tag:blogger.com,1999:blog-8091649968684074242024-03-05T17:38:22.671-08:00Computational Physicsmghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.comBlogger74125tag:blogger.com,1999:blog-809164996868407424.post-48228194208363970792018-08-11T00:07:00.000-07:002018-08-11T00:07:26.607-07:00Monte Carlo Crude Integration (User Defined Function)<div dir="ltr" style="text-align: left;" trbidi="on">
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<pre class="codeinput"><span class="comment">% _________________________________________________________________________</span>
<span class="comment">% Monte Carlo crude integration</span>
<span class="comment">% By Mahesha MG, MIT</span>
<span class="comment">% Date: 11/08/2018</span>
<span class="comment">% _________________________________INPUT___________________________________</span>
clc;
clear;
f=input(<span class="string">'Enter a valid MATLAB expression in x : '</span>,<span class="string">'s'</span>);
a=input(<span class="string">'Enter lower limit: '</span>);
b=input(<span class="string">'Enter upper limit: '</span>);
n=input(<span class="string">'Enter sampling number: '</span>);
x=a+(b-a)*rand(1,n);
s=sum(eval(f));
result=(b-a)*s/n
<span class="comment">% ______________________________SAMPLE OUTPUT______________________________</span>
<span class="comment">% Enter a valid MATLAB expression in x : x.^2+x</span>
<span class="comment">% Enter lower limit: 2</span>
<span class="comment">% Enter upper limit: 5</span>
<span class="comment">% Enter sampling number: 10000</span>
<span class="comment">%</span>
<span class="comment">% result =</span>
<span class="comment">%</span>
<span class="comment">% 49.3144</span>
<span class="comment">% _________________________________________________________________________</span>
</pre>
<div class="footer">
<br />
Published with MATLAB® </div>
</div>
<!--
##### SOURCE BEGIN #####
% _________________________________________________________________________
% Monte Carlo crude integration
% By Mahesha MG, MIT
% Date: 11/08/2018
% _________________________________INPUT___________________________________
clc;
clear;
f=input('Enter a valid MATLAB expression in x : ','s');
a=input('Enter lower limit: ');
b=input('Enter upper limit: ');
n=input('Enter sampling number: ');
x=a+(b-a)*rand(1,n);
s=sum(eval(f));
result=(b-a)*s/n
% ______________________________SAMPLE OUTPUT______________________________
% Enter a valid MATLAB expression in x : x.^2+x
% Enter lower limit: 2
% Enter upper limit: 5
% Enter sampling number: 10000
%
% result =
%
% 49.3144
% _________________________________________________________________________
##### SOURCE END #####
-->
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-35160588934918670502016-06-10T03:01:00.000-07:002016-06-10T03:10:51.866-07:00Optical Ray Tracing<div dir="ltr" style="text-align: left;" trbidi="on">
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<pre class="codeinput"><span class="comment">%==========================================================================</span>
<span class="comment">% Title: Ray tracing by matrix technique</span>
<span class="comment">% Author: Mahesha MG, Manipal Intitute of Technology Manipal University</span>
<span class="comment">% Date: 10/08/2015</span>
<span class="comment">%==========================================================================</span>
<span class="comment">% Variables</span>
<span class="comment">% r0 --> initial height from optic axis</span>
<span class="comment">% theta0 --> initial angle with normal</span>
<span class="comment">% M --> Propagation/Refraction matrix</span>
<span class="comment">%==========================================================================</span>
clear;
clc;
D=zeros(1,20);
R=zeros(1,20);
r0 = input(<span class="string">'Enter initial height from optic axis (in m): '</span>);
theta0 = input(<span class="string">'Enter initial angle with normal (in radian): '</span>);
R0=[r0;theta0];
D=0;
td=0;
R=r0;
<span class="keyword">while</span>(1)
display(<span class="string">'__________________OPTIONS__________________'</span>);
display(<span class="string">'0 --> Exit'</span>);
display(<span class="string">'1 --> Propagation'</span>);
display(<span class="string">'2 --> Refraction'</span>);
display(<span class="string">'3 --> Thin lens'</span>);
display(<span class="string">'4 --> Reflection'</span>);
display(<span class="string">'5 --> Spherical Mirror'</span>);
display(<span class="string">'____________________________________________'</span>);
ch=input(<span class="string">'Enter option: '</span>);
<span class="keyword">if</span> ch == 0
<span class="keyword">break</span>;
<span class="keyword">else</span> <span class="keyword">if</span> ch == 1
d=input(<span class="string">'Enter distance (in m): '</span>);
M=[1 d; 0 1]; <span class="comment">%Propagation matrix</span>
<span class="keyword">else</span> <span class="keyword">if</span> ch == 2
n0=input(<span class="string">'Refractive index of first medium: '</span>);
n1=input(<span class="string">'Refractive index of second medium: '</span>);
d=0;
M=[1 0; 0 n0/n1]; <span class="comment">%Refraction matrix</span>
<span class="keyword">else</span> <span class="keyword">if</span> ch == 3
f=input(<span class="string">'Focal length of the lens: '</span>);
d=0;
M=[1 0; -1/f 1]; <span class="comment">%Thin lens matrix</span>
<span class="keyword">else</span> <span class="keyword">if</span> ch == 4
d=0;
M=[1 0; 0 -1]; <span class="comment">%Reflection matrix</span>
<span class="keyword">else</span> <span class="keyword">if</span> ch == 5
d=0;
R=input(<span class="string">'Enter radius of curvature of spherical mirror: '</span>);
M=[1 0; -2/R -1];
<span class="keyword">else</span> warning(<span class="string">'Entered option is invalid'</span>);
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
<span class="keyword">end</span>
R1=M*R0;
td=td+d;
D=[D;td];
R=[R;R1(1)];
R0=R1;
<span class="keyword">end</span>
figure(<span class="string">'color'</span>,<span class="string">'white'</span>);
plot(D,R,<span class="string">'b-+'</span>,D,-R,<span class="string">'r-+'</span>);
<span class="comment">%==========================SAMPLE INPUT====================================</span>
<span class="comment">% Enter initial height from optic axis (in m): 0.02</span>
<span class="comment">% Enter initial angle with normal (in radian): 0.01</span>
<span class="comment">% __________________OPTIONS__________________</span>
<span class="comment">% 0 --> Exit</span>
<span class="comment">% 1 --> Propagation</span>
<span class="comment">% 2 --> Refraction</span>
<span class="comment">% 3 --> Thin lens</span>
<span class="comment">% 4 --> Reflection</span>
<span class="comment">% 5 --> Spherical Mirror</span>
<span class="comment">% ____________________________________________</span>
<span class="comment">% Enter option: 1</span>
<span class="comment">% Enter distance (in m): 0.1</span>
<span class="comment">% __________________OPTIONS__________________</span>
<span class="comment">% 0 --> Exit</span>
<span class="comment">% 1 --> Propagation</span>
<span class="comment">% 2 --> Refraction</span>
<span class="comment">% 3 --> Thin lens</span>
<span class="comment">% 4 --> Reflection</span>
<span class="comment">% 5 --> Spherical Mirror</span>
<span class="comment">% ____________________________________________</span>
<span class="comment">% Enter option: 3</span>
<span class="comment">% Focal length of the lens: 0.06</span>
<span class="comment">% __________________OPTIONS__________________</span>
<span class="comment">% 0 --> Exit</span>
<span class="comment">% 1 --> Propagation</span>
<span class="comment">% 2 --> Refraction</span>
<span class="comment">% 3 --> Thin lens</span>
<span class="comment">% 4 --> Reflection</span>
<span class="comment">% 5 --> Spherical Mirror</span>
<span class="comment">% ____________________________________________</span>
<span class="comment">% Enter option: 1</span>
<span class="comment">% Enter distance (in m): 0.1</span>
<span class="comment">% __________________OPTIONS__________________</span>
<span class="comment">% 0 --> Exit</span>
<span class="comment">% 1 --> Propagation</span>
<span class="comment">% 2 --> Refraction</span>
<span class="comment">% 3 --> Thin lens</span>
<span class="comment">% 4 --> Reflection</span>
<span class="comment">% 5 --> Spherical Mirror</span>
<span class="comment">% ____________________________________________</span>
<span class="comment">% Enter option: 0</span>
<span class="comment">% =========================================================================</span>
</pre>
<div class="footer">
<br />
Published with MATLAB® 7.5</div>
</div>
<!--
##### SOURCE BEGIN #####
%==========================================================================
% Title: Ray tracing by matrix technique
% Author: Mahesha MG, Manipal Intitute of Technology Manipal University
% Date: 10/08/2015
%==========================================================================
% Variables
% r0 REPLACE_WITH_DASH_DASH> initial height from optic axis
% theta0 REPLACE_WITH_DASH_DASH> initial angle with normal
% M REPLACE_WITH_DASH_DASH> Propagation/Refraction matrix
%==========================================================================
clear;
clc;
D=zeros(1,20);
R=zeros(1,20);
r0 = input('Enter initial height from optic axis (in m): ');
theta0 = input('Enter initial angle with normal (in radian): ');
R0=[r0;theta0];
D=0;
td=0;
R=r0;
while(1)
display('__________________OPTIONS__________________');
display('0 REPLACE_WITH_DASH_DASH> Exit');
display('1 REPLACE_WITH_DASH_DASH> Propagation');
display('2 REPLACE_WITH_DASH_DASH> Refraction');
display('3 REPLACE_WITH_DASH_DASH> Thin lens');
display('4 REPLACE_WITH_DASH_DASH> Reflection');
display('5 REPLACE_WITH_DASH_DASH> Spherical Mirror');
display('____________________________________________');
ch=input('Enter option: ');
if ch == 0
break;
else if ch == 1
d=input('Enter distance (in m): ');
M=[1 d; 0 1]; %Propagation matrix
else if ch == 2
n0=input('Refractive index of first medium: ');
n1=input('Refractive index of second medium: ');
d=0;
M=[1 0; 0 n0/n1]; %Refraction matrix
else if ch == 3
f=input('Focal length of the lens: ');
d=0;
M=[1 0; -1/f 1]; %Thin lens matrix
else if ch == 4
d=0;
M=[1 0; 0 -1]; %Reflection matrix
else if ch == 5
d=0;
R=input('Enter radius of curvature of spherical mirror: ');
M=[1 0; -2/R -1];
else warning('Entered option is invalid');
end
end
end
end
end
end
R1=M*R0;
td=td+d;
D=[D;td];
R=[R;R1(1)];
R0=R1;
end
figure('color','white');
plot(D,R,'b-+',D,-R,'r-+');
%==========================SAMPLE INPUT====================================
% Enter initial height from optic axis (in m): 0.02
% Enter initial angle with normal (in radian): 0.01
% __________________OPTIONS__________________
% 0 REPLACE_WITH_DASH_DASH> Exit
% 1 REPLACE_WITH_DASH_DASH> Propagation
% 2 REPLACE_WITH_DASH_DASH> Refraction
% 3 REPLACE_WITH_DASH_DASH> Thin lens
% 4 REPLACE_WITH_DASH_DASH> Reflection
% 5 REPLACE_WITH_DASH_DASH> Spherical Mirror
% ____________________________________________
% Enter option: 1
% Enter distance (in m): 0.1
% __________________OPTIONS__________________
% 0 REPLACE_WITH_DASH_DASH> Exit
% 1 REPLACE_WITH_DASH_DASH> Propagation
% 2 REPLACE_WITH_DASH_DASH> Refraction
% 3 REPLACE_WITH_DASH_DASH> Thin lens
% 4 REPLACE_WITH_DASH_DASH> Reflection
% 5 REPLACE_WITH_DASH_DASH> Spherical Mirror
% ____________________________________________
% Enter option: 3
% Focal length of the lens: 0.06
% __________________OPTIONS__________________
% 0 REPLACE_WITH_DASH_DASH> Exit
% 1 REPLACE_WITH_DASH_DASH> Propagation
% 2 REPLACE_WITH_DASH_DASH> Refraction
% 3 REPLACE_WITH_DASH_DASH> Thin lens
% 4 REPLACE_WITH_DASH_DASH> Reflection
% 5 REPLACE_WITH_DASH_DASH> Spherical Mirror
% ____________________________________________
% Enter option: 1
% Enter distance (in m): 0.1
% __________________OPTIONS__________________
% 0 REPLACE_WITH_DASH_DASH> Exit
% 1 REPLACE_WITH_DASH_DASH> Propagation
% 2 REPLACE_WITH_DASH_DASH> Refraction
% 3 REPLACE_WITH_DASH_DASH> Thin lens
% 4 REPLACE_WITH_DASH_DASH> Reflection
% 5 REPLACE_WITH_DASH_DASH> Spherical Mirror
% ____________________________________________
% Enter option: 0
% =========================================================================
##### SOURCE END #####
-->
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-80373133895511350902015-09-21T23:05:00.001-07:002015-09-21T23:18:29.182-07:00Simulink - Damped Oscillation<div dir="ltr" style="text-align: left;" trbidi="on">
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<h2 class="subtitle">
Details for damped_oscillation</h2>
<h2 class="subtitle">
ODE for damped oscillation</h2>
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<div class="pubdate">
22-Sep-2015 11:20:13</div>
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<hr />
</div>
<div class="toc">
<b>Table of Contents</b><br />
<dl>
<dt><span class="chapter"><a href="https://www.blogger.com/null">Model - damped_osc</a></span></dt>
<dt><span class="chapter"><a href="https://www.blogger.com/null">System - damped_osc</a></span></dt>
<dt><span class="chapter"><a href="https://www.blogger.com/null">Appendix</a></span></dt>
</dl>
</div>
<div class="list-of-tables">
<b>List of Tables</b><br />
<dl>
<dt>1. <a href="https://www.blogger.com/null">Gain Block Properties</a></dt>
<dt>2. <a href="https://www.blogger.com/null">Integrator Block Properties</a></dt>
<dt>3. <a href="https://www.blogger.com/null">Sum Block Properties</a></dt>
<dt>4. <a href="https://www.blogger.com/null">Block Type Count</a></dt>
</dl>
</div>
<div class="chapter" title="Model - damped_osc">
<div class="titlepage">
<div>
<div>
<h2 class="title">
<a href="https://www.blogger.com/null" name="d0e25"></a>Model - damped_osc</h2>
</div>
</div>
</div>
<a href="https://www.blogger.com/null" name="b986cfe0ceec2a99afcdaddc6626775c"></a><br />
<div class="orderedlist" title="Full Model Hierarchy">
<div class="title">
<b>Full Model Hierarchy</b></div>
<ol class="orderedlist" compact="compact" type="1">
<li class="listitem"><a class="link" href="https://www.blogger.com/null">damped_osc</a></li>
</ol>
</div>
<a href="https://www.blogger.com/null" name="d0e37"></a><br />
<div class="table">
<div class="table-contents">
<table border="1" cellspacing="0" style="width: 100%px;" summary=""><colgroup><col width="23.076923076923077%"></col><col width="76.92307692307693%"></col></colgroup><thead>
<tr><th align="left">Simulation Parameter</th><th align="left">Value</th></tr>
</thead><tbody>
<tr><td align="left">Solver</td><td align="left">ode45</td></tr>
<tr><td align="left">RelTol</td><td align="left">1e-3</td></tr>
<tr><td align="left">Refine</td><td align="left">1</td></tr>
<tr><td align="left">MaxOrder</td><td align="left">5</td></tr>
<tr><td align="left">ZeroCross</td><td align="left">on</td></tr>
</tbody></table>
</div>
</div>
<a class="link" href="https://www.blogger.com/null"><span class="emphasis"><i>[more info]</i></span></a></div>
<div class="chapter" title="System - damped_osc">
<div class="titlepage">
<div>
<div>
<h2 class="title">
<a href="https://www.blogger.com/null" name="d0e76"></a>System - damped_osc</h2>
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<div class="table">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGJzYPt7mVhlGLeA48zx7VK8yQb0kIF-b7FwuS58h8vFFQS8JE6BkAvIu0C7kfZnN2STVl6UIFCloGRmRJg40YEqi1mh9W7a6T6rb2tO_zMv7WihzxAmJcQ2pkZIGZsU_y1gbn6nxgpQqy/s1600/image-005-sl.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="93" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGJzYPt7mVhlGLeA48zx7VK8yQb0kIF-b7FwuS58h8vFFQS8JE6BkAvIu0C7kfZnN2STVl6UIFCloGRmRJg40YEqi1mh9W7a6T6rb2tO_zMv7WihzxAmJcQ2pkZIGZsU_y1gbn6nxgpQqy/s320/image-005-sl.png" width="320" /></a></div>
<div class="title">
<br /></div>
<div class="title">
<b>Table 1. Gain Block Properties</b></div>
<div class="table-contents">
<table border="1" cellspacing="0" style="width: 100%px;" summary="Gain Block Properties"><colgroup><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col><col width="12.5%"></col></colgroup><thead>
<tr><th align="left">Name</th><th align="left">Gain</th><th align="left">Multiplication</th><th align="left">Param Data Type Str</th><th align="left">Out Data Type Str</th><th align="left">Lock Scale</th><th align="left">Rnd Meth</th><th align="left">Saturate On Integer Overflow</th></tr>
</thead><tbody>
<tr><td align="left"><a href="https://www.blogger.com/null" name="8684596003174c1c49b57b50e45b4004"></a>Gain</td><td align="left">1/m</td><td align="left">Element-wise(K.*u)</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">off</td><td align="left">Floor</td><td align="left">off</td></tr>
<tr><td align="left"><a href="https://www.blogger.com/null" name="1140882e6996c0c871c048c3d7ee36f7"></a>Gain1</td><td align="left">k</td><td align="left">Element-wise(K.*u)</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">off</td><td align="left">Floor</td><td align="left">off</td></tr>
<tr><td align="left"><a href="https://www.blogger.com/null" name="588587d6d307d975a62e3a537c6ef076"></a>Gain2</td><td align="left">c</td><td align="left">Element-wise(K.*u)</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">off</td><td align="left">Floor</td><td align="left">off</td></tr>
</tbody></table>
</div>
</div>
<a href="https://www.blogger.com/null" name="d0e177"></a><br />
<div class="table">
<div class="title">
<b>Table 2. Integrator Block Properties</b></div>
<div class="table-contents">
<table border="1" cellspacing="0" style="width: 100%px;" summary="Integrator Block Properties"><colgroup><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col><col width="14.285714285714285%"></col></colgroup><thead>
<tr><th align="left">Name</th><th align="left">External Reset</th><th align="left">Initial Condition Source</th><th align="left">Initial Condition</th><th align="left">Absolute Tolerance</th><th align="left">Zero Cross</th><th align="left">Continuous State Attributes</th></tr>
</thead><tbody>
<tr><td align="left"><a href="https://www.blogger.com/null" name="7aa2e32b884a27bc02814fc228d7c898"></a>Integrator</td><td align="left">none</td><td align="left">internal</td><td></td><td align="left">auto</td><td align="left">on</td><td align="left">''</td></tr>
<tr><td align="left"><a href="https://www.blogger.com/null" name="6b3394cc78438db5f194eb8d773ab5ba"></a>Integrator1</td><td align="left">none</td><td align="left">internal</td><td align="left">1</td><td align="left">auto</td><td align="left">on</td><td align="left">''</td></tr>
</tbody></table>
</div>
</div>
<a href="https://www.blogger.com/null" name="d0e235"></a><br />
<div class="table">
<div class="title">
<b>Table 3. Sum Block Properties</b></div>
<div class="table-contents">
<table border="1" cellspacing="0" style="width: 100%px;" summary="Sum Block Properties"><colgroup><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col><col width="9.090909090909092%"></col></colgroup><thead>
<tr><th align="left">Name</th><th align="left">Icon Shape</th><th align="left">Inputs</th><th align="left">Collapse Mode</th><th align="left">Collapse Dim</th><th align="left">Input Same DT</th><th align="left">Accum Data Type Str</th><th align="left">Out Data Type Str</th><th align="left">Lock Scale</th><th align="left">Rnd Meth</th><th align="left">Saturate On Integer Overflow</th></tr>
</thead><tbody>
<tr><td align="left"><a href="https://www.blogger.com/null" name="c1ba9a34240f6e97b502979feb3a19db"></a>Add</td><td align="left">rectangular</td><td align="left">--</td><td align="left">All dimensions</td><td align="left">1</td><td align="left">off</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">Inherit: Inherit via internal rule</td><td align="left">off</td><td align="left">Floor</td><td align="left">off</td></tr>
</tbody></table>
</div>
</div>
</div>
<div class="chapter" title="Appendix">
<div class="titlepage">
<div>
<div>
<h2 class="title">
<a href="https://www.blogger.com/null" name="d0e298"></a>Appendix</h2>
</div>
</div>
</div>
<a href="https://www.blogger.com/null" name="appendix-sl"></a><a href="https://www.blogger.com/null" name="d0e303"></a><br />
<div class="table">
<div class="title">
<b>Table 4. Block Type Count</b></div>
<div class="table-contents">
<table border="1" cellspacing="0" style="width: 100%px;" summary="Block Type Count"><colgroup><col width="28.57142857142857%"></col><col width="14.285714285714285%"></col><col width="57.14285714285714%"></col></colgroup><thead>
<tr><th align="left">BlockType</th><th align="left">Count</th><th align="left">Block Names</th></tr>
</thead><tbody>
<tr><td align="left">Gain</td><td align="left">3</td><td align="left"><a class="link" href="https://www.blogger.com/null">Gain</a>, <a class="link" href="https://www.blogger.com/null">Gain1</a>, <a class="link" href="https://www.blogger.com/null">Gain2</a></td></tr>
<tr><td align="left">Integrator</td><td align="left">2</td><td align="left"><a class="link" href="https://www.blogger.com/null">Integrator</a>, <a class="link" href="https://www.blogger.com/null">Integrator1</a></td></tr>
<tr><td align="left">Sum</td><td align="left">1</td><td align="left"><a class="link" href="https://www.blogger.com/null">Add</a></td></tr>
<tr><td align="left">Scope</td><td align="left">1</td><td align="left">Scope</td></tr>
</tbody></table>
</div>
</div>
<a href="https://www.blogger.com/null" name="appendix-sf"></a></div>
</div>
</div>
mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-41125926641013460062015-05-10T22:51:00.001-07:002015-05-10T22:51:57.385-07:00Particle Diffusion - Monte Carlo Simulation<iframe allowfullscreen="" frameborder="0" height="344" src="https://www.youtube.com/embed/Z13hxcNX3-s" width="459"></iframe>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-88762260011617822222015-02-17T20:56:00.000-08:002015-02-17T20:56:31.986-08:00Fermi Energy<div dir="ltr" style="text-align: left;" trbidi="on">
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.footer { width:auto; padding:10px 0px; margin:25px 0px 0px; border-top:1px dotted #878787; font-size:0.8em; line-height:140%; font-style:italic; color:#878787; text-align:left; float:none; }
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% =========================================================================</span>
<span class="comment">%To plot Fermi-Dirac distribution</span>
<span class="comment">% By Mahesha MG, MIT Manipal</span>
<span class="comment">% Date:16/02/2015</span>
<span class="comment">% =========================================================================</span>
clc;
figure(<span class="string">'color'</span>,<span class="string">'white'</span>);
<span class="keyword">while</span>(1)
T=input(<span class="string">'Enter temperature in kelvin: '</span>);
Ef=input(<span class="string">'Enter Fermi level in ev: '</span>);
E=0:0.01:Ef+3;
E=E';
size=length(E);
k=1.38e-23;
e=1.6e-19;
fE=zeros(size,1);
<span class="keyword">for</span> i=1:size
fE(i)=1/(exp((E(i)-Ef)*e/(k*T))+1);
<span class="keyword">end</span>
plot(E,fE,<span class="string">'-'</span>);
xlabel(<span class="string">'Energy in eV'</span>);
title(<span class="string">'By Mahesha MG E-mail: maheshamg@gmail.com'</span>);
ylabel(<span class="string">'f(E)'</span>);
hold <span class="string">all</span>;
ch= input(<span class="string">'Press 1 to continue and 0 to exit: '</span>);
<span class="keyword">if</span> ch == 0
<span class="keyword">break</span>;
<span class="keyword">end</span>
<span class="keyword">end</span>
</pre><p class="footer"><br><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB® R2014b</a><br></p></div><!--
##### SOURCE BEGIN #####
% =========================================================================
%To plot Fermi-Dirac distribution
% By Mahesha MG, MIT Manipal
% Date:16/02/2015
% =========================================================================
clc;
figure('color','white');
while(1)
T=input('Enter temperature in kelvin: ');
Ef=input('Enter Fermi level in ev: ');
E=0:0.01:Ef+3;
E=E';
size=length(E);
k=1.38e-23;
e=1.6e-19;
fE=zeros(size,1);
for i=1:size
fE(i)=1/(exp((E(i)-Ef)*e/(k*T))+1);
end
plot(E,fE,'-');
xlabel('Energy in eV');
title('By Mahesha MG E-mail: maheshamg@gmail.com');
ylabel('f(E)');
hold all;
ch= input('Press 1 to continue and 0 to exit: ');
if ch == 0
break;
end
end
##### SOURCE END #####
--></body></html>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPMGJ8RWngq0Ow_Kod9H2gJfc-nIoiAplyiMwkuxCd8yTUXQg3AetfEi7jA2bAs63kVRWSMAf6d5M9ptX4THhmAhERPs-ftydSo_SmDPo7p_vXDgycTiWcdE0Xei9SeVII3SRTTFfgeUYn/s1600/FE.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPMGJ8RWngq0Ow_Kod9H2gJfc-nIoiAplyiMwkuxCd8yTUXQg3AetfEi7jA2bAs63kVRWSMAf6d5M9ptX4THhmAhERPs-ftydSo_SmDPo7p_vXDgycTiWcdE0Xei9SeVII3SRTTFfgeUYn/s320/FE.png" /></a></div>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-29484380468089755382015-02-12T22:12:00.001-08:002015-02-12T22:18:06.448-08:00Blackbody Radiation<div dir="ltr" style="text-align: left;" trbidi="on">
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h2 { padding:0px; margin:0px 0px 8px; font-family:Arial, Helvetica, sans-serif; font-size:1.2em; color:#000; font-weight:bold; line-height:140%; border-bottom:1px solid #d6d4d4; display:block; }
h3 { padding:0px; margin:0px 0px 5px; font-family:Arial, Helvetica, sans-serif; font-size:1.1em; color:#000; font-weight:bold; line-height:140%; }
a { color:#005fce; text-decoration:none; }
a:hover { color:#005fce; text-decoration:underline; }
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p { padding:0px; margin:0px 0px 20px; }
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</style></head><body><div class="content">
<pre class="codeinput"><span class="comment">% =========================================================================</span>
<span class="comment">%To plot intensity graph for blackbody</span>
<span class="comment">% By Mahesha MG, MIT Manipal</span>
<span class="comment">% Date:13/02/2015</span>
<span class="comment">% =========================================================================</span>
clc;
figure(<span class="string">'color'</span>,<span class="string">'white'</span>);
<span class="keyword">while</span>(1)
T=input(<span class="string">'Enter blackbody temperature in kelvin: '</span>);
lm=2.898e-3/T;
l=1e-9:1e-9:5000e-9;
l=l';
h=6.626e-34;
c=3e8;
k=1.38e-23;
I=zeros(5000,1);
<span class="keyword">for</span> i=1:5000
I(i)=2*pi*h*c^2/(l(i)^5*(exp((h*c)/(l(i)*k*T))-1));
<span class="keyword">end</span>
display(lm);
plot(l,I,<span class="string">'-'</span>);
xlabel(<span class="string">'Wavelength'</span>);
title(<span class="string">'By Mahesha MG E-mail: maheshamg@gmail.com'</span>);
ylabel(<span class="string">'Intensity'</span>);
hold <span class="string">all</span>;
ch= input(<span class="string">'Press 1 to continue and 0 to exit: '</span>);
<span class="keyword">if</span> ch == 0
<span class="keyword">break</span>;
<span class="keyword">end</span>
<span class="keyword">end</span>
</pre>
<div class="footer">
<br /><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB® R2014b</a></div>
</div>
<!--
##### SOURCE BEGIN #####
% =========================================================================
%To plot intensity graph for blackbody
% By Mahesha MG, MIT Manipal
% Date:13/02/2015
% =========================================================================
clc;
figure('color','white');
while(1)
T=input('Enter blackbody temperature in kelvin: ');
lm=2.898e-3/T;
l=1e-9:1e-9:5000e-9;
l=l';
h=6.626e-34;
c=3e8;
k=1.38e-23;
I=zeros(5000,1);
for i=1:5000
I(i)=2*pi*h*c^2/(l(i)^5*(exp((h*c)/(l(i)*k*T))-1));
end
display(lm);
plot(l,I,'-');
xlabel('Wavelength');
title('By Mahesha MG E-mail: maheshamg@gmail.com');
ylabel('Intensity');
hold all;
ch= input('Press 1 to continue and 0 to exit: ');
if ch == 0
break;
end
end
##### SOURCE END #####
--></body></html></div>
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMaKgy8jTZ6wx1-Ap4tTAX5Ww5DhFeMJJsjUWJ1nDeY1b4t8Q43Jwfznih4I2Pi9eSGLcnvu6nf4rl45pbhaWD7FiZXx0Xqc8RKz0f07NBoal8NCsDYjxjoLbiZmk-U2z4LYE9-KTYeEgH/s1600/bb.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMaKgy8jTZ6wx1-Ap4tTAX5Ww5DhFeMJJsjUWJ1nDeY1b4t8Q43Jwfznih4I2Pi9eSGLcnvu6nf4rl45pbhaWD7FiZXx0Xqc8RKz0f07NBoal8NCsDYjxjoLbiZmk-U2z4LYE9-KTYeEgH/s320/bb.png" /></a></div>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-35594006986406745172014-11-19T21:35:00.000-08:002014-11-19T21:35:58.478-08:00MATLAB Code - Propagating Sine Wave<div dir="ltr" style="text-align: left;" trbidi="on">
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% _____________________________________________________</span>
<span class="comment">% Progression of sine wave and sinusoidal oscillation</span>
<span class="comment">% Developed by Mahesha MG, MIT Manipal</span>
<span class="comment">%______________________________________________________</span>
figure(<span class="string">'color'</span>,<span class="string">'white'</span>)
x1=0;
x=0:.1:10;
<span class="keyword">for</span> t=0:.01:100
y=sin(2*x-1*t);
h= plot(x,y,<span class="string">'bo'</span>,x(51),y(51),<span class="string">'r*'</span>);
title(<span class="string">'Progression of sine wave'</span>)
xlabel(<span class="string">'By: Mahesha MG maheshamg@gmail.com'</span>);
h=getframe;
getframe;
<span class="keyword">end</span>
</pre><p class="footer"><br><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB® R2014b</a><br></p></div><!--
##### SOURCE BEGIN #####
% _____________________________________________________
% Progression of sine wave and sinusoidal oscillation
% Developed by Mahesha MG, MIT Manipal
%______________________________________________________
figure('color','white')
x1=0;
x=0:.1:10;
for t=0:.01:100
y=sin(2*x-1*t);
h= plot(x,y,'bo',x(51),y(51),'r*');
title('Progression of sine wave')
xlabel('By: Mahesha MG maheshamg@gmail.com');
h=getframe;
getframe;
end
##### SOURCE END #####
--></body></html>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-51092284547734374772014-03-19T22:49:00.000-07:002014-03-19T22:49:00.537-07:00C code - Particle Diffusion by Monte Carlo Method<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-26379745611415908122014-03-18T00:20:00.001-07:002014-03-18T00:26:51.817-07:00C code - Monte-Carlo crude integration<div dir="ltr" style="text-align: left;" trbidi="on">
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<div style="text-align: center;">
<span style="color: blue;">______________________________________________________________________ </span></div>
<div style="text-align: center;">
<span style="color: red;">SAMPLE OUTPUTS:</span></div>
<br />
<div style="text-align: center;">
<span style="color: blue;">Enter number of samples: 100<br />Integral value is 0.927600</span></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<span style="color: blue;"> </span><span style="color: blue;">Enter number of samples: 1000<br />Integral value is 0.987179 </span><br />
<br />
<span style="color: blue;"> </span><span style="color: blue;">Enter number of samples: 10000<br />Integral value is 0.995588</span></div>
</div>
mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-4131832536814587142014-03-14T00:51:00.002-07:002014-03-14T00:51:41.694-07:00C Code - Driven Oscillator by Euler's Method<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-52590148822879731162014-03-11T04:55:00.004-07:002014-03-11T04:55:54.829-07:00C code - RC Charging/discharging by Euler's method<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-65573098306528316422014-03-11T03:51:00.003-07:002014-03-11T03:51:56.280-07:00C Code - Simpson's Rule<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-13009903930100295482014-02-21T19:56:00.001-08:002014-02-21T19:56:35.691-08:00C code - Numerical Integration by Trapezoidal Rule<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-26854950431718523872014-02-20T23:39:00.000-08:002014-02-20T23:42:18.596-08:00MATLAB - Radioactive Decay by Monte Carlo Method<div dir="ltr" style="text-align: left;" trbidi="on">
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<pre class="codeinput"><span class="comment">% _________________________________________________________________________</span>
<span class="comment">% To simulate radio active decay by Monte Carlo method</span>
<span class="comment">% It gives nuclides number upto 10000 time steps</span>
<span class="comment">% By Mahesha MG, MIT</span>
<span class="comment">% Date: 15/02/2014</span>
<span class="comment">% _________________________________INPUT___________________________________</span>
clc;
clear;
lambda=input('Enter decay constant in /s: ');
n=input('Enter total number of nuclides: ');
dt=0.0001/lambda;
nt=zeros(10000,1); <span class="comment">%nt holds MC result</span>
nta=zeros(10000,1); <span class="comment">%nta holds analytic result</span>
tmax=10000*dt;
t=(0:dt:tmax)';
nta=n*exp(-lambda*t); <span class="comment">%Analytic solution</span>
nt(1)=n;
<span class="comment">% __________________________Monte Carlo Method_____________________________</span>
<span class="keyword">for</span> i=2:10001
random=rand(n,1);
count=length(random(random<=0.0001));
n=n-count;
<span class="keyword">if</span>(n<=0)
<span class="keyword">break</span>;
<span class="keyword">end</span>
nt(i)=n;
<span class="keyword">end</span>
<span class="comment">% _________________________________________________________________________</span>
plot(t,nt,<span class="string">'r'</span>,t,nta,<span class="string">'b'</span>);
xlabel(<span class="string">'Time'</span>);
ylabel(<span class="string">'No. of nuclides'</span>);
</pre>
<img alt="" hspace="5" src="radio_decay_01.png" vspace="5" />
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<div class="footer">
<br /><a href="http://www.mathworks.com/products/matlab/">Published with MATLAB® R2013b</a></div>
</div>
<!--
##### SOURCE BEGIN #####
% _________________________________________________________________________
% To simulate radio active decay by Monte Carlo method
% It gives nuclides number upto 10000 time steps
% By Mahesha MG, MIT
% Date: 15/02/2014
% _________________________________INPUT___________________________________
clc;
clear;
lambda=input('Enter decay constant in /s: ');
n=input('Enter total number of nuclides: ');
dt=0.0001/lambda;
nt=zeros(10000,1); %nt holds MC result
nta=zeros(10000,1); %nta holds analytic result
tmax=10000*dt;
t=(0:dt:tmax)';
nta=n*exp(-lambda*t); %Analytic solution
nt(1)=n;
% __________________________Monte Carlo Method_____________________________
for i=2:10001
random=rand(n,1);
count=length(random(random<=0.0001));
n=n-count;
if(n<=0)
break;
end
nt(i)=n;
end
% _________________________________________________________________________
plot(t,nt,'r',t,nta,'b');
xlabel('Time');
ylabel('No. of nuclides');
##### SOURCE END #####
--></body></html></div>
mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com3tag:blogger.com,1999:blog-809164996868407424.post-34675198616611034222014-02-14T03:53:00.001-08:002014-02-14T03:54:07.280-08:00C code - Newton's forward difference interpolation<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-21936096714005653882014-01-28T03:48:00.002-08:002014-01-28T03:48:59.258-08:00C code - Secant Method<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com2tag:blogger.com,1999:blog-809164996868407424.post-34038869880831568032014-01-26T23:58:00.003-08:002014-01-26T23:58:43.187-08:00C code - False Position Method<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-69635745718176789502014-01-24T22:47:00.000-08:002014-01-24T22:47:43.868-08:00C code - Linear least square fit<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-70058596000706510102014-01-24T04:24:00.000-08:002014-01-24T04:24:21.434-08:00C Code - Newton's Backward Interpolation<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-41593642784932808452014-01-23T22:16:00.000-08:002014-01-23T22:17:19.608-08:00C Code - Bisection Method [New]<div dir="ltr" style="text-align: left;" trbidi="on">
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mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-74303048973685616122013-10-24T23:02:00.001-07:002013-10-24T23:02:55.780-07:00MATLAB - Bisection [NEW]<div dir="ltr" style="text-align: left;" trbidi="on">
<br /></div>
<title>new</title><meta name="generator" content="MATLAB 7.13"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2013-10-25"><meta name="DC.source" content="new.m"><style type="text/css">
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% _______________________________ About ___________________________________</span>
<span class="comment">% To find root of a given equation by bisection method</span>
<span class="comment">% By Mahesha MG, MIT Manipal</span>
<span class="comment">% Date: 24/10/2013</span>
<span class="comment">% ________________________________Input____________________________________</span>
clc;
clear;
display(<span class="string">'Enter the equation. eg: x^2+x-1'</span>);
f1=input(<span class="string">'Enter a valid MATLAB expression in x : '</span>,<span class="string">'s'</span>);
e=input(<span class="string">'Enter the accuracy : '</span>);
<span class="comment">% _____________________To get upper and lower range________________________</span>
x=0;
f0=eval(f1);
<span class="keyword">if</span> abs(f0)<e
display(<span class="string">'Root of the equation is zero'</span>);
<span class="keyword">else</span>
i=1;
<span class="keyword">while</span>(i)
x=x+1;
<span class="keyword">if</span> (f0*eval(f1))<0
xl=0;
xu=x;
i=0;
<span class="keyword">end</span>
x=-x;
<span class="keyword">if</span> (f0*eval(f1))<0
xl=x;
xu=0;
i=0;
<span class="keyword">end</span>
x=abs(x);
<span class="keyword">end</span>
x=xl;
<span class="keyword">if</span> eval(f1)<0
xn=xl;
xp=xu;
<span class="keyword">else</span>
xn=xu;
xp=xl;
<span class="keyword">end</span>
<span class="comment">% ________________________________Bisection________________________________</span>
<span class="keyword">while</span> (abs(xn-xp)>e)
x=(xn+xp)/2;
<span class="keyword">if</span> eval(f1)<0
xn=x;
<span class="keyword">else</span>
xp=x;
<span class="keyword">end</span>
<span class="keyword">end</span>
Root=x
<span class="keyword">end</span>
<span class="comment">% _________________________________________________________________________</span>
</pre><p class="footer"><br>
Published with MATLAB® 7.13<br></p></div><!--
##### SOURCE BEGIN #####
% _______________________________ About ___________________________________
% To find root of a given equation by bisection method
% By Mahesha MG, MIT Manipal
% Date: 24/10/2013
% ________________________________Input____________________________________
clc;
clear;
display('Enter the equation. eg: x^2+x-1');
f1=input('Enter a valid MATLAB expression in x : ','s');
e=input('Enter the accuracy : ');
% _____________________To get upper and lower range________________________
x=0;
f0=eval(f1);
if abs(f0)<e
display('Root of the equation is zero');
else
i=1;
while(i)
x=x+1;
if (f0*eval(f1))<0
xl=0;
xu=x;
i=0;
end
x=-x;
if (f0*eval(f1))<0
xl=x;
xu=0;
i=0;
end
x=abs(x);
end
x=xl;
if eval(f1)<0
xn=xl;
xp=xu;
else
xn=xu;
xp=xl;
end
% ________________________________Bisection________________________________
while (abs(xn-xp)>e)
x=(xn+xp)/2;
if eval(f1)<0
xn=x;
else
xp=x;
end
end
Root=x
end
% _________________________________________________________________________
##### SOURCE END #####
--></body></html>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-74578782555174852012013-05-11T01:38:00.000-07:002013-05-11T01:38:15.351-07:00Video on Particle Diffusion - Monte Carlo<iframe src="https://docs.google.com/file/d/0B3UAkOgw1Qn8Y0dJUXJJSjFuV2s/preview" width="640" height="385"></iframe>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-19167068486795267012013-05-02T23:04:00.000-07:002013-05-02T23:32:57.218-07:00MATLAB - Parabolic Equation<title>parabolic</title><meta name="generator" content="MATLAB 7.13"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2013-05-03"><meta name="DC.source" content="parabolic.m"><style type="text/css">
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/* Make the text shrink to fit narrow windows, but not stretch too far in
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background: #EEEEEE;
padding: 10px;
}
@media print {
pre.codeinput {word-wrap:break-word; width:100%;}
}
span.keyword {color: #0000FF}
span.comment {color: #228B22}
span.string {color: #A020F0}
span.untermstring {color: #B20000}
span.syscmd {color: #B28C00}
pre.codeoutput {
color: #666666;
padding: 10px;
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color: red;
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p.footer {
text-align: right;
font-size: xx-small;
font-weight: lighter;
font-style: italic;
color: gray;
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% _________________________________________________________________________</span>
<span class="comment">% To study heat flow in one-dimensional system (insulated rod)</span>
<span class="comment">% ie finite difference solution to parabolic equation</span>
<span class="comment">% By Mahesha MG, MIT</span>
<span class="comment">% Date: 02/05/2013</span>
<span class="comment">% _________________________________INPUT___________________________________</span>
clc;
clear;
k1=input(<span class="string">'Enter thermal conductivity of the material of rod: '</span>);
cp=input(<span class="string">'Enter specific heat of the material of rod: '</span>);
rho=input(<span class="string">'Enter density of the material of rod: '</span>);
l=input(<span class="string">'Enter length of the rod: '</span>);
h=input(<span class="string">'Enter step length: '</span>);
Tl=input(<span class="string">'Enter temperature at left side of the rod: '</span>);
Tr=input(<span class="string">'Enter temperature at right side of the rod: '</span>);
tmax=input(<span class="string">'Enter tmax: '</span>);
f1=input(<span class="string">'Enter initial condition (a valid MATLAB expression in x): '</span>,<span class="string">'s'</span>);
<span class="comment">% ___________________________INITIAL CONDITION_____________________________</span>
k=k1/(cp*rho);
tou=h^2/(2*k); <span class="comment">%time step</span>
r=(tou*k)/h^2;
x=0:h:l;
temp=eval(f1);
temp(1)=Tl;
temp(size(x))=Tr;
temp2=temp;
temp1=zeros(size(temp));
temp1(1)=Tl;
temp1(size(x))=Tr;
t0=0;
<span class="comment">% _________________________FINITE DIFFERENCE METHOD________________________</span>
<span class="keyword">while</span> t0<tmax
t0=t0+tou;
<span class="keyword">for</span> i=2:size(x')-1
temp1(i)=0.5*(temp2(i-1)+temp2(i+1));
<span class="keyword">end</span>
temp2=temp1;
temp=[temp;temp1];
<span class="keyword">end</span>
temp <span class="comment">%temperature at different interior points with time</span>
t=0:tou:tmax;
surf(x,t,temp)
xlabel(<span class="string">'length in m'</span>)
ylabel(<span class="string">'Time in s'</span>)
zlabel(<span class="string">'Temperature in C'</span>)
<span class="comment">% _________________________SAMPLE INPUT AND RESULT_________________________</span>
<span class="comment">% Enter thermal conductivity of the material of rod: 2</span>
<span class="comment">% Enter specific heat of the material of rod: 1</span>
<span class="comment">% Enter density of the material of rod: 1</span>
<span class="comment">% Enter length of the rod: 4</span>
<span class="comment">% Enter step length: 1</span>
<span class="comment">% Enter temperature at left side of the rod: 0</span>
<span class="comment">% Enter temperature at right side of the rod: 0</span>
<span class="comment">% Enter tmax: 1.5</span>
<span class="comment">% Enter initial condition (a valid MATLAB expression in x): 50*(4-x)</span>
<span class="comment">%</span>
<span class="comment">% temp =</span>
<span class="comment">%</span>
<span class="comment">% 0 150.0000 100.0000 50.0000 0</span>
<span class="comment">% 0 50.0000 100.0000 50.0000 0</span>
<span class="comment">% 0 50.0000 50.0000 50.0000 0</span>
<span class="comment">% 0 25.0000 50.0000 25.0000 0</span>
<span class="comment">% 0 25.0000 25.0000 25.0000 0</span>
<span class="comment">% 0 12.5000 25.0000 12.5000 0</span>
<span class="comment">% 0 12.5000 12.5000 12.5000 0</span>
<span class="comment">% Problem taken from Numerical Methods by E Balagurusamy</span>
<span class="comment">% _________________________________________________________________________</span>
</pre><p class="footer"><br>
Published with MATLAB® 7.13<br></p></div><!--
##### SOURCE BEGIN #####
% _________________________________________________________________________
% To study heat flow in one-dimensional system (insulated rod)
% ie finite difference solution to parabolic equation
% By Mahesha MG, MIT
% Date: 02/05/2013
% _________________________________INPUT___________________________________
clc;
clear;
k1=input('Enter thermal conductivity of the material of rod: ');
cp=input('Enter specific heat of the material of rod: ');
rho=input('Enter density of the material of rod: ');
l=input('Enter length of the rod: ');
h=input('Enter step length: ');
Tl=input('Enter temperature at left side of the rod: ');
Tr=input('Enter temperature at right side of the rod: ');
tmax=input('Enter tmax: ');
f1=input('Enter initial condition (a valid MATLAB expression in x): ','s');
% ___________________________INITIAL CONDITION_____________________________
k=k1/(cp*rho);
tou=h^2/(2*k); %time step
r=(tou*k)/h^2;
x=0:h:l;
temp=eval(f1);
temp(1)=Tl;
temp(size(x))=Tr;
temp2=temp;
temp1=zeros(size(temp));
temp1(1)=Tl;
temp1(size(x))=Tr;
t0=0;
% _________________________FINITE DIFFERENCE METHOD________________________
while t0<tmax
t0=t0+tou;
for i=2:size(x')-1
temp1(i)=0.5*(temp2(i-1)+temp2(i+1));
end
temp2=temp1;
temp=[temp;temp1];
end
temp %temperature at different interior points with time
t=0:tou:tmax;
surf(x,t,temp)
xlabel('length in m')
ylabel('Time in s')
zlabel('Temperature in C')
% _________________________SAMPLE INPUT AND RESULT_________________________
% Enter thermal conductivity of the material of rod: 2
% Enter specific heat of the material of rod: 1
% Enter density of the material of rod: 1
% Enter length of the rod: 4
% Enter step length: 1
% Enter temperature at left side of the rod: 0
% Enter temperature at right side of the rod: 0
% Enter tmax: 1.5
% Enter initial condition (a valid MATLAB expression in x): 50*(4-x)
%
% temp =
%
% 0 150.0000 100.0000 50.0000 0
% 0 50.0000 100.0000 50.0000 0
% 0 50.0000 50.0000 50.0000 0
% 0 25.0000 50.0000 25.0000 0
% 0 25.0000 25.0000 25.0000 0
% 0 12.5000 25.0000 12.5000 0
% 0 12.5000 12.5000 12.5000 0
% Problem taken from Numerical Methods by E Balagurusamy
% _________________________________________________________________________
##### SOURCE END #####
--></body></html>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com0tag:blogger.com,1999:blog-809164996868407424.post-83570793733306654382013-04-08T21:44:00.000-07:002013-04-08T21:44:28.693-07:00MATLAB - Secant Method<title>secant</title><meta name="generator" content="MATLAB 7.13"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2013-04-09"><meta name="DC.source" content="secant.m"><style type="text/css">
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% _________________________________________________________________________</span>
<span class="comment">% To get accurate root of given equation by Secant method</span>
<span class="comment">% By Mahesha MG, MIT</span>
<span class="comment">% Date: 09/04/2013</span>
<span class="comment">% _________________________________INPUT___________________________________</span>
clc;
clear;
y = inline(<span class="string">'x^2+x-2.5'</span>); <span class="comment">%Equation</span>
x0=input(<span class="string">'Enter first approximate root: '</span>); <span class="comment">%Example: 3</span>
x1=input(<span class="string">'Enter second approximate root: '</span>); <span class="comment">%Example: 4</span>
e=input(<span class="string">'Enter the accuracy: '</span>); <span class="comment">%Example: 1e-5</span>
<span class="comment">% _____________________________Secant method_______________________________</span>
<span class="keyword">while</span> abs(feval(y,x1))>e
x2=((x0*feval(y,x1))-(x1*feval(y,x0)))/(feval(y,x1)-feval(y,x0));
x0=x1;
x1=x2;
<span class="keyword">end</span>
<span class="comment">% _________________________________________________________________________</span>
root=x2
</pre><p class="footer"><br>
Published with MATLAB® 7.13<br></p></div><!--
##### SOURCE BEGIN #####
% _________________________________________________________________________
% To get accurate root of given equation by Secant method
% By Mahesha MG, MIT
% Date: 09/04/2013
% _________________________________INPUT___________________________________
clc;
clear;
y = inline('x^2+x-2.5'); %Equation
x0=input('Enter first approximate root: '); %Example: 3
x1=input('Enter second approximate root: '); %Example: 4
e=input('Enter the accuracy: '); %Example: 1e-5
% _____________________________Secant method_______________________________
while abs(feval(y,x1))>e
x2=((x0*feval(y,x1))-(x1*feval(y,x0)))/(feval(y,x1)-feval(y,x0));
x0=x1;
x1=x2;
end
% _________________________________________________________________________
root=x2
##### SOURCE END #####
--></body></html>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com3tag:blogger.com,1999:blog-809164996868407424.post-89443512117994807142013-03-14T20:47:00.001-07:002013-03-14T20:47:49.430-07:00MATLAB - Newton Raphson Method<title>newton</title><meta name="generator" content="MATLAB 7.13"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2013-03-14"><meta name="DC.source" content="newton.m"><style type="text/css">
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</style></head><body><div class="content"><pre class="codeinput"><span class="comment">% _________________________________________________________________________</span>
<span class="comment">% To get accurate root of given equation by Newton-Raphson method</span>
<span class="comment">% By Mahesha MG, MIT</span>
<span class="comment">% Date: 14/03/2013</span>
<span class="comment">% _________________________________INPUT___________________________________</span>
clc;
clear;
y = inline(<span class="string">'x^2+x-2'</span>); <span class="comment">%Equation</span>
dy = inline(<span class="string">'2*x+1'</span>); <span class="comment">%Derivative of the equation</span>
x0=input(<span class="string">'Enter approximate root: '</span>);
e=input(<span class="string">'Enter the accuracy: '</span>); <span class="comment">%Example: 1e-5</span>
<span class="comment">% _________________________Newton Raphson method___________________________</span>
<span class="keyword">while</span> abs(feval(y,x0))>e
h=-feval(y,x0)/feval(dy,x0);
x0=x0+h;
<span class="keyword">end</span>
<span class="comment">% _________________________________________________________________________</span>
root=x0
</pre><p class="footer"><br>
Published with MATLAB® 7.13<br></p></div><!--
##### SOURCE BEGIN #####
% _________________________________________________________________________
% To get accurate root of given equation by Newton-Raphson method
% By Mahesha MG, MIT
% Date: 14/03/2013
% _________________________________INPUT___________________________________
clc;
clear;
y = inline('x^2+x-2'); %Equation
dy = inline('2*x+1'); %Derivative of the equation
x0=input('Enter approximate root: ');
e=input('Enter the accuracy: '); %Example: 1e-5
% _________________________Newton Raphson method___________________________
while abs(feval(y,x0))>e
h=-feval(y,x0)/feval(dy,x0);
x0=x0+h;
end
% _________________________________________________________________________
root=x0
##### SOURCE END #####
--></body></html>mghttp://www.blogger.com/profile/17389270050642663796noreply@blogger.com1