Multiscale Model. Simul.最新文献_第8页

Derivation and Closure of Baer and Nunziato Type Multiphase Models by Averaging a Simple Stochastic Model Baer和Nunziato型多相模型的简单随机平均推导和闭合

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/19M1306609

V. Perrier, Enrique Gutiérrez

引用次数: 4

Strain and Defects in Oblique Stripe Growth 斜条纹生长中的应变和缺陷

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/21m1397210

Ke-Ming Chen, Zachary Deiman, Ryan N. Goh, S. Jankovic, A. Scheel

引用次数: 3

On Continuum Approximations of Discrete-State Markov Processes of Large System Size 大系统规模离散状态马尔可夫过程的连续统逼近

Multiscale Model. Simul. Pub Date : 2021-01-01 DOI: 10.1137/20M1332293

D. Lunz

{"title":"On Continuum Approximations of Discrete-State Markov Processes of Large System Size","authors":"D. Lunz","doi":"10.1137/20M1332293","DOIUrl":"https://doi.org/10.1137/20M1332293","url":null,"abstract":"Discrete-state continuous-time Markov processes are an important class of models employed broadly across the sciences. When the system size becomes large, standard approaches can become intractable to exact solution and numerical simulation. Approximations posed on a continuous state space are often more tractable and are presumed to converge in the limit as the system size tends to infinity. For example, an expansion of the master equation truncated at second order yields the Fokker--Planck equation, a widely used continuum approximation equipped with an underlying process of continuous state. Surprisingly, in [Doering textit{et. al.} Multiscale Model. Sim. 2005 3:2, p.283--299] it is shown that the Fokker--Planck approximation may exhibit exponentially large errors, even in the infinite system-size limit. Crucially, the source of this inaccuracy has not been addressed. In this paper, we focus on the family of continuous-state approximations obtained by arbitrary-order truncations. We uncover how the exponentially large error stems from the truncation by quantifying the rapid error decay with increasing truncation order. Furthermore, we explain why this discrepancy only comes to light in a subset of problems. The approximations produced by finite truncation beyond second order lack underlying stochastic processes. Nevertheless, they retain valuable information that explains the previously observed discrepancy by bridging the gap between the continuous and discrete processes. The insight conferred by this broader notion of ``continuum approximation'', where we do not require an underlying stochastic process, prompts us to revisit previously expressed doubts regarding continuum approximations. In establishing the utility of higher-order truncations, this approach also contributes to the extensive discussion in the literature regarding the second-order truncation: while recognising the appealing features of an associated stochastic process, in certain cases it may be advantageous to dispense of the process in exchange for the increased approximation accuracy guaranteed by higher-order truncations.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126290427","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

An Adaptive Planewave Method for Electronic Structure Calculations 电子结构计算的自适应平面波法

Multiscale Model. Simul. Pub Date : 2020-12-29 DOI: 10.1137/21m1396241

Beilei Liu, Huajie Chen, Geneviève Dusson, Jun Fang, Xingyu Gao

引用次数: 2

Gradient Flow Based Kohn-Sham Density Functional Theory Model 基于梯度流的Kohn-Sham密度泛函理论模型

Multiscale Model. Simul. Pub Date : 2020-12-17 DOI: 10.1137/19m1276170

X. Dai, Qiao Wang, Aihui Zhou

引用次数: 5

A Low-Rank Approximated Multiscale Method for Pdes With Random Coefficients 带随机系数偏微分方程的低秩近似多尺度方法

Multiscale Model. Simul. Pub Date : 2020-12-08 DOI: 10.1137/19m1288565

Na Ou, G. Lin, Lijian Jiang

引用次数: 5

Modeling and Computation of Kubo Conductivity for Two-Dimensional Incommensurate Bilayers 二维不相称双层Kubo电导率的建模与计算

Multiscale Model. Simul. Pub Date : 2020-12-03 DOI: 10.1137/19m1273499

S. Etter, Daniel Massatt, M. Luskin, C. Ortner

引用次数: 2

Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks 宽带蝴蝶网络:通过多频神经网络实现稳定高效的反演

Multiscale Model. Simul. Pub Date : 2020-11-24 DOI: 10.1137/20m1383276

Matthew Li, L. Demanet, Leonardo Zepeda-N'unez

引用次数: 2

Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation 基于瞬子展开的低温自由能近似最优控制

Multiscale Model. Simul. Pub Date : 2020-11-22 DOI: 10.1137/20m1385809

Gr'egoire Ferr'e, T. Grafke

{"title":"Approximate Optimal Controls via Instanton Expansion for Low Temperature Free Energy Computation","authors":"Gr'egoire Ferr'e, T. Grafke","doi":"10.1137/20m1385809","DOIUrl":"https://doi.org/10.1137/20m1385809","url":null,"abstract":"The computation of free energies is a common issue in statistical physics. A natural technique to compute such high dimensional integrals is to resort to Monte Carlo simulations. However these techniques generally suffer from a high variance in the low temperature regime, because the expectation is dominated by high values corresponding to rare system trajectories. A standard way to reduce the variance of the estimator is to modify the drift of the dynamics with a control enhancing the probability of rare event, leading to so-called importance sampling estimators. In theory, the optimal control leads to a zero-variance estimator; it is however defined implicitly and computing it is of the same difficulty as the original problem. We propose here a general strategy to build approximate optimal controls, with the first goal to reduce the variance of free energy Monte Carlo estimators. Our construction builds upon low noise asymptotics by expanding the optimal control around the instanton, which is the path describing most likely fluctuations at low temperature. This technique not only helps reducing variance, but it is also interesting as a theoretical tool since it differs from usual small temperature expansions (WKB ansatz). As a complementary consequence of our expansion, we provide a perturbative formula for computing the free energy in the small temperature regime, which refines the now standard Freidlin-Wentzell asymptotics. We compute this expansion explicitly for lower orders, and explain how our strategy can be extended to an arbitrary order of accuracy. We support our findings with illustrative numerical examples.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130596781","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: 6

Asymptotic Analysis of Target Fluxes in the Three-Dimensional Narrow Capture Problem 三维窄捕获问题中目标通量的渐近分析

Multiscale Model. Simul. Pub Date : 2020-11-15 DOI: 10.1137/20M1380326

P. Bressloff

{"title":"Asymptotic Analysis of Target Fluxes in the Three-Dimensional Narrow Capture Problem","authors":"P. Bressloff","doi":"10.1137/20M1380326","DOIUrl":"https://doi.org/10.1137/20M1380326","url":null,"abstract":"We develop an asymptotic analysis of target fluxes in the three-dimensional (3D) narrow capture problem. The latter concerns a diffusive search process in which the targets are much smaller than the size of the search domain. The small target assumption allows us to use matched asymptotic expansions and Green's functions to solve the diffusion equation in Laplace space. In particular, we derive an asymptotic expansion of the Laplace transformed flux into each target in powers of the non-dimensionalized target size $epsilon$. One major advantage of working directly with fluxes is that one can generate statistical quantities such as splitting probabilities and conditional first passage time moments without having to solve a separate boundary value problem in each case. However, in order to derive asymptotic expansions of these quantities, it is necessary to eliminate Green's function singularities that arise in the limit $srightarrow 0$, where $s$ is the Laplace variable. We achieve this by considering a triple expansion in $epsilon$, $s$ and $Lambdasim epsilon /s$. This allows us to perform partial summations over infinite power series in $Lambda$, which leads to multiplicative factors of the form $Lambda^n/(1+Lambda)^n $. Since $Lambda^n/(1+Lambda)^n rightarrow 1$ as $srightarrow 0$, the singularities in $s$ are eliminated. We then show how corresponding asymptotic expansions of the splitting probabilities and conditional MFPTs can be derived in the small-$s$ limit. Finally, we illustrate the theory by considering a pair of targets in a spherical search domain, for which the Green's functions can be calculated explicitly.","PeriodicalId":313703,"journal":{"name":"Multiscale Model. Simul.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130840785","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: 13