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415 changes: 415 additions & 0 deletions _sources/lecture-18-adsorption.md

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<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
Expand Down Expand Up @@ -419,6 +420,7 @@ <h1>Welcome to Computational Problem Solving in the Chemical Sciences<a class="h
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>
</div>
</section>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
Expand Down Expand Up @@ -659,9 +664,9 @@ <h4>Generating Arrays with Specific Properties<a class="headerlink" href="#gener
[[1. 1. 1.]
[1. 1. 1.]
[1. 1. 1.]]
[[0.38020829 0.21567557 0.80942245]
[0.64521477 0.95713798 0.25298782]
[0.42812882 0.40446243 0.79382746]]
[[0.54445861 0.74080792 0.94093989]
[0.00189169 0.07722415 0.51145732]
[0.18499263 0.06097679 0.19381219]]
</pre></div>
</div>
</div>
Expand Down Expand Up @@ -742,7 +747,7 @@ <h4>Scatter Plots<a class="headerlink" href="#scatter-plots" title="Link to this
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/3813eb41bfc0b094fb0deeaf223a3589ba8299ceeb1f77815e9aef63ea3780bd.png" src="_images/3813eb41bfc0b094fb0deeaf223a3589ba8299ceeb1f77815e9aef63ea3780bd.png" />
<img alt="_images/a5ffdd948ab8f9628ae26b2d416ebd99b9454edb8a83ca765076fa903b0bfd95.png" src="_images/a5ffdd948ab8f9628ae26b2d416ebd99b9454edb8a83ca765076fa903b0bfd95.png" />
</div>
</div>
</section>
Expand Down Expand Up @@ -787,7 +792,7 @@ <h4>Histograms<a class="headerlink" href="#histograms" title="Link to this headi
</div>
</div>
<div class="cell_output docutils container">
<img alt="_images/26b6cd7c500fe8ffc2e502b476e09ebc4148f22520a235ae40ea139cd0caa0aa.png" src="_images/26b6cd7c500fe8ffc2e502b476e09ebc4148f22520a235ae40ea139cd0caa0aa.png" />
<img alt="_images/afdd3af4e706ec33c4d4f01c8d6b3042534fc3d0bdbd99698f1c6c4ba100e70c.png" src="_images/afdd3af4e706ec33c4d4f01c8d6b3042534fc3d0bdbd99698f1c6c4ba100e70c.png" />
</div>
</div>
</section>
Expand Down Expand Up @@ -870,11 +875,11 @@ <h3>4.2 Series: The 1D Data Structure<a class="headerlink" href="#series-the-1d-
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0 2.804001
1 -0.258769
2 1.045537
3 0.985343
4 -0.646079
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0 -0.231752
1 0.281163
2 -0.926110
3 -0.623194
4 0.588479
dtype: float64
</pre></div>
</div>
Expand Down Expand Up @@ -906,11 +911,11 @@ <h3>4.3 DataFrame: The 2D Data Structure<a class="headerlink" href="#dataframe-t
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> A B
0 -0.661308 0.093195
1 0.009564 0.094149
2 0.444864 0.048416
3 -0.797464 0.281626
4 -0.059068 0.607767
0 2.309414 0.694430
1 -0.671326 0.515353
2 -1.005650 0.102987
3 -0.084647 0.952898
4 0.639877 0.712845
</pre></div>
</div>
</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
Expand Down Expand Up @@ -742,7 +747,7 @@ <h3>Step 2: Minimizing the Equilibrium Equation<a class="headerlink" href="#step
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>25%
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/n9/q030dl3x6qgfqffys4wc7d4c0000gn/T/ipykernel_75226/1733916972.py:1: OptimizeWarning: Initial guess is not within the specified bounds
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/n9/q030dl3x6qgfqffys4wc7d4c0000gn/T/ipykernel_86439/1733916972.py:1: OptimizeWarning: Initial guess is not within the specified bounds
result = minimize(
</pre></div>
</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1"><a class="reference internal" href="lecture-11-ensembles.html">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

</div>
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<li class="toctree-l1 current active"><a class="current reference internal" href="#">Lecture 11: Ensembles and Ergodicity</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-12-monte-carlo.html">Lecture 12: The Monte Carlo Method</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-13-mc-integration.html">Lecture 13: Monte Carlo Integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-14-metropolis.html">Lecture 14: A Basic Monte Carlo Algorithm</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-15-nanoparticles.html">Lecture 15: Nanoparticle Shape and Simulated Annealing</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-16-tech-details.html">Lecture 16: Technical Details: Boundary Conditions, Truncation of Interactions, <em>Etc.</em></a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-17-lipids.html">Lecture 17: Lipid Interactions in Membranes and Monte Carlo Simulations</a></li>
<li class="toctree-l1"><a class="reference internal" href="lecture-18-adsorption.html">Lecture 18: Introduction to Project 1: Monte Carlo Simulations of Adsorption on Surfaces</a></li>
</ul>

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