AI 中文总结
本研究针对无精确解析解的一维里维埃拉模型，推导其无穷级数动力学方程并引入系统闭合方案，证明其动力学快速收敛至精确行为，高阶时可高精度估计堵塞密度且保留时间演化显式解析表达式。
AI 中文摘要
里维埃拉模型是一种用于晶格上房屋建造的随机顺序沉积模型，规则为当目标位点的两个最近邻位点均已被占用时，无法在该位点建造房屋；在一维情况下，若目标位点为孤立空位，沉积尝试会被拒绝。尽管该规则看似简单，但目前尚无原始模型的精确解析解。我们推导了描述其动力学的无穷级数动力学方程，并引入了可在任意有限阶实施的系统闭合方案。逐阶求解所得方程组后，我们证明对应的动力学快速收敛至精确行为。该方法在高阶时能给出极高精度的堵塞密度估计，同时保留完整时间演化的显式解析表达式。
英文摘要
The Riviera model is a random sequential deposition model for house building on a lattice, in which a house cannot be built when both nearest-neighbor sites are already occupied. In one dimension, an attempted deposition is therefore rejected whenever the target site is an isolated vacancy. Despite the apparent simplicity of this rule, no exact analytical solution of the original model is currently known. We derive an infinite hierarchy of kinetic equations governing its dynamics and introduce a systematic closure scheme that can be implemented at arbitrary finite order. Solving the resulting systems order by order, we show that the corresponding kinetics converges rapidly toward the exact behavior. At high order, the method yields an exceptionally accurate estimate of the jamming density while retaining explicit analytical expressions for the full time-dependent evolution.
Comments16 pages, 5
