Applied mathematics research express : AMRX最新文献_第5页

General Fractal Conservation Laws Arising from a Model of Detonations in Gases 由气体爆轰模型引起的一般分形守恒定律

Applied mathematics research express : AMRX Pub Date : 2011-10-25 DOI: 10.1093/AMRX/ABR015

M. Alfaro, J. Droniou

引用次数: 10

Resonant Uniqueness of Radial Semiclassical Schrödinger Operators 径向半经典Schrödinger算子的共振唯一性

Applied mathematics research express : AMRX Pub Date : 2011-07-05 DOI: 10.1093/amrx/abr017

K. Datchev, Hamid Hezari

引用次数: 6

Asymptotic Expansion of the Homogenized Matrix in Two Weakly Stochastic Homogenization Settings 渐近展开的均质两弱矩阵随机均匀化设置

Applied mathematics research express : AMRX Pub Date : 2011-02-18 DOI: 10.1093/AMRX/ABR011

Ronan Costaouec

{"title":"Asymptotic Expansion of the Homogenized Matrix in Two Weakly Stochastic Homogenization Settings","authors":"Ronan Costaouec","doi":"10.1093/AMRX/ABR011","DOIUrl":"https://doi.org/10.1093/AMRX/ABR011","url":null,"abstract":"This article studies some numerical approximations of the homogenized matrix for stochastic linear elliptic partial differential equations in divergence form. We focus on the case when the underlying random field is a small perturbation of a reference periodic tensor. The size of such a perturbation is encoded by a real parameter eta. In this case, it has already been theoretically shown in the literature that the exact homogenized matrix possesses an expansion in powers of the parameter eta for both models considered in this article, the coefficients of which are deterministic. In practice, one cannot manipulate the exact terms of such an expansion. All objects are subjected to a discretization approach. Thus we need to derive a similar expansion for the approximated random homogenized matrix. In contrast to the expansion of the exact homogenized matrix, the expansion of the approximated homogenized matrix contains intrinsically random coefficients. In particular, the second order term is random in nature. The purpose of this work is to derive and study this expansion in function of the parameters of the approximation procedure (size of the truncated computational domain used, meshsize of the finite elements approximation).","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"63 1","pages":"76-104"},"PeriodicalIF":0.0,"publicationDate":"2011-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83163669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

DNA Unzipping via Stopped Birth and Death Processes with Unknown Transition Probabilities DNA解压缩通过停止出生和死亡过程与未知的过渡概率

Applied mathematics research express : AMRX Pub Date : 2011-01-03 DOI: 10.1093/AMRX/ABS008

P. Andreoletti, R. Diel

引用次数: 1

Convergence to Homogenized or Stochastic Partial Differential Equations 均匀化或随机偏微分方程的收敛性

Applied mathematics research express : AMRX Pub Date : 2011-01-01 DOI: 10.1093/AMRX/ABR006

G. Bal

{"title":"Convergence to Homogenized or Stochastic Partial Differential Equations","authors":"G. Bal","doi":"10.1093/AMRX/ABR006","DOIUrl":"https://doi.org/10.1093/AMRX/ABR006","url":null,"abstract":"We consider the behavior of solutions to parabolic equations with large, highly oscillatory, possibly time dependent, random potential with Gaussian statistics. The Gaussian potential fluctuates in the spatial variables and possibly in the temporal variable. We seek the limit of the solution to the parabolic equation as the scale ε at which the random medium oscillates converges to zero. Depending on spatial dimension and on the decorrelation properties of the Gaussian potential, we show that the solution converges, as ε tends to 0, either to the solution of a deterministic, homogenized, equation with negative effective medium potential or to the solution of a stochastic partial differential equation with multiplicative noise that should be interpreted as a Stratonovich integral. The transition between the deterministic and stochastic limits depends on the elliptic operator in the parabolic equation and on the decorrelation properties of the random potential. In the setting of convergence to a deterministic solution, we characterize the random corrector, which asymptotically captures the stochasticity in the solution. Such models can be used to calibrate upscaling schemes that aim at understanding the influence of microscopic structures in macroscopic calculations.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"270 1","pages":"215-241"},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83714094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14

Efficient Boundary Tracking Through Sampling 通过采样的有效边界跟踪

Applied mathematics research express : AMRX Pub Date : 2011-01-01 DOI: 10.1093/AMRX/ABR002

Alex Chen, Todd Wittman, A. Tartakovsky, A. Bertozzi

引用次数: 9

Radial Spreading of a Surfactant on a Thin Liquid Film 表面活性剂在液体薄膜上的径向扩散

Applied mathematics research express : AMRX Pub Date : 2010-09-13 DOI: 10.1093/AMRX/ABQ015

E. Peterson, M. Shearer

引用次数: 16

Annular Bose-Einstein Condensates in the Lowest Landau Level 环状玻色-爱因斯坦凝聚在最低朗道能级

Applied mathematics research express : AMRX Pub Date : 2010-09-10 DOI: 10.1093/AMRX/ABQ020

N. Rougerie

引用次数: 7

Phase Transitions in a Relaxation Model of Mixed Type with Periodic Boundary Condition 具有周期边界条件的混合型松弛模型中的相变

Applied mathematics research express : AMRX Pub Date : 2010-07-09 DOI: 10.1093/AMRX/ABM006

M. Gander, Ming Mei, E. Schmidt

{"title":"Phase Transitions in a Relaxation Model of Mixed Type with Periodic Boundary Condition","authors":"M. Gander, Ming Mei, E. Schmidt","doi":"10.1093/AMRX/ABM006","DOIUrl":"https://doi.org/10.1093/AMRX/ABM006","url":null,"abstract":"We study the asymptotic behavior of solutions for a 2×2 relaxation model of mixed type with periodic initial and boundary conditions. We prove that the asymptotic behavior of the solutions and their phase transitions are dependent on the location of the initial data and the size of the viscosity. If the average of the initial data is in the hyperbolic region and the initial data does not deviate too much from its average,we prove that there exists a unique global solution and that it converges time-asymptotically to the average in the same hyperbolic region. No phase transition occurs after initial oscillations. If the average of the initial data is in the elliptic region and the initial data does not deviate too much from its average, and in addition if the viscosity is big, then the solution converges to the average in the same elliptic region, and does not exhibit phase transitions after initial oscillations. If, however, the viscosity is small, numerical evidence indicates that the solution oscillates across the hyperbolic and elliptic regions for all time, exhibiting phase transitions. In this case, we conjecture that the solution converges to an oscillatory standing wave (steady-state solution).","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"6 1","pages":"1-34"},"PeriodicalIF":0.0,"publicationDate":"2010-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84919779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls 一类线性动力学有界微分对策的完全解

Applied mathematics research express : AMRX Pub Date : 2010-07-09 DOI: 10.1093/AMRX/ABM012

V. Glizer, V. Turetsky

引用次数: 16