Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions

We study a nonlinear pseudodifferential equation describing the dynamics of dislocations in crystals. The long time asymptotics of solutions is described by the self-similar profiles.     

Diffusion Dynamics of Cux Cluster on Cu(111) Surface

利用分子动力学与修正分析型嵌入原子模型研究了从200K至800 K范围内,Cux (1·x·8)小团簇在(111)面的自扩散动力学行为,计算了Cu小团簇的扩散系数与激活能. 计算结果表明,密排的Cu7团簇的激活能最高,其扩散前因子比单个吸附原子的高3个数量级,这与其他类似金属的实验结果一致. 另外,还定量讨论了薄膜生长与团簇扩散的关系.     

金属团簇在单晶表面的稳定性和扩散行为的Monte Carlo研究

采用MonteCarlo方法,研究了正二十面体结构的Cu、Ni、Pd和Pt等金属团簇在Pd(001)表面的稳定性和扩散行为.研究表明,载体对负载型金属团簇的稳定性和扩散性质有明显的影响.由于载体表面和金属团簇的振动偶合,金属团簇结构变化的温度要低于自由团簇的结构转化温度.负载型金属团簇的稳定性不仅取决于团簇内部原子之间的相互作用而且取决于团簇与载体之间的相互作用.对金属团簇扩散的研究表明,金属团簇的扩散常数与单金属原子的扩散常数相差不大,通过比较金属团簇的结构变化温度和扩散常数发现,团簇的稳定性和扩散行为有密切的联系.     

Surface Distribution of Topological Defects on Axisymmetric

We propose a general method of deterrnining the distribution of topological defects on axisymmetric surface, and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface： four defects charged with 1/2, two defects charged with ＋1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.     

Distribution of Topological Defects on Axisymmetric Surface

We propose a general method of determining the distribution of topological defects on axisymmetric surface,and study the distribution of topological defects on biconcave-discoid surface, which is the geometric configuration of red blood cell. There are three most possible cases of the distribution of the topological defects on the biconcave surface:four defects charged with 1/2, two defects charged with 1, or one defect charged with 2. For the four defect charged with 1/2, they sit at the vertices of a square imbedded in the equator of biconcave surface.     

On the Stability of Self-Similar Solutions to Nonlinear Wave Equations

We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.     

轴对称钝体后湍流扩散燃烧的PDF模拟

在无结构网格中,对轴对称钝体驻定的湍流扩散火焰进行数值模拟．采用有限容积(FV)／Monte Carlo(MC)混合算法求解湍流燃烧问题的混合算法．Monte Carlo法求解脉动速度一标量．频率的联合概率密度函数方程,有限容积法求解平均质量、动量和能量方程．求解的两组方程是相容的,合理的耦合方式可以减少统计偏差,计算精度和效率显著优于单独的颗粒方法．文中对化学反应采用层流火焰面模型,并将数值计算结果与实验结果作了比较和分析．     

Axisymmetric Stagnation-Point Flow of Nanofluid over a Stretching Surface

This paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet. Nanofluid model exhibiting Brownian motion and thermophoresis is used. Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method (HAM). Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement. Velocity, temperature and mass fraction are displayed for various values of parameters. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are computed. It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid. It is found that the convective heat transfer coefficient (Nusselt number) is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.     

Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact

The axisymmetric time-fractional diffusion equation with mass absorption is studied in a circle under the time-harmonic Dirichlet boundary condition. The Caputo derivative of the order 0<α≤2 is used. The investigated equation can be considered as the time-fractional generalization of the bioheat equation and the Klein–Gordon equation. Different formulations of the problem for integer values of the time-derivatives α=1 and α=2 are also discussed. The integral transform technique is employed. The outcomes of numerical calculations are illustrated graphically for different values of the parameters.     

Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion

In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics.     

Self-Similar Cosmological model: Introduction and empirical tests

After calling attention to the empirical and theoretical motivations for considering the hypothesis of a self-similar cosmos, the basic concepts and scaling rules of the Self-Similar Cosmological Model are presented. The results of a diverse set of 20 falsification tests are then shown to provide strong quantitative support for the uniqueness and broad applicability of the self-similar scale transformation equations, which successfully correlate physical parameters of atomic, stellar, and galactic scale systems. Possible implications of these results are discussed.     

Outflow Probability for Drift–Diffusion Dynamics

The proposed explanations are provided for the one–dimensional diffusion process with constant drift by using forward Fokker–Planck technique. We present the exact calculations and numerical evaluation to get the outflow probability in a finite interval, i.e. first passage time probability density distribution taking into account reflecting boundary on left hand side and absorbing border on right hand side. This quantity is calculated from balance equation which follows from conservation of probability. At first, the initial-boundary-value problem is solved analytically in terms of eigenfunction expansion which relates to Sturm–Liouville analysis. The results are obtained for all possible values of drift (positive, zero, negative). As application we get the cumulative breakdown probability which is used in theory of traffic flow. PACS numbers: 02.60.Lj, 02.50.–r, 02.50.Fz, 02.50.Ga     

Letter: Self-Similar Bianchi Type VIII and IX Models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admits a four dimensional group of homotheties is given.     

Diffusion on a Curved Surface Coupled to Diffusion in the Volume: Application to Cell Biology

An algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume, a problem often arising in cell biology. It applies to pixilated surfaces obtained from experimental images and performs at low computational cost. In the method, the Laplace-Beltrami operator is approximated locally by the Laplacian on the tangential plane and then a finite volume discretization scheme based on a Voronoi decomposition is applied. Convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2. The method is applied to a cell-biological problem where a signaling molecule, G-protein Rac, cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior. Simulations on realistic cell geometry are performed to validate, and determine the accuracy of, a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching. The method is implemented within the Virtual Cell computational framework freely accessible at www.vcell.org.     

Modeling of Surface Diffusion in hcp Zr and Ti

The statics and dynamics of vacancies and adatoms on different surface orientations in two hcp materials are studied by using static relaxation techniques and many-body potentials. Formation and migration energies and entropies as well as attempt frequencies are evaluated and used in the random walk approach to obtain correlation factors and diffusivities. It is found that the main features of surface diffusion are dominated by jumps on and between a few atomic layers, so that a consistent comparison between the two mechanisms is feasible. The activation energies and the diffusivities for different environments, namely, bulk Q _b, D _b, symmetric grain boundaries Q _gb, D _gb, and surfaces, Q _s, D _s, calculated using the same simulation technique and interatomic potentials, fulfil the expected relationships Q _s < Q _gb < Q _b and D _s > D _gb > D _b. It is also found that generally adatoms are faster surface diffusers than vacancies.     

Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion

The stability of asymptotic profiles of solutions to the Cauchy–Dirichlet problem for fast diffusion equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy. It is noteworthy that this result can cover non-isolated profiles, e.g., those for thin annular domain cases. The method of proof is based on the ?ojasiewicz–Simon inequality, which is usually used to prove the convergence of solutions to prescribed limits, as well as a uniform extinction estimate for solutions to FDE. Besides, local minimizers of an energy functional associated with this issue are characterized. Furthermore, the instability of positive radial asymptotic profiles in thin annular domains is also proved by applying the ?ojasiewicz–Simon inequality in a different way.     

Dynamics and Stability of a Weak Detonation Wave

One dimensional weak detonation waves of a basic reactive shock wave model are proved to be nonlinearly stable, i.e. initially perturbed waves tend asymptotically to translated weak detonation waves. This model system was derived as the low Mach number limit of the one component reactive Navier-Stokes equations by Majda and Roytburd [SIAM J. Sci. Stat. Comput. 43, 1086–1118 (1983)], and its weak detonation waves have been numerically observed as stable. The analysis shows in particular the key role of the new nonlinear dynamics of the position of the shock wave, The shock translation solves a nonlinear integral equation, obtained by Green's function techniques, and its solution is estimated by observing that the kernel can be split into a dominating convolution operator and a remainder. The inverse operator of the convolution and detailed properties of the traveling wave reduce, by monotonicity, the remainder to a small L ₁ perturbation. Received: 17 August 1998 / Accepted: 13 November 1998     

Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.