平均抽样约束：Hugoniot曲线的例子
Sampling constraints in average: The example of Hugoniot curves
摘要：
我们提出了一种方法，用于采样微观配置的物理系统分布根据一个典型的（玻尔兹曼-吉布斯）措施，与约束平均持有。假设约束可以由系统的体积和/或温度控制，并将控制参数视为动态变量，提出了一种基于非线性随机过程的采样策略。作为应用，我们考虑了冲击波作用下材料平衡后的平衡态，即Hugoniot曲线上的点的计算。
英文摘要：
We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann-Gibbs) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering the control parameter as a dynamical variable, a sampling strategy based on a nonlinear stochastic process is proposed. Convergence results for this dynamics are proved using entropy estimates.As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.
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