二维带反射吸收边界的布朗运动仿真

清华大学随机过程的课程大作业，主要内容是带反射吸收壁的二维布朗运动理论建模与仿真，压缩包里面含有matlab的源代码，我自己写的详细的课程报告，还有代码的说明文档，相当详细而且一定可以运行，还有我详细的理论推导。是学习布朗运动非常好的资料

clear all; clc; close all;
%length of wall
xmax=10;
ymax=20;
%probality of absorption
p = 0.5;
%num of particles
totalnum=1000; 
totaltime=1000;
%resistance flag
f_flag =1;%ref:0:no resis; 1:resis
%prelocate length
x（totalnum） = 0;
y（totalnum） = 0;
x_x（totaltime） = 0;% var for tracking
y_y（totaltime） = 0;% var for tracking
direction（totalnum）=0;  

for i=1:totalnum
    x（i）=xmax*rand; 
    y（i）=ymax*rand; 
end
figure;%initial
scatter（xy）;    

for m = 1:totaltime
    for i=1:totalnum
        direction（i）=fix（4*rand）+1; 
    end
    
    for i=1:totalnum
     if（direction（i）==1）
         if（f_flag == 1）
            x（i）=x（i）+（1-m/1000）*randn;
         else
            x（i）=x（i）+randn; 
         end
         %---partial_border-----
         probability=rand;
            %absorotion
            if（probability<=p）   
                directionabsorb=fix（3*rand）+1;
                if（x（i）<=0）
                   switch directionabsorb
                        case 1
                            x（i）=xmax-abs（randn）;                
                        case 2                
                            x（i）=xmax-abs（randn）/sqrt（2）;
                            y（i）=y（i）+abs（randn）/sqrt（2）;       
                        case 3               
                            x（i）=xmax-abs（randn）/sqrt（2）;
                            y（i）=y（i）-abs（randn）/sqrt（2）;   
                    end 
                end

                 if（x（i）>=xmax）
                   switch directionabsorb          
                        case 1
                            x（i）=abs（randn）;               
                        case 2                
                            x（i）=abs（randn）/sqrt（2）;
                            y（i）=y（i）-abs（randn）/sqrt（2）;
                        case 3                
                            x（i）=abs（randn）/sqrt（2）;
                            y（i）=y（i）+abs（randn）/sqrt（2）;     
                  end
                 end

                 if（y（i）>=ymax）
                   switch directionabsorb
                        case 1                
                            y（i）=abs（randn）;                
                        case 2                
                            x（i）=x（i）+abs（randn）/sqrt（2）;
                            y（i）=abs（randn）/sqrt（2）;               
                        case 3               
                            x（i）=x（i）-abs（randn）/sqrt（2）;
                            y（i）=abs（randn）/sqrt（2）;   
                    end
                end

                if（y（i）<=0）
                   switch directionabsorb
                        case 1                
                            y（i）=ymax-abs（randn）;                
                        case 2               
                            x（i）=x（i）+abs（randn）/sqrt（2）;
                            y（i）=ymax-abs（randn）/sqrt（2）;               
                        case 3 

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     文件       13537  2015-12-04 19:33  Main.m
     文件          82  2015-12-04 19:36  main说明.txt
     文件      774996  2015-12-04 19:24  随机过程实验报告.pdf