On the Theory of KM2O-Langevin Equations for Stationary Flows (2): Construction Theorem

The aim of the present paper is to construct the KM₂O-Langevin matrix LM([X,Y]) directly from the correlation matrix function R by using (DDT), (FDT) and (PAC) as an algorithm.     

Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.      

On Nonhomogeneous Slip Boundary Conditions for 2D Incompressible Exterior Fluid Flows

The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in ℝ². The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence of weak solutions for arbitrary data.      

Collapsing in the L 2 Curvature Flow

We show some results for the L² curvature flow linked by the theme of addressing collapsing phenomena. First we show long time existence and convergence of the flow for SO(3)-invariant initial data on S³, as well as a long time existence and convergence statement for three-manifolds with initial L² norm of curvature chosen small with respect only to the diameter and volume, which are both necessary dependencies for a result of this kind. In the critical dimension n = 4 we show a related low-energy convergence statement with an additional hypothesis. Finally we exhibit some finite time singularities in dimension n ≥ 5, and show examples of finite time singularities in dimension n ≥ 6 which are collapsed on the scale of curvature.     

Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation

This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropolar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each case. As special consequences, the 2D Navier-Stokes equations, the 2D magnetohydrodynamic equations, and the 2D micropolar equations with several types of partial dissipation always possess global classical solutions. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms.     

Diffusion approximation for slow motion in fully coupled averaging

In systems which combine fast and slow motions it is usually impossible to study directly corresponding two scale equations and the averaging principle suggests to approximate the slow motion by averaging in fast variables. We consider the averaging setup when both fast and slow motions are diffusion processes depending on each other (fully coupled) and show that there exists a diffusion process which approximates the slow motion in the $L^2$ sense much better than the averaged motion prescribed by the averaging principle.The authors are partially supported by INTAS, project No. 99-00559 and by US-Israel BSF, respectively. Part of the work was done during the visit of the 1st author to the Hebrew University.Mathematics Subject Classification (2000): Primary 34C29; Secondary 60F15, 58J65     

Loss of Smoothness and Inherent Instability of 2D Inviscid Fluid Flows

The paper is focused on the loss of smoothness hypothesis which claims that vorticity (or vorticity gradients in the 2D case) grows unboundedly for the substantial part of the inviscid incompressible flows. At least, every steady flow is supposed to belong to the closure of this set (relative to a reasonably strong topology). We approach the problem involving both direct Lyapunov method and some sort of the linearization. We present new (and rather wide) classes of 2D flows in a generic domains which admit the loss of smoothness and related phenomena.     

Prediction and Conditional Simulation of a 2D Lognormal Diffusion Random Field

This paper describes techniques for estimation, prediction and conditional simulation of two-parameter lognormal diffusion random fields which are diffusions on each coordinate and satisfy a particular Markov property. The estimates of the drift and diffusion coefficients, which characterize the lognormal diffusion random field under certain conditions, are used for obtaining kriging predictors. The conditional simulations are obtained using the estimates of the drift and diffusion coefficients, kriging prediction and unconditional simulation for the lognormal diffusion random field.      

3D Anisotropic Diffusion on GPUs by Closed-Form Local Tensor Computations

We present an efficient implementation of volumetric anisotropic image diffusion filters on modern programmable graphics processing units (GPUs), where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images. We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in $\mathbb{R}^3$. Instead, we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors. We derive closed formulas to achieve this and prevent the GPU code from branching. We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution.     

180°弯曲方管牛顿流体及一种非牛顿流体湍性流动的数值模拟

运用湍流k-ε模式及实测壁面函数分别模拟牛顿流体(清水)及一种非牛顿流体(聚合物稀薄减阻溶液)流经180°弯曲方管的湍性流动,取得与实测速度分布吻合较好的结果.对于湍流模式对存在大涡的复杂流动的适应性,根据计算和试验结果进行了分析和讨论.     

Queuing Systems with Semi-Markov Flow in Average and Diffusion Approximation Schemes

We study asymptotic average and diffusion approximation schemes for semi-Markov queuing systems by a random evolution approach and using compensating operator of the corresponding extended Markov renewal process. These results generalize Markov and renewal flow queuing systems.      

有界域上具有部分耗散和磁扩散的二维磁流体方程的全局适定性

探究了具有部分耗散和磁扩散的二维不可压缩磁流体(MHD)方程的初边值问题.在有界区域上,当系统的各个方向上的耗散系数和磁扩散系数都非负时,我们得到了该模型的强解是整体存在且唯一的.此外,对周期域而言,其解仍是全局适定的.     

Global Well-Posedness of the 2D Incompressible Micropolar Fluid Flows with Partial Viscosity and Angular Viscosity

This paper is concerned with the two-dimensional equations of incompressible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established.     

Stability analysis of linear parabolic systems and removement of singularities in substructure: Static feedback

We analyze stability property of a class of linear parabolic systems via static feedback. Stabilization via static feedback scheme is most difficult and challenging when both actuators and observation weights admit spillovers. This arises typically in the boundary observation-boundary feedback scheme. We propose a simple static feedback law containing a parameter γ, and enhance the stability property or achieve (slightly) stabilization. In some situations, the evolution of the substructure of finite dimension contains singularities regarding γ. We show that these singularities are removed as long as the dimension is not large.     

The Gradient Flow of <Emphasis Type="Italic">∫</Emphasis><Subscript><Emphasis Type="Italic">M</Emphasis></Subscript>|Rm|<Superscript>2</Superscript>

We study the gradient flow of the Riemannian functional ℱ(g):=∫ _M |Rm|². This flow corresponds to a fourth-order degenerate parabolic equation for a Riemannian metric. We prove that the degeneracies may be accounted for entirely by diffeomorphism flow, and hence we show short-time existence using the DeTurck method. We prove L ² derivative estimates of Bernstein-Bando-Shi type and use these to give a basic obstruction to long time existence and prove a compactness theorem.      

Reaction–Diffusion models: From particle systems to SDE’s

Let $V$ be any finite set and $p(?,?)$ a transition kernel on it. We present a construction of a family of Reaction–Diffusion models that converge after scaling to the solution to the $\left|V\right|$-dimensional SDE: $d{\zeta }_t=\left[{\Delta }_p{\zeta }_t?\beta ?{\zeta }_t^k\right]dt+\sqrt{\alpha ?{\zeta }_t^{?}}d{B}_t$with arbitrary initial condition ${\zeta }_0\in {\mathbb{R}}^V$. Here, ${\Delta }_p$ is the diffusion on $V$ corresponding to $p$, $\alpha$, $\beta$ are positive real numbers and $k$, $?$ are positive integers.     

Fluid Flow Equations with Thermal Effects in Complex-Quaternionic Setting

This article considers the Boussinesq approximation of Poisson–Stokes equations under given initial value and boundary value conditions. Using a quaternionic operator calculus representations of solutions are presented. If the boundedness of the velocity can be assumed then a stable semi-discretisation procedure approximates the problem. Received: October, 2007. Accepted: February, 2008.     

电渗驱动微通道流中的扩散

利用差分方法对电渗驱动微通道中的脉冲样品的浓度扩散进行了数值模拟,结果说明外加电场和缓冲液浓度对样品的扩散起着重要的作用,而水力直径及其通道的高宽比对扩散的影响甚微．采用减小外加电场和减小缓冲液浓度的办法,可以防止样品带宽的增大、增强检测和分离的效果,同时又保持比较快的输送速度．该结论对于微通道的优化设计具有参考价值．     

带干扰的双Poisson风险模型的破产概率

首先将[3]的双Possion风险模型推广到带干扰的一种新模型。然后运用鞅论的方法得出破产概率满足Lundberg不等式和一般公式。以及当个体所赔服从指数分布时的破产概率的具体表达式。