周期性悬浮体有效粘滞率的第一性原理研究

在本文中我们导出一组积分方程,借此可以确定不可压缩牛顿流体中位于周期点阵上的任意形状粒子的有效粘滞率张量,而且解的有效性不再受低粒子浓度的限制,并建立了等价流体的最普遍的本构方程。利用简单近似,我们导出了立方对称悬浮体的有效粘滞率的简便公式,并在相当宽的粒子浓度区间给出合理的结果。我们用多项式近似精确地计算了柱列阵的有效粘滞率张量。     

Steady State and Long Time Convergence of Spirals Moving by Forced Mean Curvature Motion

In this paper, we prove the existence and uniqueness of a “steady” spiral moving with forced mean curvature motion. This spiral has a stationary shape and rotates with constant angular velocity. Under appropriate conditions on the initial data, we also show the long time convergence (up to some subsequence in time) of the solution of the Cauchy problem to the steady state. This result is based on a new Liouville result which is of independent interest.     

拓扑量子场理论与相交指标

该文构造了一新的上同调型拓扑量子场理论并证明了其配分函数是相交指标 (crossingindex)     

The Liouville Field Theory Zero-Mode Problem

We quantize the canonical free-field zero modes p, q on the half-plane p > 0 for both Liouville field theory and its reduced Liouville particle dynamics. We describe the particle dynamics in detail, calculate one-point functions of particle vertex operators, deduce their zero-mode realization on the half-plane, and prove that the particle vertex operators act self-adjointly on the Hilbert space L ²(₊) because of symmetries generated by the S-matrix. Similarly, we obtain the self-adjointness of the corresponding Liouville field theory vertex operator in the zero-mode sector by applying the Liouville reflection amplitude, which is derived by the operator method.     

The Collineation Groups of Generalized Twisted Field Planes

We investigate autotopisms and isotopisms of generalized twisted field planes. A revision of Alberts results is developed using a mixture of group-theoretical and algebraic methods. In particular, transitivity conditions of the autotopism group on the nonvertex points of one or more sides of the autotopism triangle are determined. Also, correlations and polarities in generalized twisted field planes are examined in detail. These results allow us to obtain several improvements of recent results in semifield planes.     

Stability of Solutions of Parabolic PDEs with Random Drift and Viscosity Limit

Let u _α be the solution of the It? stochastic parabolic Cauchy problem , where ξ is a space—time noise. We prove that u _α depends continuously on α , when the coefficients in L _α converge to those in L ₀ . This result is used to study the diffusion limit for the Cauchy problem in the Stratonovich sense: when the coefficients of L _α tend to 0 the corresponding solutions u _α converge to the solution u ₀ of the degenerate Cauchy problem . These results are based on a criterion for the existence of strong limits in the space of Hida distributions (S) ^* . As a by-product it is proved that weak solutions of the above Cauchy problem are in fact strong solutions. Accepted 22 May 1998     

Modular Data: The Algebraic Combinatorics of Conformal Field Theory

This paper is primarily intended as an introduction for mathematicians to some of the rich algebraic combinatorics arising in for instance conformal field theory (CFT). It tries to refine, modernise, and bridge the gap between papers [6] and [55]. Our paper is essentially self-contained, apart from some of the background motivation (Section 1) and examples (Section 3) which are included to give the reader a sense of the context. Detailed proofs will appear elsewhere. The theory is still a work-in-progress, and emphasis is given here to several open questions and problems.     

New Perturbation Theory for Quantum Field Theory: Convergent Series Instead of Asymptotic Expansions

We present a new approach to perturbation theory for quantum field theory based on convergent series instead of asymptotic expansions. This approach could be considered as the next step after traditional perturbation theory calculations, which allows more comprehensive use of previously obtained information in finding numerical values with greater accuracy.