Papers by Keyword: Fokker-Planck Equation

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Authors: H.Q. Nguyen, C.D. Tran, N. Pham-Sy, T. Tran-Cong
Abstract: This paper presents a numerical method for the Fokker-Planck Equation (FPE) based on mesoscopic modelling of dilute polymer solutions using Radial Basis Function (RBF) approaches. The stress is determined by the solution of a FPE while the velocity field is locally calculated via the solution of conservation Differential Equations (DEs) [1,2]. The FPE and PDEs are approximated separately by two different Integrated RBF methods. The time implicit discretisation of both FPE and PDEs is carried out using collocation methods where the high order RBF approximants improve significantly the accuracy of the numerical solutions and the convergence rate. As an illustration of the method, the time evolution of a start-up flow is studied for the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model.
Authors: Andriy Gusak, A.O. Bogatyrev, A.O. Kovalchuk
Authors: Yuri Estrin, László S. Tóth, Yves Bréchet, Hyoung Seop Kim
Abstract: A model describing the evolution of the misorientation angle between dislocation cells with plastic strain is proposed. The model is applied to the case of equal channel angular pressing (ECAP) of copper. In a basic version of the model, the evolution of the average misorientation angle is traced. A way of handling the evolution of the misorientation angle distribution function using a probabilistic description is also outlined.
Authors: Katayun Barmak, Eva Eggeling, M. Emelianenko, Y. Epshteyn, David Kinderlehrer, R. Sharp, Shlomo Ta'asan
Abstract: Mesoscale experiment and simulation permit harvesting information about both geometric featuresand texture in material microstructures. The grain boundary character distribution (GBCD) is an em-pirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misori-entation and grain boundary normal. During the growth process, an initially random texture distribu-tion reaches a steady state that is strongly correlated to the interfacial energy density [9]. In simulation,it is found that if the given energy depends only on lattice misorientation, then the steady state GBCDand the energy are related by a Boltzmann distribution. This is among the simplest non-random dis-tributions, corresponding to independent trials with respect to the energy. Why does such a simpledistribution arise from such a complex system?.
Authors: Andriy Gusak, Yu.A. Lyashenko, A.O. Bogatyrev
Authors: Jing Bo He, Sheng Liang Hu
Abstract: In this paper stochastic resonance was studied in radar driven by noise frequency modulation signal. According to the intrinsic relations between the stochastic differential and the radar jamming signal processing, the stochastic calculus was used in the radar jamming signal processing in this paper. The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given.
Authors: A.O. Bogatyrev, Andriy Gusak, Yu.A. Lyashenko
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