Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction*

This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type A or a. Under suitable scaling, the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wrig...     

A dynamical characterization of contact circles

A simple dynamical condition is given for line fields within a contact structure, which is satisfied exactly by those line fields which are common kernels of contact circles. Some convexity properties are established which are useful in the study of contact circles up to homotopy. A necessary condition for extending a contact form to a contact circle is given. Based on work of Lisca–Matić and Honda, concrete examples are given which show that the condition is not just homotopic but a geometric one. The paper ends with an open question. Dedicated to Fernando Varela, for many reasons.     

Perturbations of Pseudodifferential Operators with Negative Definite Symbol

Pseudodifferential operators with negative definite symbols appear as generators of jump-type Markov processes. The purpose of this paper is to treat the large jumps of the process by a perturbation approach for the generator. This is of particular interest since in this way the generators are made accessible to a symbolic calculus of pseudodifferential operators. The main auxiliary result consists of a characterization of tightness of the jump measures in terms of the symbol.     

Weak solutions to stochastic 3D Navier-Stokes-α model of turbulence: α-Asymptotic behavior

We study the asymptotic behavior of weak solutions to the stochastic 3D Navier-Stokes-α model as α approaches zero. The main result provides a new construction of the weak solutions of stochastic 3D Navier-Stokes equations as approximations by sequences of solutions of the stochastic 3D Navier-Stokes-α model.     

Envelopes of Sets of Measures, Tightness, and Markov Control Processes

We introduce upper and lower envelopes for sets of measures on an arbitrary topological space, which are then used to give a tightness criterion. These concepts are applied to show the existence of optimal policies for a class of Markov control processes. Accepted 22 May 1998     

A moderate deviation principle for 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noises

In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier–Stokes equations driven by multiplicative Lévy noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in [3] plays a key role.     

Some remarks on Euclidean tight designs

In this paper we present a new 4-dimensional tight Euclidean 5-design on 3 concentric spheres, together with a list of all known tight Euclidean designs which has been updated since the last survey paper by Bannai and Bannai (2009) [6]. We also examine whether each of all known tight Euclidean designs has the structure of a coherent configuration.     

Convergence of Weighted Empirical Measures

This article considers a system with infinitely many interacting particles, starting with a system of n interacting particles that is described by a system of n stochastic differential equations for the time-varying locations and weights. Any particle in the system interacts with others through the weighted empirical measure Uⁿ formed by the sum of weighted Dirac measures on the n particles. Weak convergence of the weighted empirical measure is studied under suitable conditions, such as bounded initial values, and linear growth of drift and diffusion coefficients. Thereafter, the limit of the weighted empirical measures is identified to be a martingale solution of the infinite interacting system.     

Convergence for a Splitting-Up Scheme for the 3D Stochastic Navier-Stokes-α Model

We propose and analyze a splitting-up scheme for the numerical approximation of the 3D stochastic Navier-Stokes-α model. We prove the convergence of the scheme to the unique variational solution of the 3D stochastic Navier-Stokes-α model when the time step tends to zero.     

低温高强度复合材料绝缘子的研制和性能测试

在EAST全超导核聚变实验装置中,绝缘子担负着超导磁体冷却回路和带电回路之间的绝缘重任,是保证超导磁体稳定运行的关键部件,EAST装置进行放电实验时绝缘子必须承受4.2K低温、高氦气压(5MPa)和高电压环境的多重考验。文中介绍了一种使用环氧树脂和玻璃纤维复合材料制作的高强度绝缘子的研制工艺,并对该绝缘子在室温和低温下的机械性能测试、冷热循环测试、耐氦气压测试和电绝缘性能测试进行了详细的介绍,一系列测试结果表明,该类型绝缘子能满足EAST复杂条件下的绝缘性能要求。