An approach to control the spurious currents in a multiphase lattice Boltzmann method and to improve the implementation of initial condition

Multiphase lattice Boltzmann methods are known to generate spurious or parasitic currents at the fluid–fluid interfaces. This nonphysical phenomenon has to be avoided, or at least controlled, in order to achieve reliable solutions. In this article, a method to control these fictitious velocities via lattice refinement is proposed, which is based on interface thickness control for which both the spurious currents and the physical fluid–fluid interface thickness vanishes as the spatial resolution increases. It has been found that a proper interface thickness adjustment is required as the lattice refinement is applied, or an increase in spurious currents, instead of a reduction, can occur. By combining the new method with an appropriate multiphase flow initialization, the overall stability for high density O(1000) and viscosity O(100) ratios is greatly improved. Although this research has been conducted with a Rothman and Keller type lattice Boltzmann model, it is believed that other types of multiphase lattice Boltzmann models could benefit from the basic ideas underlying this research. Copyright © 2015 John Wiley & Sons, Ltd.     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Fatness and thinness of uniform Cantor sets for doubling measures

Let E = E({nk},{ck}) be a fat uniform Cantor set. We prove that E is a minimally fat set for doubling measures if and only if (nkck)p = ∞ for all p < 1 and that E is a fairly fat set for doubling measures if and only if there are constants 0 < p < q < 1 such that (nkck)q < ∞ and (nkck)p = ∞. The classes of minimally thin uniform Cantor sets and of fairly thin uniform Cantor sets are also characterized.     

二元函数连续性条件之探析

对二元函数连续性判定条件给出了详细分析，强调有关问题的关键点，纠正了常见的模糊认识，得到一系列连续性充分条件及其推广形式．     

Mid-infrared InAsSb-based nBn photodetectors with AlGaAsSb barrier layers – Grown on GaAs,using an interfacial misfit array,and on native GaSb

InAsSb-based nBn photodetectors were fabricated on GaAs, using the interfacial misfit (IMF) array growth mode, and on native GaSb. At −0.1 V operating bias, 200 K dark current densities of 1.4 × 10⁻⁵ A cm⁻² (on GaAs) and 4.8 × 10⁻⁶ A cm⁻² (on GaSb) were measured. At the same temperature, specific detectivity (D^*) figures of 1.2 × 10¹⁰ Jones (on GaAs) and 7.2 × 10¹⁰ Jones (on GaSb) were calculated. Arrhenius plots of the dark current densities yielded activation energies of 0.37 eV (on GaAs) and 0.42 eV (on GaSb). These values are close to the 4 K bandgap of the absorption layers (0.32–0.35 eV) indicating diffusion limited dark currents and small valence band offsets. Significantly, these devices could be used for mid-infrared focal plane arrays operating within the temperature range of cost-effective thermoelectric coolers.     

Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference

This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102 and 10432030) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335107)     

Dynamical Localization II with an Application to the Almost Mathieu Operator

Several recent works have established dynamical localization for Schrödinger operators, starting from control on the localization length of their eigenfunctions, in terms of their centers of localization. We provide an alternative way to obtain dynamical localization, without resorting to such a strong condition on the exponential decay of the eigenfunctions. Furthermore, we illustrate our purpose with the almost Mathieu operator, H _{, ,} =–+ cos(2(+x)), 15 and with good Diophantine properties. More precisely, for almost all , for all q>0, and for all functions ²( ) of compact support, we show that The proof applies equally well to discrete and continuous random Hamiltonians. In all cases, it uses as input a repulsion principle of singular boxes, supplied in the random case by the multi-scale analysis.     

Uniform dimension results of multi-parameter stable processes

The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic Hölder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z _t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.     

Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.