台球中随机射线追踪的边界积分形式
A boundary integral formalism for stochastic ray tracing in billiards
摘要：
确定由力或速度场驱动的射线或粒子的流动是模拟许多物理过程的基础，包括天气预报和分子动力学模拟。高频波能量分布也可以近似使用流动或传输方程。应用出现在水下和室内声学，振动声学，地震学，电磁学，量子力学和产生计算机生成的图像。在许多实际应用中，驱动场并不确切知道，动力学仅在一定程度的不确定性下确定。本文提出了一种边界积分框架，包括不确定性的传播流，这是系统的插值之间的确定性和完全随机的轨迹传播的描述。一个简单而有效的离散化方法是适用于模型不确定台球动态可积矩形域。
英文摘要：
Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy distributions can also be approximated using flow or transport equations. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, quantum mechanics and in producing computer generated imagery. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain.
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