Matlab：利用Matlab编程实现模拟分子布朗运动的动画展示

Matlab：利用Matlab编程实现模拟分子布朗运动的动画展示

目录

输出结果

实现代码

输出结果

实现代码

  

   

    

     

    
    

     

      %Brownian motion 
     
    
   

    

     

    
    

     

      clf; 
     
    
   

    

     

    
    

     

      n=20; 
     
    
   

    

     

    
    

     

      s=0.02; 
     
    
   

    

     

    
    

     

      x = rand(n,1)-0.5; 
     
    
   

    

     

    
    

     

      y = rand(n,1)-0.5; 
     
    
   

    

     

    
    

     

      h = plot(x,y,'.'); 
     
    
   

    

     

    
    

     

      axis([-1 1 -1 1]) 
     
    
   

    

     

    
    

     

      axis square 
     
    
   

    

     

    
    

     

      grid off 
     
    
   

    

     

    
    

     

      set(h,'EraseMode','xor','MarkerSize',18) 
     
    
   

    

     

    
    

     

      grid on; 
     
    
   

    

     

    
    

     

      title('Press Ctl-C to stop'); 
     
    
   

    

     

    
    

     

      while 1 
     
    
   

    

     

    
    

     

       drawnow 
     
    
   

    

     

    
    

     

       x = x + s*randn(n,1); 
     
    
   

    

     

    
    

     

       y = y + s*randn(n,1); 
     
    
   

    

     

    
    

     

       set(h,'XData',x,'YData',y) 
     
    
   

    

     

    
    

     

      end
     
    
  
 

  

   

    

     

    
    

     

      clear;clc;
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      %Initializetherandngenerator
     
    
   

    

     

    
    

     

      randn('state',1)
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      %SettheparameterHandthesamplelength
     
    
   

    

     

    
    

     

      H=0.7;lg=10000;
     
    
   

    

     

    
    

     

      %Generateandplotwavelet-basedfBmforH=0.7
     
    
   

    

     

    
    

     

      fBm=wfbm(H,lg);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      n=0:10;
     
    
   

    

     

    
    

     

      dt=2.^n;
     
    
   

    

     

    
    

     

      v=zeros(1,length(n));
     
    
   

    

     

    
    

     

      fori=1:11
     
    
   

    

     

    
    

     

       d=fBm(1+dt(i):end)-fBm(1:end-dt(i));
     
    
   

    

     

    
    

     

       v(i)=sum(d.^2)./(length(d)-1);
     
    
   

    

     

    
    

     

       cleard;
     
    
   

    

     

    
    

     

      end
     
    
   

    

     

    
    

     

      p=polyfit(log(dt),log(v),1);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      loglog(dt,v,'ko');
     
    
   

    

     

    
    

     

      holdon;
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      sH=p(1)./2;
     
    
   

    

     

    
    

     

      ch=exp(p(2));
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      plot(dt,ch.*dt.^(2.*sH),'b','LineWidth',1);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      %% 
     
    
   

    

     

    
    

     

      clc;
     
    
   

    

     

    
    

     

      clearvars-exceptchsH;
     
    
   

    

     

    
    

     

      mch=ch;
     
    
   

    

     

    
    

     

      msH=sH;
     
    
   

    

     

    
    

     

      clearchsH;
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      %Initializetherandngenerator
     
    
   

    

     

    
    

     

      randn('state',1)
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      %SettheparameterHandthesamplelength
     
    
   

    

     

    
    

     

      H=0.7;lg=10000;
     
    
   

    

     

    
    

     

      fBm=fbm1d(H,lg);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      n=0:10;
     
    
   

    

     

    
    

     

      dt=2.^n;
     
    
   

    

     

    
    

     

      v=zeros(1,length(n));
     
    
   

    

     

    
    

     

      fori=1:11
     
    
   

    

     

    
    

     

       d=fBm(1+dt(i):end)-fBm(1:end-dt(i));
     
    
   

    

     

    
    

     

       v(i)=sum(d.^2)./(length(d)-1);
     
    
   

    

     

    
    

     

       cleard;
     
    
   

    

     

    
    

     

      end
     
    
   

    

     

    
    

     

      p=polyfit(log(dt./lg),log(v),1);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      holdon;
     
    
   

    

     

    
    

     

      loglog(dt,v,'ks');
     
    
   

    

     

    
    

     

      sH=p(1)./2;
     
    
   

    

     

    
    

     

      ch=exp(p(2));
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      plot(dt,ch.*(dt./lg).^(2.*sH),'r','LineWidth',1);
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      legend('matlab',strcat('Var=',num2str(mch),'*dt^{2.*',num2str(msH),'}'),'KB',strcat('Var=',num2str
     
    
   

    

     

    
    

     

      (ch),'*dt^{2.*',num2str(sH),'}'),'Location','SouthEast');
     
    
   

    

     

    
    

     

      saveas(gcf,'test1.jpg');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
  
 

相关文章
Fractional Brownian motion generator

分数布朗运动及其模拟PDF参考文件

文章来源: yunyaniu.blog.csdn.net，作者：一个处女座的程序猿，版权归原作者所有，如需转载，请联系作者。

原文链接：yunyaniu.blog.csdn.net/article/details/83758429