Matlab模拟布朗运动

1 简介

利用matlab工具模拟了布朗运动测量的实验。通过一正态随机数产生函数模拟从而产生布朗运动步距。在假定粒子所受拖曳力满足斯托克斯关系的情况下,通过拟合多个粒子的均方位移随时间的变化曲线得到斜率,从而进一步可得出扩散系数和波尔兹曼常数。同时,根据模拟结果也对如何减小实验误差作了分析。

2 完整代码

function varargout = bulang(varargin)% BULANG M-file for bulang.fig%      BULANG, by itself, creates a new BULANG or raises the existing%      singleton*.%%      H = BULANG returns the handle to a new BULANG or the handle to%      the existing singleton*.%%      BULANG('CALLBACK',hObject,eventData,handles,...) calls the local%      function named CALLBACK in BULANG.M with the given input arguments.%%      BULANG('Property','Value',...) creates a new BULANG or raises the%      existing singleton*.  Starting from the left, property value pairs are%      applied to the GUI before bulang_OpeningFcn gets called.  An%      unrecognized property name or invalid value makes property application%      stop.  All inputs are passed to bulang_OpeningFcn via varargin.%%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one%      instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES% Edit the above text to modify the response to help bulang% Last Modified by GUIDE v2.5 13-Sep-2021  13:42:21% Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name',       mfilename, ...                   'gui_Singleton',  gui_Singleton, ...                   'gui_OpeningFcn', @bulang_OpeningFcn, ...                   'gui_OutputFcn',  @bulang_OutputFcn, ...                   'gui_LayoutFcn',  [] , ...                   'gui_Callback',   []);if nargin && ischar(varargin{1})    gui_State.gui_Callback = str2func(varargin{1});end​if nargout    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});else    gui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT​% --- Executes just before bulang is made visible.function bulang_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject    handle to figure% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% varargin   command line arguments to bulang (see VARARGIN)% Choose default command line output for bulanghandles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes bulang wait for user response (see UIRESUME)% uiwait(handles.figure1);​% --- Outputs from this function are returned to the command line.function varargout = bulang_OutputFcn(hObject, eventdata, handles) % varargout  cell array for returning output args (see VARARGOUT);% hObject    handle to figure% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Get default command line output from handles structurevarargout{1} = handles.output;​​​function edit1_Callback(hObject, eventdata, handles)% hObject    handle to edit1 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)% Hints: get(hObject,'String') returns contents of edit1 as text%        str2double(get(hObject,'String')) returns contents of edit1 as a doubleglobal k;k=str2double(get(hObject,'string'));% --- Executes during object creation, after setting all properties.function edit1_CreateFcn(hObject, eventdata, handles)% hObject    handle to edit1 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    empty - handles not created until after all CreateFcns called% Hint: edit controls usually have a white background on Windows.%       See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))    set(hObject,'BackgroundColor','white');end​% --- Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObject    handle to pushbutton1 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)axes(handles.axes1);global k;n=50;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',24);if k>=0;    for i=linspace(1,10,10000)        drawnow        x=x+k/10000.*randn(n,1);        y=y+k/10000.*randn(n,1);        set(h,'xdata',x,'ydata',y);    end        else        input('Error');end   ​​% --------------------------------------------------------------------function Quit_Callback(hObject, eventdata, handles)% hObject    handle to Quit (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)close​​

3 仿真结果

4 参考文献

[1]冉诗勇. 利用Matlab模拟布朗运动测量实验[J]. 大学物理实验, 2011, 24(6):4.

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