, Francois

1975-01-01

Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

Non-local quasi-linear parabolic equations

International Nuclear Information System (INIS)

Amann, H

2005-01-01

This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing

A constitutive equation for creep fracture under constant, variable or cyclic positive stress

International Nuclear Information System (INIS)

Snedden, J.D.

1977-01-01

Prediction of creep fracture of metals under variable stress is one of the most difficult problems of applied mechanics. At NEL this problem is under investigation using an approach in which creep is represented by two macroscopic components: an anelastic (reversible) component and a plastic (irreversible) component. Under variable loading conditions, the anelastic component's behaviour will be most important and, if an experimental programme is logically planned, the structural processes responsible will be implicit in the resulting constitutive equation describing the material's behaviour. The present paper deals with the development and application of a constitutive equation for creep fracture of RR58 Aluminium alloy at 180 0 C under variable stress and such a constitutive equation can be extrapolated to cover long-time behaviour just as with conventional constant stress creep fracture equations. Constant stress, in fact, is one of the boundary conditions of the general constitutive equation, representing zero prior damage. The other boundary condition is that of 'cadence loading' in which the stress is completely removed and then re-applied in a cyclic fashion. (Auth.)

The Cauchy problem for non-linear Klein-Gordon equations

International Nuclear Information System (INIS)

Simon, J.C.H.; Taflin, E.

1993-01-01

We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

Hamiltonian structures of some non-linear evolution equations

International Nuclear Information System (INIS)

Tu, G.Z.

1983-06-01

The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

Solving polynomial differential equations by transforming them to linear functional-differential equations

OpenAIRE

Nahay, John Michael

2008-01-01

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

Science.gov (United States)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

Constitutive equations for describing high-temperature inelastic behavior of structural alloys

International Nuclear Information System (INIS)

Robinson, D.N.; Pugh, C.E.; Corum, J.M.

1976-01-01

This paper addresses constitutive equations for the description of inelastic behavior of LMFBR structural alloys at elevated temperatures. Both elastic-plastic (time-independent) and creep (time-dependent) deformations are considered for types 304 and 316 stainless steel and 2 1 / 4 Cr--1 Mo steel. The constitutive equations identified for interim use in design analyses are described along with the assumptions and data on which they are based. Areas where improvements are needed are identified, and some alternate theories that are being pursued are outlined

Linear differential equations to solve nonlinear mechanical problems: A novel approach

OpenAIRE

Nair, C. Radhakrishnan

2004-01-01

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

Linear measure functional differential equations with infinite delay

OpenAIRE

Monteiro, G. (Giselle Antunes); Slavík, A.

2014-01-01

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

Science.gov (United States)

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.

Saturation and linear transport equation

International Nuclear Information System (INIS)

Kutak, K.

2009-03-01

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)

Validation of constitutive equations for steel

International Nuclear Information System (INIS)

Valentin, T.; Magain, P.; Quik, M.; Labibes, K.; Albertini, C.

1997-01-01

High strain rate mechanical properties are a major concern for each steel manufacturer, especially with respect to thin sheet steel used in the automotive branch. We began to study this topic by starting a project with the following goals: acquiring reliable experimental data, understanding in depth the energy absorption in thin sheet steel and finding the right constitutive material equation. The first part of the project has been presented in. In this paper we present data computation and comparison with the existing material model theories to exploit the experimental data. (orig.)

Linearized pseudo-Einstein equations on the Heisenberg group

Science.gov (United States)

Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard

2017-02-01

We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.

Linear causal modeling with structural equations

CERN Document Server

Mulaik, Stanley A

2009-01-01

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

Systems of Inhomogeneous Linear Equations

Science.gov (United States)

Scherer, Philipp O. J.

Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

Nonlocal constitutive equations of elasto-visco-plasticity coupled with damage and temperature

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Liu Weijie

2016-01-01

Full Text Available In this paper, the nonlocal anisothermal elasto-visco-plastic constitutive equations strongly coupled with ductile isotropic damage, nonlinear isotropic hardening and kinematic hardening are developed to model the material behaviour under finite strain. The new micromorphic variable of damage is introduced into the principle of virtual power and new additional balance equations are obtained. Thermodynamically-consistent nonlocal constitutive equations are then deduced. The evolution equations are deduced from the generalized normality rule for the Norton-Hoff visco-plastic potential. This model is used to simulate various material responses under different velocities at high temperature. The micromorphic parameters of damage: micromorphic density and H moduli are studied to examine the effects of micromorphic damage. Biaxial tension is performed to make a comparison between the local damage model and the micromorphic damage model.

Diffusion phenomenon for linear dissipative wave equations

KAUST Repository

Said-Houari, Belkacem

2012-01-01

In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

A new linearized equation for servo valve in hydraulic control systems

International Nuclear Information System (INIS)

Kim, Tae Hyung; Lee, Ill Yeong

2002-01-01

In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. And, as of now, there are no general standards on how to determine the operating point of a servo valve in the process of applying the linearized equation. So, in this study, a new linearized equation for valve characteristics is proposed as a modified form of the existing linearized equation. And, a method for selecting an optimal operating point is proposed for the new linearized equation. The effectiveness of the new linearized equation is confirmed through numerical simulations and experiments for a model hydraulic control system

Evaluation of high temperature mechanical properties and constitutive equation of austenitic stainless steels

International Nuclear Information System (INIS)

Blanchard, P.; Tortel, J.

1985-08-01

A large amount of experimental data (tensile tests, creep tests, cyclic strain tests, relaxation experiments and biaxial experiments) on 17-12 Mo SPH (316 L SPH) stainless steel used for building the primary loop of Super Phenix Reactor have been obtained during the last years. The aim of this paper is to illustrate by a few examples the work done in the constitutive equations area using this powerful data base. Numerous semiempirical equations have been developed to represent tensile, cyclic, creep or relaxation tests on 17-12 Mo SPH (316 L SPH) stainless steel. These equations, althrough not being able to be properly called ''constitutive equations'' in the full sense of the word, are nevertheless very useful for design studies. Actually these semiempirical equations are necessary tools for building elastic analysis's rules. Some examples of these equations are given along with specific applications (creep-fatigue rules). The qualitative and semiquantitative comparisons of the stress-strain behaviour (both uniaxial and biaxial) predicted by the most common constitutive equations (PRAGER, MEIJERS, HART, CHABOCHE, KRIEB, MILLER, ROBINSON) with the actual behaviour of 17-12 Mo SPH (316 L SPH) steel, allows us to shed some light on the strengths and weaknesses of these equations. This comparison is presented and discussed. The way to more realistic equations is shown. A detailed and quantitative comparison of the capabilities of two models, the CHABOCHE model and the multilayer unified model which has been developed is presented

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

OpenAIRE

Nakamura, Gen; Vashisth, Manmohan

2017-01-01

In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

On establishing constitutive equations for use in design of high-temperature fast-reactor structures

International Nuclear Information System (INIS)

Pugh, C.E.

1978-01-01

The presentation describes the approach being used to establish constitutive equations for wide use in the design of fast breeder reactor (FBR) components in the US. The approach combines exploratory experiments, constitutive model studies, studies of computational techniques, and tests of simple structural configurations. Short-time (elastic-plastic) behavior, long-time (creep) behavior, and their interactions are considered, and some of the background to equations now identified for use in current FBR design applications involving three structural alloys is discussed. Comments are also given on current efforts aimed at identifying improved constitutive equations for these alloys and on properties data required for design applications. References are cited which have addressed the status of the process at various times. (Auth.)

The numerical solution of linear multi-term fractional differential equations: systems of equations

Science.gov (United States)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Development and validation of constitutive equation of HBS irradiation swelling considering hydrostatic pressure

International Nuclear Information System (INIS)

Gao Lijun; Jiang Shengyao; Yu Jiyang; Chen Bingde; Xiao Zhong

2014-01-01

The mechanism of hydrostatic pressure affecting the irradiation swelling of UO_2 high burnup structure was analyzed. Three basic assumptions used to develop the constitutive equation of irradiation swelling were made accordingly. It is concluded that hydrostatic pressure imposes an important impact on irradiation swelling mainly through compressing the UO_2 high burnup structure pores. Based on the already developed correlation of the irradiation swelling of UO_2 high burnup structure, pore shrinkage due to the application of hydrostatic pressure and thus the reduction of irradiation swelling of UO_2 high burnup structure were determined quantitatively, and the constitutive equation of irradiation swelling of UO_2 high burnup structure considering the hydrostatic pressure was constructed successfully. The constitutive equation is validated using available irradiation swelling data of UO_2 high burnup structure, which demonstrates its reasonability. (authors)

Infinite sets of conservation laws for linear and non-linear field equations

International Nuclear Information System (INIS)

Niederle, J.

1984-01-01

The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation

Invariant imbedding equations for linear scattering problems

International Nuclear Information System (INIS)

Apresyan, L.

1988-01-01

A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation

Linear Einstein equations and Kerr-Schild maps

International Nuclear Information System (INIS)

Gergely, Laszlo A

2002-01-01

We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

Analytical exact solution of the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

2011-01-01

Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

A regression approach for Zircaloy-2 in-reactor creep constitutive equations

International Nuclear Information System (INIS)

Yung Liu, Y.; Bement, A.L.

1977-01-01

In this paper the methodology of multiple regressions as applied to Zircaloy-2 in-reactor creep data analysis and construction of constitutive equation are illustrated. While the resulting constitutive equation can be used in creep analysis of in-reactor Zircaloy structural components, the methodology itself is entirely general and can be applied to any creep data analysis. The promising aspects of multiple regression creep data analysis are briefly outlined as follows: (1) When there are more than one variable involved, there is no need to make the assumption that each variable affects the response independently. No separate normalizations are required either and the estimation of parameters is obtained by solving many simultaneous equations. The number of simultaneous equations is equal to the number of data sets. (2) Regression statistics such as R 2 - and F-statistics provide measures of the significance of regression creep equation in correlating the overall data. The relative weights of each variable on the response can also be obtained. (3) Special regression techniques such as step-wise, ridge, and robust regressions and residual plots, etc., provide diagnostic tools for model selections. Multiple regression analysis performed on a set of carefully selected Zircaloy-2 in-reactor creep data leads to a model which provides excellent correlations for the data. (Auth.)

Creep constitutive equation of dual phase 9Cr-ODS steel

International Nuclear Information System (INIS)

Sakasegawa, Hideo; Ukai, Shigeharu; Tamura, Manabu; Ohtsuka, Satoshi; Tanigawa, Hiroyasu; Ogiwara, Hiroyuki; Kohyama, Akira; Fujiwara, Masayuki

2008-01-01

9Cr-ODS (oxide dispersion strengthened) steels developed by JAEA (Japan Atomic Energy Agency) have superior creep properties compared with conventional heat resistant steels. The ODS steels can enormously contribute to practical applications of fast breeder reactors and more attractive fusion reactors. Key issues are developments of material processing procedures for mass production and creep life prediction methods in present R and D. In this study, formulation of creep constitutive equation was performed against the backdrop. The 9Cr-ODS steel displaying an excellent creep property is a dual phase steel. The ODS steel is strengthened by the δ ferrite which has a finer dispersion of oxide particles and shows a higher hardness than the α' martensite. The δ ferrite functions as a reinforcement in the dual phase 9Cr-ODS steel. Its creep behavior is very unique and cannot be interpreted by conventional theories of heat resistant steels. Alternative qualitative model of creep mechanism was formulated at the start of this study using the results of microstructural observations. Based on the alternative creep mechanism model, a novel creep constitutive equation was formulated using the exponential type creep equation extended by a law of mixture

Non-linear wave equations:Mathematical techniques

International Nuclear Information System (INIS)

1978-01-01

An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

International Nuclear Information System (INIS)

Gene Golub; Kwok Ko

2009-01-01

The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.

Dynamical symmetries of semi-linear Schrodinger and diffusion equations

International Nuclear Information System (INIS)

Stoimenov, Stoimen; Henkel, Malte

2005-01-01

Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed

Evaluation of high temperature mechanical properties and constitutive equation of austenitic stainless steels

International Nuclear Information System (INIS)

Blanchard, P.; Tortel, J.

1986-07-01

A large amount of experimental data on 17-12 Mo SPH (316 L SPH) stainless steel have been obtained during the last years. The aim of this paper is to illustrate by a few examples the work done in the constitutive equations area using this powerful data base. Numerous semiempirical equations have been developed to represent tensile, cyclic, creep or relaxation tests on 17-12 Mo SPH (316 L SPH) stainless steel used for building the primary loop of the SUPER PHENIX 1 reactor. These equations are necessary tools for building elastic analysis's rules. Some examples are given with specific applications. The qualitative and semiquantitative comparisons of the stress-strain behaviour (both uniaxial and biaxial) predicted by the most common constitutive equations with the actual behaviour of 17-12 Mo SPH (316 L SPH) steel, shed some light on the strengths and weaknesses of these equations. This comparison is presented and discussed. The way to more realistic equations is shown. A detailed and quantitative comparison of the capabilities of two models, the CHABOCHE model and the multilayer unified model, is presented

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2012-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Half-trek criterion for generic identifiability of linear structural equation models

NARCIS (Netherlands)

Foygel, R.; Draisma, J.; Drton, M.

2011-01-01

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

Introduction to linear systems of differential equations

CERN Document Server

Adrianova, L Ya

1995-01-01

The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...

GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.

Geometric Insight into Scalar Combination of Linear Equations

Indian Academy of Sciences (India)

... Journals; Resonance – Journal of Science Education; Volume 14; Issue 11. Geometric Insight into Scalar Combination of Linear Equations. Ranjit Konkar. Classroom Volume 14 Issue 11 November 2009 pp 1092-1097 ... Keywords. Linear algebra; linear dependence; linear combination; family of lines; family of planes.

What happens to linear properties as we move from the Klein-Gordon equation to the sine-Gordon equation

International Nuclear Information System (INIS)

Kovalyov, Mikhail

2010-01-01

In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.

Emmy Noether and Linear Evolution Equations

Directory of Open Access Journals (Sweden)

P. G. L. Leach

2013-01-01

Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.

Simplified Linear Equation Solvers users manual

Energy Technology Data Exchange (ETDEWEB)

Gropp, W. [Argonne National Lab., IL (United States); Smith, B. [California Univ., Los Angeles, CA (United States)

1993-02-01

The solution of large sparse systems of linear equations is at the heart of many algorithms in scientific computing. The SLES package is a set of easy-to-use yet powerful and extensible routines for solving large sparse linear systems. The design of the package allows new techniques to be used in existing applications without any source code changes in the applications.

A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

NARCIS (Netherlands)

Dorren, H.J.S.

1998-01-01

It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

Constitutive equation of butter at static loading

Directory of Open Access Journals (Sweden)

Šárka Nedomová

2008-01-01

Full Text Available This study focuses on the constitutive modelling of finite deformation in the commercially obtained butter (composition is 83 % of milk fat at the temperature 17–20 °C. The specimens from the butter (height L0=14.6 mm and diameter 20 mm have been compressed between two parallel metal plates at a fixed crosshead speed 20 mm/min using of the testing device TIRA TEST. The force F and the deformation ∆L are measured during compression and both quantities are recorded. The experimental records force F – displacement (deformation were obtained. These records have been transformed into stress–strain dependences and into true stress–true strain. The basic data on the strain behaviour of a butter under low strain rates have been obtained. Experimental results show that the behaviour of butter can be described by a hyperelastic material model. In this model, the quasi–static response is defined by compressible hyperelasticity, whereby the strain energy potential is assumed to be representable by a newly proposed polynomial series with three independent parameters. The material parameters in the constitutive model are determined from compression test. A comparison of predictions based on the proposed constitutive equation with experiments shows that the model is able to describe the strain behaviour of the butter examined.

Construction of a Roe linearization for the ideal MHD equations

International Nuclear Information System (INIS)

Cargo, P.; Gallice, G.; Raviart, P.A.

1996-01-01

In [3], Munz has constructed a Roe linearization for the equations of gas dynamics in Lagrangian coordinates. We extend this construction to the case of the ideal magnetohydrodynamics equations again in Lagrangian coordinates. As a consequence we obtain a Roe linearization for the MHD equations in Eulerian coordinates. (author)

Variational linear algebraic equations method

International Nuclear Information System (INIS)

Moiseiwitsch, B.L.

1982-01-01

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

Non-linear effects in the Boltzmann equation

International Nuclear Information System (INIS)

Barrachina, R.O.

1985-01-01

The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

Asymptotic properties for half-linear difference equations

Czech Academy of Sciences Publication Activity Database

Cecchi, M.; Došlá, Z.; Marini, M.; Vrkoč, Ivo

2006-01-01

Roč. 131, č. 4 (2006), s. 347-363 ISSN 0862-7959 R&D Projects: GA ČR(CZ) GA201/04/0580 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear second order difference equation * nonoscillatory solutions * Riccati difference equation Subject RIV: BA - General Mathematics

The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

Directory of Open Access Journals (Sweden)

Eitzinger B

2014-12-01

Full Text Available This study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

Students' errors in solving linear equation word problems: Case ...

African Journals Online (AJOL)

The study examined errors students make in solving linear equation word problems with a view to expose the nature of these errors and to make suggestions for classroom teaching. A diagnostic test comprising 10 linear equation word problems, was administered to a sample (n=130) of senior high school first year Home ...

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

High-order quantum algorithm for solving linear differential equations

International Nuclear Information System (INIS)

Berry, Dominic W

2014-01-01

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt 2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution. (paper)

Periodic feedback stabilization for linear periodic evolution equations

CERN Document Server

Wang, Gengsheng

2016-01-01

This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

A regression approach for zircaloy-2 in-reactor creep constitutive equations

International Nuclear Information System (INIS)

Yung Liu, Y.; Bement, A.L.

1977-01-01

In this paper the methodology of multiple regressions as applied to zircaloy-2 in-reactor creep data analysis and construction of constitutive equation are illustrated. While the resulting constitutive equation can be used in creep analysis of in-reactor zircaloy structural components, the methodology itself is entirely general and can be applied to any creep data analysis. From data analysis and model development point of views, both the assumption of independence and prior committment to specific model forms are unacceptable. One would desire means which can not only estimate the required parameters directly from data but also provide basis for model selections, viz., one model against others. Basic understanding of the physics of deformation is important in choosing the forms of starting physical model equations, but the justifications must rely on their abilities in correlating the overall data. The promising aspects of multiple regression creep data analysis are briefly outlined as follows: (1) when there are more than one variable involved, there is no need to make the assumption that each variable affects the response independently. No separate normalizations are required either and the estimation of parameters is obtained by solving many simultaneous equations. The number of simultaneous equations is equal to the number of data sets, (2) regression statistics such as R 2 - and F-statistics provide measures of the significance of regression creep equation in correlating the overall data. The relative weights of each variable on the response can also be obtained. (3) Special regression techniques such as step-wise, ridge, and robust regressions and residual plots, etc., provide diagnostic tools for model selections

Infinite sets of conservation laws for linear and nonlinear field equations

International Nuclear Information System (INIS)

Mickelsson, J.

1984-01-01

The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)

A constitutive equation for hot deformation range of 304 stainless steel considering grain sizes

International Nuclear Information System (INIS)

Parsa, M.H.; Ohadi, D.

2013-01-01

Highlights: • A hot deformation constitutive equation based on invariant theory is proposed. • Deformation variables are evaluated based on objectivity, entropy principle, etc. • Using hot compression tests, coefficients of equation have been found. • The ability of equation to show the variation of stress with strain is examined. - Abstract: A general constitutive equation based on the framework of invariant theory by consideration of hot deformation key variables and also the properties of the material such as initial grain size is presented in the current work. Soundness of the considered parameters to be used in the developed formula was initially verified based on the important axioms such as objectivity, entropy principle, and thermodynamics stability. To access the prediction ability of the method, the formula was simplified for the simple hot compression test. To evaluate the simplified formula, single-hit hot compression tests were carried out at the temperature range of 900–1100 °C under true strain rate of 0.01–1 s −1 on a AISI 304 stainless steel. The capability of proposed formula for reproducing the variation of flow stress with strain and the strain hardening rate with stress for the resultant flow stress data was examined. The good agreement between model predictions and actual results signified the applicability of this method as a general constitutive equation in hot deformation studies

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

Dual exponential polynomials and linear differential equations

Science.gov (United States)

Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

2018-01-01

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

Exact non-linear equations for cosmological perturbations

Energy Technology Data Exchange (ETDEWEB)

Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

2017-10-01

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

International Nuclear Information System (INIS)

Alvarez-Estrada, R.F.

1979-01-01

A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

HESS Opinions: Linking Darcy's equation to the linear reservoir

Science.gov (United States)

Savenije, Hubert H. G.

2018-03-01

In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological timescales. This drainage network provides equally distributed resistance for water to access the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the timescale of the linear reservoir appears to be inversely proportional to Darcy's conductance, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

Science.gov (United States)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

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

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

Science.gov (United States)

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

On formal structure of constitutive equations for materials exhibiting shape memory effects

International Nuclear Information System (INIS)

Dobovsek, I.

2000-01-01

A derivation of constitutive equations in a general three-dimensional setting is described, based on an additive decomposition of the rate of deformation tensor. The rate of deformation tensor is assumed to consist of an elastic part, a thermoelastic part, a plastic part, a part due to shape memory transformation, and a part due to phase transformation. The thermoelastic part due to thermoelastic coupling accounts for the influence of temperature near phase transformation, while the plastic part is taken in the form of classical J 2 flow theory of plasticity with combined isotropic and kinematic hardening, where the back stress represents a tensor of orientational microstresses. It is assumed that the phase transformation part depends on the first and the second invariant of the tensor of crystallographic distortion, on the deviatoric part of the stress tensor, and on a special evolution parameter describing the rate of forming of a new phase. The elastic part of the rate of deformation tensor is connected with the objective rate of Cauchy stress through the tensor of elastic compliance. As a result, a general form of derived constitutive equations exhibits a similar structure as constitutive relations in finite deformation plasticity. (orig.)

Linear matrix differential equations of higher-order and applications

Directory of Open Access Journals (Sweden)

Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

Science.gov (United States)

Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco

2017-11-01

The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.

A General Linear Method for Equating with Small Samples

Science.gov (United States)

Albano, Anthony D.

2015-01-01

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

A local-global problem for linear differential equations

NARCIS (Netherlands)

Put, Marius van der; Reversat, Marc

2008-01-01

An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

Iterative solution of linear equations in ODE codes. [Krylov subspaces

Energy Technology Data Exchange (ETDEWEB)

Gear, C. W.; Saad, Y.

1981-01-01

Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

Runge-Kutta Methods for Linear Ordinary Differential Equations

Science.gov (United States)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Dissipative behavior of some fully non-linear KdV-type equations

Science.gov (United States)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Darboux transformations and linear parabolic partial differential equations

International Nuclear Information System (INIS)

Arrigo, Daniel J.; Hickling, Fred

2002-01-01

Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

OpenAIRE

Leibov Roman

2017-01-01

This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...

Solvable linear potentials in the Dirac equation

International Nuclear Information System (INIS)

Dominguez-Adame, F.; Gonzalez, M.A.

1990-01-01

The Dirac equation for some linear potentials leading to Schroedinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones

On some perturbation techniques for quasi-linear parabolic equations

Directory of Open Access Journals (Sweden)

Igor Malyshev

1990-01-01

Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

On some constitutive equations for inelastic materials and their application

International Nuclear Information System (INIS)

Valeva, V.V.; Karagiozova, D.D.; Baltov, A.A.; Hadjikov, L.M.

1987-01-01

The problems of the mechano-mathematical modelling of the behaviour of materials under irradiation become more topical with development of atomic energetics. Many protective and technological structures could be subjected to irradiation in case of operation or average. The irradiation affects the process of deformation by causing inelastic swelling of materials, it affects their physico-mechanical properties, i.e. it changes their elastic, plastic, viscous, thermal, etc. properties. This effect varies depending on the material. Due to this reason it is very important to indicate exactly the class of materials for which a mechano-mathematical model is created. Grounding on the analysis of experimental data about the behaviour of different types of steel used in nuclear reactors and on the existing models, the present paper proposes constitutive equations for inelastic materials which account temperature, strain rate and radiation effects. The thermodynamic theory of systems with internal state parameters is utilized and for the description of the radiation effects two scalar parameters are introduced - dose φ r and temperature θ r of irradiation. Problem of the behaviour of irradiated structure element in stress concentrator zone is solved on the basis of these constitutive equations and of Boundary Element Method (BEM). (orig.)

Linearized gyro-kinetic equation

International Nuclear Information System (INIS)

Catto, P.J.; Tsang, K.T.

1976-01-01

An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated

Experimental quantum computing to solve systems of linear equations.

Science.gov (United States)

Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

2013-06-07

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Oscillation and non-oscillation criterion for Riemann–Weber type half-linear differential equations

Directory of Open Access Journals (Sweden)

Petr Hasil

2016-08-01

Full Text Available By the combination of the modified half-linear Prüfer method and the Riccati technique, we study oscillatory properties of half-linear differential equations. Taking into account the transformation theory of half-linear equations and using some known results, we show that the analysed equations in the Riemann–Weber form with perturbations in both terms are conditionally oscillatory. Within the process, we identify the critical oscillation values of their coefficients and, consequently, we decide when the considered equations are oscillatory and when they are non-oscillatory. As a direct corollary of our main result, we solve the so-called critical case for a certain type of half-linear non-perturbed equations.

Solution methods for large systems of linear equations in BACCHUS

International Nuclear Information System (INIS)

Homann, C.; Dorr, B.

1993-05-01

The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

Perturbations of linear delay differential equations at the verge of instability.

Science.gov (United States)

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Local energy decay for linear wave equations with variable coefficients

Science.gov (United States)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

Science.gov (United States)

Mallet, D. G.; McCue, S. W.

2009-01-01

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

Linear orbit parameters for the exact equations of motion

International Nuclear Information System (INIS)

Parzen, G.

1995-01-01

This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

Constitutive error based parameter estimation technique for plate structures using free vibration signatures

Science.gov (United States)

Guchhait, Shyamal; Banerjee, Biswanath

2018-04-01

In this paper, a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig-natures. It has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity. Complying with this idea, an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature/strain and moment/stress fields. Unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration, we generate these incompatible fields via two linear solves. A simple, yet effective, penalty based approach is followed to incorporate measured data. The penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill-posedness of the inverse problem. Explicit linear update formulas are then developed for anisotropic linear elastic material. Numerical examples are provided to show the applicability of the proposed technique. Finally, an experimental validation is also provided.

Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

Directory of Open Access Journals (Sweden)

S. Narayanamoorthy

2015-01-01

Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

A canonical form of the equation of motion of linear dynamical systems

Science.gov (United States)

Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

2018-03-01

The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

An implicit spectral formula for generalized linear Schroedinger equations

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan

2009-01-01

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

Science.gov (United States)

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

An Evaluation of Five Linear Equating Methods for the NEAT Design

Science.gov (United States)

Mroch, Andrew A.; Suh, Youngsuk; Kane, Michael T.; Ripkey, Douglas R.

2009-01-01

This study uses the results of two previous papers (Kane, Mroch, Suh, & Ripkey, this issue; Suh, Mroch, Kane, & Ripkey, this issue) and the literature on linear equating to evaluate five linear equating methods along several dimensions, including the plausibility of their assumptions and their levels of bias and root mean squared difference…

Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements

International Nuclear Information System (INIS)

Bal, Guillaume; Bellis, Cédric; Imperiale, Sébastien; Monard, François

2014-01-01

Within the framework of linear elasticity we assume the availability of internal full-field measurements of the continuum deformations of a non-homogeneous isotropic solid. The aim is the quantitative reconstruction of the associated moduli. A simple gradient system for the sought constitutive parameters is derived algebraically from the momentum equation, whose coefficients are expressed in terms of the measured displacement fields and their spatial derivatives. Direct integration of this system is discussed to finally demonstrate the inexpediency of such an approach when dealing with noisy data. Upon using polluted measurements, an alternative variational formulation is deployed to invert for the physical parameters. Analysis of this latter inversion procedure provides existence and uniqueness results while the reconstruction stability with respect to the measurements is investigated. As the inversion procedure requires differentiating the measurements twice, a numerical differentiation scheme based on an ad hoc regularization then allows an optimally stable reconstruction of the sought moduli. Numerical results are included to illustrate and assess the performance of the overall approach. (paper)

The flow behavior and constitutive equation in isothermal compression of FGH4096-GH4133B dual alloy

International Nuclear Information System (INIS)

Liu, Yanhui; Yao, Zekun; Ning, Yongquan; Nan, Yang; Guo, Hongzhen; Qin, Chun; Shi, Zhifeng

2014-01-01

Highlights: • Hot compression behaviors of the FGH4096-GH4133B dual alloy were investigated. • Constitutive equation also represented deformation behavior of a dual alloy. • The effects of deformation activation energy on the microstructures were discussed. • Constitutive equation represented an accurate and precise estimate of flow stress. - Abstract: The electron beam welding of superalloy FGH4096 and GH4133B was conducted, and the cylindrical compression specimens were machined from the central part of the electron beam weldments. Isothermal compression tests were carried out on electron beam weldments FGH4096-GH4133B alloy at the temperatures of 1020–11140 °C (the nominal γ′-transus temperature is about 1080 °C) and the strain rates of 0.001–1.0 s −1 with the height reduction of 50%. True stress–true strain curves are sensitive to the deformation temperature and strain rate, and the flow stress decreases with the increasing deformation temperature and the decreasing strain rate. The true stress–true strain curves can indicate the intrinsic relationship between the flow stress and the thermal-dynamic behavior. The apparent activation energy of deformation at the strain of 0.6 was calculated to be 550 kJ/mol, and the apparent activation energy has a great effect on the microstructure. The constitutive equation that describes the flow stress as a function of strain rate and deformation temperature was proposed for modeling the hot deformation process of FGH4096-GH4133B electron beam weldments. The constitutive equation at the strain of 0.6 was established using the hyperbolic law. The relationship between the strain and the values of parameters was studied, and the cubic functions were built. The constitutive equation during the whole process can be obtained based on the parameters under different strains. Comparing the experimental flow stress and the calculated flow stress, the constitutive equation obtained in this paper can be very good

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT DOI: http://dx.doi.org/10.22342/jme.7.1.2814.19-30

New approach to solve fully fuzzy system of linear equations using ...

Indian Academy of Sciences (India)

This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...

Growth of meromorphic solutions of higher-order linear differential equations

Directory of Open Access Journals (Sweden)

Wenjuan Chen

2009-01-01

Full Text Available In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.

Multiaxial probabilistic elastic-plastic constitutive simulations of soils

Science.gov (United States)

Sadrinezhad, Arezoo

Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to simulate elastic-plastic constitutive behaviors of materials with uncertain material properties. The FPK equation approach transforms the stochastic constitutive rate equation, which is a stochastic, nonlinear, ordinary differential equation (ODE) in the stress-pseudo time space into a second-order accurate, deterministic, linear FPK partial differential equation (PDE) in the probability density of stress-pseudo time space. This approach does not suffer from the drawbacks of the traditional approaches such as the Monte Carlo approach and the perturbation approach for solving nonlinear ODEs with random coefficients. In this study, the existing one dimensional FPK framework for probabilistic constitutive modeling of soils is extended to multi--dimension. However, the multivariate FPK PDEs cannot be solved using the traditional mathematical techniques such as finite difference techniques due to their high computational cost. Therefore, computationally efficient algorithms based on the Fourier spectral approach are developed for solving a class of FPK PDEs that arises in probabilistic elasto-plasticity. This class includes linear FPK PDEs in (stress) space and (pseudo) time - having space-independent but time-dependent, and both space- and time-dependent coefficients - with impulse initial conditions and reflecting boundary conditions. The solution algorithms, rely on first mapping the stress space of the governing PDE between 0 and 2pi using the change of coordinates rule, followed by approximating the solution of the PDE in the 2pi-periodic domain by a finite Fourier series in the stress space and unknown time-dependent solution coefficients. Finally, the time-dependent solution coefficients are obtained from the initial condition. The accuracy and efficiency of the developed algorithms are tested. The developed algorithms are used to simulate uniaxial and multiaxial, monotonic and cyclic

A generic validation methodology and its application to a set of multi-axial creep damage constitutive equations

International Nuclear Information System (INIS)

Xu Qiang

2005-01-01

A generic validation methodology for a set of multi-axial creep damage constitutive equations is proposed and its use is illustrated with 0.5Cr0.5Mo0.25V ferritic steel which is featured as brittle or intergranular rupture. The objective of this research is to develop a methodology to guide systematically assess the quality of a set of multi-axial creep damage constitutive equations in order to ensure its general applicability. This work adopted a total quality assurance approach and expanded as a Four Stages procedure (Theories and Fundamentals, Parameter Identification, Proportional Load, and Non-proportional load). Its use is illustrated with 0.5Cr0.5Mo0.25V ferritic steel and this material is chosen due to its industry importance, the popular use of KRH type of constitutive equations, and the available qualitative experimental data including damage distribution from notched bar test. The validation exercise clearly revealed the deficiencies existed in the KRH formulation (in terms of mathematics and physics of damage mechanics) and its incapability to predict creep deformation accurately. Consequently, its use should be warned, which is particularly important due to its wide use as indicated in literature. This work contributes to understand the rational for formulation and the quality assurance of a set of constitutive equations in creep damage mechanics as well as in general damage mechanics. (authors)

On the constitutive law of environment assisted fatigue: The physical meaning of the Paris type equations. Pt. 1

International Nuclear Information System (INIS)

Krausz, K.; Wu Xijia; Krausz, A.S.; Lian Zhiwen

1992-01-01

Environment assisted fatigue crack growth is a complex of thermally activated processes. Accordingly, the framework for the expression of rational constitutive law is developed from fracture kinetics theory. The correlation of the constitutive law with the Paris equation is discussed and the empirical parameters in the Paris equation are expressed explicitly in terms of activation energy, stress intensity factor range, temperature, stress ratio, and other physically rigorous engineering quantities. The theory assures and facilitates, the rigorous quantitative evaluation of the effects of the microstructure: the constitutive law gives guidance to its measurement and expresses it in terms of energy-related quantities. (orig.) [de

Stochastic equivalent linearization in 3-D hysteretic frames

International Nuclear Information System (INIS)

Casciati, F.; Faravelli, L.

1987-01-01

Stochastic equivalent linearization technique for hysteretic systems is extended to study the dynamic response of 3-D frames with hysteretic constitutive laws in the potential plastic hinges. The constitutive law is idealized by an appropriate endochronic model. A general purpose finite element code is adopted in order to generate the matrices by which the equations of motion to be linearized are built. (orig./HP)

SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

Directory of Open Access Journals (Sweden)

Sari Saraswati

2016-01-01

Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.

New non-linear modified massless Klein-Gordon equation

Energy Technology Data Exchange (ETDEWEB)

Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

2017-11-15

The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)

A discrete homotopy perturbation method for non-linear Schrodinger equation

Directory of Open Access Journals (Sweden)

H. A. Wahab

2015-12-01

Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

On index-2 linear implicit difference equations

NARCIS (Netherlands)

Nguyen Huu Du, [No Value; Le Cong Loi, [No Value; Trinh Khanh Duy, [No Value; Vu Tien Viet, [No Value

2011-01-01

This paper deals with an index-2 notion for linear implicit difference equations (LIDEs) and with the solvability of initial value problems (IVPs) for index-2 LIDEs. Besides, the cocycle property as well as the multiplicative ergodic theorem of Oseledets type are also proved. (C) 2010 Elsevier Inc.

Singular Linear Differential Equations in Two Variables

NARCIS (Netherlands)

Braaksma, B.L.J.; Put, M. van der

2008-01-01

The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

A unified inelastic constitutive equation in terms of anisotropic yield function

International Nuclear Information System (INIS)

Inoue, T.; Imatani, S.

1989-01-01

In order to describe the material behavior under complicated loading conditions, inelastic constitutive equations accounting for the plasticity-creep interaction have been proposed by several researchers. However, these models are developed to predict the hardening and/or softening phenomena during the inelastic deformation processes, and two important features still remain to be considered; material anisotropy induced by the prior deformation history and inelastic flow or, in another word, directionality of the inelastic strain rate. This paper deals with a unified constitutive model capable of expressing both the deformation-induced anisotropy and the anisotropic flow. In the first part of the paper, an anisotropic yield function which can simulate both the Bauschinger effect and the cross effect is proposed. Then, the excess stress theory is applied to a viscoplastic constitutive relationship so as to describe the plasticity-creep interaction behavior. The experimental verification is carried out for SUS304 stainless steel at 650 degrees C in a biaxial stress state. Moreover, a generalized flow rule of the inelastic strain rate is also developed, by which the description of the ratcheting process can be improved

Visual construction of characteristic equations of linear electric circuits

Directory of Open Access Journals (Sweden)

V.V. Kostyukov

2013-12-01

Full Text Available A visual identification method with application of partial circuits is developed for characteristic equation coefficients of transients in linear electric circuits. The method is based on interrelationship between the roots of algebraic polynomial and its coefficients. The method is illustrated with an example of a third-order linear electric circuit.

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.

Nonoscillation of half-linear dynamic equations

Czech Academy of Sciences Publication Activity Database

Matucci, S.; Řehák, Pavel

2010-01-01

Roč. 60, č. 5 (2010), s. 1421-1429 ISSN 0898-1221 R&D Projects: GA AV ČR KJB100190701 Grant - others:GA ČR(CZ) GA201/07/0145 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear dynamic equation * time scale * (non)oscillation * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 1.472, year: 2010 http://www.sciencedirect.com/science/article/pii/S0898122110004384

Subroutine for series solutions of linear differential equations

International Nuclear Information System (INIS)

Tasso, H.; Steuerwald, J.

1976-02-01

A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de

A fast iterative scheme for the linearized Boltzmann equation

Science.gov (United States)

Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

2017-06-01

Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

Simulating sympathetic detonation using the hydrodynamic models and constitutive equations

Energy Technology Data Exchange (ETDEWEB)

Kim, Bo Hoon; Kim, Min Sung; Yoh, Jack J. [Dept. of Mechanical and Aerospace Engineering, Seoul National University, Seoul (Korea, Republic of); Sun, Tae Boo [Hanwha Corporation Defense Rand D Center, Daejeon (Korea, Republic of)

2016-12-15

A Sympathetic detonation (SD) is a detonation of an explosive charge by a nearby explosion. Most of times it is unintended while the impact of blast fragments or strong shock waves from the initiating donor explosive is the cause of SD. We investigate the SD of a cylindrical explosive charge (64 % RDX, 20 % Al, 16 % HTPB) contained in a steel casing. The constitutive relations for high explosive are obtained from a thermo-chemical code that provides the size effect data without the rate stick data typically used for building the rate law and equation of state. A full size SD test of eight pallet-packaged artillery shells is performed that provides the pressure data while the hydrodynamic model with proper constitutive relations for reactive materials and the fragmentation model for steel casing is conducted to replicate the experimental findings. The work presents a novel effort to accurately model and reproduce the sympathetic detonation event with a reduced experimental effort.

Appearance of eigen modes for the linearized Vlasov-Poisson equation

International Nuclear Information System (INIS)

Degond, P.

1983-01-01

In order to determine the asymptotic behaviour, when the time goes to infinity, of the solution of the linearized Vlasov-Poisson equation, we use eigen modes, associated to continuous linear functionals on a Banach space of analytic functions [fr

Linear algebra a first course with applications to differential equations

CERN Document Server

Apostol, Tom M

2014-01-01

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

International Nuclear Information System (INIS)

Goreac, D.

2009-01-01

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case

Spectrum of the linearized operator for the Ginzburg-Landau equation

Directory of Open Access Journals (Sweden)

Tai-Chia Lin

2000-06-01

Full Text Available We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.

Stability of numerical method for semi-linear stochastic pantograph differential equations

Directory of Open Access Journals (Sweden)

Yu Zhang

2016-01-01

Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

Constitutive modelling in the range of inelastic deformations

International Nuclear Information System (INIS)

Bruhns, O.T.; White, P.S.; Chaboche, J.L.; Eikhoff, J.V.D.

1988-01-01

The main objective of this report is to describe the state of the art in constitutive modelling in the range of inelastic deformations, with particular consideration of the practical use of these models in the field of fast reactors, rather than to formulate new models. An outline is given of the constitutive equations for high-temperature reactor materials developed at the Oak Ridge National Laboratory. Two forms of equations are considered, a semi-classical treatment in terms of separate plasticity and creep and unified equations in which the classical plasticity does not explicitly occur. The fraction model originally proposed by Besseling is described. The basic concept of this model is that the material is thought to be subdivided into a number of parallel fractions, each with simple conventional properties. The more complicated behaviour of real material is thus approximated by choosing a number of parallel fractions with suitable models and model parameters. Three time-independent formulations of plasticity are considered and compared. Attention is focused on the kinematic hardening in the multi-yield surface theory of Mroz and the non-linear kinematic rule intensively used at Enset and Onera. Some connections are pointed out with the two-surface model of Dafalias and Popov, and the range of applicability of the different models is studied in detail. Finally, the constitutive equations of the Interatom model are presented. They are mainly based on the concept of overstresses, expressing the rate-dependence of the material by the magnitude of these overstresses. This model furthermore comprises a combination of general non-linear isotropic and kinematic hardening, with a smooth transition from isotropic to kinematic hardening as a function of process time

Quantum osp-invariant non-linear Schroedinger equation

International Nuclear Information System (INIS)

Kulish, P.P.

1985-04-01

The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

Science.gov (United States)

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

Novel algorithm of large-scale simultaneous linear equations

International Nuclear Information System (INIS)

Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

2010-01-01

We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

Dark energy cosmology with generalized linear equation of state

International Nuclear Information System (INIS)

Babichev, E; Dokuchaev, V; Eroshenko, Yu

2005-01-01

Dark energy with the usually used equation of state p = wρ, where w const 0 ), where the constants α and ρ 0 are free parameters. This non-homogeneous linear equation of state provides the description of both hydrodynamically stable (α > 0) and unstable (α < 0) fluids. In particular, the considered cosmological model describes the hydrodynamically stable dark (and phantom) energy. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by using phase trajectories analysis. For the dark energy case, some distinctive types of cosmological scenarios are possible: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the big rip and with the anti-big rip. In the framework of a linear equation of state the universe filled with a phantom energy, w < -1, may have either the de Sitter attractor or the big rip

POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

Focal decompositions for linear differential equations of the second order

Directory of Open Access Journals (Sweden)

L. Birbrair

2003-01-01

two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.

Hot workability of γ + α2 titanium aluminide: Development of processing map and constitutive equations

International Nuclear Information System (INIS)

Gupta, R.K.; Narayana Murty, S.V.S.; Pant, Bhanu; Agarwala, Vijaya; Sinha, P.P.

2012-01-01

Highlights: ► Deformation studies of five TiAl alloys carried out through processing map. ► DRX domain and superplastic domain identified in power efficiency map. ► Safe working zone for alloys found at 1223–1423 K at strain rates (10 −2 –10 −3 s −1 ). ► Strain rate sensitivity, activation energy, Zener Hollomon parameter (Z) are obtained. ► Constitutive equations derived and verified. DRX grain size correlated with Z. - Abstract: Gamma titanium alumindes are intermetallics, which have very narrow working range. Hot isothermal working is the most suitable process for hot working of alloy. Accordingly, hot isothermal compression test is carried out on reaction synthesized and homogenized titanium aluminide alloys at different temperatures and strain rates using Gleeble thermomechanical simulator. Three alloys of Ti48Al2Cr2Nb0.1B (atom%) have been used in the study. Stress–strain data obtained from the test has been used to construct processing map, which indicates the safe and unsafe working zone. Strain rate sensitivity and Zener–Hollomon parameter has been calculated. Further, constitutive equations have been generated and verified. It is found that alloy has good workability in the temperature range of 1223–1423 K at strain rates of 0.01–0.001 s −1 . In this range of parameters, the alloys nearly follow the constitutive equations.

Creep-recovery constitutive equation and its time-independent limit

International Nuclear Information System (INIS)

Chang, S.J.

1978-01-01

The effect of strain recovery is taken into consideration in establishing a constitutive equation for metals at elevated temperatures. Internal state variables and Rice's flow potential are used in the representation. Growth law for the state variables is discussed and interpreted to be a more general form of the kinematic hardening condition. Yield condition is obtained from the flow law. Accordingly, the flow rule is established with the effect of the recovery mechanism, as a slightly general version of the time-independent theory with the kinematic hardening rule. In the discussion of the time-independent limit, the duration of time required for the inelastic strain to reach its saturated value is defined

An anisotropic linear thermo-viscoelastic constitutive law - Elastic relaxation and thermal expansion creep in the time domain

Science.gov (United States)

Pettermann, Heinz E.; DeSimone, Antonio

2017-09-01

A constitutive material law for linear thermo-viscoelasticity in the time domain is presented. The time-dependent relaxation formulation is given for full anisotropy, i.e., both the elastic and the viscous properties are anisotropic. Thereby, each element of the relaxation tensor is described by its own and independent Prony series expansion. Exceeding common viscoelasticity, time-dependent thermal expansion relaxation/creep is treated as inherent material behavior. The pertinent equations are derived and an incremental, implicit time integration scheme is presented. The developments are implemented into an implicit FEM software for orthotropic material symmetry under plane stress assumption. Even if this is a reduced problem, all essential features are present and allow for the entire verification and validation of the approach. Various simulations on isotropic and orthotropic problems are carried out to demonstrate the material behavior under investigation.

Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

International Nuclear Information System (INIS)

Kramer, D.; Neugebauer, G.

1981-01-01

The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

From the hypergeometric differential equation to a non-linear Schrödinger one

International Nuclear Information System (INIS)

Plastino, A.; Rocca, M.C.

2015-01-01

We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

Construction of local and non-local conservation laws for non-linear field equations

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1984-08-01

A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

Determination of parameters for a stress-strain constitutive equation considering time-dependent behavior of Toki granite

International Nuclear Information System (INIS)

Hirano, Toru; Seno, Yasuhiro; Nakama, Shigeo; Okubo, Seisuke

2008-01-01

Toki granite was tested to obtain parameters for the constitutive equation. The testing method was uniaxial compressive loading at the moderate a constant strain rate that is decreased after yielding to obtain the complete stress-strain curve. In addition, two kinds of the strain rate were alternately switched to obtain the parameter n from one specimen. The n represents the strength time-dependence in the constitutive equation. The second parameter m can be obtained by fitting the experimental stress-strain curve to the calculated curve. The m accounts for the behavior after yielding. According to the results, Toki granite has n=52 and m=60, showing relatively weak time-dependence of creep failure. (author)

A Hamiltonian structure for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1991-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

Collective spin by linearization of the Schrodinger equation for nuclear collective motion

International Nuclear Information System (INIS)

Greiner, M.; Scheid, W.; Herrmann, R.

1988-01-01

The free Schrodinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, the authors demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. The authors derive the operator of the collective spin and its eigen values depending on multipolarity

Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

International Nuclear Information System (INIS)

Ravi Kanth, A.S.V.; Aruna, K.

2009-01-01

In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case

International Nuclear Information System (INIS)

Schmidt, H.J.

1985-01-01

The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)

On a representation of linear differential equations

Czech Academy of Sciences Publication Activity Database

Neuman, František

2010-01-01

Roč. 52, 1-2 (2010), s. 355-360 ISSN 0895-7177 Grant - others:GA ČR(CZ) GA201/08/0469 Institutional research plan: CEZ:AV0Z10190503 Keywords : Brandt and Ehresmann groupoinds * transformations * canonical forms * linear differential equations Subject RIV: BA - General Mathematics Impact factor: 1.066, year: 2010 http://www.sciencedirect.com/science/article/pii/S0895717710001184

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

Science.gov (United States)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)

2016-07-05

In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

GDTM-Padé technique for the non-linear differential-difference equation

Directory of Open Access Journals (Sweden)

Lu Jun-Feng

2013-01-01

Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

Energy Technology Data Exchange (ETDEWEB)

Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki

1996-11-01

In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

International Nuclear Information System (INIS)

Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.

1996-11-01

In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

International Nuclear Information System (INIS)

Man, Yiu-Kwong

2010-01-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)

On the economical solution method for a system of linear algebraic equations

Directory of Open Access Journals (Sweden)

Jan Awrejcewicz

2004-01-01

Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

Inhomogeneous linear equation in Rota-Baxter algebra

OpenAIRE

Pietrzkowski, Gabriel

2014-01-01

We consider a complete filtered Rota-Baxter algebra of weight $\\lambda$ over a commutative ring. Finding the unique solution of a non-homogeneous linear algebraic equation in this algebra, we generalize Spitzer's identity in both commutative and non-commutative cases. As an application, considering the Rota-Baxter algebra of power series in one variable with q-integral as the Rota-Baxter operator, we show certain Eulerian identities.

Solution of systems of linear algebraic equations by the method of summation of divergent series

International Nuclear Information System (INIS)

Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

2015-01-01

A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

International Nuclear Information System (INIS)

Grigoriu, Mircea; Samorodnitsky, Gennady

2004-01-01

Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

Factorization of a class of almost linear second-order differential equations

International Nuclear Information System (INIS)

Estevez, P G; Kuru, S; Negro, J; Nieto, L M

2007-01-01

A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations

Phenomenological inelastic constitutive equations for SiC and SiC fibers under irradiation

International Nuclear Information System (INIS)

El-Azab, A.; Ghoniem, N.M.

1994-01-01

Experimental data on irradiation-induced dimensional changes and creep in β-SiC and SiC fibers is analyzed, with the objective of studying the constitutive behavior of these materials under high-temperature irradiation. The data analysis includes empirical representation of irradiation-induced dimensional changes in SiC matrix and SiC fibers as function of time and irradiation temperature. The analysis also includes formulation of simple scaling laws to extrapolate the existing data to fusion conditions on the basis of the physical mechanisms of radiation effects on crystalline solids. Inelastic constitutive equations are then developed for SCS-6 SiC fibers, Nicalon fibers and CVD SiC. The effects of applied stress, temperature, and irradiation fields on the deformation behavior of this class of materials are simultaneously represented. Numerical results are presented for the relevant creep functions under the conditions of the fusion reactor (ARIES IV) first wall. The developed equations can be used in estimating the macro mechanical properties of SiC-SiC composite systems as well as in performing time-dependent micro mechanical analysis that is relevant to slow crack growth and fiber pull-out under fusion conditions

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

Science.gov (United States)

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

A Proposed Method for Solving Fuzzy System of Linear Equations

Directory of Open Access Journals (Sweden)

Reza Kargar

2014-01-01

Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

On a class of fourth order linear recurrence equations

Directory of Open Access Journals (Sweden)

Sui-Sun Cheng

1984-01-01

Full Text Available This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences.

Could solitons be adiabatic invariants attached to certain non linear equations

International Nuclear Information System (INIS)

Lochak, P.

1984-01-01

Arguments are given to support the claim that solitons should be the adiabatic invariants associated to certain non linear partial differential equations; a precise mathematical form of this conjecture is then stated. As a particular case of the conjecture, the Korteweg-de Vries equation is studied. (Auth.)

On a Linear Equation Arising in Isometric Embedding of Torus-like Surface

Institute of Scientific and Technical Information of China (English)

Chunhe LI

2009-01-01

The solvability of a linear equation and the regularity of the solution are discussed.The equation is arising in a geometric problem which is concerned with the realization of Alexandroff's positive annul in R3.

Stochastic modeling of mode interactions via linear parabolized stability equations

Science.gov (United States)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

KAM for the non-linear Schroedinger equation

CERN Document Server

Eliasson, L H

2006-01-01

We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep|u|^2u;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it If $|\\ep|$ is sufficiently small, then there is a large subset $U'$ of $U$ such that for all $...

Minimal solution of linear formed fuzzy matrix equations

Directory of Open Access Journals (Sweden)

Maryam Mosleh

2012-10-01

Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

Science.gov (United States)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution

International Nuclear Information System (INIS)

Hamdi, Adel

2009-01-01

The aim of this paper is to localize the position of a point source and recover the history of its time-dependent intensity function that is both unknown and constitutes the right-hand side of a 1D linear transport equation. Assuming that the source intensity function vanishes before reaching the final control time, we prove that recording the state with respect to the time at two observation points framing the source region leads to the identification of the source position and the recovery of its intensity function in a unique manner. Note that at least one of the two observation points should be strategic. We establish an identification method that determines quasi-explicitly the source position and transforms the task of recovering its intensity function into solving directly a well-conditioned linear system. Some numerical experiments done on a variant of the water pollution BOD model are presented

Some Additional Remarks on the Cumulant Expansion for Linear Stochastic Differential Equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumulant expansions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Some additional remarks on the cumulant expansion for linear stochastic differential equations

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1984-01-01

We summarize our previous results on cumular expasions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

Hyers-Ulam stability for second-order linear differential equations with boundary conditions

Directory of Open Access Journals (Sweden)

Pasc Gavruta

2011-06-01

Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.

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.

On oscillation of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, A.; Šremr, Jiří

2011-01-01

Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm

An inhomogeneous wave equation and non-linear Diophantine approximation

DEFF Research Database (Denmark)

Beresnevich, V.; Dodson, M. M.; Kristensen, S.

2008-01-01

A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...

Improved harmonic balance approach to periodic solutions of non-linear jerk equations

International Nuclear Information System (INIS)

Wu, B.S.; Lim, C.W.; Sun, W.P.

2006-01-01

An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach

Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

Science.gov (United States)

Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

2018-03-01

The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

Nonoscillation criteria for half-linear second order difference equations

Czech Academy of Sciences Publication Activity Database

Došlý, Ondřej; Řehák, Pavel

2001-01-01

Roč. 42, - (2001), s. 453-464 ISSN 0898-1221 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : half-linear difference equation%nonoscillation criteria%variational principle Subject RIV: BA - General Mathematics Impact factor: 0.383, year: 2001

Lie symmetries and differential galois groups of linear equations

NARCIS (Netherlands)

Oudshoorn, W.R.; Put, M. van der

2002-01-01

For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In

Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model

NARCIS (Netherlands)

Boek, E.S.; Padding, J.T.; Anderson, V.J.; Tardy, P.M.J.; Crawshaw, J.P.; Pearson, J.R.A.

2005-01-01

We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real

Solving Fully Fuzzy Linear System of Equations in General Form

Directory of Open Access Journals (Sweden)

A. Yousefzadeh

2012-06-01

Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

Linear fractional diffusion-wave equation for scientists and engineers

CERN Document Server

Povstenko, Yuriy

2015-01-01

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

Local linearization methods for the numerical integration of ordinary differential equations: An overview

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)

On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

Institute of Scientific and Technical Information of China (English)

Chunhe LI

2013-01-01

In the present paper,the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given.In the meantime,the Solvability of a relevant linearized Darboux equation is given.The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov's positive annulus in R3.

Modification of Flow Stress Curves and Constitutive Equations During Hot Compression Deformation of 5083 Aluminum Alloy

Directory of Open Access Journals (Sweden)

FU Ping

2017-08-01

Full Text Available The flow stress behavior of 5083 aluminum alloy was investigated under hot compression deformation at 523-723K,strain rates of 0.01-10s-1 and true strains of 0-0.7 with Gleeble-3800 thermal simulator. Based on the heat transfer effect on alloy deformation heat effect, the flow stress curves were corrected. The results show that influence of heat conduction can not be neglected and becomes more obvious with the increase of true strain. The corrected flow stress has little influence on the peak stress, but the steady flow stress softening trends to be diminished to some degree. The flow stress can be predicted by the Zener-Hollomon parameters in the constitutive equation. The corrected measured value exhibits a good agreement with the flow stress predicted by the constitutive equation, and the average relative error is only 5.21%.

Non-linear partial differential equations an algebraic view of generalized solutions

CERN Document Server

Rosinger, Elemer E

1990-01-01

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

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

Asymptotic formulae for solutions of half-linear differential equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2017-01-01

Roč. 292, January (2017), s. 165-177 ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www.sciencedirect.com/science/article/pii/S0096300316304581

Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

International Nuclear Information System (INIS)

Edery, D.

1983-11-01

The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

International Nuclear Information System (INIS)

Misguich, J.H.

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

Energy Technology Data Exchange (ETDEWEB)

Misguich, J.H

2004-04-01

As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

Science.gov (United States)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Exponential estimates for solutions of half-linear differential equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2015-01-01

Roč. 147, č. 1 (2015), s. 158-171 ISSN 0236-5294 Institutional support: RVO:67985840 Keywords : half-linear differential equation * decreasing solution * increasing solution * asymptotic behavior Subject RIV: BA - General Mathematics Impact factor: 0.469, year: 2015 http://link.springer.com/article/10.1007%2Fs10474-015-0522-9

On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

International Nuclear Information System (INIS)

Dietrich, K.; Vautherin, D.

1985-01-01

We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

High Temperature Mechanical Constitutive Modeling of a High-Nb TiAl Alloy

Directory of Open Access Journals (Sweden)

DONG Chengli

2018-02-01

Full Text Available Uniaxial tensile, low cycle fatigue, fatigue-creep interaction and creep experiments of a novel high-Nb TiAl alloy (i.e. Ti-45Al-8Nb-0.2W-0.2B-0.02Y (atom fraction/% were conducted at 750℃ to obtain its tested data and curves. Based on Chaboche visco-plasticity unified constitutive model, Ohno-Wang modified non-linear kinematic hardening was introduced in Chaboche constitutive model to describe the cyclic hardening/softening, and Kachanov damage was coupled in Chaboche constitutive model to characterize the accelerated creep stage. The differential equations of the constitutive model discretized by explicit Euler method were compiled in to ABAQUS/UMAT to simulate the mechanical behavior of high-Nb TiAl alloy at different test conditions. The results show that Chaboche visco-plasticity unified constitutive model considering both Ohno-Wang modified non-linear kinematic hardening and Kachanov damage is able to simulate the uniaxial tensile, low cycle fatigue, fatigue-creep interaction and creep behavior of high-Nb TiAl alloy and has high accuracy.

Shifted Legendre method with residual error estimation for delay linear Fredholm integro-differential equations

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Şuayip Yüzbaşı

2017-03-01

Full Text Available In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.

Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

OpenAIRE

Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

2017-01-01

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

Science.gov (United States)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. linear model are compared to those

Students' errors in solving linear equation word problems: Case ...

African Journals Online (AJOL)

kofi.mereku

Development in most areas of life is based on effective knowledge of science and ... Problem solving, as used in mathematics education literature, refers ... word problems, on the other hand, are those linear equation tasks or ... taught LEWPs in the junior high school, many of them reach the senior high school without a.

On nonnegative solutions of second order linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2004-01-01

Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

A Hamiltonian functional for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Rosas-RodrIguez, R

2005-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

An introduction to linear ordinary differential equations using the impulsive response method and factorization

CERN Document Server

Camporesi, Roberto

2016-01-01

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Science.gov (United States)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

A linear multiple balance method for discrete ordinates neutron transport equations

International Nuclear Information System (INIS)

Park, Chang Je; Cho, Nam Zin

2000-01-01

A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

Comparison between the Norton - and Mukherjee constitutive equations in the determination of stress - strain analysis of a material under creep

International Nuclear Information System (INIS)

Bevilacqua, L.; Feijoo, R.A.; Freire, J.L.; Miranda, P.E.V. de; Monteiro, E.; Silveira, T.L. da; Taroco, E.

1981-06-01

The Norton and Mukherjee constitutive equations are used to approximate the experimental results of creep in AISI 304 steel. Both equations are applied to the stress-strain analysis of a rotating disk with a concentric circular hole. From the design point of view it is shown that the stresses obtained with both equations are equivalents, which is not true for the velocities. (Author) [pt

Development of PARA-ID Code to Simulate Inelastic Constitutive Equations and Their Parameter Identifications for the Next Generation Reactor Designs

International Nuclear Information System (INIS)

Koo, Gyeong Hoi; Lee, J. H.

2006-03-01

The establishment of the inelastic analysis technology is essential issue for a development of the next generation reactors subjected to elevated temperature operations. In this report, the peer investigation of constitutive equations in points of a ratcheting and creep-fatigue analysis is carried out and the methods extracting the constitutive parameters from experimental data are established. To perform simulations for each constitutive model, the PARA-ID (PARAmeter-IDentification) computer program is developed. By using this code, various simulations related with the parameter identification of the constitutive models are carried out

Nonlinear and linear wave equations for propagation in media with frequency power law losses

Science.gov (United States)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Numerical implementation of constitutive material law for simulating the kinkband formation in fiber composites

DEFF Research Database (Denmark)

Veluri, Badrinath; Jensen, Henrik Myhre

2011-01-01

constitutive equations for the constituent materials is adopted to model the non-linear behavior of the unidirectional layered materials. This material law is implemented as UMAT user subroutine in ABAQUS/Standard to study kinkband formation. The methodology provides a procedure to investigate the kinkband...

Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

Directory of Open Access Journals (Sweden)

Mervan Pašić

2016-10-01

Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

International Nuclear Information System (INIS)

Rizzato, F.B.

1985-01-01

Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

Directory of Open Access Journals (Sweden)

Yongjin Li

2013-08-01

Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

A three operator split-step method covering a larger set of non-linear partial differential equations

Science.gov (United States)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

Directory of Open Access Journals (Sweden)

Sankar Prasad Mondal

2016-06-01

Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

Cardona, A.V.; Vilhena, M.T.M.B. de

1994-01-01

The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

On a class of strongly degenerate and singular linear elliptic equation

International Nuclear Information System (INIS)

Duong Minh Duc, D.M.; Le Dung.

1992-11-01

We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs

A study on linear and nonlinear Schrodinger equations by the variational iteration method

International Nuclear Information System (INIS)

Wazwaz, Abdul-Majid

2008-01-01

In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Directory of Open Access Journals (Sweden)

Encinas A.M.

2018-02-01

Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Radial solutions to semilinear elliptic equations via linearized operators

Directory of Open Access Journals (Sweden)

Phuong Le

2017-04-01

Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.

Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

DEFF Research Database (Denmark)

Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik

2004-01-01

The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...

Identification of a time-varying point source in a system of two coupled linear diffusion-advection- reaction equations: application to surface water pollution

International Nuclear Information System (INIS)

Hamdi, Adel

2009-01-01

This paper deals with the identification of a point source (localization of its position and recovering the history of its time-varying intensity function) that constitutes the right-hand side of the first equation in a system of two coupled 1D linear transport equations. Assuming that the source intensity function vanishes before reaching the final control time, we prove the identifiability of the sought point source from recording the state relative to the second coupled transport equation at two observation points framing the source region. Note that at least one of the two observation points should be strategic. We establish an identification method that uses these records to identify the source position as the root of a continuous and strictly monotonic function. Whereas the source intensity function is recovered using a recursive formula without any need of an iterative process. Some numerical experiments on a variant of the surface water pollution BOD–OD coupled model are presented

Constitutive equations for energy balance evaluation in metals under inelastic deformation

Science.gov (United States)

Kostina, A.; Plekhov, O.; Venkatraman, B.

2017-12-01

The work is devoted to the development of constitutive equations for energy balance evaluation in plastically deformed metals. The evolution of the defect system is described by a previously obtained model based on the Boltzmann-Gibbs statistics. In the framework of this model, a collective behavior of mesodefect ensembles is taken into account by the introduction of an internal variable representing additional structural strain. This parameter enables the partition of plastic work into dissipated heat and stored energy. The proposed model is applied to energy balance calculation in a Ti-1Al-1Mn specimen subjected to cyclic loading. Simulation results have shown that the model is able to describe an upward trend in the stored energy value with the increase in the load ratio.

The H-N method for solving linear transport equation: theory and application

International Nuclear Information System (INIS)

Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

2002-01-01

The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

An implicit iterative scheme for solving large systems of linear equations

International Nuclear Information System (INIS)

Barry, J.M.; Pollard, J.P.

1986-12-01

An implicit iterative scheme for the solution of large systems of linear equations arising from neutron diffusion studies is presented. The method is applied to three-dimensional reactor studies and its performance is compared with alternative iterative approaches

Anisotropic constitutive equations for the viscoplastic behaviour of the single crystal superalloy CMSX-4

International Nuclear Information System (INIS)

Fleury, G.; Schubert, F.

1997-09-01

Nickel-base superalloy blades of the first rotor stage in a gas turbine have to withstand extremely severe thermomechanical loading conditions. Single crystal blades exhibit a highly anisotropic deformation behaviour and are subjected to triaxial stress fields induced by complex cooling systems. Consequently the prediction of their deformation behaviour requires constitutive equations based on multiaxial formulations. The microstructural evolution of γ/γ' superalloys during the service time modifies the material properties and has therefore to be taken into account in the constitutive equations. For the modelling of the anisotropic, viscoplastic behaviour of single crystal blades taking into account the evolution of the microstructure, a microstructure-dependent, orthotropic Hills potential, whose anisotropy coefficients are connected to the edge length of the γ'-particles, is applied. The prediction was validated by investigating the deformation behaviour of the superalloy CMSX-4 in the range of temperatures [750 C-950 C]. If the shape of γ'-particles remain cubic, for example, in creep testing at low temperatures (up to about 850 C), the microstructure-dependent potential leads to the cubic version of the Hills potential. The prediction is in good agreement with creep results for left angle 001 right angle - and left angle 111 right angle - orientated specimens but overestimates the creep resistance of left angle 011 right angle - orientated specimens. (orig.)

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

NARCIS (Netherlands)

Martini, Ruud; Kersten, P.H.M.

1983-01-01

Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

On the calculation of linear stability with the aid of asymptotic solutions of Orr-Sommerfeld equation, 1

International Nuclear Information System (INIS)

Fujimura, Kaoru

1980-11-01

The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III 1 ) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Constitutive Modelling of Resins in the Compliance Domain

Science.gov (United States)

Klasztorny, M.

2004-07-01

A rheological HWKK/H model for resins is developed taking into consideration the up-to-date analyses of experimental results. Constitutive compliance equations of linear are formulated for this model in the shear/bulk form, which describes, among other things, the first-rank reversible isothermal creep. The shear (distorsional) deformations are simulated with three independent stress history functions of fractional and normal exponential types. The volume deformations are simulated as perfectly elastic. The model is described by two elastic and six viscoelastic constants, namely three long-term creep coefficients and three retardation times. The constitutive compliance equations of viscoealsticity for resins are also formulated in the coupled form. Formulae for converting the constants of shear/bulk (uncoupled) viscoelasticity into the constants of coupled viscoelasticity are given too. An algorithm for identifying the material constants, based on the creep of uniaxially tensioned bar samples, is formulated in a way that gives unique results. The material constants are fiund for Epidian 53 epoxy and Polimal 109 polyester resins. The creep processes, simulated based on the experimental data, are presented graphically for both the resins examined.

Non self-similar collapses described by the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Berge, L.; Pesme, D.

1992-01-01

We develop a rapid method in order to find the contraction rates of the radially symmetric collapsing solutions of the nonlinear Schroedinger equation defined for space dimensions exceeding a threshold value. We explicitly determine the asymptotic behaviour of these latter solutions by solving the non stationary linear problem relative to the nonlinear Schroedinger equation. We show that the self-similar states associated with the collapsing solutions are characterized by a spatial extent which is bounded from the top by a cut-off radius

Computer programs for the solution of systems of linear algebraic equations

Science.gov (United States)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Geon-type solutions of the non-linear Heisenberg-Klein-Gordon equation

International Nuclear Information System (INIS)

Mielke, E.W.; Scherzer, R.

1980-10-01

As a model for a ''unitary'' field theory of extended particles we consider the non-linear Klein-Gordon equation - associated with a ''squared'' Heisenberg-Pauli-Weyl non-linear spinor equation - coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schroedinger type wave functions within the ''scalar geon''. For zero angular momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding ''principal quantum number'' reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particle-like structure of these ''quantized geons''. (author)

A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

Science.gov (United States)

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

Solving Linear Equations by Classical Jacobi-SR Based Hybrid Evolutionary Algorithm with Uniform Adaptation Technique

OpenAIRE

Jamali, R. M. Jalal Uddin; Hashem, M. M. A.; Hasan, M. Mahfuz; Rahman, Md. Bazlar

2013-01-01

Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxation factor, {\\omega}. Recently, hybridization of classical Gauss-Seidel based successive relaxation t...

Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

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 Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Constitutive Modelling of Resins in the Stiffness Domain

Science.gov (United States)

Klasztorny, M.

2004-09-01

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic. The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.

Insights into the School Mathematics Tradition from Solving Linear Equations

Science.gov (United States)

Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth

2015-01-01

In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

Oscillatory solutions of the Cauchy problem for linear differential equations

Directory of Open Access Journals (Sweden)

Gro Hovhannisyan

2015-06-01

Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

Role of statistical linearization in the solution of nonlinear stochastic equations

International Nuclear Information System (INIS)

Budgor, A.B.

1977-01-01

The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables

Analytical approach to linear fractional partial differential equations arising in fluid mechanics

International Nuclear Information System (INIS)

Momani, Shaher; Odibat, Zaid

2006-01-01

In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation

KAUST Repository

Almubarak, Mohammed S.

2013-05-01

The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.

Linear stochastic differential equations with anticipating initial conditions

DEFF Research Database (Denmark)

Khalifa, Narjess; Kuo, Hui-Hsiung; Ouerdiane, Habib

In this paper we use the new stochastic integral introduced by Ayed and Kuo (2008) and the results obtained by Kuo et al. (2012b) to find a solution to a drift-free linear stochastic differential equation with anticipating initial condition. Our solution is based on well-known results from...... classical Itô theory and anticipative Itô formula results from Kue et al. (2012b). We also show that the solution obtained by our method is consistent with the solution obtained by the methods of Malliavin calculus, e.g. Buckdahn and Nualart (1994)....

A general method for enclosing solutions of interval linear equations

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2012-01-01

Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Science.gov (United States)

Stone, H. S.

1971-01-01

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Some oscillation criteria for the second-order linear delay differential equation

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2011-01-01

Roč. 136, č. 2 (2011), s. 195-204 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order linear differential equation with a delay * oscillatory solution Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/141582

Refined Fuchs inequalities for systems of linear differential equations

International Nuclear Information System (INIS)

Gontsov, R R

2004-01-01

We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point

A non linear half space problem for radiative transfer equations. Application to the Rosseland approximation

International Nuclear Information System (INIS)

Sentis, R.

1984-07-01

The radiative transfer equations may be approximated by a non linear diffusion equation (called Rosseland equation) when the mean free paths of the photons are small with respect to the size of the medium. Some technical assomptions are made, namely about the initial conditions, to avoid any problem of initial layer terms

Coupling and reduction of the HAWC equations

DEFF Research Database (Denmark)

Nim, E.

2001-01-01

This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system.......This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model...

Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations VIASM 2016

CERN Document Server

Tran, Hung

2017-01-01

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the n...

Formulation and integration of constitutive models describing large deformations in thermoplasticity and thermoviscoplasticity

International Nuclear Information System (INIS)

Jansohn, W.

1997-10-01

This report deals with the formulation and numerical integration of constitutive models in the framework of finite deformation thermomechanics. Based on the concept of dual variables, plasticity and viscoplasticity models exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules are presented. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. In view of the development of an efficient numerical integration procedure, simplified versions of these constitutive models are supposed. In these versions, the thermoelastic strains are assumed to be small and a simplified kinematic hardening rule is considered. Additionally, in view of an implementation into the ABAQUS finite element code, the elasticity law is approximated by a hypoelasticity law. For the simplified onstitutive models, an implicit time-integration algorithm is developed. First, in order to obtain a numerical objective integration scheme, use is made of the HUGHES-WINGET-Algorithm. In the resulting system of ordinary differential equations, it can be distinguished between three differential operators representing different physical effects. The structure of this system of differential equations allows to apply an operator split scheme, which leads to an efficient integration scheme for the constitutive equations. By linearizing the integration algorithm the consistent tangent modulus is derived. In this way, the quadratic convergence of Newton's method used to solve the basic finite element equations (i.e. the finite element discretization of the governing thermomechanical field equations) is preserved. The resulting integration scheme is implemented as a user subroutine UMAT in ABAQUS. The properties of the applied algorithm are first examined by test calculations on a single element under tension-compression-loading. For demonstrating the capabilities of the constitutive theory

Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

DEFF Research Database (Denmark)

Mejlbro, Leif

1997-01-01

An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

Linear and nonlinear analogues of the Schroedinger equation in the contextual approach in quantum mechanics

International Nuclear Information System (INIS)

Khrennikov, A.Yu.

2005-01-01

One derived the general evolutionary differential equation within the Hilbert space describing dynamics of the wave function. The derived contextual model is more comprehensive in contrast to a quantum one. The contextual equation may be a nonlinear one. Paper presents the conditions ensuring linearity of the evolution and derivation of the Schroedinger equation [ru

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional-differential equations * functional-differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076. xml

Multi-point boundary value problems for linear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

2017-01-01

Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional- differential equations * functional- differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076.xml

Some trends in constitutive equation model development for high-temperature behavior of fast-reactor structural alloys

International Nuclear Information System (INIS)

Pugh, C.E.; Robinson, D.N.

1977-01-01

The paper addresses some important features of the inelastic behavior of 2 1 / 4 Cr--1Mo steel and indicates a mathematical framework that is capable of representing these types of response. While the constitutive model discussed embraces capabilities beyond those of equations presently used in design analyses; their implementation into practicable analysis methods (such as finite-element programs) is more demanding. For example, in the case of slow time-dependent deformations, the equations governing accumulation of the inelastic strain components and the evolution of the tensorial state variable α are intimately coupled. A part of recommending any such model for use in design must be a quantitative assessment of the economic feasibility of implementation

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

First order linear ordinary differential equations in associative algebras

Directory of Open Access Journals (Sweden)

Gordon Erlebacher

2004-01-01

Full Text Available In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t x b_i(t + f(t $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.

Myshkis type oscillation criteria for second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2015-01-01

Roč. 178, č. 1 (2015), s. 143-161 ISSN 0026-9255 Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillation criteria Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2015 http://link.springer.com/article/10.1007%2Fs00605-014-0719-y

Comparison of nonlinearities in oscillation theory of half-linear differential equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2008-01-01

Roč. 121, č. 2 (2008), s. 93-105 ISSN 0236-5294 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential equation * comparison theorem * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 0.317, year: 2008

Linear hyperbolic functional-differential equations with essentially bounded right-hand side

Czech Academy of Sciences Publication Activity Database

Domoshnitsky, A.; Lomtatidze, Alexander; Maghakyan, A.; Šremr, Jiří

2011-01-01

Roč. 2011, - (2011), s. 242965 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear functional-differential equation of hyperbolic type * Darboux problem * unique solvability Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/242965/

Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

Directory of Open Access Journals (Sweden)

Matt Challacombe

2014-03-01

Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

A novel algebraic procedure for solving non-linear evolution equations of higher order

International Nuclear Information System (INIS)

Huber, Alfred

2007-01-01

We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

Linear absorptive dielectrics

Science.gov (United States)

Tip, A.

1998-06-01

Starting from Maxwell's equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations D(x,t)=ɛ1(x)E(x,t)+∫t-∞dsχ(x,t-s)E(x,s) and H(x,t)=B(x,t), a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability ɛ(x,ω), no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An S-matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.

Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

Science.gov (United States)

Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

2018-01-01

This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

Hadronic equation of state in the statistical bootstrap model and linear graph theory

International Nuclear Information System (INIS)

Fre, P.; Page, R.

1976-01-01

Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed

On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

International Nuclear Information System (INIS)

Aristov, Anatoly I

2011-01-01

We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

A generalized variational algebra and conserved densities for linear evolution equations

International Nuclear Information System (INIS)

Abellanas, L.; Galindo, A.

1978-01-01

The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)

Peculiarities in power type comparison results for half-linear dynamic equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2012-01-01

Roč. 42, č. 6 (2012), s. 1995-2013 ISSN 0035-7596 R&D Projects: GA AV ČR KJB100190701 Institutional support: RVO:67985840 Keywords : half-linear dynamic equation * time scale * comparison theorem Subject RIV: BA - General Mathematics Impact factor: 0.389, year: 2012 http://projecteuclid.org/euclid.rmjm/1361800616

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

Energy Technology Data Exchange (ETDEWEB)

Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

2013-03-15

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Chaotic dynamics and diffusion in a piecewise linear equation

International Nuclear Information System (INIS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-01-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems

Chaotic dynamics and diffusion in a piecewise linear equation

Science.gov (United States)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Dyson-Schwinger equations for the non-linear σ-model

International Nuclear Information System (INIS)

Drouffe, J.M.; Flyvbjerg, H.

1989-08-01

Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)

An Improved Recurrent Neural Network for Complex-Valued Systems of Linear Equation and Its Application to Robotic Motion Tracking.

Science.gov (United States)

Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua

2017-01-01

To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

Solutions of half-linear differential equations in the classes Gamma and Pi

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel; Taddei, V.

2016-01-01

Roč. 29, 7-8 (2016), s. 683-714 ISSN 0893-4983 Institutional support: RVO:67985840 Keywords : half-linear differential equation * positive solution * asymptotic formula Subject RIV: BA - General Mathematics Impact factor: 0.565, year: 2016 http://projecteuclid.org/euclid.die/1462298681

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

Science.gov (United States)

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

International Nuclear Information System (INIS)

Granita; Bahar, A.

2015-01-01

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)

2015-03-09

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

A structure-based constitutive equation for filler-reinforced rubber-like networks and for the description of the Mullins effect

Czech Academy of Sciences Publication Activity Database

Meissner, Bohumil; Matějka, Libor

2006-01-01

Roč. 47, č. 23 (2006), s. 7997-8012 ISSN 0032-3861 R&D Projects: GA ČR GA203/05/2252 Institutional research plan: CEZ:AV0Z40500505 Keywords : elastomers * fillers * constitutive equation Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.773, year: 2006

Disformal invariance of continuous media with linear equation of state

Energy Technology Data Exchange (ETDEWEB)

Celoria, Marco [Gran Sasso Science Institute (INFN), Viale Francesco Crispi 7, L' Aquila, I-67100 Italy (Italy); Matarrese, Sabino [Dipartimento di Fisica e Astronomia ' G. Galilei' , Università degli Studi di Padova, via Marzolo 8, Padova, I-35131 Italy (Italy); Pilo, Luigi, E-mail: marco.celoria@gssi.infn.it, E-mail: sabino.matarrese@pd.infn.it, E-mail: luigi.pilo@aquila.infn.it [Dipartimento di Fisica, Università di L' Aquila, L' Aquila, I-67010 Italy (Italy)

2017-02-01

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form p = w ρ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of w =1/3 (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, irrotational dust (mimetic matter) and homogeneous and isotropic solids are discussed.

A three-dimensional constitutive model for shape memory alloy

International Nuclear Information System (INIS)

Zhou, Bo; Yoon, Sung-Ho; Leng, Jin-Song

2009-01-01

Shape memory alloy (SMA) has a wide variety of practical applications due to its unique super-elasticity and shape memory effect. It is of practical interest to establish a constitutive model which predicts its phase transformation and mechanical behaviors. In this paper, a new three-dimensional phase transformation equation, which predicts the phase transformation behaviors of SMA, is developed based on the results of a differential scanning calorimetry (DSC) test. It overcomes both limitations: that Zhou's phase transformation equations fail to describe the phase transformation from twinned martensite to detwinned martensite of SMA and Brinson's phase transformation equation fails to express the influences of phase transformation peak temperatures on the phase transformation behaviors of SMA. A new three-dimensional constitutive equation, which predicts the mechanical behaviors associated with the super-elasticity and shape memory effect of SMA, is developed on the basis of thermodynamics and solid mechanics. Results of numerical simulations show that the new constitutive model, which includes the new phase transformation equation and constitutive equation, can predict the phase transformation and mechanical behaviors associated with the super-elasticity and shape memory effect of SMA precisely and comprehensively. It is proved that Brinson's constitutive model of SMA can be considered as one special case of the new constitutive model

Path integral solution of linear second order partial differential equations I: the general construction

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

Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

Science.gov (United States)

Tisdell, Christopher C.

2017-11-01

For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT

Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations

International Nuclear Information System (INIS)

Ehsani, Amir

2015-01-01

Algebras with a pair of non-associative binary operations (f, g) which are satisfy in the balanced quadratic functional equations with four object variables considered. First, we obtain a linear representation for the operations, of this kind of binary algebras (A,f,g), over an abelian group (A, +) and then we generalize the linear representation of operations, to an algebra (A,F) with non-associative binary operations which are satisfy in the balanced quadratic functional equations with four object variables. (paper)

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

2005-07-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

KAM for the non-linear Schroedinger equation a short presentation

CERN Document Server

Eliasson, H L

2006-01-01

We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep \\frac{\\p F}{\\p \\bar u}(x,u,\\bar u) ;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real and $F$ is a real analytic function in $\\Re u$, $\\Im u$ and $x$. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it ...

Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

KAUST Repository

Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

2014-01-01

This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

DEFF Research Database (Denmark)

Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

Science.gov (United States)

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

An Explicit Enclosure of the Solution Set of Overdetermined Interval Linear Equations

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2017-01-01

Roč. 24, February (2017), s. 1-10 ISSN 1573-1340 Institutional support: RVO:67985807 Keywords : interval linear equations * interval hull * unit midpoint * enclosure Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://interval.louisiana.edu/ reliable -computing-journal/volume-24/ reliable -computing-24-pp-001-010.pdf

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations

Science.gov (United States)

Müller, Ingo

2008-12-01

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Scilab software as an alternative low-cost computing in solving the linear equations problem

Science.gov (United States)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

International Nuclear Information System (INIS)

Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

2012-05-01

We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.

q-analogue of summability of formal solutions of some linear q-difference-differential equations

Directory of Open Access Journals (Sweden)

Hidetoshi Tahara

2015-01-01

Full Text Available Let \\(q\\gt 1\\. The paper considers a linear \\(q\\-difference-differential equation: it is a \\(q\\-difference equation in the time variable \\(t\\, and a partial differential equation in the space variable \\(z\\. Under suitable conditions and by using \\(q\\-Borel and \\(q\\-Laplace transforms (introduced by J.-P. Ramis and C. Zhang, the authors show that if it has a formal power series solution \\(\\hat{X}(t,z\\ one can construct an actual holomorphic solution which admits \\(\\hat{X}(t,z\\ as a \\(q\\-Gevrey asymptotic expansion of order \\(1\\.

A Solution to the Fundamental Linear Fractional Order Differential Equation

Science.gov (United States)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Time-independent limit of a creep-recovery constitutive equation

International Nuclear Information System (INIS)

Chang, S.J.

1984-01-01

The effect of strain recovery is taken into consideration in ORNL efforts to establish unified constitutive equations for time-dependent plastic deformation for metals at elevated temperatures. Representation by internal state variables and Rice's flow potential are under consideration. Here the growth law for the internal state variables is discussed and interpreted in terms of a generalized form of the kinematic hardening condition of Prager. The yield condition is obtained from the flow potential representation of the inelastic strain rate. A consistency condition is derived from the yield condition and leads to a flow rule which assumes a slightly general form as compared with that of the classical plasticity due to the effect of strain recovery and the time-dependent property of the yield condition. Based on this representation, the time-independent limit is discussed. From a vanishing effect of recovery and a rate-independent limit for the yield condition at low temperature, this flow rule reduces to the well-known form of time-independent plasticity with a kinematic hardening condition. The duration of time (the characteristic time) required for the inelastic strain to reach its saturated value is defined for the inelastic loading condition. It provides the measure of a minimum duration of time which is required for a valid approximation made by the time-independent plasticity model

Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

Directory of Open Access Journals (Sweden)

Luo Li-Qin

2016-01-01

Full Text Available In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

International Nuclear Information System (INIS)

Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

1990-01-01

Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

Science.gov (United States)

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Approximate solution to neutron transport equation with linear anisotropic scattering

International Nuclear Information System (INIS)

Coppa, G.; Ravetto, P.; Sumini, M.

1983-01-01

A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

International Nuclear Information System (INIS)

Zhou, B.

1997-01-01

The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

Implementation of constitutive equations for creep damage mechanics into the ABAQUS finite element code - some practical cases in high temperature component design and life assessment

International Nuclear Information System (INIS)

Segle, P.; Samuelson, L.Aa.; Andersson, Peder; Moberg, F.

1996-01-01

Constitutive equations for creep damage mechanics are implemented into the finite element program ABAQUS using a user supplied subroutine, UMAT. A modified Kachanov-Rabotnov constitutive equation which accounts for inhomogeneity in creep damage is used. With a user defined material a number of bench mark tests are analyzed for verification. In the cases where analytical solutions exist, the numerical results agree very well. In other cases, the creep damage evolution response appear to be realistic in comparison with laboratory creep tests. The appropriateness of using the creep damage mechanics concept in design and life assessment of high temperature components is demonstrated. 18 refs

Oscillation of solutions of some higher order linear differential equations

Directory of Open Access Journals (Sweden)

Hong-Yan Xu

2009-11-01

Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.

Hardy inequality on time scales and its application to half-linear dynamic equations

Directory of Open Access Journals (Sweden)

Řehák Pavel

2005-01-01

Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

Science.gov (United States)

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

TBA equations for the mass gap in the O(2r) non-linear σ-models

International Nuclear Information System (INIS)

Balog, Janos; Hegedues, Arpad

2005-01-01

We propose TBA integral equations for 1-particle states in the O(n) non-linear σ-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system

Equations for the non linear evolution of the resistive tearing modes in toroidal plasmas

International Nuclear Information System (INIS)

Edery, D.; Pellat, R.; Soule, J.L.

1979-09-01

Following the tokamak ordering, we simplify the resistive MHD equations in toroidal geometry. We obtain a closed system of non linear equations for two scalar potentials of the magnetic and velocity fields and for plasma density and temperature. If we expand these equations in the inverse of aspect ratio they are exact to the two first orders. Our formalism should correctly describe the mode coupling by curvature effects /1/ and the toroidal displacement of magnetic surfaces /2/. It provides a natural extension of the well known cylindrical model /3/ and is now being solved on computer

Anisotropic compacts stars on paraboloidal spacetime with linear equation of state

Energy Technology Data Exchange (ETDEWEB)

Thomas, V.O. [The Maharaja Sayajirao University of Baroda, Department of Mathematics, Faculty of Science, Vadodara, Gujarat (India); Pandya, D.M. [Pandit Deendayal Petroleum University, Department of Mathematics and Computer Science, Gandhinagar, Gujarat (India)

2017-06-15

New exact solutions of Einstein's field equations (EFEs) by assuming a linear equation of state, p{sub r} = α(ρ-ρ{sub R}), where p{sub r} is the radial pressure and ρ{sub R} is the surface density, are obtained on the background of a paraboloidal spacetime. By assuming estimated mass and radius of strange star candidate 4U 1820-30, various physical and energy conditions are used for estimating the range of parameter α. The suitability of the model for describing pulsars like PSR J1903+327, Vela X-1, Her X-1 and SAX J1808.4-3658 has been explored and respective ranges of α, for which all physical and energy conditions are satisfied throughout the distribution, are obtained. (orig.)

Method to determine the optimal constitutive model from spherical indentation tests

Science.gov (United States)

Zhang, Tairui; Wang, Shang; Wang, Weiqiang

2018-03-01

The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE) calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang's modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in) into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study.

Method to determine the optimal constitutive model from spherical indentation tests

Directory of Open Access Journals (Sweden)

Tairui Zhang

2018-03-01

Full Text Available The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang’s modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study. Keywords: Optimal constitutive model, Spherical indentation test, Finite Element calculations, Yang’s modulus

The potential in general linear electrodynamics. Causal structure, propagators and quantization

Energy Technology Data Exchange (ETDEWEB)

Siemssen, Daniel [Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw (Poland); Pfeifer, Christian [Institute for Theoretical Physics, Leibniz Universitaet Hannover (Germany); Center of Applied Space Technology and Microgravity (ZARM), Universitaet Bremen (Germany)

2016-07-01

From an axiomatic point of view, the fundamental input for a theory of electrodynamics are Maxwell's equations dF=0 (or F=dA) and dH=J, and a constitutive law H=F, which relates the field strength 2-form F and the excitation 2-form H. In this talk we consider general linear electrodynamics, the theory of electrodynamics defined by a linear constitutive law. The best known application of this theory is the effective description of electrodynamics inside (linear) media (e.g. birefringence). We analyze the classical theory of the electromagnetic potential A before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (instead of a metric) and a discussion of the classical phase space. This classical analysis sets the stage for the construction of the quantum field algebra and quantum states, including a (generalized) microlocal spectrum condition.

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml

A General Construction of Linear Differential Equations with Solutions of Prescribed Properties

Czech Academy of Sciences Publication Activity Database

Neuman, František

2004-01-01

Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004

An Empirical Comparison of Five Linear Equating Methods for the NEAT Design

Science.gov (United States)

Suh, Youngsuk; Mroch, Andrew A.; Kane, Michael T.; Ripkey, Douglas R.

2009-01-01

In this study, a data base containing the responses of 40,000 candidates to 90 multiple-choice questions was used to mimic data sets for 50-item tests under the "nonequivalent groups with anchor test" (NEAT) design. Using these smaller data sets, we evaluated the performance of five linear equating methods for the NEAT design with five levels of…

Linear Equating for the NEAT Design: A Rejoinder and Some Further Comments

Science.gov (United States)

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2010-01-01

This article presents the authors' rejoinder to commentaries on linear equating and the NEAT design. The authors appreciate the insightful work of the commentary writers. Each has made a number of interesting points, many of which the authors had not considered at all. Before responding to some of those points, the authors reiterate what they see…

On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients

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P. I. Kogut

2011-12-01

Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.

On the prolongation structure and Backlund transformation for new non-linear Klein-Gordon equations

International Nuclear Information System (INIS)

Roy Chowdhury, A.; Mukherjee, J.

1986-07-01

We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual Sine-Gordon and Sinh-Gordon equations. The first one is of non-autonomous version of Sinh-Gordon system and the second is closely related to the usual Sine-Gordon theory. The first problem indicates how (x,t) dependent non-linear equations can be treated in the prolongation theory and how a Backlund map can be constructed. The second one is a variation of the usual Sine-Gordon equation and suggests that there may be other equations (similar to Sine-Gordon) which are completely integrable. In both cases we have been able to construct the Lax pair. We then construct an auto-Backlund map by following the idea of Konno and Wadati, for the generation of multisolution states. (author)

A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

Science.gov (United States)

Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

2010-02-01

Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

The creep compliance, the relaxation modulus and the complex compliance of linear viscoelastic, homogeneous, isotropic materials

International Nuclear Information System (INIS)

Wong, P.K.

1989-01-01

This paper reports on a study to obtain the creep compliance, the relaxation modulus and the complex compliance derived from the concept of mechanical resistance for the constitutive equation of a class of linear viscoelastic, homogeneous, isotropic materials

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations; Sur la stabilite, les solutions periodiques et la resolution de certaines categories d'equations et systemes d'equations differentielles couplees non lineaires apparaissant dans les oscillations betatroniques

Energy Technology Data Exchange (ETDEWEB)

Valat, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1960-12-15

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de trouver des solutions generales. Pour les

TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

International Nuclear Information System (INIS)

Garbow, B.

1984-01-01

Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

Science.gov (United States)

Hoover, Wm G; Hoover, Carol G

2010-04-01

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Excited-state lifetime measurements: Linearization of the Foerster equation by the phase-plane method

International Nuclear Information System (INIS)

Love, J.C.; Demas, J.N.

1983-01-01

The Foerster equation describes excited-state decay curves involving resonance intermolecular energy transfer. A linearized solution based on the phase-plane method has been developed. The new method is quick, insensitive to the fitting region, accurate, and precise

Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆

Directory of Open Access Journals (Sweden)

Rubio Gerardo

2011-03-01

Full Text Available We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem. Nous considérons le problème de Cauchy dans ℝd pour une classe d’équations aux dérivées partielles paraboliques semi linéaires qui se pose dans certains problèmes de contrôle stochastique. Nous supposons que les coefficients ne sont pas bornés et sont localement Lipschitziennes, pas nécessairement différentiables, avec des données continues et ellipticité local uniforme. Nous construisons une solution classique par approximation avec les équations paraboliques linéaires. Les équations linéaires impliquées ne peuvent être résolues avec les résultats traditionnels. Par conséquent, nous construisons une solution classique au problème de Cauchy linéaire sous les mêmes hypothèses sur les coefficients pour l’équation semi-linéaire. Notre approche utilise les équations différentielles stochastiques et les équations différentielles paraboliques dans les domaines bornés. Enfin, nous appliquons les résultats à un problème stochastique de consommation optimale.

On the solution of a class of fuzzy system of linear equations

Indian Academy of Sciences (India)

J. Mathematics and Comput. Sci. 1: 1–5. Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing 15: 953–961. Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. S¯adhan¯a 36: 933–940. Wang K and Zheng B 2007 Block iterative methods ...

Scaling and constitutive relationships in downcomer modeling

International Nuclear Information System (INIS)

Daly, B.J.; Harlow, F.H.

1978-12-01

Constitutive relationships to describe mass and momentum exchange in multiphase flow in a pressurized water reactor downcomer are presented. Momentum exchange between the phases is described by the product of the flux of momentum available for exchange and the effective area for interaction. The exchange of mass through condensation is assumed to occur along a distinct condensation boundary separating steam at saturation temperature from water in which the temperature falls off roughly linearly with distance from the boundary. Because of the abundance of nucleation sites in a typical churning flow in a downcomer, we propose an equilibrium evaporation process that produces sufficient steam per unit time to keep the water perpetually cooled to the saturation temperature. The transport equations, constitutive models, and boundary conditions used in the K-TIF numerical method are nondimensionalized to obtain scaling relationships for two-phase flow in the downcomer. The results indicate that, subject to idealized thermodynamic and hydraulic constraints, exact mathematical scaling can be achieved. Experiments are proposed to isolate the effects of parameters that contribute to mass, momentum, and energy exchange between the phases

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

Science.gov (United States)

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Operational matrices with respect to Hermite polynomials and their applications in solving linear dierential equations with variable coecients

Directory of Open Access Journals (Sweden)

A. Aminataei

2014-05-01

Full Text Available In this paper, a new and ecient approach is applied for numerical approximation of the linear dierential equations with variable coecients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem. In addition, two experiments are given to demonstrate the validity and applicability of the method

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Science.gov (United States)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument

Czech Academy of Sciences Publication Activity Database

Drábek, P.; Kufner, Alois; Kuliev, K.

2017-01-01

Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

Science.gov (United States)

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.

Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

Science.gov (United States)

Le, Nam Q.

2018-05-01

We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

Directory of Open Access Journals (Sweden)

Jinsong Hu

2013-01-01

Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

Decoherence of histories and hydrodynamic equations for a linear oscillator chain

International Nuclear Information System (INIS)

Halliwell, J.J.

2003-01-01

We investigate the decoherence of histories of local densities for linear oscillators models. It is shown that histories of local number, momentum and energy density are approximately decoherent, when coarse grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally induced decoherence. We discuss the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities

A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

Science.gov (United States)

Liu, Tao; Huang, Jie

2017-04-17

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

Constitutive relations for nuclear reactor core materials

International Nuclear Information System (INIS)

Zaverl, F. Jr.; Lee, D.

1978-01-01

A strain rate dependent constitutive equation is proposed which is capable of describing inelastic deformation behavior of anisotropic metals, such as Zircaloys, under complex loading conditions. The salient features of the constitutive equations are that they describe history dependent inelastic deformation behaviour of anisotropic metals under three-dimensional stress states in the presence of fast neutron flux. It is shown that the general form of the constitutive relations is consistent with experimental observations made under both unirradiated and irradiated conditions. The utility of the model is demonstrated by examining the analytical results obtained for a segment of tubing undergoing different loading histories in a reactor. (Auth.)

Remark on periodic boundary-value problem for second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2018-01-01

Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients

OpenAIRE

Casas Pérez, Fernando; Chiralt Monleon, Cristina

2014-01-01

A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic ...

Constitutive behavior of as-cast AA1050, AA3104, and AA5182

Science.gov (United States)

van Haaften, W. M.; Magnin, B.; Kool, W. H.; Katgerman, L.

2002-07-01

Recent thermomechanical modeling to calculate the stress field in industrially direct-chill (DC) cast-aluminum slabs has been successful, but lack of material data limits the accuracy of these calculations. Therefore, the constitutive behavior of three aluminum alloys (AA1050, AA3104, and AA5182) was determined in the as-cast condition using tensile tests at low strain rates and from room temperature to solidus temperature. The parameters of two constitutive equations, the extended Ludwik equation and a combination of the Sellars-Tegart equation with a hardening law, were determined. In order to study the effect of recovery, the constitutive behavior after prestraining at higher temperatures was also investigated. To evaluate the quantified constitutive equations, tensile tests were performed simulating the deformation and cooling history experienced by the material during casting. It is concluded that both constitutive equations perform well, but the combined hardening-Sellars-Tegart (HST) equation has temperature-independent parameters, which makes it easier to implement in a DC casting model. Further, the deformation history of the ingot should be taken into account for accurate stress calculations.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

2008-04-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

International Nuclear Information System (INIS)

Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

2008-01-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

Directory of Open Access Journals (Sweden)

N. S. Dzhaliuk

2017-07-01

Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

A linear evolution for non-linear dynamics and correlations in realistic nuclei

International Nuclear Information System (INIS)

Levin, E.; Lublinsky, M.

2004-01-01

A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model-dependent way, correlations inside the nuclei. The third equation is a non-linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings

A critical oscillation constant as a variable of time scales for half-linear dynamic equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2010-01-01

Roč. 60, č. 2 (2010), s. 237-256 ISSN 0139-9918 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : dynamic equation * time scale * half-linear equation * (non)oscillation criteria * Hille-Nehari criteria * Kneser criteria * critical constant * oscillation constant * Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0009-7

On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

Directory of Open Access Journals (Sweden)

Yoshitsugu Takei

2015-01-01

Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

A parallel algorithm for solving linear equations arising from one-dimensional network problems

International Nuclear Information System (INIS)

Mesina, G.L.

1991-01-01

One-dimensional (1-D) network problems, such as those arising from 1- D fluid simulations and electrical circuitry, produce systems of sparse linear equations which are nearly tridiagonal and contain a few non-zero entries outside the tridiagonal. Most direct solution techniques for such problems either do not take advantage of the special structure of the matrix or do not fully utilize parallel computer architectures. We describe a new parallel direct linear equation solution algorithm, called TRBR, which is especially designed to take advantage of this structure on MIMD shared memory machines. The new method belongs to a family of methods which split the coefficient matrix into the sum of a tridiagonal matrix T and a matrix comprised of the remaining coefficients R. Efficient tridiagonal methods are used to algebraically simplify the linear system. A smaller auxiliary subsystem is created and solved and its solution is used to calculate the solution of the original system. The newly devised BR method solves the subsystem. The serial and parallel operation counts are given for the new method and related earlier methods. TRBR is shown to have the smallest operation count in this class of direct methods. Numerical results are given. Although the algorithm is designed for one-dimensional networks, it has been applied successfully to three-dimensional problems as well. 20 refs., 2 figs., 4 tabs

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

Science.gov (United States)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

Science.gov (United States)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Linear indices in nonlinear structural equation models : best fitting proper indices and other composites

NARCIS (Netherlands)

Dijkstra, T.K.; Henseler, J.

2011-01-01

The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with

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.

Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

DEFF Research Database (Denmark)

Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

1994-01-01

perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

Stationary distributions of stochastic processes described by a linear neutral delay differential equation

International Nuclear Information System (INIS)

Frank, T D

2005-01-01

Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

On one two-point BVP for the fourth order linear ordinary differential equation

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Manjikashvili, M.

2017-01-01

Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml

On one two-point BVP for the fourth order linear ordinary differential equation

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Manjikashvili, M.

2017-01-01

Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml

Oscillation theory of linear differential equations

Czech Academy of Sciences Publication Activity Database

Došlý, Ondřej

2000-01-01

Roč. 36, č. 5 (2000), s. 329-343 ISSN 0044-8753 R&D Projects: GA ČR GA201/98/0677 Keywords : discrete oscillation theory %Sturm-Liouville equation%Riccati equation Subject RIV: BA - General Mathematics

Resummation of the 1/N-expansion of the non-linear σ-model by Dyson-Schwinger equations

International Nuclear Information System (INIS)

Drouffe, J.M.; Flyvbjerg, H.

1988-02-01

Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived and expanded in 1/N. A closed set of equations is obtained by keeping only the leading term and the first correction term in this expansion. These equations are solved numerically in 2 dimensions on square lattices of sizes 50x50 and 100x100. Results for the magnetic susceptibility and the mass gap are compared with predictions of the ordinary 1/N-expansion and with Monte Carlo results. The results obtained with the Dyson-Schwinger equations show the same scaling behavior as found in the Monte Carlo results. This is not the behavior predicted by the perturbative renormalization group. (orig.)

Inhomogeneous Linear Random Differential Equations with Mutual Correlations between Multiplicative, Additive and Initial-Value Terms

NARCIS (Netherlands)

Roerdink, J.B.T.M.

1981-01-01

The cumulant expansion for linear stochastic differential equations is extended to the general case in which the coefficient matrix, the inhomogeneous part and the initial condition are all random and, moreover, statistically interdependent. The expansion now involves not only the autocorrelation

Occupational doses due to photoneutrons in medical linear accelerators rooms; Doses ocupacionais devido a neutrons em salas de aceleradores lineares de uso medico

Energy Technology Data Exchange (ETDEWEB)

Soares, Alessandro Facure Neves de Salles

2006-04-15

Medical linear accelerators, with maximum photon energies above 10 MeV, are becoming of common use in Brazil. Although desirable in the therapeutic point of view, the increase in photon energies causes the generation of undesired neutrons, which are produced through nuclear reactions between photons and the high Z target nuclei of the materials that constitute the accelerator head. In this work, MCNP simulation was undertaken to examine the neutron equivalent doses around the accelerators head and at the entrance of medical linear accelerators treatment rooms, some of them licensed in Brazil by the National Regulatory Agency (CNEN). The simulated neutron dose equivalents varied between 2 e 26 {mu} Sv/Gy{sub RX}, and the results were compared with calculations performed with the use of some semi-empirical equations found in literature. It was found that the semi-empirical equations underestimate the simulated neutron doses in the majority of the cases, if compared to the simulated values, suggesting that these equations must be revised, due to the increasing number of high energy machines in the country. (author)

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

Science.gov (United States)

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

NARCIS (Netherlands)

Bochev, Mikhail A.

2013-01-01

We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

Development and adjustment of programs for solving systems of linear equations

International Nuclear Information System (INIS)

Fujimura, Toichiro

1978-03-01

Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)

"Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

Science.gov (United States)

Casasent, David; Jackson, James

1986-03-01

A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

Higher derivative discontinuous solutions to linear ordinary differential equations: a new route to complexity?

International Nuclear Information System (INIS)

Datta, Dhurjati Prasad; Bose, Manoj Kumar

2004-01-01

We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz., 2nd, 4th, 8th, 16th,.... The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new dynamical principle for understanding complex phenomena in nature

Engineering equations for characterizing non-linear laser intensity propagation in air with loss.

Science.gov (United States)

Karr, Thomas; Stotts, Larry B; Tellez, Jason A; Schmidt, Jason D; Mansell, Justin D

2018-02-19

The propagation of high peak-power laser beams in real atmospheres will be affected at long range by both linear and nonlinear effects contained therein. Arguably, J. H. Marburger is associated with the mathematical characterization of this phenomenon. This paper provides a validated set of engineering equations for characterizing the self-focusing distance from a laser beam propagating through non-turbulent air with, and without, loss as well as three source configurations: (1) no lens, (2) converging lens and (3) diverging lens. The validation was done against wave-optics simulation results. Some validated equations follow Marburger completely, but others do not, requiring modification of the original theory. Our results can provide a guide for numerical simulations and field experiments.

The linearized pressure Poisson equation for global instability analysis of incompressible flows

Science.gov (United States)

Theofilis, Vassilis

2017-12-01

The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

Chemical Equation Balancing.

Science.gov (United States)

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

On the Evaluation of Computational Results Obtained from Solving System of linear Equations With matlab The Dual affine Scalling interior Point

International Nuclear Information System (INIS)

Murfi, Hendri; Basaruddin, T.

2001-01-01

The interior point method for linear programming has gained extraordinary interest as an alternative to simplex method since Karmarkar presented a polynomial-time algorithm for linear programming based on interior point method. In implementation of the algorithm of this method, there are two important things that have impact heavily to performance of the algorithm; they are data structure and used method to solve linear equation system in the algorithm. This paper describes about solving linear equation system in variants of the algorithm called dual-affine scaling algorithm. Next, we evaluate experimentally results of some used methods, either direct method or iterative method. The experimental evaluation used Matlab

An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

KAUST Repository

Bourantas, Georgios

2013-07-01

A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

KAUST Repository

Bourantas, Georgios; Burganos, Vasilis N.

2013-01-01

A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

Science.gov (United States)

Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.

2008-01-01

Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…

Obtention of the constitutive equation of hydride blisters in fuel cladding from nanoindentation tests

Energy Technology Data Exchange (ETDEWEB)

Martin Rengel, M.A., E-mail: mamartin.rengel@upm.es [E.T.S.I. Caminos, Canales y Puertos, Universidad Politécnica de Madrid, c/ Profesor Aranguren, 3, E-28040 Madrid (Spain); Gomez, F.J., E-mail: javier.gomez@amsimulation.com [Advanced Material Simulation, AMS, Bilbao (Spain); Rico, A., E-mail: alvaro.rico@urjc.es [DIMME, Universidad Rey Juan Carlos, Mostoles (Spain); Ruiz-Hervias, J. [E.T.S.I. Caminos, Canales y Puertos, Universidad Politécnica de Madrid, c/ Profesor Aranguren, 3, E-28040 Madrid (Spain); Rodriguez, J. [DIMME, Universidad Rey Juan Carlos, Mostoles (Spain)

2017-04-15

It is well known that the presence of hydrides in nuclear fuel cladding may reduce its mechanical and fracture properties. This situation may be worsened as a consequence of the formation of hydride blisters. These blisters are zones with an extremely high hydrogen concentration and they are usually associated to the oxide spalling which may occur at the outer surface of the cladding. In this work, a method which allows us to reproduce, in a reliable way, hydride blisters in the laboratory has been devised. Depth-sensing indentation tests with a spherical indenter were conducted on a hydride blister produced in the laboratory with the aim of measuring its mechanical behaviour. The plastic stress-strain curve of the hydride blister was calculated for first time by combining depth-sensing indentation tests results with an iterative algorithm using finite element simulations. The algorithm employed reduces, in each iteration, the differences between the numerical and the experimental results by modifying the stress-strain curve. In this way, an almost perfect adjustment of the experimental data was achieved after several iterations. The calculation of the constitutive equation of the blister from nanoindentation tests, may involve a lack of uniqueness. To evaluate it, a method based on the optimization of parameters of analytical equations has been proposed in this paper. An estimation of the error which involves this method is also provided.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

Science.gov (United States)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

On the Use of Linearized Euler Equations in the Prediction of Jet Noise

Science.gov (United States)

Mankbadi, Reda R.; Hixon, R.; Shih, S.-H.; Povinelli, L. A.

1995-01-01

Linearized Euler equations are used to simulate supersonic jet noise generation and propagation. Special attention is given to boundary treatment. The resulting solution is stable and nearly free from boundary reflections without the need for artificial dissipation, filtering, or a sponge layer. The computed solution is in good agreement with theory and observation and is much less CPU-intensive as compared to large-eddy simulations.

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

Science.gov (United States)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

Science.gov (United States)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Difference equations theory, applications and advanced topics

CERN Document Server

Mickens, Ronald E

2015-01-01

THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

Dynamic constitutional frameworks for DNA biomimetic recognition.

Science.gov (United States)

Catana, Romina; Barboiu, Mihail; Moleavin, Ioana; Clima, Lilia; Rotaru, Alexandru; Ursu, Elena-Laura; Pinteala, Mariana

2015-02-07

Linear and cross-linked dynamic constitutional frameworks generated from reversibly interacting linear PEG/core constituents and cationic sites shed light on the dominant coiling versus linear DNA binding behaviours, closer to the histone DNA binding wrapping mechanism.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

Science.gov (United States)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

International Nuclear Information System (INIS)

Hernandez-Walls, R; Martín-Atienza, B; Salinas-Matus, M; Castillo, J

2017-01-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations. (paper)

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

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Heinz Toparkus

2014-04-01

Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

Using constitutive equation gap method for identification of elastic material parameters: Technical insights and illustrations

KAUST Repository

Florentin, Éric

2011-08-09

The constitutive equation gap method (CEGM) is a well-known concept which, until now, has been used mainly for the verification of finite element simulations. Recently, CEGM-based functional has been proposed to identify local elastic parameters based on experimental full-field measurement. From a technical point of view, this approach requires to quickly describe a space of statically admissible stress fields. We present here the technical insights, inspired from previous works in verification, that leads to the construction of such a space. Then, the identification strategy is implemented and the obtained results are compared with the actual material parameters for numerically generated benchmarks. The quality of the identification technique is demonstrated that makes it a valuable tool for interactive design as a way to validate local material properties. © 2011 Springer-Verlag.

Occupational doses due to photoneutrons in medical linear accelerators rooms

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Soares, Alessandro Facure Neves de Salles

2006-04-01

Medical linear accelerators, with maximum photon energies above 10 MeV, are becoming of common use in Brazil. Although desirable in the therapeutic point of view, the increase in photon energies causes the generation of undesired neutrons, which are produced through nuclear reactions between photons and the high Z target nuclei of the materials that constitute the accelerator head. In this work, MCNP simulation was undertaken to examine the neutron equivalent doses around the accelerators head and at the entrance of medical linear accelerators treatment rooms, some of them licensed in Brazil by the National Regulatory Agency (CNEN). The simulated neutron dose equivalents varied between 2 e 26 μ Sv/Gy RX , and the results were compared with calculations performed with the use of some semi-empirical equations found in literature. It was found that the semi-empirical equations underestimate the simulated neutron doses in the majority of the cases, if compared to the simulated values, suggesting that these equations must be revised, due to the increasing number of high energy machines in the country. (author)

Linear analysis of neoclassical tearing mode based on the four-field reduced neoclassical MHD equation

International Nuclear Information System (INIS)

Furuya, Atsushi; Yagi, Masatoshi; Itoh, Sanae-I.

2003-01-01

The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if Δ' > 0. (author)

Asymptotically linear Schrodinger equation with zero on the boundary of the spectrum

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