Odd fluids from chiral cellular automata
来自手性元胞自动机的奇流体
Andrew A. Allocca, Shiva Heidari, Thomas Iadecola, Armin Rahmani, Pouyan Ghaemi, Sriram Ganeshan
AI总结 通过修改FHP模型引入手性二体碰撞规则和旋转粒子速度,构建了奇粘性流体元胞自动机,并通过泊肃叶流模拟验证了奇粘性系数。
Comments 10 pages, 2 figures
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元胞自动机是定义在晶格上的离散动力系统,其中每个位点携带一组有限状态,这些状态根据局部确定性规则随时间演化。元胞自动机的一个重要应用是流体格子气模型,其中元胞自动机框架提供了基于粒子的流体动力学行为的微观描述。宏观流体方程在粗粒化多个晶格点和时间步后出现,提供了从下到上的流体动力学途径。一个著名的例子是Frisch-Hasslacher-Pomeau (FHP)模型,这是一个定义在二维三角晶格上的自动机,在粗粒化后产生二维Navier-Stokes方程。在这项工作中,我们通过两个修改构建了FHP模型的宇称破缺推广:引入手性二体碰撞规则并系统旋转粒子速度以模拟背景磁场的影响。我们展示了这个自动机产生了一个具有奇粘性的流体动力学模型,奇粘性是一种横向输运系数,是奇流体的标志。我们通过手性FHP自动机的泊肃叶流模拟验证了解析输运系数。我们的结果表明,这里引入的手性自动机在微观宇称破缺散射过程和宏观奇流体动力学之间架起了一座桥梁。
Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.