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Characterization of the most probable transition paths of stochastic dynamical systems with stable Lévy noise

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arXiv 2018年

作者： Huang, Yuanfei Chao, Ying Yuan, Shenglan Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric α-stable Lévy motion (0 Copyright © 2018, The Authors. All rights r... 详细信息

关键词： Brownian movement

A parameter estimator based on Smoluchowski-Kramers approximation 1

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arXiv 2018年

作者： He, Ziying Duan, Jinqiao Cheng, Xiujun Center for Mathematical Sciences School of Mathematics and Statistics Hubei Key Laboratory for Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China Department of Applied Mathematics Illinois Institute of Technology ChicagoIL60616 United States

We devise a simplified parameter estimator for a second order stochastic differential equation by a first order system based on the Smoluchowski-Kramers approximation. We establish the consistency of the estimator by using Γ-convergence theory. We further illustrate our estimation method by an experimentally studied movement model of a colloidal particle immersed in water under conservative force and constant diffusion. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

Analysis of multivariate Gegenbauer approximation in the hypercube

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arXiv 2018年

作者： Wang, Haiyong Zhang, Lun School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematical Sciences Fudan University Shanghai200433 China

In this paper, we are concerned with multivariate Gegenbauer approximation of analytic functions defined in the d-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion are presented based on two different extensions of the Bernstein ellipse. We then establish an explicit error bound for the multivariate Gegenbauer approximation associated with an q ball index set in the uniform norm. As an application, we extend our arguments to obtain some new tight bounds for the coefficients of tensorized Legendre expansions in the context of polynomial approximation of parameterized *** Codes 41A10, 41A63, 41A25 Copyright © 2018, The Authors. All rights reserved.

关键词： Geometry

A spectral penalty method for two-sided fractional differential equations with general boundary conditions

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arXiv 2018年

作者： Wang, Nan Mao, Zhiping Huang, Chengming Karniadakis, George Em School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Division of Applied Mathematics Brown University ProvidenceRI02912 United States Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We consider spectral approximations to the conservative form of the two-sided Riemann-Liouville (R-L) and Caputo fractional differential equations (FDEs) with nonhomogeneous Dirichlet (fractional and classical, respectively) and Neumann (fractional) boundary conditions. In particular, we develop a spectral penalty method (SPM) by using the Jacobi poly-fractonomial approximation for the conservative R-L FDEs while using the polynomial approximation for the conservative Caputo FDEs. We establish the well-posedness of the corresponding weak problems and analyze sufficient conditions for the coercivity of the SPM for different types of fractional boundary value problems. This analysis allows us to estimate the proper values of the penalty parameters at boundary points. We present several numerical examples to verify the theory and demonstrate the high accuracy of SPM, both for stationary and time dependent FDEs. Moreover, we compare the results against a Petrov-Galerkin spectral tau method (PGS-τ, an extension of [23]) and demonstrate the superior accuracy of SPM for all cases considered. Copyright © 2018, The Authors. All rights reserved.

关键词： Constrained optimization

Modelling brain-wide neuronal morphology via rooted Cayley trees

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arXiv 2018年

作者： Lin, Congping Huang, Yuanfei Quan, Tingwei Zhang, Yiwei Center for Mathematical Sciences Huazhong University of Science and Technology Wuhan China Hubei Key Lab of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China Britton Chance Center for Biomedical Photonics Wuhan National Laboratory for Optoelectronics-Huazhong University of Science and Technology Wuhan China MoE Key Laboratory for Biomedical Photonics Collaborative Innovation Center for Biomedical Engineering School of Engineering Sciences Huazhong University of Science and Technology Wuhan China

Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide neuron topology. Based on estimated order-dependent branching probability from actual axonal and dendritic trees, our inhomogeneous model quantitatively captures a number of topological features including size and shape of both axons and dendrites. This sheds lights on a universal mechanism behind the topological formation of brain-wide axonal and dendritic trees. Copyright © 2018, The Authors. All rights reserved.

关键词： Brain

Two-scale sparse finite element approximations

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Science China Mathematics 2016年第4期59卷 789-808页

作者： LIU Fang ZHU JinWei School of Statistics and Mathematics Central University of Finance and Economics The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and ScientificEngineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general *** any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper *** applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.

关键词： combination discretization eigenvalue finite element postprocessing two-scale

A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem

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arXiv 2017年

作者： Diao, Rui Liu, Ya-Feng Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals {[ai,1, ai,2]}ni=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard. Then, we propose a new fully polynomial time approximation scheme (FPTAS) for solving the general ISSP problem. The time and space complexities of the proposed scheme are O (n max {1/ǫ, log n}) and O (n + 1/ǫ), respectively, where ǫ is the relative approximation error. To the best of our knowledge, the proposed scheme has almost the same time complexity but a significantly lower space complexity compared to the best known scheme. Both the correctness and efficiency of the proposed scheme are validated by numerical simulations. In particular, the proposed scheme successfully solves ISSP instances with n = 100, 000 and ǫ = 0.1% within one second. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity

Reshaping the Cathodic Catalyst Layer for Anion Exchange Membrane Fuel Cells: From Heterogeneous Catalysis to Homogeneous Catalysis

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Angewandte Chemie 2020年第8期133卷

作者： Dr. Rong Ren Xiaojiang Wang Dr. Hengquan Chen Dr. Hamish Andrew Miller Dr. Ihtasham Salam Prof. John Robert Varcoe Dr. Liang Wu Dr. Youhu Chen Prof. Hong-Gang Liao Dr. Ershuai Liu Dr. Francesco Bartoli Dr. Francesco Vizza Dr. Qingying Jia Dr. Qinggang He College of Chemical and Biological Engineering Zhejiang University Hangzhou Zhejiang 310027 China Institute of Chemistry of Organometallic Compounds ICCOM-CNR Polo Scientifico Area CNR 50019 Sesto Fiorentino Italy Department of Chemistry University of Surrey Guildford Surrey GU2 7XH UK School of Chemistry and Chemical Engineering and Key Laboratory of Scientific and Engineering Computing of Ministry of Education Shanghai Jiao Tong University Shanghai China State Key Laboratory of Physical Chemistry of Solid Surfaces College of Chemistry and Chemical Engineering Xiamen University Xiamen 361005 P. R. China Department of Chemistry and Chemical Biology Northeastern University Center for Renewable Energy Technology Boston MA 02115 USA Ningbo Research Institute Zhejiang University Ningbo Zhejiang 315100 China

In anion exchange membrane fuel cells, catalytic reactions occur at a well-defined three-phase interface, wherein conventional heterogeneous catalyst layer structures exacerbate problems, such as low catalyst utilization and limited mass transfer. We developed a structural engineering strategy to immobilize a molecular catalyst tetrakis(4-methoxyphenyl)porphyrin cobalt(II) (TMPPCo) on the side chains of an ionomer (polyfluorene, PF) to obtain a composite material (PF-TMPPCo), thereby achieving a homogeneous catalysis environment inside ion-flow channels, with greatly improved mass transfer and turnover frequency as a result of 100 % utilization of the catalyst molecules. The unique structure of the homogeneous catalysis system comprising interconnected nanoreactors exhibits advantages of low overpotential and high fuel-cell power density. This strategy of reshaping of the catalyst layer structure may serve as a new platform for applications of many molecular catalysts in fuel cells.

关键词： anion exchange membrane fuel cell cathodic catalyst layer homogeneous catalysis oxygen reduction reaction

Improvements in continuum modeling for biomolecular systems

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Chinese Physics B 2016年第1期25卷 333-338页

作者：乔瑜卢本卓 State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.

关键词： Poisson-Boltzmann equation Poisson-Nernst-Planck equations ionic size effects density func-tional theory