Self-Similar Decay in the Kraichnan Model of a Passive Scalar

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field that is stationary and white noise in time, but fractional Brownian in space with roughness exponent 0<<2, appropriate to the inertial-convective range of the scalar. We find all self-similar solutions by transforming the scaling equation to Kummer's equation. It is shown that only those scaling solutions with scalar energy decay exponent a(d/)+1 are statistically realizable, where d is space dimension and =2–. An infinite sequence of invariants J _p, p=0, 1, 2,..., is pointed out, where J ₀ is Corrsin's integral invariant but the higher invariants appear to be new. We show that at least one of the invariants J ₀ or J ₁ must be nonzero (possibly infinite) for realizable initial data. Initial datum with a finite, nonzero invariant—the first being J _p—converges at long times to a scaling solution _p with a=(d/)+p, p=0, 1. The latter belongs to an exceptional series of self-similar solutions with stretched-exponential decay in space. However, the domain of attraction includes many initial data with power-law decay. When the initial datum has all invariants zero or infinite and also it exhibits power-law decay, then the solution converges at long times to a nonexceptional scaling solution with the same power-law decay. These results support a picture of a two-scale decay with breakdown of self-similarity for a range of exponents (d+)/<a<(d+2)/, analogous to what has recently been found in the decay of Burgers turbulence.     

Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

A Numerical Study of Characteristic Slow-Transient Behavior of a Compressible 2D Gas-Liquid Two-Fluid Model

The purpose of this paper is to gain some insight into the characteristic behavior of a general compressible two-fluid gas-liquid model in 2D by using numerical computations. Main focus is on mass transport phenomena. Relatively few numerical results in higher dimensions can be found in the literature for this two-fluid model, in particular, for cases where mass transport dynamics are essential. We focus on natural extensions to 2D of known 1D benchmark test cases, like water faucet and gas-liquid separation, previously employed by many researchers for the purpose of testing various numerical schemes. For the numerical investigations, the WIMF discretization method introduced in [SIAM J. Sci. Comput. 26 (2005), 1449] is applied, in combination with a standard dimensional splitting approach. Highly complicated flow patterns are observed reflecting the balance between acceleration forces, gravity, interfacial forces, and pressure gradients. An essential ingredient in these results is the appearance of single-phase regions in combination with mixture regions (dispersed flow). Solutions are calculated and shown from early times until a steady state is reached. Grid refinement studies are included to demonstrate that the obtained solutions are not grid-sensitive.     

Dynamo Effect in the Kraichnan Magnetohydrodynamic Turbulence

The existence of a dynamo effect in a simplified magnetohydrodynamic model of turbulence is considered when the magnetic Prandtl number approaches zero or infinity. The magnetic field is interacting with an incompressible Kraichnan-Kazantsev model velocity field which incorporates also a viscous cutoff scale. An approximate system of equations in the different scaling ranges can be formulated and solved, so that the solution tends to the exact one when the viscous and magnetic-diffusive cutoffs approach zero. In this approximation we are able to determine analytically the conditions for the existence of a dynamo effect and give an estimate of the dynamo growth rate. Among other things we show that in the large magnetic Prandtl number case the dynamo effect is always present. Our analytical estimates are in good agreement with previous numerical studies of the Kraichnan-Kazantsev dynamo by Vincenzi (J. Stat. Phys. 106:1073–1091, 2002).     

方形颗粒在黏弹性流体中的沉降特性

采用有限元任意拉格朗日-欧拉(ALE)法对方形颗粒在黏弹性流体中的沉降特性进行研究。通过直接数值模拟得到了不同弹性数下方形颗粒的稳定取向角的变化情况,并讨论了颗粒长宽比和通道宽度对其沉降特性的影响。结果表明,当方形颗粒在黏弹性流体中沉降时,弹性数存在一个临界值。当弹性数小于临界值时,颗粒的稳定取向为长轴方向垂直于重力方向;当弹性数大于临界值时,颗粒的稳定取向为长轴方向平行于重力方向。颗粒长宽比和通道宽度对其沉降特性都有一定的影响。长宽比大的颗粒在沉降过程中的取向角和横向漂移的振幅更大。弹性数的临界值随着长宽比的增大而减小,随着阻塞比的增大而增大。     

Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid

We define a lattice Boltzmann model of solid, deformable suspensions immersed in a fluid itself described in terms of the lattice Boltzmann method. We discuss the rules governing the internal dynamics of the solid object as well as the rules specifying the interaction between solid and fluid particle. We perform a numerical drag experiment to validate the model. Finally we consider the case of a population of flexible chains in suspension in a shear stress flow and study the influence on the velocity profile.     

电流变液中的旋光现象

根据光波在介质中的传播理论,由麦克斯韦方程出发,对非均相结构电流变流导出在外电场与光场交互作用下旋光角ψ与入射线偏振光振动方向与外加电场方向间夹角θ及ζ（取决于电流变液材料本身及外加电场强度）的函数关系式。对不同浓度、不同场强下的SiO2电为液的旋光进行了测量,实验发现,同一场强作用下,旋光角ψ随浓度c的增大而增大;对于同一浓度,旋光角ψ随场强E增大而增大;在浓度c与场强E一定的情况下,旋光角ψ还随θ角而变化。实验结果与理论预测吻合较好。     

Asymptotic Behavior of Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

In this paper, we study the one-dimensional Navier-Stokes equations connecting to vacuum state with a jump in density when the viscosity depends on the density. Precisely, when the viscosity coefficient μ(ρ) is proportional to ρ ^θ with θ > 0, where ρ is the density, we give the asymptotic behavior and the decay rate of the density function ρ(x, t). Furthermore, the behavior of the density function ρ(x, t) near the interfaces separating the gas from vacuum and the expanding rate of the interfaces are also studied. The analysis is based on some new mathematical techniques and some new useful estimates. This fills a final gap on studying Navier-Stokes equations with the viscosity coefficient μ(ρ) dependent on the density ρ.     

Boltzmann Model for Viscoelastic Particles: Asymptotic Behavior,Pointwise Lower Bounds and Regularity

We investigate the long-time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state with explicit rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as a generalization of several classical results holding for the pseudo-Maxwellian and constant normal restitution models.     

Phase Behavior of Bow-Shaped Hard Particles in Two Dimensions

The phase behavior of a two-dimensional hard-particle model is studied via Monte Carlo simulations using the grand canonical, the isobaric and the canonical ensembles. This model consists of a three-segmented line whose geometry resembles a bow shape. The model reduces to some limiting cases: hard needles and bent-core particles. Manipulating the molecular parameters, a variety of molecular shapes were generated. As a result, several liquid crystalline structures like nematic and tetratic were obtained. Additionally, there are some other regions where the molecules form curvilinear paths. As the density increases, the formation of clusters of two or more particles is observed, producing assemblies with different shapes depending on the particular values of the molecular parameters. One interesting example is when the clusters have chiral features despite the particles are achiral. The two-dimensional tetratic, nematic and polar order parameters as well as the orientational correlation functions g ₂(r ^?) and g ₄(r ^?) and the distribution functions g _∥ and g _⊥ were calculated to describe the resulting mesophases. Besides this, the Gibbs ensemble was used to investigate some cases where indications of first-order phase transitions appeared. The mesophases diagrams are also reported.     

Kraichnan Flow in a Square: An Example of Integrable Chaos

The Kraichnan flow provides an example of a random dynamical system accessible to an exact analysis. We study the evolution of the infinitesimal separation between two Lagrangian trajectories of the flow. Its long-time asymptotics is reflected in the large deviation regime of the statistics of stretching exponents. Whereas in the flow that is isotropic at small scales the distribution of such multiplicative large deviations is Gaussian, this does not have to be the case in the presence of an anisotropy. We analyze in detail the flow in a two-dimensional periodic square where the anisotropy generally persists at small scales. The calculation of the large deviation rate function of the stretching exponents reduces in this case to the study of the ground state energy of an integrable periodic Schrödinger operator of the Lamé type. The underlying integrability permits to explicitly exhibit the non-Gaussianity of the multiplicative large deviations and to analyze the time-scales at which the large deviation regime sets in. In particular, we indicate how the divergence of some of those time scales when the two Lyapunov exponents become close allows a discontinuity of the large deviation rate function in the parameters of the flow. The analysis of the two-dimensional anisotropic flow permits to identify the general scenario for the appearance of multiplicative large deviations together with the restrictions on its applicability.     

Stochastic Behavior of Particles in a Circularly Polarized Standing Wave

The particle motion in a standing left circularly polarized wave is studied. For wave frequency lower than the ion cyclotron frequency ?ci, the slow varying trajectory is given by the ponderomotive force FNL=q2?|E|2/[m?(?-?ci)]. However, for ? close to ?ci, stochastic trajectories occur. These stochastic trajectories are due to the overlapping of closed orbits due to each of the propagating waves which form the standing wave.     

全尺度方法对颗粒与流体之间相交换量研究

本文采用了内嵌边界多重直接力算法全尺度计算研究了三维空间中颗粒群在重力作用下沉降时,颗粒群与流体之间的相互作用过程。结合多相流的欧拉-欧拉双流体模型方法中对颗粒群与流体之间相互作用力的处理方式,分析了颗粒与流体之间的相交换量。并把全尺度计算得到的颗粒群与流体之间的相交换量与本文中提到的单颗粒受力模型(SPM)和颗粒群受力模型(GPM)对相互作用力进行了比较分析。     

Settling Behavior Characterization of Submicron Particles in Dilute and Concentrated Suspensions

In separation processes, the knowledge of particle size and density arc often not enough to describe the settling behaviour in a concentrated suspension. Therefore, a direct method for the characterization of the settling behavior of submicron particles in concentrated suspensions is introduced in a centrifugal field by a manometric sedimentation analysis. By means of this cumulative method in a homogeneous suspension, the analyses of both the interfacial settling rate and the settling rate of the particles within the concentrated suspension are possible. This permits a differential examination of settling processes in a broad concentration range. First, the influence of the solid concentration on the settling rate at the interface and within a monodisperse suspension with a range from 0.01 to 30 vol.% is represented. The relationship between the increase in settling rate through particles settling in a cluster and a concentration decrease in the suspension is also represented. Consideration of the possibilities of the analysis of polydisperse suspensions demonstrates the field of applications for this method.     

Remarks on the Tunneling Behavior of Scalar Particles Across Einsein-Born-Infeld Black Holes

Motived by the recent work, we discuss the tunneling radiation of the scalar particle from the Einsein-Born-Infeld black hole. The self-gravitional interaction is taken into account in this paper. The result shows that the tunneling rate is related to the exponential of the change of Bekenstein-Hawking entropy and the corrected emission spectrum deviates from the thermnal one. The unitary theory is satisfied.     

Fluid Model of Waveguide Transverse Coupling

In this paper, optical fluid is firstly defined. By using the movement law of hydrodynamics, the transverse coupling of waveguides is discussed. The result fully coincides with the electromagnetic solution.     

Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier–Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L ^p ?L ^q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier–Stokes fluid-rigid disk system.     

脉动流化床内球柱形颗粒流动行为研究

本文结合离散单元模型和计算流体力学方法对脉动流化床内气固流动特性进行数值模拟.结果表明,脉动气流的波形和振幅对球柱形颗粒的流动行为有明显的影响.方波脉动气流作用下的时均颗粒总平动和旋转动能最大,其次是正弦波脉动和三角波脉动,恒定气流下的最小.功率谱分析结果可以发现方波气流下主频幅度最大,其次是正弦波、三角波和恒定气流....