This is Computational-Physics-A Course Programs in fall 2022 in USTC

Author: Rainzor

Code：Python

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Mainly having some assignments and lecture notes.

RandomNumGenerator.py is a random number generator based on 16807 method. This random number generator is continuously improving as the tasks progress. It can generate random numbers with a uniform distribution in [0,1], create random number matrices of specified sizes, and generate normally distributed random numbers.

For methods of generating random numbers with more distributions, please see DistributionGenerator.py.

本项目主要包括一些作业和讲义。

RandomNumGenerator.py 是一个基于16807方法的随机数生成器。这个随机数生成器随着课程的进行在不断完善。它能够随机产生[0,1]均匀分布的随机数，或者产生指定大小的随机数矩阵，也能产生正态分布随机数。

更多的分布随机数产生方法可以查看 DistributionGenerator.py

Create a random numbers generator by 16807 Method

Test 16807 generation's uniformity and independence

通过16807方法创建一个随机数生成器,测试16807生成的均匀性和独立性

Compare the 16807 generator and Lagged Fibonacci generator

比较16807生成器和滞后Fibonacci生成器

Sampling uniform distribution on the hemisphere

在半球上采样均匀分布

Using selection method sampling of a given function

使用选择法采样给定函数

Marsaglia sampling method which is used to sampling cos and sin function as usual

利用Marsaglia方法采样球面分布

Sampling the Gaussian and Lorentz-like function

采样Gauss分布和Lorentz分布

Sampling a dataset from realistic physics experiments

从真实物理实验中采样数据集，构造概率密度函数

Simple Monte Carlo Method to calculate the integral

使用简单的蒙特卡洛方法计算积分

Verifying the Central Limit Theorem using Poisson Distribution，Binomial distribution，Exponential distribution and Uniform distribution

使用泊松分布、二项分布、指数分布和均匀分布验证中心极限定理

Using Monte Carlo method studies the random walk of charged particles in a sinusoidal external electric field (sin(wt)) on a two-dimensional plane.

Derive the expression for the velocity autocorrelation function

使用蒙特卡洛方法研究带电粒子在二维平面上的正弦外电场(sin(wt))中的随机行走

Simulate 2D DLA and Dielectric Breakdown (DBM) patterns and discuss their growth patterns

模拟2D DLA和电介质击穿(DBM)模式，并讨论它们的生长模式

Derivation of Renormalized Group Transform Expressions, Critical Points and Critical Exponents for Bond Percolation on Square Lattice Lattice

对正方格子上键渗透的重整化群变换表达式、临界点和临界指数的推导

Compute the integral using Metropolis-Hasting sampling

使用Metropolis-Hasting采样计算积分

A question about Ising model.

Experiment about the phase transition between one-dimensional Ising model and two-dimensional XY model system.

讨论一维伊辛模型和二维XY模型系统之间的相变。

Mark the distribution of Markov chain points in turn on the 2-dimensional plane during sampling, so as to understand the Markov chain visually

根据 Metropolis-Hasting 抽样抽样能量函数的分布，绘制马尔科夫链点在二维平面上的分布，以便直观理解马尔科夫链

Finding Chaos from Newton's Iterative Equation

从牛顿迭代方程找到定值状态、倍周期分叉和混沌状态

Analysis of Fractal and Fractal Dimension Features from DLA Model

从DLA模型中分析分形和分形维度特征

Some notes and cheat sheet about this course