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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=1024" />
<meta name="apple-mobile-web-app-capable" content="yes" />
<title>2013 BLCS Annual Meeting</title>
<script src="js/prefixfree.min.js"></script>
<script src="js/jquery-1.9.1.min.js"></script>
<!-- <script src="js/lightbox.js"></script> -->
<link rel="stylesheet" type="text/css" href="css/presentation.css" />
<link rel="stylesheet" type="text/css" href="css/prettify.css" />
<!-- <link href="css/lightbox.css" rel="stylesheet" /> -->
<link rel="shortcut icon" href="favicon.png" />
<link rel="apple-touch-icon" href="apple-touch-icon.png" />
</head>
<body class="impress-not-supported">
<div id="timeline"></div>
<div id="impress">
<div id="title" class="step">
<h1>Forces Between Nanoparticles in a Nematic Host</h1>
<img id="uob-logo" src="img/logo-screen.gif" />
<p>Tom Fenech</p>
</div>
<div id="introduction" class="step" >
<h1>Introduction</h1>
<ul>
<li>Monte Carlo simulations of nematic liquid crystals</li>
<li>Supporting experimental work</li>
<li>Explore continuous parameter space
<ul>
<li>Shape</li>
<li>Size</li>
<li>Aspect ratio</li>
<li>Surface anchoring</li>
</ul>
</li>
</ul>
</div>
<!--<div id="motivation" class="step" >
<h1>Motivation</h1>
<img src="img/lcd-tv.jpg" class="right"/>
<ul>
<li>Technological applications
<ul>
<li>High precision displays</li>
<li>Self-assembled structures</li>
</ul>
</li>
<li>Two-way process
<ul>
<li>Control liquid crystal ↔ manipulate particles</li>
</ul>
</li>
<li>Forces → behaviour</li>
</ul>
<span class="footnote">Source: http://www.flickr.com/photos/jvcamerica/3660100511/in/photostream/</span>
</div>-->
<!--<div id="liquid-crystal" class="step">
<h1>Liquid Crystals</h1>
<img class="right" src="img/nematic.jpg"/>
<ul>
<li>A state of matter between solid and liquid
<ul>
<li>Properties of both states</li>
</ul>
</li>
<li>Only exists in certain molecules</li>
<li>Rod-like molecular structure</li>
<li>Ordering of molecules</li>
</ul>
<span class="footnote">Source: http://en.wikipedia.org/wiki/File:LiquidCrystal-MesogenOrder-Nematic.jpg</span>
</div>-->
<div id="method" class="step">
<h1>Method</h1>
<ul>
<li>Static simulations</li>
<li>Range of separations, orientations</li>
<li>Calculate energy
<ul>
<li>Gradient of energy → force</li>
</ul>
</li>
</ul>
</div>
<div id="continuum" class="step">
<h1>Continuum Theory</h1>
<ul>
<li>Not interested in individual molecules
<ul>
<li>Just their average orientation</li>
</ul>
</li>
<li>Coarse-grained approach
<ul>
<li>Access to much larger size scales</li>
</ul>
</li>
</ul>
</div>
<!--<div id="director" class="step" >
<h1>The Director</h1>
<img class="right" src="img/director.png" />
<ul>
<li>Direction of preferred orientation</li>
<li>Average alignment of molecules</li>
</ul>
</div>-->
<div id="frank" class="step" >
<h1>Frank Equation</h1>
<ul>
<li>Elastic potential energy between directors</li>
<li id="sum">Sum of three components:</li>
</ul>
</div>
<div id="frank-components" class="step" data-y="400">
<div class="splay left">
<h1>Splay</h1>
<p class="math">(∇⋅<strong>n</strong>)<sup>2</sup></p>
<img class="no-trans" src="img/splay.png"/>
</div>
<div class="twist left">
<h1>+ Twist</h1>
<p class="math">(<strong>n</strong>⋅∇×<strong>n</strong>)<sup>2</sup></p>
<img src="img/twist.png"/>
</div>
<div class="bend left">
<h1>+ Bend</h1>
<p class="math">(<strong>n</strong>×∇×<strong>n</strong>)<sup>2</sup></p>
<img src="img/bend.png" />
</div>
</div>
<div id="setup" class="step" >
<h1>Simulation Setup</h1>
<ul>
<li>Lattice of directors</li>
</ul>
<div class="center-image">
<img src="img/arrows.png" />
</div>
</div>
<div id="algorithm" class="step">
<h1>The Algorithm</h1>
<pre class="prettyprint"><code class="language-cpp">for (t = 0; t < num_its; ++t) {
for (k = 0; k < z_size; ++k) {
for (j = 0; k < y_size; ++j) {
for (i = 0; k < x_size; ++i) {
e_old = calc_energy(i, j, k);
trial_move(i, j, k);
e_new = calc_energy(i, j, k);
if (accept_reject(e_old, e_new))
accept(i, j, k);
}
}
}
}</code></pre>
</div>
<!--<div id="energy" class="step">
<h1>Energy Calculation</h1>
<object class="right" height="400" data="img/energy-centre.svg" type="image/svg+xml"></object>
<ul>
<li>Splay, Twist and Bend calculated</li>
<li>Nearest-neighbour derivatives</li>
<li>Average taken of forward and backward</li>
</ul>
</div>-->
<!--<div id="move" class="step" >
<h1>Monte Carlo Moves</h1>
<img class="right" src="img/coning.png" />
<ul>
<li>Old director <strong>n</strong></li>
<li>New director selected from <br />
<em>θ [0, γ], <br/>
φ [0, 2 π]</em></li>
<li><em>γ</em> tuned to keep Monte Carlo acceptance ratio at ½
<ul>
<li>Lower <em>γ</em> → higher acceptance</li>
</ul>
</li>
</ul>
</div>-->
<!--<div id="energy-calc" class="step">
<h1>Energy Calculation (cont.)</h1>
<object class="right" height="400" data="img/energy-5-part.svg" type="image/svg+xml"></object>
<ul>
<li>Move at cell (i, j, k) → energy change at (i, j, k)</li>
<li>But also changes energy of neighbouring cells</li>
<li>Energy change at these cells must also be calculated</li>
</ul>
</div>-->
<div id="accept" class="step">
<h1>Move Acceptance</h1>
<ul>
<li>Lower energy → always accepted</li>
<li>Higher energy → accepted with probability
<p><em>p = exp<span class="math">(-β(E<sub>new</sub> - E<sub>old</sub>))</span></em></p>
</li>
<li><em>β</em>: Monte Carlo temperature <br/>
(≠ thermodynamic temperature)</li>
</ul>
</div>
<div id="ghost" class="step">
<h1>Ghost Particles</h1>
<img id="ghost-particle" src="img/cylinder.png" />
<ul>
<li>Introduced after the system has equilibrated</li>
<li>A mixing parameter <em>G</em>
<ul>
<li><em>U<sub>Frank</sub> = G U<sub>no particle</sub> + (1 - G) U<sub>particle</sub></em></li>
</ul>
</li>
<li><em>G</em> is gradually decreased → particle gradually introduced</li>
</ul>
</div>
<div id="annealing" class="step">
<h1>Simulated Annealing</h1>
<ul>
<li>Minimisation of free energy</li>
<li>Monte Carlo temperature is gradually decreased → <em>β</em> gradually increases</li>
<li>Looking for global minimum
<ul>
<li>Maximise alignment</li>
<li>Minimise defects</li>
</ul>
</li>
<li>Rate of cooling is critical
<ul>
<li>Too fast → defects are annealed into system</li>
<li>Too slow → simulations take forever!</li>
</ul>
</li>
</ul>
</div>
<div id="defects" class="step">
<h1>Defects</h1>
<img src="img/defect.png" class="right"/>
<ul>
<li>Points where the director is undefined</li>
<li>High energy regions</li>
<li>Cause: conflicting boundary conditions
<ul>
<li>e.g. Particle surface vs. simulation walls</li>
</ul>
</li>
</ul>
</div>
<!--<div id="parallel" class="step">
<h1>Parallelisation</h1>
<h2>Considerations</h2>
<ul>
<li>Monte Carlo moves are interdependent</li>
<li>Acceptance of move depends on state of neighbours</li>
</ul>
<h2>Measures</h2>
<ul>
<li>Concurrent moves are suitably spaced</li>
<li>Accepted moves are reflected globally</li>
</ul>
</div>-->
<!--<div id="mpi-parallel" class="step">
<h1>Parallelisation (MPI)</h1>
<img class="right" src="img/mpi-decomp.png"/>
<ul>
<li>1D domain decomposition</li>
<li>Two phases
<ul>
<li>Each process operates on half of slice</li>
<li>Inter-process communication</li>
</ul>
</li>
</ul>
</div>-->
<!--<div id="results-2d" class="step" >
<h1>2D Results</h1>
<img class="fit right" src="img/final-2d.png" />
<ul>
<li>Pairs of circular particles</li>
<li>Finite box</li>
<li>Change in energy as a function of separation, orientation</li>
<li>Gradient in energy → force between particles</li>
</ul>
</div>-->
<!--<div id="final-2d-zoom" class="step" >
<img class="no-trans fit" src="img/final-2d-zoom.png" />
</div>-->
<!--<div id="contour-par" class="step" >
<h1>Energy Contour Map (Parallel)</h1>
<ul>
<li>Distance from origin: separation</li>
<li>Polar angle: orientation</li>
</ul>
<div class="center-image">
<img class="fit" src="img/contour-par.png" />
<img class="colourbar" src="img/colourbar.png" />
</div>
</div>-->
<!--<div id="contour-perp" class="step" >
<h1>Energy Contour Map (Perpendicular)</h1>
<div class="center-image">
<img class="fit" src="img/contour-perp.png" />
<img class="colourbar" src="img/colourbar.png" />
</div>
</div>-->
<!--<div id="graph-3d" class="step" >
<h1>Preferred Orientation of a Cylindrical Particle</h1>
<ul>
<li>Perpendicular to field → lower energy</li>
</ul>
<div class="center-image">
<img src="img/aspect.png" />
</div>
</div>-->
<!--<div id="mpi-summary" class="step">
<h1>Summary (MPI)</h1>
<ul>
<li>Method can be parallelised</li>
<li>Still takes a long time</li>
<li>Limit to size of system
<ul>
<li>Would like to look at much larger simulations</li>
</ul>
</li>
</ul>
</div>-->
<div id="opencl" class="step">
<h1>OpenCL™</h1>
<img class="right" src="img/OpenCL_Logo.png"/>
<ul>
<li>Based on C99
<ul>
<li>C++ bindings</li>
</ul>
</li>
<li>General purpose computation</li>
<li>Variety of platforms
<ul>
<li>Including (but not limited to) GPUs</li>
</ul>
</li>
</ul>
</div>
<div id="performance-mpi-opencl" class="step" >
<h1>Performance Comparison</h1>
<table>
<tbody>
<tr><th>CPU</th><th>GPU</th><th>Simulation Size</th><th>Time (hours)</th></tr>
<tr><td>8×Xeon E5462 @ 2.8Ghz</td><td>N/A</td><td>64<sup>3</sup> = 262144</td><td>50</td></tr>
<tr><td>1×Xeon X5650 @ 2.67Ghz</td><td>1 x NVIDIA M2090<td>80<sup>3</sup> = 512000</td><td>32</td></tr>
</tbody>
</table>
</div>
<!--<div id="performance-mpi-opencl-graph" class="step">
<h1>Performance Per Cell</h1>
<object data="img/mpi-opencl.svg" type="image/svg+xml"></object>
<ul>
<li>3× speedup</li>
<li>Possible to run 8 of these jobs per node</li>
</ul>
</div>-->
<div id="graph-final" class="step">
<object data="img/tuning-final.svg" type="image/svg+xml"></object>
<ul>
<!--<li>On the M2090, the global size can be made even bigger</li>-->
<li>>3× speedup after tuning</li>
<li>>10× compared to MPI on 8 CPUs</li>
</ul>
</div>
<div id="results-3d" class="step" >
<h1>Results</h1>
<img class="right" src="img/cylinders.png" />
<ul>
<li>Preferred orientation to field of a cylindrical particle</li>
<li>Homeotropic and homogeneous surface anchoring</li>
<li>Range of aspect ratios</li>
</ul>
</div>
<div id="cl-single-homeotropic" class="step">
<h1>Single Homeotropic Particle</h1>
<object data="img/homeotropic.svg" type="image/svg+xml"></object>
<ul>
<li>Higher aspect ratio rods and discs show greater variation in energy</li>
</ul>
</div>
<div id="cl-single-homogeneous" class="step">
<h1>Single Homogeneous Particle</h1>
<object data="img/homogeneous.svg" type="image/svg+xml"></object>
<ul>
<li>Long rods → parallel</li>
<li>Flat discs → perpendicular</li>
</ul>
</div>
<div id="current-work" class="step">
<h1>Current Work</h1>
<img src="img/grid-animation.gif" class="animated right"/>
<ul>
<li>Pairs of particles</li>
<li>Aspect Ratios 1/5, 1/2, 2, 5</li>
<li>Energy variation with separation and rotation</li>
</ul>
</div>
<div id="homeotropic-rods-ar5" class="step">
<h1>Pairs of Rods</h1>
<object id="homeotropic-rods-graph" data="img/l40_r4_a90.svg" type="image/svg+xml"></object>
<ul>
<li>Aspect Ratio 5
<ul>
<li>Length 100nm, Radius 10nm</li>
</ul>
</li>
<li>Homeotropic surface anchoring</li>
<li>Long axis perpendicular to bulk director</li>
</ul>
</div>
<div id="ar5-s0" class="step defect-pics" data-scale="0.2" data-exclude="true" data-for="homeotropic-rods-ar5">
<img src="img/rad10_len100_theta90/s0/1.png"/>
<img src="img/rad10_len100_theta90/s0/2.png"/>
<img src="img/rad10_len100_theta90/s0/3.png"/>
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<img src="img/rad10_len100_theta90/s1/1.png"/>
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<h1>Pairs of Discs</h1>
<object id="homeotropic-discs-graph" data="img/l20_r20_a90.svg" type="image/svg+xml"></object>
<ul>
<li>Aspect Ratio 1/2
<ul>
<li>Length 20nm, Radius 20nm</li>
</ul>
</li>
<li>Homeotropic surface anchoring</li>
<li>Face normal perpendicular to bulk director</li>
</ul>
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<div id="larger" class="step">
<h1>Future Work: Larger Simulations</h1>
<ul>
<li>Simulations containing many particles</li>
<li>Aggregation of colloidal particles
<ul>
<li>Observed experimentally</li>
<li>Not entirely understood</li>
</ul>
</li>
</ul>
</div>
<div id="opencl-summary" class="step">
<h1>Conclusions</h1>
<ul>
<li>OpenCL method enables modelling of much larger systems</li>
<li>Wide range of particles
<ul>
<li>Shape, size, aspect ratio, surface alignment</li>
</ul>
</li>
<li>Wide range of geometries
<ul>
<li>Separation, orientation</li>
</ul>
</li>
</ul>
</div>
<div id="acknowledge" class="step" >
<h1>Thanks To</h1>
<ul>
<li>Supervisors
<ul>
<li>Dr. Simon Hanna</li>
<li>Prof. Rob Richardson</li>
</ul>
</li>
<li>EPSRC</li>
<li>Nanophysics and Soft Matter Group</li>
</ul>
<p>and thanks for listening.</p>
<span class="footnote">OpenCL and the OpenCL logo are trademarks of Apple Inc. used by permission by Khronos.</span>
</div>
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<h1>Questions?</h1>
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