iMechanica - negative density
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enMetamaterials: negative mass density and anisotropic mass
https://imechanica.org/node/870
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/128">education</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/632">metamaterials</a></div><div class="field-item odd"><a href="/taxonomy/term/639">negative mass</a></div><div class="field-item even"><a href="/taxonomy/term/640">negative density</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
<strong>Update: February 2012</strong>
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1) The lecture notes are on Wikiversity at <a href="http://en.wikiversity.org/wiki/Waves_in_composites_and_metamaterials"> http://en.wikiversity.org/wiki/Waves_in_composites_and_metamaterials</a>
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2) The book on the topic can be bought from Amazon at <a href="http://www.amazon.com/Introduction-Metamaterials-Waves-Composites/dp/1439841578">http://www.amazon.com/Introduction-Metamaterials-Waves-Composites/dp/1439841578</a>
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3) Solutions and errata can be found at <a href="node/9727">node/9727</a>
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Is it possible for materials to have negative mass densities, anisotropic masses, and other such unintuitive characteristics? Recent work on certain composite material has shown that that indeed such things are possible (see for example <a href="http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRBMDO000071000001014103000001&idtype=cvips&prog=normal">Liu, Chan, Sheng, (2005), Physical Review B, 71, 014103</a>).</p>
<p>The study of metamaterials is just beginning and will probably lead to interesting new discoveries. Mechanicians have somewhat of a head start in the matter because researchers in the field of classical electrodynamics have already made some significant strides with metamaterials.</p>
<p><a href="http://www.math.utah.edu/~milton/">Prof. Graeme Milton</a> has been teaching a class on metamaterials this semester (Spring, 2007). I have typeset his lecture notes and added in some details for the beginner. You can find the lecture notes <a href="http://www.eng.utah.edu/~banerjee/MATH7875/notes.html">here</a>. Please let me know how the notes can be improved and if you find any mistakes.
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<strong>Update: 27 June, 2007</strong>:
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Here's a <a href="http://vmsstreamer1.fnal.gov/VMS_Site_03/Lectures/Colloquium/070221Schurig/index.htm" target="_blank">link</a> to <a href="http://www.ece.duke.edu/~dschurig/" target="_blank">David Schurig</a> 's talk at the <a href="http://www-ppd.fnal.gov/EPPOffice-w/colloq/colloq.html" target="_blank">Fermilab Colloquium</a> Lectures. The talk is titled "<em>The Transformation Design Method and Metamaterials: Tools to realize Invibility and Other Interesting Effects</em>". The talk discusses the contents of Lecture 5 and Lectures 22/23 without most of the mathematical details.
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<strong>Links to lecture notes from Prof. Milton's course:</strong>
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<dl><dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 1</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture1.pdf">Rainbows [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 2</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture2.pdf">Airy Theory [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 3</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture3.pdf">Maxwell's Equations in Media [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 4</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture4.pdf">Fresnel's Equations [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 5</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture5.pdf">Perfect Lenses and Negative Density Materials [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 6</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture6.pdf">Anisotropic Mass and Generalization [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 7</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture7.pdf">Elastodynamics and Electrodynamics [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 8</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture8.pdf">Acoustic Metamaterials and Negative Moduli [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 9</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture9.pdf">Fading Memory/Waves in Layered Media [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 10</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture10.pdf">Airy solution and WKB solution [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 11</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture11.pdf">TE waves in multilayered media [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 12</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture12.pdf">Continuum limit and propagator matrix [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 13</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture13.pdf">Waves in layered media and point sources [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 14</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture14.pdf">Point sources and EM vector potentials [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 15</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture15.pdf">Mie Theory and Bloch's Theorem [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 16</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture16.pdf">Bloch Waves and the Quasistatic Limit [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 17</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture17.pdf">Bloch Waves in Elastodynamics and Bubbly Fluids [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 18</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture18.pdf">Duality Relations/Phase Interchange Identity/Laminates [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 19</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture19.pdf">Backus Formula for Laminates/Rank-1 Laminates [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 20</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture20.pdf">Hierarchical Laminates/Hilbert space formalism [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 21</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture21.pdf">Effective tensors using Hilbert space formalism [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 22</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture22.pdf">Transformation-based Cloaking in Electromagnetism [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 23</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture23.pdf">Transformation-based Cloaking continued [pdf]</a> <br /></dt>
<dt><img src="http://www.eng.utah.edu/~banerjee/MATH7875/redball.gif" border="0" alt="o" /><strong>Lecture 24</strong>: <a href="http://www.eng.utah.edu/~banerjee/MATH7875/Lecture24.pdf">Willis equations for Elastodynamics [pdf]</a></dt>
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</dl></div></div></div>Mon, 19 Feb 2007 00:26:41 +0000Biswajit Banerjee870 at https://imechanica.orghttps://imechanica.org/node/870#commentshttps://imechanica.org/crss/node/870Error | iMechanica