复合材料特征值的高阶多尺度Rayleigh商校正

本文讨论了周期结构复合材料特征值的多尺度计算,提出了高阶多尺度Rayleigh商校正算法,并给出了收敛性分析. 最后,通过大量数值实验结果表明,新算法是有效且必要的.     

Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville equation can be decomposed via an expansion in terms of a smallness parameter , wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to O(²) for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker–Planck equation up to O(²). This approach has applications to a broad range of problems in the nanosciences.     

多尺度Retinex截断区间对图像质量影响的分析

研究了多尺度Retinex算法对曝光量不足的彩色图像增强处理的结果。改进型多尺度Retinex算法是使用多尺度Retinex增强后在亮度平均值附近以k倍标准差进行截取、拉伸。采用亮度与对比度乘积、图像信息熵等2个判据,实验结果表明在亮度平均值附近k=1倍标准差进行截取后再拉伸得到的图像其2个判据的值都较大,图像最佳。     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Domain decomposition methods in a geometrical multiscale domain using finite volume schemes

The heat equation is solved by using a finite volume discretization in a domain that consists of a two-dimensional central node and several one-dimensional outgoing branches. Several interface connection options to match the submodels set on the node and on the branches, with or without continuity, are looked at. For each of them, a monolithic scheme is defined, and existence and uniqueness of the solution is proved. New schemes are deduced, which are obtained through domain decomposition methods in the form of interface systems, with one or two unknowns per interface. A comparative systematic study is carried out from an algebraic and numerical point of view according to the interface conditions: Dirichlet, Neumann, or Robin. An efficient diagonal preconditioning is proposed.     

POD enriched boundary models and their optimal stabilisation

Modes obtained using the Proper Orthogonal Decomposition are used as boundary enrichment functions within a variational multiscale method for the stochastically forced Burgers equation. Initially, large increases in accuracy are obtained using the enrichment functions without stabilisation terms. Then, optimal coefficients for the stabilisation parameter τ of the unresolved scale model are calibrated using a goal‐oriented model‐constrained optimisation technique, resulting in further improvements. As both the determination of the enrichment functions and the optimisation of the coefficients requires high‐accuracy reference data, a scaling procedure is introduced to allow their use over range of conditions. Numerical experiments confirm that the scaling procedure is effective. Copyright © 2014 John Wiley & Sons, Ltd.     

The Nanoparticle Size Effect in Graphene Cutting: A “Pac‐Man” Mechanism

Metal‐nanoparticle‐catalyzed cutting is a promising way to produce graphene nanostructures with smooth and well‐aligned edges. Using a multiscale simulation approach, we unambiguously identified a “Pac‐Man” cutting mechanism, characterized by the metal nanoparticle “biting off” edge carbon atoms through a synergetic effect of multiple metal atoms. By comparing the reaction rates at different types of edge sites, we found that etching of an entire edge carbon row could be triggered by a single zigzag‐site etching event, which explains the puzzling linear dependence of the overall carbon‐atom etching rate on the nanoparticle surface area observed experimentally. With incorporation of the nanoparticle size effect, the mechanisms revealed herein open a new avenue to improve controllability in graphene cutting.     

A new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions

In this paper, we consider second order elliptic problems with rapidly oscillating coefficients. On basis of [O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992; Wen-ming He, Jun-zhi Cui, A pointwise estimate on the 1-order approximation of , IMA J. Appl. Math. 70 (2005) 241-269] we propose a new approximate method to solve these problems. Of course, we present its error estimate.     

Adaptive frame methods for elliptic operator equations: the steepest descent approach

Massimo Fornasier^¶ Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università "La Sapienza" in Roma, Via Antonio Scarpa, 16/B, I-00161 Roma, Italy Rob Stevenson^|| Department of Mathematics, Utrecht University, PO Box 80.010, NL-3508 TA Utrecht, The Netherlands ^{This paper is concerned with the development of adaptive numericalmethods for elliptic operator equations. We are particularlyinterested in discretization schemes based on wavelet frames.We show that by using three basic subroutines an implementable,convergent scheme can be derived, which, moreover, has optimalcomputational complexity. The scheme is based on adaptive steepestdescent iterations. We illustrate our findings by numericalresults for the computation of solutions of the Poisson equationwith limited Sobolev smoothness on intervals in 1D and L-shapeddomains in 2D.}     

A Multiscale Network Model for Simulating Moisture Transfer Properties of Porous Media

A multiscale network model is presented to model unsaturated moisture transfer in hygroscopic capillary-porous materials showing a broad pore-size distribution. Both capillary effects and water sorption phenomena, water vapour and liquid water transfer are considered. The multiscale approach is based on the concept of examining the porous space at different levels of magnification. The conservation of the water vapour permeability of dry material is used as scaling criterion to link the different pore scales. A macroscopic permeability is deduced from the permeabilities calculated at the different levels of magnification. Each level of magnification is modelled using an isotropic nonplanar 2D cross-squared network. The multiscale network simulates the enhancement of water vapour permeability due to capillary condensation, the hysteresis phenomenon between wetting and drying, and the steep increase of moisture permeability at the critical moisture saturation level. The calculated network permeabilities are compared with experimental data for calcium silicate and ceramic brick and a good agreement is observed.