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backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay

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Science China Mathematics 2019年第3期62卷 597-616页

作者： Chengjian Zhang Ying Xie School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology

In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.

关键词： nonlinear hybrid stochastic differential equations time-variable delay backward Euler-Maruyama method strong convergence almost surely exponential stability

Compact finite difference schemes for the backward fractional Feynman–Kac equation with fractional substantial derivative

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Chinese Physics B 2019年第10期28卷 226-236页

作者： Jiahui Hu Jungang Wang Yufeng Nie Yanwei Luo Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710129China College of Science Henan University of TechnologyZhengzhou 450001China

The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.

关键词： backward fractional Feynman-Kac equation fractional substantial derivative compact finite difference scheme numerical inversion of Laplace transforms

Non-equilibrium turbulent phenomena in the ?ow over a backward-facing ramp

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Applied Mathematics and Mechanics(English Edition) 2019年第2期40卷 215-236页

作者： Le FANG Hongkai ZHAO Weidan NI Jian FANG Lipeng LU Laboratoire de Mecanique Physique (LMP) Ecole Centrale de P'ekinBeihang University National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics School of Energy and Power Engineering Beihang University Scientific Computing Department Science and Technology Facilities Council (STFC)Daresbury Laboratory

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid turbulence, turbulent wakes, and homogeneous isotropic turbulence(HIT). The non-equilibrium turbulence in non-canonical flows, however, has rarely been studied due to the complexity of the flows. In the present contribution, a directnumerical simulation(DNS) database of a turbulent flow is analyzed over a backwardfacing ramp, the flow near the boundary is demonstrated, and the non-equilibrium turbulent properties of the flow in the wake of the ramp are presented by using the characteristic parameters such as the dissipation coefficient C and the skewness of longitudinal velocity gradient Sk, but with opposite underlying turbulent energy transfer properties. The equation of Lagrangian velocity gradient correlation is examined, and the results show that non-equilibrium turbulence is the result of phase de-coherence phenomena, which is not taken into account in the modeling of non-equilibrium turbulence. These findings are expected to inspire deeper investigation of different non-equilibrium turbulence phenomena in different flow conditions and the improvement of turbulence modeling.

关键词： non-equilibrium turbulence backward ramp direct numerical simulation(DNS)

backward SCATTERING OF POLARIZED γ+e → H+e REACTION—A SUGGESTION FOR SEARCHING HIGGS BOSONS IN WEINBERG-SALAM MODEL

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Chinese Physics Letters 1984年第1期1卷 39-42页

作者： PENG Hong-an LI Jia-rong QIU Zhong-ping Peking University Hua-Zhong Teachers College

Using the extremely sharp peak of backward cross section for polarized γ+e → H+e processes one could hopefully detect Higgs bosons in W-S model.

关键词： model. backward polarized

A Novel Spacetime Collocation Meshless Method for Solving Two- Dimensional backward Heat Conduction Problems

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Computer Modeling in Engineering & Sciences 2019年第1期118卷 229-252页

作者： Chihyu Liu Chengyu Ku Jingen Xiao Weichung Yeih Department of Harbor and River Engineering National Taiwan Ocean UniversityKeelung20224Taiwan Center of Excellence for Ocean Engineering National Taiwan Ocean UniversityKeelung20224Taiwan.

In this article,a meshless method using the spacetime collocation for solving the two-dimensional backward heat conduction problem(BHCP)is *** spacetime collocation meshless method(SCMM)is to derive the general solutions as the basis functions for the two-dimensional transient heat equation using the separation of *** solutions of the heat conduction problem are expressed as a series using the addition *** the basis functions are the general solutions of the governing equation,the boundary points may be collocated on the spacetime boundary of the *** proposed method is verified by conducting several heat conduction *** also carry out numerical applications to compare the SCMM with other meshless *** results show that the SCMM is accurate and ***,it is found that the recovered boundary data on inaccessible boundary can be obtained with high accuracy even though the over specified data are provided only at a 1/6 portion of the spacetime boundary.

关键词： Spacetime collocation meshless method backward heat conduction problem basis functions.

Rheological behavior,microstructure and hardness of A356 aluminum alloy in semisolid state using backward extrusion process

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中国有色金属学会会刊：英文版 2010年第S3期20卷 906-910页

作者： S.A.SADOUGH M.R.RAHMANI V.POUYAFAR Center of Excellence in Termoelasticity Amir Kabir University of Technology Department of Mechanical Engineering Islamic Azad University Science and Research Branch

The influence of temperature on the flow behavior and rheological characteristics of an A356 alloy in the semi-solid state was investigated using backward extrusion *** were performed at 5 temperatures and 4 different wall *** were determined using the force-displacement graphs obtained form back extrusion *** observed experimentally,at a constant temperature,the increase of shear rate results in the decrease of alloy viscosity *** the temperature increases the liquid fraction hence reduces the semi-solid alloy *** and image analyses show that,because of low forming speed,liquid has time to escape from solid phase forward the sample *** condition is the main reason for the segregation phenomenon seen in the base and *** hardness test on samples reveals that the hardness increases with the decrease of temperature and wall thickness.

关键词： aluminum alloy A356 backward extrusion semisolid forming rheology

Partially-Observed Maximum Principle for backward Stochastic Differential Delay Equations

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1524-1526页

作者： Shuang Wu Department of Applied Mathematics China University of PetroleumQingdao 266580China

Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is *** adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional *** backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed *** corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].

关键词： stochastic backward convex

Distribution of displacement in backward spinning of tube

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Chinese Science Bulletin 1997年第11期42卷 962-965页

作者： Li, KZ Lu, Y School of Materials Science and Engineering Harbin Institute of Technology Harbin China

TUBE spinning technology is one of the effective methods of manufacturing the large diameterthin-wall cylindrical workpieces *** has been widely used in practical production *** the tube spinning process is complicate... 详细信息

关键词： backward spinning displacement field cylindrical workpieces FEM elasto-plasticity.

In-plane bistatic backward scattering from seabottom with randomly inhomogeneous sediment and rough interface

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Science China(Physics,Mechanics & Astronomy) 2004年第6期47卷 702-716页

作者： PENG Zhaohui1,,ZHOU Jixun1,& ZHANG Renhe1 2 2 1.Institute of Acoustics,Chinese Academy of Sciences,Beijing 100080,China 2.School of Mechanical Engineering,Georgia Institute of Technology,Atlanta,GA 30332,USA Institute of Acoustics Chinese Academy of Sciences Beijing China School of Mechanical Engineering Georgia Institute of Technology Atlanta USA

The in-plane bistatic backward scattering caused by seabottom with random inhomogeneities and rough interface is studied. This work combines the ray tube integral method of Ivakin et al. and the complex-ray/steepest descent method of Hines. For a given incident grazing angle, the theoretical expression can easily be used to calculate scattering strength for different backward scattering angles. (This is essential for modeling shallow water reverberation by the normal mode approach.) The model is tested against published scattering measurements. The frequency/angle dependence of backward scattering and effects of volume inhomogeneity parameters on backward scattering are also discussed.

关键词： in-plane bistatic backward scattering, inhomogeneous sediment, rough interface.