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		<title>Particles at 10:09, 20 July 2016</title>
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				<updated>2016-07-20T10:09:53Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:09, 20 July 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Abstract==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The numerical simulation of complex dynamical systems is an important way for studying phenomena that are difficult to investigate experimentally. We could then speak about numerical granular media as a specific scientific field similarly to the numerical fluids twenty years ago. The numerical investigation progresses so quickly with respect with the experiments that the comparison between simulations and experiments is often rather coarse. Moreover the numerical tools may be used beyond their limits of validity. We propose to analyse the contributions, but also the limits of the NonSmooth Contact Dynamics (NSCD), developed by J.J. Moreau, applied to the granular systems starting from some experiences and from the numerous remarks given by Moreau himself in his papers.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The numerical simulation of complex dynamical systems is an important way for studying phenomena that are difficult to investigate experimentally. We could then speak about numerical granular media as a specific scientific field similarly to the numerical fluids twenty years ago. The numerical investigation progresses so quickly with respect with the experiments that the comparison between simulations and experiments is often rather coarse. Moreover the numerical tools may be used beyond their limits of validity. We propose to analyse the contributions, but also the limits of the NonSmooth Contact Dynamics (NSCD), developed by J.J. Moreau &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[&amp;lt;span id='cite-1'&amp;gt;&amp;lt;/span&amp;gt;[[#1|1]]]&lt;/ins&gt;, applied to the granular systems starting from some experiences and from the numerous remarks given by Moreau himself in his papers &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[&amp;lt;span id='cite-2'&amp;gt;&amp;lt;/span&amp;gt;[[#2|2]]]&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NSCD method has been developed for dealing with large collections of packed bodies and then for simulating the behaviour of granular materials. The Nonlinear Gauss-Seidel (NLGS) algorithm is the generic solver applied to the NSCD formulation. This combination allows simulation of the behaviour of a collection of (especially rigid) bodies involving different and mixed regimes: static, slow dynamics (solid), fast dynamics (fluid). Some examples illustrate the ability of the Moreau’s approach for dealing with a large range of granular problems.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NSCD method has been developed for dealing with large collections of packed bodies and then for simulating the behaviour of granular materials. The Nonlinear Gauss-Seidel (NLGS) algorithm is the generic solver applied to the NSCD formulation. This combination allows simulation of the behaviour of a collection of (especially rigid) bodies involving different and mixed regimes: static, slow dynamics (solid), fast dynamics (fluid). Some examples illustrate the ability of the Moreau’s approach for dealing with a large range of granular problems.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot; &gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[&amp;lt;span id='cite-3'&amp;gt;&amp;lt;/span&amp;gt;[[#3|3]]]&lt;/ins&gt;. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Recording of the presentation ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Recording of the presentation ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l26&quot; &gt;Line 26:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 26:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;div id=&amp;quot;1&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[#cite-1|[1]]] J.J. Moreau, “Numerical aspects of the sweeping process”, Comp. Meth. Appl. Mech. Engng.,&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;177, Issues 3-4, 329–349 (1999).&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;div id=&amp;quot;2&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[#cite-2|[2]]] J.J. Moreau, “Facing to the plurality of solutions in nonsmooth mechanics”, in&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Nosmooth/Nonconvex mechanics with applications in Engineering, Editions Ziti,&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Thessaloniki,3-12 (2006)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;div id=&amp;quot;3&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[#cite-3|[3]]] N.S. Nguyen, B. Brogliato, Multiple impacts in dissipative granular chains, Springer, (2014)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<title>Scipediacontent at 11:46, 19 July 2016</title>
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 11:46, 19 July 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l11&quot; &gt;Line 11:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 11:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| style=&amp;quot;font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| style=&amp;quot;font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-U3J6mahU alignment=center}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-U3J6mahU &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;| &lt;/ins&gt;alignment=center}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- style=&amp;quot;text-align: center;&amp;quot; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- style=&amp;quot;text-align: center;&amp;quot; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Location: Technical University of Catalonia (UPC), Vertex Building. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Location: Technical University of Catalonia (UPC), Vertex Building. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=3034&amp;oldid=prev</id>
		<title>Scipediacontent at 11:37, 19 July 2016</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=3034&amp;oldid=prev"/>
				<updated>2016-07-19T11:37:20Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
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				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 11:37, 19 July 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Abstract==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The numerical simulation of complex dynamical systems is an important way for studying phenomena that are difficult to investigate experimentally. We could then speak about numerical granular media as a specific scientific field similarly to the numerical fluids twenty years ago. The numerical investigation progresses so quickly with respect with the experiments that the comparison between simulations and experiments is often rather coarse. Moreover the numerical tools may be used beyond their limits of validity. We propose to analyse the contributions, but also the limits of the NonSmooth Contact Dynamics (NSCD), developed by J.J. Moreau, applied to the granular systems starting from some experiences and from the numerous remarks given by Moreau himself in his papers.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The NSCD method has been developed for dealing with large collections of packed bodies and then for simulating the behaviour of granular materials. The Nonlinear Gauss-Seidel (NLGS) algorithm is the generic solver applied to the NSCD formulation. This combination allows simulation of the behaviour of a collection of (especially rigid) bodies involving different and mixed regimes: static, slow dynamics (solid), fast dynamics (fluid). Some examples illustrate the ability of the Moreau’s approach for dealing with a large range of granular problems.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Recording of the presentation ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| style=&amp;quot;font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| style=&amp;quot;font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|- style=&amp;quot;border-bottom: 1px solid darkgray; text-align: center;&amp;quot;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;| Recording of the presentation&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-U3J6mahU alignment=center}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-U3J6mahU alignment=center}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l9&quot; &gt;Line 9:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 17:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Date: 28 - 30 September 2015, Barcelona, Spain.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Date: 28 - 30 September 2015, Barcelona, Spain.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== General Information ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== General Information ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Location: Technical University of Catalonia (UPC), Barcelona, Spain.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Location: Technical University of Catalonia (UPC), Barcelona, Spain.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Date: 28 - 30 September 2015&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Date: 28 - 30 September 2015&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Secretariat: [//www.cimne.com/ CIMNE] &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;Centre Internacional de Metodes Numerics&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Secretariat: [//www.cimne.com/ &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;International Center for Numerical Methods in Engineering (&lt;/ins&gt;CIMNE&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;)&lt;/ins&gt;].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== External Links ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== External Links ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//congress.cimne.com/particles2015/frontal/default.asp Particles 2015] Official Website of the Conference.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2660&amp;oldid=prev</id>
		<title>Particles at 08:40, 18 July 2016</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2660&amp;oldid=prev"/>
				<updated>2016-07-18T08:40:38Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 08:40, 18 July 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot; &gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Recording of the presentation&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Recording of the presentation&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;U3J6mahUalignment&lt;/del&gt;=center}}&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| {{#evt:service=youtube|id=https://youtu.be/1t-&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;U3J6mahU alignment&lt;/ins&gt;=center}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- style=&amp;quot;text-align: center;&amp;quot; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|- style=&amp;quot;text-align: center;&amp;quot; &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Location: Technical University of Catalonia (UPC), Vertex Building. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Location: Technical University of Catalonia (UPC), Vertex Building. &amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Particles</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2122&amp;oldid=prev</id>
		<title>Particles: Particles moved page Draft Contents 361260168 to Contents 2016q</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2122&amp;oldid=prev"/>
				<updated>2016-06-29T10:43:40Z</updated>
		
		<summary type="html">&lt;p&gt;Particles moved page &lt;a href=&quot;/public/Draft_Contents_361260168&quot; class=&quot;mw-redirect&quot; title=&quot;Draft Contents 361260168&quot;&gt;Draft Contents 361260168&lt;/a&gt; to &lt;a href=&quot;/public/Contents_2016q&quot; title=&quot;Contents 2016q&quot;&gt;Contents 2016q&lt;/a&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;tr style='vertical-align: top;' lang='en'&gt;
				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:43, 29 June 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan='2' style='text-align: center;' lang='en'&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Particles</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2121&amp;oldid=prev</id>
		<title>Particles at 10:43, 29 June 2016</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2121&amp;oldid=prev"/>
				<updated>2016-06-29T10:43:27Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;a href=&quot;https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;amp;diff=2121&amp;amp;oldid=2120&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Particles</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2120&amp;oldid=prev</id>
		<title>Particles: Created page with &quot;==1 Title, abstract and keywords==  Your paper should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations a...&quot;</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Contents_2016q&amp;diff=2120&amp;oldid=prev"/>
				<updated>2016-06-29T10:40:02Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot;==1 Title, abstract and keywords==  Your paper should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations a...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;==1 Title, abstract and keywords==&lt;br /&gt;
&lt;br /&gt;
Your paper should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.&lt;br /&gt;
&lt;br /&gt;
Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.&lt;br /&gt;
&lt;br /&gt;
An abstract is required for every paper; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.&lt;br /&gt;
&lt;br /&gt;
==2 The main text==&lt;br /&gt;
&lt;br /&gt;
You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.&lt;br /&gt;
&lt;br /&gt;
Most of the papers in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific journals in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.&lt;br /&gt;
&lt;br /&gt;
===2.1 Subsections===&lt;br /&gt;
&lt;br /&gt;
Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.&lt;br /&gt;
&lt;br /&gt;
===2.2 General guidelines===&lt;br /&gt;
&lt;br /&gt;
Some general guidelines that should be followed in your manuscripts are:&lt;br /&gt;
&lt;br /&gt;
:*  Avoid hyphenation at the end of a line.&lt;br /&gt;
&lt;br /&gt;
:*  Symbols denoting vectors and matrices should be indicated in bold type. Scalar variable names should normally be expressed using italics.&lt;br /&gt;
&lt;br /&gt;
:*  Use decimal points (not commas); use a space for thousands (10 000 and above).&lt;br /&gt;
&lt;br /&gt;
:*  Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.&lt;br /&gt;
&lt;br /&gt;
===2.3 Tables, figures, lists and equations===&lt;br /&gt;
&lt;br /&gt;
Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text (&amp;lt;span id='cite-_Ref382560620'&amp;gt;&amp;lt;/span&amp;gt;[[#_Ref382560620|table 1]], table 2, etc.) and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span id='_Ref382560620'&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
{| style=&amp;quot;margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|Thickness&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|3.175 mm&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|Young Modulus&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|12.74 MPa&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|Poisson coefficient&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|0.25&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|Density&lt;br /&gt;
| style=&amp;quot;text-align: center;&amp;quot;|1107 kg/m&amp;lt;sup&amp;gt;3&amp;lt;/sup&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&amp;lt;div class=&amp;quot;center&amp;quot; style=&amp;quot;width: auto; margin-left: auto; margin-right: auto;&amp;quot;&amp;gt;&lt;br /&gt;
&amp;lt;span style=&amp;quot;text-align: center; font-size: 75%;&amp;quot;&amp;gt;Table 1: Material properties&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span id='_Ref448852946'&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;center&amp;quot; style=&amp;quot;width: auto; margin-left: auto; margin-right: auto;&amp;quot;&amp;gt;&lt;br /&gt;
[[Image:Scipedia.gif|center|480px]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;div class=&amp;quot;center&amp;quot; style=&amp;quot;width: auto; margin-left: auto; margin-right: auto;&amp;quot;&amp;gt;&lt;br /&gt;
&amp;lt;span style=&amp;quot;text-align: center; font-size: 75%;&amp;quot;&amp;gt;Figure 1. Scipedia logo.&amp;lt;/span&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Number the figures according to their sequence in the text (&amp;lt;span id='cite-_Ref448852946'&amp;gt;&amp;lt;/span&amp;gt;[[#_Ref448852946|figure 1]], figure 2, etc.). Ensure that each illustration has a caption. A caption should comprise a brief title. Keep text in the illustrations themselves to a minimum but explain all symbols and abbreviations used. Try to keep the resolution of the figures to a minimum of 300 dpi. If a finer resolution is required, the figure can be inserted as supplementary material&lt;br /&gt;
&lt;br /&gt;
For tabular summations that do not deserve to be presented as a table, lists are often used. Lists may be either numbered or bulleted. Below you see examples of both.&lt;br /&gt;
&lt;br /&gt;
1. The first entry in this list&lt;br /&gt;
&lt;br /&gt;
2. The second entry&lt;br /&gt;
&lt;br /&gt;
2.1. A subentry&lt;br /&gt;
&lt;br /&gt;
3. The last entry&lt;br /&gt;
&lt;br /&gt;
* A bulleted list item&lt;br /&gt;
&lt;br /&gt;
* Another one&lt;br /&gt;
&lt;br /&gt;
You may choose to number equations for easy referencing. In that case they must be numbered consecutively with Arabic numerals in parentheses on the right hand side of the page. Below is an example of formulae that should be referenced as eq. &amp;lt;span id='cite-_Ref424030152'&amp;gt;&amp;lt;/span&amp;gt;[[#_Ref424030152|(1)]].&lt;br /&gt;
&lt;br /&gt;
{| style=&amp;quot;width: 100%;&amp;quot;&lt;br /&gt;
|-&lt;br /&gt;
| style=&amp;quot;vertical-align: top;&amp;quot;| &amp;lt;math&amp;gt;{\nabla }^{2}\phi =0&amp;lt;/math&amp;gt;&lt;br /&gt;
| style=&amp;quot;text-align: right;&amp;quot;|&amp;lt;span id='_Ref424030152'&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
(1)&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===2.4 Supplementary material===&lt;br /&gt;
&lt;br /&gt;
Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file.&lt;br /&gt;
&lt;br /&gt;
==3 Bibliography==&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span id='_Ref449344604'&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the paper is [&amp;lt;span id='cite-1'&amp;gt;&amp;lt;/span&amp;gt;[[#1|1]]], the second [&amp;lt;span id='cite-2'&amp;gt;&amp;lt;/span&amp;gt;[[#2|2]]], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen (e.g. [&amp;lt;span id='cite-1'&amp;gt;&amp;lt;/span&amp;gt;[[#1|1]], &amp;lt;span id='cite-3'&amp;gt;&amp;lt;/span&amp;gt;[[#3|3]]] or [&amp;lt;span id='cite-2'&amp;gt;&amp;lt;/span&amp;gt;[[#2|2]]-&amp;lt;span id='cite-2'&amp;gt;&amp;lt;/span&amp;gt;[[#4|4]]]).&lt;br /&gt;
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&amp;lt;span id='_Ref449084254'&amp;gt;&amp;lt;/span&amp;gt;&lt;br /&gt;
You should ensure that all references are cited in the text and that the reference list. References should preferably refer to papers published in Scipedia. Unpublished results should not be included in the reference list, but can be mentioned in the text. The reference data must be updated once publication is ready. Complete bibliographic information for all cited references must be given following the standards in the field (IEEE and ISO 690 standards are recommended). If possible, a hyperlink to the referenced publication should be given. See examples for Scipedia’s articles [&amp;lt;span id='cite-1'&amp;gt;&amp;lt;/span&amp;gt;[[#1|1]]], other journal articles [&amp;lt;span id='cite-2'&amp;gt;&amp;lt;/span&amp;gt;[[#2|2]]], books [&amp;lt;span id='cite-3'&amp;gt;&amp;lt;/span&amp;gt;[[#3|3]]], book chapter [&amp;lt;span id='cite-4'&amp;gt;&amp;lt;/span&amp;gt;[[#4|4]]], conference proceedings [&amp;lt;span id='cite-5'&amp;gt;&amp;lt;/span&amp;gt;[[#5|5]]], and online documents [&amp;lt;span id='cite-6'&amp;gt;&amp;lt;/span&amp;gt;[[#6|6]]], shown in references section below.&lt;br /&gt;
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==4 Acknowledgments==&lt;br /&gt;
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Acknowledgments should be inserted at the end of the paper, before the references section.&lt;br /&gt;
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==5 References==&lt;br /&gt;
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&amp;lt;div id=&amp;quot;1&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-1|[1]]] Author, A. and Author, B. (Year) Title of the article. Title of the Journal. Article code. Available: [http://www.scipedia.com/ucode. http://www.scipedia.com/ucode.]&lt;br /&gt;
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&amp;lt;div id=&amp;quot;2&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-2|[2]]] Author, A. and Author, B. (Year) Title of the article. Title of the Journal. Volume number, first page-last page.&lt;br /&gt;
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&amp;lt;div id=&amp;quot;3&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-3|[3]]] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.&lt;br /&gt;
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&amp;lt;div id=&amp;quot;4&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-4|[4]]] Author of Part, D. (Year). Title of chapter or part. In A. Editor &amp;amp; B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.&lt;br /&gt;
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&amp;lt;div id=&amp;quot;5&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-5|[5]]] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.&lt;br /&gt;
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&amp;lt;div id=&amp;quot;6&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
[[#cite-6|[6]]] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: [http://www.scipedia.com/document.pdf http://www.scipedia.com/document.pdf]. [Accessed day, month and year].&lt;/div&gt;</summary>
		<author><name>Particles</name></author>	</entry>

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