Torres Francis A, Gauthier Michel G, Slater Gary W
Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario K1N 6N5, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):065701. doi: 10.1103/PhysRevE.78.065701. Epub 2008 Dec 1.
The migration of a particle in a system of obstacles under the action of an external field is often modeled using lattice Monte Carlo algorithms. For example, such simulation methods have been used to study the electrophoresis of charged molecules in sieving gels and the separation of particles using ratchet systems. In the case of constant fields or low-frequency alternating fields, the Monte Carlo simulation method can be mapped onto a numerical or algebraic matrix problem that can be solved exactly. In this Rapid Communication, we generalize this matrix approach to treat periodic time-dependent fields. The evolution of the spatial distribution function during a period is computed using a sequence of transfer matrices, and a steady-state closure relation allows us to calculate the exact mean velocity of the particle during a complete cycle. As an example, we examine the properties of a simple spatially asymmetric ratchet system in the presence of periodic alternating fields (symmetric and asymmetric) as well as random telegraph signals.
在外部场作用下，粒子在障碍物系统中的迁移通常使用晶格蒙特卡罗算法进行建模。例如，此类模拟方法已被用于研究筛分凝胶中带电分子的电泳以及使用棘轮系统分离粒子。在恒定场或低频交变场的情况下，蒙特卡罗模拟方法可以映射到一个可以精确求解的数值或代数矩阵问题上。在本快报中，我们将这种矩阵方法推广到处理周期性随时间变化的场。使用一系列转移矩阵计算一个周期内空间分布函数的演化，并且一个稳态闭合关系使我们能够计算粒子在一个完整周期内的精确平均速度。作为一个例子，我们研究了在周期性交变场（对称和不对称）以及随机电报信号存在的情况下，一个简单的空间不对称棘轮系统的性质。
