diff --git a/homework3/.idea/workspace.xml b/homework3/.idea/workspace.xml
index d31a6fb..47d6603 100644
--- a/homework3/.idea/workspace.xml
+++ b/homework3/.idea/workspace.xml
@@ -1,394 +1,501 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
   <component name="CMakeRunConfigurationManager" shouldGenerate="true" shouldDeleteObsolete="true" buildAllGenerated="false">
     <generated />
   </component>
   <component name="CMakeSettings">
     <configurations>
       <configuration PROFILE_NAME="Debug" CONFIG_NAME="Debug" />
     </configurations>
   </component>
   <component name="ChangeListManager">
     <list default="true" id="4ffcf8b4-3f90-4054-ad57-61ff4d03c055" name="Default" comment="" />
     <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
     <option name="TRACKING_ENABLED" value="true" />
     <option name="SHOW_DIALOG" value="false" />
     <option name="HIGHLIGHT_CONFLICTS" value="true" />
     <option name="HIGHLIGHT_NON_ACTIVE_CHANGELIST" value="false" />
     <option name="LAST_RESOLUTION" value="IGNORE" />
   </component>
   <component name="FileEditorManager">
     <leaf SIDE_TABS_SIZE_LIMIT_KEY="300">
       <file leaf-file-name="compute_temperature.hh" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.hh">
           <provider selected="true" editor-type-id="text-editor">
             <state relative-caret-position="255">
               <caret line="17" column="11" selection-start-line="17" selection-start-column="11" selection-end-line="17" selection-end-column="11" />
             </state>
           </provider>
         </entry>
       </file>
-      <file leaf-file-name="compute_temperature.cc" pinned="false" current-in-tab="false">
+      <file leaf-file-name="compute_temperature.cc" pinned="false" current-in-tab="true">
         <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.cc">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="62">
-              <caret line="47" lean-forward="true" selection-start-line="47" selection-end-line="47" />
+            <state relative-caret-position="396">
+              <caret line="62" selection-start-line="62" selection-end-line="62" />
             </state>
           </provider>
         </entry>
       </file>
       <file leaf-file-name="CMakeLists.txt" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/CMakeLists.txt">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="15">
+            <state relative-caret-position="75">
               <caret line="5" selection-start-line="5" selection-end-line="5" />
             </state>
           </provider>
         </entry>
       </file>
-      <file leaf-file-name="matrix.hh" pinned="false" current-in-tab="true">
+      <file leaf-file-name="matrix.hh" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/matrix.hh">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="874">
+            <state relative-caret-position="1095">
               <caret line="73" column="4" selection-start-line="73" selection-start-column="4" selection-end-line="73" selection-end-column="4" />
             </state>
           </provider>
         </entry>
       </file>
       <file leaf-file-name="my_types.hh" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/my_types.hh">
           <provider selected="true" editor-type-id="text-editor" />
         </entry>
       </file>
       <file leaf-file-name="compute_verlet_integration.hh" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/compute_verlet_integration.hh">
           <provider selected="true" editor-type-id="text-editor">
             <state relative-caret-position="300">
               <caret line="20" column="26" selection-start-line="20" selection-start-column="26" selection-end-line="20" selection-end-column="26" />
             </state>
           </provider>
         </entry>
       </file>
       <file leaf-file-name="README.md" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/README.md">
           <provider selected="true" editor-type-id="text-editor">
             <state relative-caret-position="420">
               <caret line="28" selection-start-line="28" selection-end-line="28" />
             </state>
           </provider>
         </entry>
       </file>
       <file leaf-file-name="material_points_factory.cc" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.cc">
           <provider selected="true" editor-type-id="text-editor">
             <state relative-caret-position="510">
-              <caret line="34" column="27" lean-forward="true" selection-start-line="34" selection-start-column="27" selection-end-line="34" selection-end-column="27" />
+              <caret line="34" column="27" selection-start-line="34" selection-start-column="27" selection-end-line="34" selection-end-column="27" />
             </state>
           </provider>
         </entry>
       </file>
       <file leaf-file-name="material_points_factory.hh" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.hh">
           <provider selected="true" editor-type-id="text-editor" />
         </entry>
       </file>
       <file leaf-file-name="main.cc" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/starting_point/main.cc">
           <provider selected="true" editor-type-id="text-editor">
             <state>
               <folding>
                 <element signature="e#0#29#0" expanded="true" />
               </folding>
             </state>
           </provider>
         </entry>
       </file>
     </leaf>
   </component>
   <component name="IdeDocumentHistory">
     <option name="CHANGED_PATHS">
       <list>
         <option value="$PROJECT_DIR$/README.md" />
         <option value="$PROJECT_DIR$/starting_point/compute_temperature.hh" />
         <option value="$PROJECT_DIR$/starting_point/material_points_factory.cc" />
         <option value="$PROJECT_DIR$/starting_point/matrix.hh" />
         <option value="$PROJECT_DIR$/starting_point/compute_temperature.cc" />
         <option value="$PROJECT_DIR$/starting_point/CMakeLists.txt" />
       </list>
     </option>
   </component>
   <component name="JsBuildToolGruntFileManager" detection-done="true" sorting="DEFINITION_ORDER" />
   <component name="JsBuildToolPackageJson" detection-done="true" sorting="DEFINITION_ORDER" />
   <component name="JsGulpfileManager">
     <detection-done>true</detection-done>
     <sorting>DEFINITION_ORDER</sorting>
   </component>
   <component name="NodePackageJsonFileManager">
     <packageJsonPaths />
   </component>
   <component name="ProjectFrameBounds">
     <option name="y" value="23" />
     <option name="width" value="1440" />
     <option name="height" value="800" />
   </component>
   <component name="ProjectView">
     <navigator proportions="" version="1">
       <foldersAlwaysOnTop value="true" />
     </navigator>
     <panes>
+      <pane id="Scope" />
       <pane id="ProjectPane">
         <subPane>
           <expand>
             <path>
               <item name="homework3" type="b2602c69:ProjectViewProjectNode" />
               <item name="homework3" type="462c0819:PsiDirectoryNode" />
             </path>
             <path>
               <item name="homework3" type="b2602c69:ProjectViewProjectNode" />
               <item name="homework3" type="462c0819:PsiDirectoryNode" />
               <item name="starting_point" type="462c0819:PsiDirectoryNode" />
             </path>
           </expand>
           <select />
         </subPane>
       </pane>
-      <pane id="Scope" />
     </panes>
   </component>
   <component name="PropertiesComponent">
     <property name="WebServerToolWindowFactoryState" value="false" />
     <property name="last_opened_file_path" value="$PROJECT_DIR$" />
     <property name="nodejs_interpreter_path.stuck_in_default_project" value="undefined stuck path" />
     <property name="nodejs_npm_path_reset_for_default_project" value="true" />
     <property name="settings.editor.selected.configurable" value="configurable.group.build" />
   </component>
   <component name="RunDashboard">
     <option name="ruleStates">
       <list>
         <RuleState>
           <option name="name" value="ConfigurationTypeDashboardGroupingRule" />
         </RuleState>
         <RuleState>
           <option name="name" value="StatusDashboardGroupingRule" />
         </RuleState>
       </list>
     </option>
   </component>
   <component name="SvnConfiguration">
     <configuration />
   </component>
   <component name="TaskManager">
     <task active="true" id="Default" summary="Default task">
       <changelist id="4ffcf8b4-3f90-4054-ad57-61ff4d03c055" name="Default" comment="" />
       <created>1544395045595</created>
       <option name="number" value="Default" />
       <option name="presentableId" value="Default" />
       <updated>1544395045595</updated>
       <workItem from="1544395046856" duration="12959000" />
       <workItem from="1544618537533" duration="1158000" />
     </task>
     <servers />
   </component>
   <component name="TimeTrackingManager">
-    <option name="totallyTimeSpent" value="14117000" />
+    <option name="totallyTimeSpent" value="14122000" />
   </component>
   <component name="ToolWindowManager">
     <frame x="0" y="23" width="1440" height="800" extended-state="0" />
     <editor active="true" />
     <layout>
       <window_info active="true" content_ui="combo" id="Project" order="0" visible="true" weight="0.24947146" />
       <window_info anchor="bottom" id="TODO" order="6" />
       <window_info anchor="bottom" id="Event Log" order="7" side_tool="true" />
-      <window_info anchor="bottom" id="Version Control" order="7" show_stripe_button="false" />
       <window_info anchor="bottom" id="Run" order="2" />
+      <window_info anchor="bottom" id="Version Control" order="7" show_stripe_button="false" />
       <window_info id="Structure" order="1" side_tool="true" weight="0.25" />
       <window_info anchor="bottom" id="Terminal" order="7" />
-      <window_info id="Favorites" order="2" side_tool="true" />
       <window_info anchor="bottom" id="Debug" order="3" weight="0.4" />
+      <window_info id="Favorites" order="2" side_tool="true" />
       <window_info anchor="right" content_ui="combo" id="Hierarchy" order="2" weight="0.25" />
       <window_info anchor="right" id="Commander" order="0" weight="0.4" />
       <window_info anchor="right" id="Ant Build" order="1" weight="0.25" />
       <window_info anchor="bottom" id="Message" order="0" />
       <window_info anchor="bottom" id="Inspection" order="5" weight="0.4" />
       <window_info anchor="bottom" id="Cvs" order="4" weight="0.25" />
       <window_info anchor="bottom" id="Find" order="1" />
     </layout>
   </component>
   <component name="TypeScriptGeneratedFilesManager">
     <option name="version" value="1" />
   </component>
   <component name="VcsContentAnnotationSettings">
     <option name="myLimit" value="2678400000" />
   </component>
   <component name="XDebuggerManager">
     <breakpoint-manager>
       <option name="time" value="2" />
     </breakpoint-manager>
   </component>
   <component name="editorHistoryManager">
+    <entry file="file://$PROJECT_DIR$/starting_point/CMakeLists.txt">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="75">
+          <caret line="5" lean-forward="true" selection-start-line="5" selection-end-line="5" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/particles_factory_interface.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_interaction.cc">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/system_evolution.cc">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/system.hh">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="-207" />
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/system_evolution.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_contact.cc">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_boundary.cc">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_verlet_integration.cc">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="30">
+          <caret line="2" column="71" lean-forward="true" selection-start-line="2" selection-end-line="2" selection-end-column="71" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/fft.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_verlet_integration.hh">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="300">
+          <caret line="20" column="26" selection-start-line="20" selection-start-column="26" selection-end-line="20" selection-end-column="26" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/README.md">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="420">
+          <caret line="28" selection-start-line="28" selection-end-line="28" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/main.cc">
+      <provider selected="true" editor-type-id="text-editor">
+        <state>
+          <folding>
+            <element signature="e#0#29#0" expanded="true" />
+          </folding>
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/my_types.hh">
+      <provider selected="true" editor-type-id="text-editor" />
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.hh">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="255">
+          <caret line="17" column="11" selection-start-line="17" selection-start-column="11" selection-end-line="17" selection-end-column="11" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.cc">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="510">
+          <caret line="34" column="27" lean-forward="true" selection-start-line="34" selection-start-column="27" selection-end-line="34" selection-end-column="27" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/CMakeLists.txt">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="15">
+          <caret line="5" selection-start-line="5" selection-end-line="5" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/matrix.hh">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="1095">
+          <caret line="73" column="4" selection-start-line="73" selection-start-column="4" selection-end-line="73" selection-end-column="4" />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.cc">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="92">
+          <caret line="49" column="4" selection-start-line="49" selection-start-column="4" selection-end-line="49" selection-end-column="4" />
+        </state>
+      </provider>
+    </entry>
     <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.hh">
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="255">
           <caret line="17" column="11" selection-start-line="17" selection-start-column="11" selection-end-line="17" selection-end-column="11" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.cc">
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="1050">
           <caret line="70" selection-start-line="70" selection-end-line="70" />
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     <entry file="file://$PROJECT_DIR$/starting_point/matrix.hh">
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="1095">
           <caret line="73" column="4" selection-start-line="73" selection-start-column="4" selection-end-line="73" selection-end-column="4" />
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       <provider selected="true" editor-type-id="text-editor" />
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       <provider selected="true" editor-type-id="text-editor">
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     <entry file="file://$PROJECT_DIR$/README.md">
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     <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.cc">
       <provider selected="true" editor-type-id="text-editor">
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     <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.hh">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/main.cc">
       <provider selected="true" editor-type-id="text-editor">
         <state>
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             <element signature="e#0#29#0" expanded="true" />
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     <entry file="file://$PROJECT_DIR$/starting_point/CMakeLists.txt">
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     <entry file="file://$PROJECT_DIR$/starting_point/particles_factory_interface.hh">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute_interaction.cc">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/system_evolution.cc">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/system.hh">
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     <entry file="file://$PROJECT_DIR$/starting_point/system_evolution.hh">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute.hh">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute_contact.cc">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute_boundary.cc">
       <provider selected="true" editor-type-id="text-editor" />
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       <provider selected="true" editor-type-id="text-editor">
         <state>
           <folding>
             <element signature="e#0#29#0" expanded="true" />
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       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/my_types.hh">
       <provider selected="true" editor-type-id="text-editor" />
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     <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.hh">
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     <entry file="file://$PROJECT_DIR$/starting_point/material_points_factory.cc">
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+          <caret line="34" column="27" selection-start-line="34" selection-start-column="27" selection-end-line="34" selection-end-column="27" />
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     <entry file="file://$PROJECT_DIR$/starting_point/CMakeLists.txt">
       <provider selected="true" editor-type-id="text-editor">
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           <caret line="5" selection-start-line="5" selection-end-line="5" />
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       </provider>
     </entry>
     <entry file="file://$PROJECT_DIR$/starting_point/compute_temperature.cc">
       <provider selected="true" editor-type-id="text-editor">
-        <state relative-caret-position="62">
-          <caret line="47" lean-forward="true" selection-start-line="47" selection-end-line="47" />
+        <state relative-caret-position="396">
+          <caret line="62" selection-start-line="62" selection-end-line="62" />
         </state>
       </provider>
     </entry>
     <entry file="file://$PROJECT_DIR$/starting_point/matrix.hh">
       <provider selected="true" editor-type-id="text-editor">
-        <state relative-caret-position="874">
+        <state relative-caret-position="1095">
           <caret line="73" column="4" selection-start-line="73" selection-start-column="4" selection-end-line="73" selection-end-column="4" />
         </state>
       </provider>
     </entry>
   </component>
 </project>
\ No newline at end of file
diff --git a/homework3/TH_gen.py b/homework3/TH_gen.py
index 927935e..2a91177 100644
--- a/homework3/TH_gen.py
+++ b/homework3/TH_gen.py
@@ -1,98 +1,98 @@
 #!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 """
 Created on Thu Dec 13 10:53:07 2018
 
 @author: alessia
 """
 
 import numpy as np
 import math as m
 from mpl_toolkits.mplot3d import Axes3D
 import matplotlib.pyplot as plt
 from matplotlib import cm
 from matplotlib.ticker import LinearLocator, FormatStrFormatter
 
 
 #=======================================================================================
 #
 # This program generates the initial conditions for Temperature and Heat-rate to
 # be used to solve the heat-equation with zero homogeneous boundary conditions.
 
 # The heat-rate is uniformly distributed within a given radius R and zero elsewhere
 # The Temperature can either have a zero homogeneous distribution or a Gaussian distrib.
 
 #---------------------------------------------------------------------------------------
 
 
 
-N2=100*100                                  #Number of particles
-R=0.5                                       #Radius
+N2=10*10                                  #Number of particles 
+R=0.5                                      #Radius
 L=1.                                        #half-lenght of the domain
 C=1.0                                       #Constant val for the uniform distrib. of h
 TGauss=1                                    #Gaussian initial distr. for T
 
 N=int(m.sqrt(N2))
 dx=2*L/N
 
-x, y = np.mgrid[-L:L:N*1j, -L:L:N*1j]
+x, y = np.mgrid[-L:(L-dx):N*1j, -L:(L-dx):N*1j]
 xy = np.column_stack([x.flat, y.flat])
 
 
 if(TGauss == 1):
     mu = np.array([0.0, 0.0])
     sigma = np.array([.15, .15])
     covariance = np.diag(sigma**2)
     T = multivariate_normal.pdf(xy, mean=mu, cov=covariance)
 
 #create the trivial initial condition for T
 else:
     T = (np.zeros(N2))                       
 
 
 #homogeneous distr. for heat-rate within R
 h = np.zeros(N2)
 h = UniformR(R, N, L, C)                    
 
 z=np.column_stack((xy,T.T,h.T))
 
 #Write the output to file N2 lines 4 columns (xpos, ypos, T, hrate) 
 out_file = open("particles.txt","w")
 for i in range (0,N2): 
     out_file.write('\n')
     for j in range(0,4):
         out_file.write('%.20f' % z[i,j] + '\t')
 out_file.close()
 
 
 
 #----------------------Visualization of T and h distributions---------------------------
 
 h = h.reshape(x.shape)
 T = T.reshape(x.shape)
 fig = plt.figure()
 ax = fig.add_subplot(111, projection='3d')
 surf=ax.plot_surface(x,y,h.T)
-surf=ax.plot_surface(x,y,T.T,alpha=0.3)
+#surf=ax.plot_surface(x,y,T.T,alpha=1)
 plt.show()
 
 #=======================================================================================
 #---------------------------------------- END ------------------------------------------
 #=======================================================================================
 
 
 
 def UniformR(R, N, L, C):
     H = np.zeros((N,N))
     dx = 2*L/N
     
     #Loop over 1/4 of the domain
     for i in range(0, int(N/2)):
         x2 = (i*dx-L)**2
         for j in range (0, int(N/2)):
             y2 = (L-j*dx)**2
             if(x2+y2<=R):
                 H[i,j] = H[i,N-j-1] = C
                 H[N-i-1,j] = H[N-i-1,N-j-1] = C  
     hh=np.reshape(H,(N*N))
     return hh
diff --git a/homework3/particles.txt b/homework3/particles.txt
index ca3be69..a7b832f 100644
--- a/homework3/particles.txt
+++ b/homework3/particles.txt
@@ -1,10001 +1,101 @@
 
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