9 research outputs found
Discrete Models Of Coupled Dynamic Thermoelasticity For Stress-Temperature Formulations
No full textIn this article, the author studies the properties of discrete approximations for mathematical models of coupled thermoelasticity in the stress-temperature formulation. Since many applied problems deal with steep gradients of thermal fields, the main emphasis is given to the investigation of non-smooth solutions of non-stationary thermoelasticity. Convergence of operator-difference schemes on weak solutions of thermoelasticity is proved, and the dispersion analysis of models is performed. Error estimates and the results of computational experiments are presented. Key words: hyperbolic-parabolic models, operator-difference schemes for thermoelasticity problems, weak solutions, optimal error control. 1 Mixed Modes in Dynamics Described by Mathematical Models of Coupled Field Theory. In essence, any mathematical model describes a transformation of different types of energy. The recognition of this fact leads to an integral reformulation of differential models. On the one hand, such a r..
Application of ALTPACK to the Solution of Nonlinear PDEs
No full textIn this article the author applies the alternating-triangular method (ATM) to the solution of a number of 2D initial-boundary value problems that can be modelled by non-linear parabolic equations with a source term. Different types of non-linearities are considered and the procedure of finding approximate solutions is explained. The main features of the ALTPACK package are outlined and the results of computational experiments are presented. Key words: non-linear parabolic equations with source terms, alternating-triangular method. 1 Introduction. The application of mathematical models based on linear and nonlinear elliptic and parabolic equations is extremely wide [2, 6, 10, 15, 23, 9, 16]. It includes such areas as heat conduction, diffusion, electron and ion thermoconductivity, combustion and porous media modelling, chemical kinetics, semiconductor device modelling, biophysics etc. Such models differ from each other only by types of dependencies of coefficients and source terms. Fr..
A Hierarchy of Hyperbolic Macrodynamic Equations as a Model for Network Training
No full textThe author proposes mathematical models of hyperbolic type for training of neural networks, and its computational implementation using the Markov Chain approximation method. I. Introduction Let a mapping x t : R ! \Sigma be a sigmoidal function (activator) coupled to a neural network defined by its neurons x t ffi ¯ : T\Omega \Sigma\Omega UT ! R; (1) where ¯ : T\Omega \Sigma\Omega UT ! R will be referred to as the decision making function. In (1) we assume that the network is trained by a dynamic system with the state space \Sigma during time defined by a set T, and UT is a set of all permissible training strategies. Let H be a mapping XT ! R M ; and HT : N ! N is a T-computable function. Then H can be in principle arbitrarily well approximated by a network implementing HT due to the Godel numeration procedure. On the one hand if XT is a compact Borel set and H 2 L 1 (XT ) then for any arbitrary small ffl ? 0 there exists a feedforward neural network (FNN) ~ H such that jj..
Intelligent Structures and Coupling in Mathematical Models: Examples from Dynamic Electroelasticity
No full textMacroscopic mathematical models for intelligent structures are discussed. Due to a fundamental connection between densities of drift and diffusion currents and inter-dependency of relaxing particles such mathematical models acquire non-local features. This requires adequate mathematical tools in description of underlying physical and chemical processes. Some such tools are considered. I Introduction. In mathematical modelling of physical and chemical processes in dielectrics many traditional assumptions appear to be incompatible with new technologies. Such assumptions are often connected with the concept of relaxation time [3, 4]. Since macroscopic mathematical models can only approximately reflect processes in question, a continuous improvement of existing mathematical models is necessary to accommodate new knowledge about the material from which a specific device or structure consists of, as well as additional knowledge about geometrical properties of this device or structure. Uncer..
Dynamic System Evolution and Markov Chain Approximation
No full textIn this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of such models is treated as a decision making process with limited available information. The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space-time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work. Key words: decision making with limited information, optimal control theory, hyperbolicity of dynamic rules, generalized dynamic systems, Markov Chain approximation. 1 Introduction Many mathematical problems in information theory and optimal control related to dynamic system studies can be formulated in the following generic form. A decision..
Steklov's Operator Technique In Coupled Dynamic Thermoelasticity
No full textIn this paper we study non-smooth solutions of coupled non-stationary problems in thermoelasticity. Since the classical tools based on the Taylor 's expansion of unknown functions may not be appropriate in obtaining a measure of quality for numerical methods, we apply the averaging Steklov operators and the technique based on the Bramble-Hilbert lemma in order to establish the convergence result for a class of generalized solutions. Effective explicit numerical schemes and error estimates are presented. Key words: Coupled field theory, dynamic thermoelasticity, Steklov's averaging technique, a-priori and a-posteriori estimates, Sobolev spaces. 1 Coupled Field Theory and Hyperbolic Modes in Dynamics. All real processes, dynamic systems and phenomena describe a transformation of different types of energy. This implies that in general, mathematical models applied to them should have integral rather than differential features. However, when engaged in mathematical modelling, we can ofte..
The Stability Condition and Energy Estimate for Non-Stationary Problems of Coupled Electroelasticity
No full textIn this paper a coupled problem of dynamic electroelasticity is investigated using the variational approach and the concept of generalized solutions. We derive a numerical procedure directly from the definition of the generalized solution of the problem. We prove the convergence of the numerical scheme (with the second order in spacetime) to the solution of the original problem from a class of generalized solutions. The stability condition is obtained from an energy estimate. It is shown that such a condition is the Courant-Friederichs-Lewy-type stability condition, being dependent on the velocity of mixed electro-elastic waves. Coupling effects are discussed with a numerical example. Key words: generalized solutions, coupling, mixed electroelastic waves, convergence and stability. 1. INTRODUCTION. Modern applications of the coupled theory of dynamic electroelasticity include situations where solutions of the underlying problems do not have to be "smooth" in a classical sense. In many ..
Closed-form expressions for computing flexoelectric coefficients in textured polycrystalline dielectrics
No full textThe volume average of the constituting properties of a textured polycrystalline aggregate (the Voigt average) provides a simple way to estimate the effective properties of such an aggregate in terms of its crystallographic symmetry, texture symmetry, and the properties of the constituting crystallites. Despite the interest in estimate or characterizing flexoelectric properties, few studies have addressed the problem of finding effective flexoelectric properties from the continuum phases of the constituents. Instead, most of them focus on single-crystals at the atomic level. This study provides, for the first time, closed-form expressions that allow the direct flexoelectric coefficients to be computed for textured polycrystalline dielectrics. Crystallites can belong to any class of cubic symmetry or to the tetragonal TI Laue group, while no restriction is imposed on texture symmetry. These expressions are reduced to very simple ones when cubic crystallites with fiber texture are considered. The proposed formulation provides information on the matrix structure of the homogenized material related to the crystallographic symmetry and texture. We close with some illustrative examples
Towards an evaluation of schema theory with reference to ESL/EFL reading comprehension.
No full textSIGLEAvailable from British Library Document Supply Centre- DSC:D93524 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
