空间噪声和Langevin方程的Monte Carlo模拟

为了能够模拟Langevin方程中具有任意关联的色噪声,克服由于不知道产生色噪声的微分方程而无法模拟的缺点,该文给出了一个模拟色噪声的方法。在离散的Fourier空间中产生一个噪声序列,再经过离散Fourier逆变换得到所需要的色噪声序列。该方法也适用于模拟空间噪声。以一维时间色噪声以及二维空间短程关联的噪声为例,讨论了用离散Fourier变换来产生色噪声的具体方法。用该方法得到的噪声实际关联,能够与理论值较好地吻合。

Monte Carlo simulations of spatial noise and Langevin equation

In order to simulate the colored noise with any correlation in the Langevin equation,and avoid the difficulty in simulating the colored noise without the differential equation to generate the noise,an algorithm was developed to simulate the colored noise.The noise is generated in Fourier space,and then the real noise can be got from an inverse transform.The algorithm is also available to simulate the spatial noise.This paper discusses the detailed technique and presents two examples such as colored noise in time and two-dimensional spatial shortrange-correlated noise.The real correlation of the noise generated from this method can tally match with the theoretic value.