We derive a mobility tensor for many cylindrical objects embedded in a viscous sheet. This tensor guarantees a positive dissipation rate for any configuration of particles and forces, analogous to the Rotne-Prager-Yamakawa tensor for spherical particles in a three-dimensional viscous fluid. We test our result for a ring of radially driven particles, demonstrating the positive-definite property at all particle densities. The derived tensor can be utilized in Brownian dynamics simulations with hydrodynamic interactions for such systems as proteins in biomembranes and inclusions in free-standing liquid films.

中文翻译：

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粘性薄片中物体的多粒子迁移率和扩散张量

我们推导了许多嵌入粘性表中的圆柱物体的运动张量。该张量可确保任何形式的颗粒和力的正耗散率，类似于三维粘性流体中球形颗粒的Rotne-Prager-Yamakawa张量。我们测试了一个径向驱动的粒子环的结果，证明了在所有粒子密度下的正定性质。导出的张量可用于具有流体动力学相互作用的布朗动力学模拟中，用于诸如生物膜中的蛋白质和独立式液膜中的内含物的系统。