MozartV1, Istex, Corpus, bibRecord, 000B89

Steady state of tapped granular polygons

Identifieur interne : 000B89 ( Istex/Corpus ); précédent : 000B88; suivant : 000B90

Steady state of tapped granular polygons

Auteurs : Carlos M. Carlevaro ; Luis A. Pugnaloni

Source :

Journal of Statistical Mechanics: Theory and Experiment [ 1742-5468 ] ; 2011.

RBID : ISTEX:FAC215E8152A70950D6B8B0D60534B5912395D59

Abstract

The steady state packing fraction of a tapped granular bed is studied for different grainshapes via a discrete element method. Grains are monosized regular polygons, fromtriangles to icosagons. Comparisons with disc packings show that the steady state packingfraction as a function of the tapping intensity presents the same general trends inpolygon packings. However, better packing fractions are obtained, as expected, forshapes that can tessellate the plane (triangles, squares and hexagons). In addition,we find a sharp transition for packings of polygons with more than 13 verticessignaled by a discontinuity in the packing fraction at a particular tapping intensity.Density fluctuations for most shapes are consistent with recent experimentalfindings in disc packing; however, a peculiar behavior is found for triangles andsquares.

Url:

https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/pdf

DOI: 10.1088/1742-5468/2011/01/P01007

Links to Exploration step

ISTEX:FAC215E8152A70950D6B8B0D60534B5912395D59

Le document en format XML

<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Steady state of tapped granular polygons</title>
<author><name sortKey="Carlevaro, Carlos M" sort="Carlevaro, Carlos M" uniqKey="Carlevaro C" first="Carlos M" last="Carlevaro">Carlos M. Carlevaro</name>
<affiliation><mods:affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>Universidad Tecnolgica Nacional-FRBA, UDB Fsica, Mozart 2300, C1407IVT Buenos Aires, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail:manuel@iflysib.unlp.edu.ar</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Pugnaloni, Luis A" sort="Pugnaloni, Luis A" uniqKey="Pugnaloni L" first="Luis A" last="Pugnaloni">Luis A. Pugnaloni</name>
<affiliation><mods:affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail:luis@iflysib.unlp.edu.ar</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:FAC215E8152A70950D6B8B0D60534B5912395D59</idno>
<date when="2011" year="2011">2011</date>
<idno type="doi">10.1088/1742-5468/2011/01/P01007</idno>
<idno type="url">https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000B89</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a">Steady state of tapped granular polygons</title>
<author><name sortKey="Carlevaro, Carlos M" sort="Carlevaro, Carlos M" uniqKey="Carlevaro C" first="Carlos M" last="Carlevaro">Carlos M. Carlevaro</name>
<affiliation><mods:affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>Universidad Tecnolgica Nacional-FRBA, UDB Fsica, Mozart 2300, C1407IVT Buenos Aires, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail:manuel@iflysib.unlp.edu.ar</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Pugnaloni, Luis A" sort="Pugnaloni, Luis A" uniqKey="Pugnaloni L" first="Luis A" last="Pugnaloni">Luis A. Pugnaloni</name>
<affiliation><mods:affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</mods:affiliation>
</affiliation>
<affiliation><mods:affiliation>E-mail:luis@iflysib.unlp.edu.ar</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Journal of Statistical Mechanics: Theory and Experiment</title>
<title level="j" type="abbrev">J. Stat. Mech.</title>
<idno type="ISSN">1742-5468</idno>
<idno type="eISSN">1742-5468</idno>
<imprint><publisher>Institute of Physics Publishing</publisher>
<date type="published" when="2011">2011</date>
<biblScope unit="volume">2011</biblScope>
<biblScope unit="issue">01</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="10">10</biblScope>
<biblScope unit="production">Printed in the UK</biblScope>
</imprint>
<idno type="ISSN">1742-5468</idno>
</series>
<idno type="istex">FAC215E8152A70950D6B8B0D60534B5912395D59</idno>
<idno type="DOI">10.1088/1742-5468/2011/01/P01007</idno>
<idno type="arXivPPT">1010.3907</idno>
<idno type="PII">S1742-5468(11)78273-5</idno>
<idno type="articleID">378273</idno>
<idno type="articleNumber">P01007</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1742-5468</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract">The steady state packing fraction of a tapped granular bed is studied for different grainshapes via a discrete element method. Grains are monosized regular polygons, fromtriangles to icosagons. Comparisons with disc packings show that the steady state packingfraction as a function of the tapping intensity presents the same general trends inpolygon packings. However, better packing fractions are obtained, as expected, forshapes that can tessellate the plane (triangles, squares and hexagons). In addition,we find a sharp transition for packings of polygons with more than 13 verticessignaled by a discontinuity in the packing fraction at a particular tapping intensity.Density fluctuations for most shapes are consistent with recent experimentalfindings in disc packing; however, a peculiar behavior is found for triangles andsquares.</div>
</front>
</TEI>
<istex><corpusName>iop</corpusName>
<author><json:item><name>Carlos M Carlevaro</name>
<affiliations><json:string>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</json:string>
<json:string>Universidad Tecnolgica Nacional-FRBA, UDB Fsica, Mozart 2300, C1407IVT Buenos Aires, Argentina</json:string>
<json:string>E-mail:manuel@iflysib.unlp.edu.ar</json:string>
</affiliations>
</json:item>
<json:item><name>Luis A Pugnaloni</name>
<affiliations><json:string>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</json:string>
<json:string>E-mail:luis@iflysib.unlp.edu.ar</json:string>
</affiliations>
</json:item>
</author>
<subject><json:item><lang><json:string>eng</json:string>
</lang>
</json:item>
<json:item><lang><json:string>eng</json:string>
</lang>
</json:item>
</subject>
<language><json:string>eng</json:string>
</language>
<abstract>The steady state packing fraction of a tapped granular bed is studied for different grainshapes via a discrete element method. Grains are monosized regular polygons, fromtriangles to icosagons. Comparisons with disc packings show that the steady state packingfraction as a function of the tapping intensity presents the same general trends inpolygon packings. However, better packing fractions are obtained, as expected, forshapes that can tessellate the plane (triangles, squares and hexagons). In addition,we find a sharp transition for packings of polygons with more than 13 verticessignaled by a discontinuity in the packing fraction at a particular tapping intensity.Density fluctuations for most shapes are consistent with recent experimentalfindings in disc packing; however, a peculiar behavior is found for triangles andsquares.</abstract>
<qualityIndicators><score>5.387</score>
<pdfVersion>1.4</pdfVersion>
<pdfPageSize>595 x 842 pts (A4)</pdfPageSize>
<refBibsNative>true</refBibsNative>
<keywordCount>2</keywordCount>
<abstractCharCount>837</abstractCharCount>
<pdfWordCount>3471</pdfWordCount>
<pdfCharCount>19000</pdfCharCount>
<pdfPageCount>10</pdfPageCount>
<abstractWordCount>118</abstractWordCount>
</qualityIndicators>
<title>Steady state of tapped granular polygons</title>
<pii><json:string>S1742-5468(11)78273-5</json:string>
</pii>
<genre><json:string>article</json:string>
<json:string>paper</json:string>
</genre>
<host><volume>2011</volume>
<pages><total>10</total>
<last>10</last>
<first>1</first>
</pages>
<issn><json:string>1742-5468</json:string>
</issn>
<issue>01</issue>
<genre></genre>
<language><json:string>unknown</json:string>
</language>
<eissn><json:string>1742-5468</json:string>
</eissn>
<title>Journal of Statistical Mechanics: Theory and Experiment</title>
</host>
<publicationDate>2011</publicationDate>
<copyrightDate>2011</copyrightDate>
<doi><json:string>10.1088/1742-5468/2011/01/P01007</json:string>
</doi>
<id>FAC215E8152A70950D6B8B0D60534B5912395D59</id>
<fulltext><json:item><original>true</original>
<mimetype>application/pdf</mimetype>
<extension>pdf</extension>
<uri>https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/pdf</uri>
</json:item>
<json:item><original>false</original>
<mimetype>application/zip</mimetype>
<extension>zip</extension>
<uri>https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Steady state of tapped granular polygons</title>
</titleStmt>
<publicationStmt><authority>ISTEX</authority>
<publisher>Institute of Physics Publishing</publisher>
<availability><p>IOP Publishing Ltd</p>
</availability>
<date>2011</date>
</publicationStmt>
<sourceDesc><biblStruct type="inbook"><analytic><title level="a">Steady state of tapped granular polygons</title>
<author><persName><forename type="first">Carlos M</forename>
<surname>Carlevaro</surname>
</persName>
<affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</affiliation>
<affiliation>Universidad Tecnolgica Nacional-FRBA, UDB Fsica, Mozart 2300, C1407IVT Buenos Aires, Argentina</affiliation>
<affiliation>E-mail:manuel@iflysib.unlp.edu.ar</affiliation>
</author>
<author><persName><forename type="first">Luis A</forename>
<surname>Pugnaloni</surname>
</persName>
<affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</affiliation>
<affiliation>E-mail:luis@iflysib.unlp.edu.ar</affiliation>
</author>
</analytic>
<monogr><title level="j">Journal of Statistical Mechanics: Theory and Experiment</title>
<title level="j" type="abbrev">J. Stat. Mech.</title>
<idno type="pISSN">1742-5468</idno>
<idno type="eISSN">1742-5468</idno>
<imprint><publisher>Institute of Physics Publishing</publisher>
<date type="published" when="2011"></date>
<biblScope unit="volume">2011</biblScope>
<biblScope unit="issue">01</biblScope>
<biblScope unit="page" from="1">1</biblScope>
<biblScope unit="page" to="10">10</biblScope>
<biblScope unit="production">Printed in the UK</biblScope>
</imprint>
</monogr>
<idno type="istex">FAC215E8152A70950D6B8B0D60534B5912395D59</idno>
<idno type="DOI">10.1088/1742-5468/2011/01/P01007</idno>
<idno type="arXivPPT">1010.3907</idno>
<idno type="PII">S1742-5468(11)78273-5</idno>
<idno type="articleID">378273</idno>
<idno type="articleNumber">P01007</idno>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><creation><date>2011</date>
</creation>
<langUsage><language ident="en">en</language>
</langUsage>
<abstract><p>The steady state packing fraction of a tapped granular bed is studied for different grainshapes via a discrete element method. Grains are monosized regular polygons, fromtriangles to icosagons. Comparisons with disc packings show that the steady state packingfraction as a function of the tapping intensity presents the same general trends inpolygon packings. However, better packing fractions are obtained, as expected, forshapes that can tessellate the plane (triangles, squares and hexagons). In addition,we find a sharp transition for packings of polygons with more than 13 verticessignaled by a discontinuity in the packing fraction at a particular tapping intensity.Density fluctuations for most shapes are consistent with recent experimentalfindings in disc packing; however, a peculiar behavior is found for triangles andsquares.</p>
</abstract>
<textClass><keywords scheme="keyword"><list><head>Keywords</head>
<item><term></term>
</item>
<item><term></term>
</item>
</list>
</keywords>
</textClass>
</profileDesc>
<revisionDesc><change when="2011">Published</change>
</revisionDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item><original>false</original>
<mimetype>text/plain</mimetype>
<extension>txt</extension>
<uri>https://api.istex.fr/document/FAC215E8152A70950D6B8B0D60534B5912395D59/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration>
<istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_2.dtd" name="istex:docType"></istex:docType>
<istex:document><article artid="jstat378273"><article-metadata><jnl-data jnlid="jstat"><jnl-fullname>Journal of Statistical Mechanics: Theory and Experiment</jnl-fullname>
<jnl-abbreviation>J. Stat. Mech.</jnl-abbreviation>
<jnl-shortname>JSTAT</jnl-shortname>
<jnl-issn>1742-5468</jnl-issn>
<jnl-coden>JSMTC6</jnl-coden>
<jnl-imprint>Institute of Physics Publishing</jnl-imprint>
<jnl-web-address>stacks.iop.org/JSTAT</jnl-web-address>
</jnl-data>
<volume-data><year-publication>2011</year-publication>
<volume-number>2011</volume-number>
</volume-data>
<issue-data><issue-number>01</issue-number>
<coverdate>January 2011</coverdate>
</issue-data>
<article-data><article-type type="paper" sort="regular"></article-type>
<type-number type="paper" numbering="article" artnum="P01007"></type-number>
<article-number>378273</article-number>
<first-page>1</first-page>
<last-page>10</last-page>
<length>10</length>
<pii>S1742-5468(11)78273-5</pii>
<doi>10.1088/1742-5468/2011/01/P01007</doi>
<arxivppt>1010.3907</arxivppt>
<copyright>IOP Publishing Ltd</copyright>
<ccc>1742-5468/11/P01007 + 10$30.00</ccc>
<printed>Printed in the UK</printed>
</article-data>
</article-metadata>
<header><title-group><title>Steady state of tapped granular polygons</title>
<short-title>Steady state of tapped granular polygons
 </short-title>
<ej-title>Steady state of tapped granular polygons
 </ej-title>
</title-group>
<author-group><author address="jstat378273ad1 jstat378273ad2" email="jstat378273ea1"><first-names>Carlos M</first-names>
<second-name>Carlevaro</second-name>
</author>
<author address="jstat378273ad1" email="jstat378273ea2"><first-names>Luis A</first-names>
<second-name>Pugnaloni</second-name>
</author>
<short-author-list>C M Carlevaro and L A Pugnaloni</short-author-list>
</author-group>
<address-group><address id="jstat378273ad1"><orgname>Instituto de Física de Líquidos y Sistemas Biológicos (CONICET La Plata, UNLP)</orgname>, Casilla
 de Correo 565, 1900, La Plata,
 <country>Argentina</country>
</address>
<address id="jstat378273ad2"><orgname>Universidad Tecnológica Nacional-FRBA, UDB Física</orgname>, Mozart 2300, C1407IVT Buenos
 Aires,
 <country>Argentina</country>
</address>
<e-address id="jstat378273ea1"><email mailto="manuel@iflysib.unlp.edu.ar">manuel@iflysib.unlp.edu.ar</email>
</e-address>
<e-address id="jstat378273ea2"><email mailto="luis@iflysib.unlp.edu.ar">luis@iflysib.unlp.edu.ar</email>
</e-address>
</address-group>
<history received="19 October 2010" accepted="10 December 2010" online="6 January 2011"></history>
<abstract-group><abstract><heading>Abstract</heading>
<p indent="no">The steady state packing fraction of a tapped granular bed is studied for different grain
 shapes via a discrete element method. Grains are monosized regular polygons, from
 triangles to icosagons. Comparisons with disc packings show that the steady state packing
 fraction as a function of the tapping intensity presents the same general trends in
 polygon packings. However, better packing fractions are obtained, as expected, for
 shapes that can tessellate the plane (triangles, squares and hexagons). In addition,
 we find a sharp transition for packings of polygons with more than 13 vertices
 signaled by a discontinuity in the packing fraction at a particular tapping intensity.
 Density fluctuations for most shapes are consistent with recent experimental
 findings in disc packing; however, a peculiar behavior is found for triangles and
 squares.</p>
</abstract>
</abstract-group>
<classifications><subject-areas type="jstat"><category code="15"></category>
</subject-areas>
<keywords type="jstat"><keyword code="15/100"></keyword>
 <keyword code="15/190"></keyword>
</keywords>
</classifications>
</header>
<body refstyle="numeric"><sec-level1 id="jstat378273s1" label="1"><heading>Introduction</heading>
<p indent="no">Granular materials settle under gravity and come to mechanical equilibrium unless an
 external excitation is provided. The properties of such static packings are difficult to
 predict, since the history of preparation of the sample is important. However, there exist
 different protocols to prepare a granular bed in a well-defined macroscopic state. In
 such state, the packing fraction (and other macroscopic observables such as the
 pressure on the container) are reproducible if the given protocol is followed. A
 canonical example of this is the steady states obtained by tapping the sample
 with a given intensity [<cite linkend="jstat378273bib1">1</cite>]. After a suitable annealing, tapping at a
 constant intensity produces mechanically stable configurations (inherent states, or
 microstates) whose ensemble has well-defined mean values of all macroscopic
 observables.</p>
<p>In recent years, the dependency of the steady state packing fraction,
 &phis;, on the tapping
 intensity, Γ, has been shown to be nonmonotonic; presenting a minimum at relatively high values of
 Γ 
 for discs and spheres [<cite linkend="jstat378273bib2">2</cite>
, <cite linkend="jstat378273bib3">3</cite>], and a maximum at very low
 Γ 
 for spheres [<cite linkend="jstat378273bib4">4</cite>]. In general, the symbol
 Γ 
 is used for the reduced peak acceleration given to the system during a tap. However, we will use
 Γ 
 in what follows to refer to any suitable parameter that characterizes the tapping
 intensity.</p>
<p>On the one hand, there exist some studies on the response to tapping of non-spherical particles [<cite linkend="jstat378273bib5" range="jstat378273bib5,jstat378273bib6,jstat378273bib7,jstat378273bib8">5–8</cite>],
 however these do not consider polygonal particles. On the other hand,
 there are some investigations on polygon packings [<cite linkend="jstat378273bib9" range="jstat378273bib9,jstat378273bib10,jstat378273bib11,jstat378273bib12">9–12</cite>]. These latter
 studies, however, do not focus on the steady state obtained after a repeated pulse excitation.
 Inspired by previous works on pentagon packings [<cite linkend="jstat378273bib16">16</cite>
, <cite linkend="jstat378273bib17">17</cite>], we investigate the
 &phis;–Γ 
 tapping curve in the steady state for monosized regular polygons with different numbers
 <italic>N</italic> of vertices; from
 triangles (<italic>N</italic> = 3)
 to icosagons (<italic>N</italic> = 20). As the number of vertices grows, we expect polygon packings to approach the properties
 of disc packings. Since depending on the number of vertices these particles may or may not
 tessellate the plane, we also expect strong deviations from the general trends for some grain
 shapes.</p>
<p>In this paper, we compare the general features found in the
 &phis;–Γ 
 curve of disc packings with those of regular polygons. Although some general trends are
 conserved, new phenomenology emerges.</p>
<p>In section <secref linkend="jstat378273s2">2</secref>
 we present the simulation technique and the model particles. In section <secref linkend="jstat378273s3.1">3.1</secref>
 we analyze the behavior of polygons with fewer than ten vertices. In section <secref linkend="jstat378273s3.2">3.2</secref>
 we present results for polygons of up to twenty vertices. Section <secref linkend="jstat378273s3.3">3.3</secref> is devoted to the study of the density fluctuations. Finally, we draw our conclusions in
 section <secref linkend="jstat378273s4">4</secref>
 and point out some interesting areas of research suggested by the new results.</p>
</sec-level1>
<sec-level1 id="jstat378273s2" label="2"><heading>Simulation</heading>
<p indent="no">We perform molecular dynamic type simulations by solving the Newton–Euler
 equations of motion for rigid bodies confined on a vertical plane. Gravity acts in the
 negative vertical direction. The bodies (particles) are placed in a rectangular box
 which is confined to move in the vertical direction. This box is high enough to
 avoid particles contacting the ceiling during the simulations. We prepare nineteen
 samples that consist of 500 monosized regular polygons of a single type (from
 triangles to icosagons) or monosized discs. Particles, initially placed at random
 without overlaps in the box, are allowed to settle until they come to rest in order to
 prepare the initial packing. Then, the same tapping protocol is applied to each
 sample.</p>
<p>We set the particle–particle interactions to yield a normal restitution coefficient
 ε = 0.058 
 and a static and dynamic friction coefficient
 μ<sub>s</sub>
 = μ<sub>d</sub> = 0.5. The confining
 box is 24.8<italic>r</italic> 
 wide and 2000<italic>r</italic> 
 tall (with <italic>r</italic> 
 the radius of the particles). The particle–box friction coefficient is
 μ<sub>s</sub>
 = μ<sub>d</sub> = 0.07 
 and the restitution coefficient is as in the particle–particle interaction. All
 polygons have the same radius and material density. Therefore, the actual
 weight of a particle depends on the number of vertices. We use as unit mass,
 <italic>m</italic>, the mass of a disc;
 as unit length <italic>r</italic>; and
 the unit time is (<italic>r</italic>
/<italic>g</italic>
)<sup>1/2</sup>
, with <italic>g</italic> 
 the acceleration of gravity.</p>
<p>Tapping is simulated by giving the box an impulse. In practice, we set the initial velocity
 <italic>v</italic>
<sub>0</sub> 
 of the box (originally at rest after deposition) to a given positive value and restart the
 dynamics. In doing so, the box and its filling move upward and fall back on top of a zero
 restitution base. While the box dissipates all its kinetic energy on contacting the base,
 particles inside the box bounce against the box walls and floor until they fully settle.
 After all particles come to rest a new tap is applied. The intensity of the taps is
 measured by the initial velocity imposed on the confining box at each tap (i.e.
 Γ = <italic>v</italic>
<sub>0</sub>). A similar parameter (the lift-off velocity) has been recently proposed as a suitable
 measure of the tap intensity [<cite linkend="jstat378273bib18">18</cite>
].</p>
<p>The tapping protocol consist in a series of 50 000 taps. Every
 250 taps we change
 the value of Γ by a
 small amount ΔΓ. We
 initially decrease Γ 
 from ≈15.0(<italic>rg</italic>
)<sup>1/2</sup> 
 down to a very low value and then increase it back to its initial high value. At each value of
 Γ the
 last 150 
 taps are used to average the packing fraction in order to plot the
 &phis;–Γ 
 curve.</p>
<p>The simulations were implemented by means of the Box2D library [<cite linkend="jstat378273bib19">19</cite>].
 Box2D uses a constraint solver to handle hard bodies. At each time step of the dynamics a
 series of iterations (typically 20) are used to resolve penetrations between bodies through a
 Lagrange multiplier scheme [<cite linkend="jstat378273bib20">20</cite>]. After resolving penetrations, the
 inelastic collision at each contact (a contact is defined by a manifold in the case of
 polygons) is solved and new linear and angular velocities are assigned. The equations
 of motion are integrated through a symplectic Euler algorithm. The time step
 δ<italic>t</italic> 
 used to integrate the equations of motion is <inline-eqn></inline-eqn>. Solid friction is also handled by means of a Lagrange multiplier scheme that implements
 the Coulomb criterion. This library achieves a high performance when handling complex
 bodies such as polygons.</p>
</sec-level1>
<sec-level1 id="jstat378273s3" label="3"><heading>Results</heading>
<sec-level2 id="jstat378273s3.1" label="3.1"><heading>From triangles to nonagons</heading>
<p indent="no">The steady state packing fraction as a function of the tapping intensity for triangles,
 squares, pentagons, hexagons, heptagons, octagons and nonagons is presented in
 figure <figref linkend="jstat378273fig1">1</figref> along with the results for discs. The packing fraction is
 estimated from the number density measured in a rectangular slab of half
 the packing height at the middle of the sample. The fact that the same
 &phis;–Γ 
 curve is obtained for decreasing and increasing
 Γ 
 indicates that these states are reversible and that
 &phis; is uniquely
 defined for each Γ. We have repeated the simulations for discs and pentagons carrying out three
 extra decreasing and increasing annealing cycles in a narrower range of
 Γ (0 < Γ < 3.0) and the same
 values of &phis; 
 were obtained each time. From these results we can see that polygon packings present
 similar features to those observed in disc packings. At low tapping intensities, a decrease of
 &phis; is observed for increasing
 Γ down to a minimum
 packing fraction &phis;<sub>min</sub>. A
 further increase of Γ 
 induces an increase of &phis; 
 until a plateau is reached at a packing fraction somewhat lower than the maximum obtained for the lowest
 values of Γ. Disks also show a not very pronounced maximum at low
 Γ 
 which is not observed in polygon packings. This maximum has been recently observed in
 sphere packings [<cite linkend="jstat378273bib4">4</cite>]. It is worth noting that the maximum packing fraction
 attained by discs is somewhat lower than the crystalline triangular close packing. This is
 due to the fact that the width of the simulation box and the diameter of the particles are
 not commensurable, which prevents perfect crystalline arrangements. Another overall trend
 is that the range of packing fractions attained by disc packings is narrower than for
 polygons.
 <figure id="jstat378273fig1" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" width="24pc" filename="images/7827301.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/7827301.jpg"></graphic-file>
</graphic>
<caption id="jstat378273fc1" type="figure" label="Figure 1"><p indent="no">Mean packing fraction &phis; as a
 function of tapping intensity Γ 
 for triangles (violet), squares (red), pentagons (green), hexagons (blue),
 heptagons (yellow), octagons (cyan), nonagons (magenta), and discs
 (black). Except for discs, all curves correspond to a progressive decrease of
 Γ 
 followed by an increase back to high values. For discs only the decreasing part
 has been carried out. Error bars correspond to the estimated error of the mean.</p>
</caption>
</figure>
</p>
<p>Beyond these general features, there are some peculiarities associated to
 the ability of a given polygonal shape to tessellate the plane. As is to be
 expected, triangles, squares and hexagons can reach packing fractions of nearly
 1 at
 the lower tapping intensities. All other shapes reach packing fractions similar to disc packings at low
 Γ. It is important to notice at this point that our results differ from those
 obtained by Vidales <italic>et al</italic>
 [<cite linkend="jstat378273bib16">16</cite>
, <cite linkend="jstat378273bib17">17</cite>] in the case of pentagons in
 the framework of a pseudo-dynamic algorithm. In [<cite linkend="jstat378273bib16">16</cite>
, <cite linkend="jstat378273bib17">17</cite>] the
 &phis;–Γ 
 curve does not present any minimum of the packing fraction.</p>
<p>In figure <figref linkend="jstat378273fig2">2</figref>, we plot the minimum steady state density,
 &phis;<sub>min</sub>, as a
 function of the number of vertices of the polygon. As the number of vertices is increased, a consistent increase
 of &phis;<sub>min</sub> 
 is found for all polygons with the exception of triangles, squares and hexagons. As
 we mentioned, these three polygons can tessellate the plane. Correspondingly,
 triangles, squares and hexagons present higher densities than expected by
 the trend showed by all other polygons. We have seen that the position,
 Γ<sub>min</sub>, of the minimum is independent of the number of vertices. The existence of
 &phis;<sub>min</sub> has
 been associated to a competition between arch formation and arch breaking [<cite linkend="jstat378273bib2">2</cite>]. The position
 Γ<sub>min</sub> 
 of such a minimum signals the crossover between a regime where arches cannot form
 due to the particles settling one by one (in a sequential manner) at very high
 Γ, and a regime where arches do form but are ‘melted down’ in
 successive taps creating a dynamic equilibrium. The fact that
 Γ<sub>min</sub> 
 is the same for all shapes is a clear indication that arching is not favored
 (nor prevented) by any particular shape at these intermediate values of
 Γ.
 <figure id="jstat378273fig2" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" width="25.6pc" filename="images/7827302.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/7827302.jpg"></graphic-file>
</graphic>
<caption id="jstat378273fc2" type="figure" label="Figure 2"><p indent="no">Minimum packing fraction &phis;<sub>min</sub> 
 as a function of the number of vertices. The blue line is drawn only to guide the eye.</p>
</caption>
</figure>
</p>
</sec-level2>
<sec-level2 id="jstat378273s3.2" label="3.2"><heading>An unforeseen sharp transition for triskaidecagons and beyond</heading>
<p indent="no">We now focus on the behavior of polygons with larger number of vertices (from nonagons
 up to icosagons). Figure <figref linkend="jstat378273fig3">3</figref> shows the &phis;–Γ 
 curves for each shape. One might have expected that a smooth change would appear in
 these curves as the number of vertices is increased up to a point where the behavior of the
 <italic>n</italic>-vertex polygon will converge to the one shown by disc packings. However, a sudden change
 is found as we move from dodecagons to triskaidecagons. While a continuous
 &phis;–Γ 
 curve is observed for polygons with up to
 12 vertices, a sharp
 discontinuity in &phis; 
 is present in all packings with polygons of
 13 
 vertices or more. A gap of ‘forbidden’ values of
 &phis; appears between
 roughly 0.80 
 and 0.83 
 in all these polygon packings with more than
 12 
 vertices. It is important to mention that fluctuations are rather large, and configurations (microstates)
 with 0.80 < &phis; < 0.83 
 are rather common. It is the mean values that present a gap.
 <figure id="jstat378273fig3" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" width="32pc" filename="images/7827303.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/7827303.jpg"></graphic-file>
</graphic>
<caption id="jstat378273fc3" type="figure" label="Figure 3"><p indent="no">Mean packing fraction &phis; as a
 function of tapping intensity Γ 
 for nonagons, decagons,... 
 and icosagons. The brown data in the lower right panel correspond to discs. A progressive decrease (red
 data) of Γ 
 is followed by an increase (blue data) back to the high initial values. Error bars as in
 figure <figref linkend="jstat378273fig1">1</figref>
.</p>
</caption>
</figure>
</p>
<p>A similar discontinuity has been seen in tapped disc packings simulated under a
 pseudo-dynamic algorithm [<cite linkend="jstat378273bib21">21</cite>]. However, this is not observed in our
 simulations of discs (see brown data in the lower right panel in figure <figref linkend="jstat378273fig3">3</figref>) nor in previous molecular dynamic simulations where the same region of
 Γ 
 was explored [<cite linkend="jstat378273bib22">22</cite>
]. The pseudo-dynamic algorithm [<cite linkend="jstat378273bib21">21</cite>] conducts a
 deposition of discs that roll on top of each other without sliding. This might mimic, rather
 realistically, the behavior of regular polygons with a large number of vertices.
 These polygons behave like gears in the sense that they interlock very easily
 just as if they were infinitely rough discs. We presume this basic characteristic
 shared by polygons with many vertices and discs that roll without sliding
 is the underlying phenomenon that leads to the emergence of a discontinuous
 &phis;–Γ 
 curve. We mention in passing that, although it is difficult to relate with the static packings
 studied here, a similar discontinuity has been reported in an oscillation experiment of a 2D
 granular sample [<cite linkend="jstat378273bib23">23</cite>
].</p>
<p>In order to have a rough indication of the nature of the transition,
 we have made a more detailed simulation for tetrakaidecagons (<italic>N</italic>
 = 14). In figure <figref linkend="jstat378273fig4">4</figref>, the steady state value of
 &phis; is plotted for
 Γ in the interval
 [2.8, 4.0] with a
 smaller ΔΓ 
 step. In panel (a), we plot two independent experiments obtained by increasing
 Γ 
 along with the corresponding results from figure <figref linkend="jstat378273fig3">3</figref> (where a larger
 ΔΓ 
 was used). The results for the reversed protocol in which
 Γ 
 is decreased is presented in panel (b) of figure <figref linkend="jstat378273fig4">4</figref>
. In figure <figref linkend="jstat378273fig4">4</figref>(a), the system seems to present a first order type transition where
 metastable branches are explored. Since fluctuations are rather large for this small system
 size, the system may explore microstates compatible with both ‘coexisting’ phases.
 Nevertheless, in figure <figref linkend="jstat378273fig4">4</figref>(b), where the protocol corresponds to decreasing
 Γ, the transition looks much smoother if the rate
 ΔΓ 
 is reduced. Although the data is noisy, we can see that the width of the transition region is
 rate dependent. We have also run a series of simulations with smaller system sizes
 (200, 300 and 400 grains) in the case of tetrakaidecagons. We observed that the
 density jump fades away as the system size is reduced. This is a common feature in
 phase transitions, since proper discontinuities only appear in the thermodynamic
 limit.
 <figure id="jstat378273fig4" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" width="31.8pc" filename="images/7827304.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/7827304.jpg"></graphic-file>
</graphic>
<caption id="jstat378273fc4" type="figure" label="Figure 4"><p indent="no">Mean packing fraction &phis; as a
 function of tapping intensity Γ 
 for tetrakaidecagons. Panel (a), increasing
 Γ. Panel (b),
 decreasing Γ. The red and blue data correspond to independent realizations of the tapping protocol.
 The black data correspond to the ones presented in figure <figref linkend="jstat378273fig3">3</figref> for tetrakaidecagons, where larger steps in
 Γ 
 are taken. The full and dashed black lines are to guide the eye. Error bars as in
 figure <figref linkend="jstat378273fig1">1</figref>
.</p>
</caption>
</figure>
</p>
</sec-level2>
<sec-level2 id="jstat378273s3.3" label="3.3"><heading>Density fluctuations</heading>
<p indent="no">Density fluctuations have recently received renewed interest as a way to measure configurational
 temperature (as defined by Edwards [<cite linkend="jstat378273bib24">24</cite>
]) and entropy [<cite linkend="jstat378273bib25">25</cite>]. It
 was in a fluidization experiment that a nonmonotonic dependence of the fluctuations
 Δ&phis; as a
 function of &phis; 
 in the steady state was first reported [<cite linkend="jstat378273bib26">26</cite>
]. In that work, Schroter <italic>et al</italic> found a
 minimum in the density fluctuations for spheres. However, a recent study on
 discs reported a maximum in fluctuations from both experiments and simulations [<cite linkend="jstat378273bib3">3</cite>
].</p>
<p>In figure <figref linkend="jstat378273fig5">5</figref> we show the steady state density fluctuations
 Δ&phis; 
 as measured by the standard deviation as a function of
 &phis; for several
 polygons and discs. The results for discs are entirely in agreement with [<cite linkend="jstat378273bib3">3</cite>]. A clear maximum
 in Δ&phis; 
 appears for discs. One can also see that states of equal
 &phis; at each
 side of &phis;<sub>min</sub> 
 present slightly different fluctuations. This indicates that these states are not equivalent and that
 &phis; 
 is not sufficient to characterize the macroscopic state. A more detailed analysis of this
 can be found in [<cite linkend="jstat378273bib3">3</cite>] where the force moment tensor is found to be a
 suitable extra macroscopic variable in accordance with theoretical suggestions [<cite linkend="jstat378273bib27">27</cite>].
 <figure id="jstat378273fig5" parts="single" width="column" position="float" printstyle="normal" orientation="port"><graphic><graphic-file version="print" format="EPS" width="31.9pc" filename="images/7827305.eps"></graphic-file>
<graphic-file version="ej" format="JPEG" filename="images/7827305.jpg"></graphic-file>
</graphic>
<caption id="jstat378273fc5" type="figure" label="Figure 5"><p indent="no">Standard deviation Δ&phis; 
 of the packing fraction in the steady state as a function of
 &phis;. The
 red line is a simple running average to guide the eye. The arrows indicate the direction of increasing
 Γ.</p>
</caption>
</figure>
</p>
<p>The behavior of the density fluctuations in the polygon packings show the signal of the transition for shapes
 with <italic>N</italic> > 12. However the same general trends as those seen for discs are observed.
 Interestingly, a peculiar behavior appears for triangles, squares and
 pentagons. Pentagons present the same fluctuations at both sides of the
 &phis; 
 minimum whereas triangles and squares present a reversed situation where fluctuations are larger for
 large Γ, instead of smaller as seen in all other shapes. This change in trend should have an
 important impact in the calculation of configurational temperature and entropy. We will
 pursue this point further elsewhere.
 </p>
</sec-level2>
</sec-level1>
<sec-level1 id="jstat378273s4" label="4"><heading>Conclusions</heading>
<p indent="no">We have carried out simulations of the tapping of assemblies of regular polygonal grains
 and studied the steady state of such systems. The comparison with more widely
 studied disc packings has shown some general similarities but also remarkable new
 phenomenology.</p>
<p>On the one hand, beyond the expected result for triangles, squares
 and hexagons that cover the space if gently tapped, polygons with
 <italic>N</italic> > 12 
 show a sharp transition with a clear density gap. On the other hand, triangles and squares
 present density fluctuations that are larger at large tapping intensities in contrast with all
 other shapes (including discs).</p>
<p>A number of questions arise from this study that can lead future research. Some of these
 questions are:
 <ordered-list id="jstat378273ol1" type="roman"><list-item id="jstat378273oli1" marker="(i)"><p>What is the true nature of the transition for polygons with a large number of
 vertices? Can this transition be effectively found in infinite rough discs? Can
 the low density coexisting
 phase be related to the so called <italic>random close packing</italic>
 state [<cite linkend="jstat378273bib13" range="jstat378273bib13,jstat378273bib14,jstat378273bib15">13–15</cite>
], [<cite linkend="jstat378273bib11">11</cite>]?
 </p>
</list-item>
<list-item id="jstat378273oli2" marker="(ii)"><p>Given that fluctuations have a different trend, is the granular (configurational)
 temperature in the case of triangles and squares radically different from that of
 other shape packings?
 </p>
</list-item>
<list-item id="jstat378273oli3" marker="(iii)"><p>Given that for pentagons the fluctuations are equivalent for states at each side of
 &phis;<sub>min</sub> 
 obtained with different Γ, which suggest that the states are equivalent, is the force moment tensor
 equivalent?
 </p>
</list-item>
</ordered-list>
</p>
</sec-level1>
<acknowledgment><heading>Acknowledgments</heading>
<p indent="no">We thank Ana María Vidales and Irene Ippolito for valuable discussions. This work has
 been supported by CONICET and ANPCyT (Argentina).
 </p>
</acknowledgment>
</body>
<back><references><heading>References</heading>
<reference-list type="numeric"><journal-ref id="jstat378273bib1" num="1"><authors><au><second-name>Nowak</second-name>
<first-names>E R</first-names>
</au>
<au><second-name>Knight</second-name>
<first-names>J B</first-names>
</au>
<au><second-name>Povinelli</second-name>
<first-names>M</first-names>
</au>
<au><second-name>Jaeger</second-name>
<first-names>H M</first-names>
</au>
<au><second-name>Nagel</second-name>
<first-names>S R</first-names>
</au>
</authors>
<year>1997</year>
<jnl-title>Powder Technol.</jnl-title>
<volume>94</volume>
<pages>79</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1016/S0032-5910(97)03291-9</cr_doi>
<cr_issn type="print">00325910</cr_issn>
<cr_issn type="electronic"></cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib2" num="2"><authors><au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
<au><second-name>Mizrahi</second-name>
<first-names>M</first-names>
</au>
<au><second-name>Carlevaro</second-name>
<first-names>M C</first-names>
</au>
<au><second-name>Vericat</second-name>
<first-names>F</first-names>
</au>
</authors>
<year>2008</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>78</volume>
<pages>051305</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.78.051305</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib3" num="3"><authors><au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
<au><second-name>Sánchez</second-name>
<first-names>I</first-names>
</au>
<au><second-name>Gago</second-name>
<first-names>P A</first-names>
</au>
<au><second-name>Damas</second-name>
<first-names>J</first-names>
</au>
<au><second-name>Zuriguel</second-name>
<first-names>I</first-names>
</au>
<au><second-name>Maza</second-name>
<first-names>D</first-names>
</au>
</authors>
<year>2010</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>82</volume>
<pages>050301(R)</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.82.050301</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib4" num="4"><authors><au><second-name>Rosato</second-name>
<first-names>A D</first-names>
</au>
<au><second-name>Dybenko</second-name>
<first-names>O</first-names>
</au>
<au><second-name>Horntrop</second-name>
<first-names>D J</first-names>
</au>
<au><second-name>Ratnaswamy</second-name>
<first-names>V</first-names>
</au>
<au><second-name>Kondic</second-name>
<first-names>L</first-names>
</au>
</authors>
<year>2010</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>81</volume>
<pages>061301</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.81.061301</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib5" num="5"><authors><au><second-name>Rankenburg</second-name>
<first-names>I C</first-names>
</au>
<au><second-name>Zieve</second-name>
<first-names>R J</first-names>
</au>
</authors>
<year>2001</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>63</volume>
<pages>061303</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.63.061303</cr_doi>
<cr_issn type="print">1063-651X</cr_issn>
<cr_issn type="electronic">1095-3787</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib6" num="6"><authors><au><second-name>Villarruel</second-name>
<first-names>F X</first-names>
</au>
<au><second-name>Lauderdale</second-name>
<first-names>B E</first-names>
</au>
<au><second-name>Mueth</second-name>
<first-names>D M</first-names>
</au>
<au><second-name>Jaeger</second-name>
<first-names>H M</first-names>
</au>
</authors>
<year>2000</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>61</volume>
<pages>6914</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.61.6914</cr_doi>
<cr_issn type="print">1063-651X</cr_issn>
<cr_issn type="electronic">1095-3787</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib7" num="7"><authors><au><second-name>Lumay</second-name>
<first-names>G</first-names>
</au>
<au><second-name>Vandewalle</second-name>
<first-names>N</first-names>
</au>
</authors>
<year>2006</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>74</volume>
<pages>021301</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.74.021301</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib8" num="8"><authors><au><second-name>Ramaioli</second-name>
<first-names>M</first-names>
</au>
<au><second-name>Pournin</second-name>
<first-names>L</first-names>
</au>
<au><second-name>Liebling</second-name>
<first-names>Th M</first-names>
</au>
</authors>
<year>2007</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>76</volume>
<pages>021304</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.76.021304</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib9" num="9"><authors><au><second-name>Cruz Hidalgo</second-name>
<first-names>R</first-names>
</au>
<au><second-name>Zuriguel</second-name>
<first-names>I</first-names>
</au>
<au><second-name>Maza</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Pagonabarraga</second-name>
<first-names>I</first-names>
</au>
</authors>
<year>2009</year>
<jnl-title>Phys. Rev. Lett.</jnl-title>
<volume>103</volume>
<pages>118001</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevLett.103.118001</cr_doi>
<cr_issn type="print">0031-9007</cr_issn>
<cr_issn type="electronic">1079-7114</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib10" num="10"><authors><au><second-name>Cruz Hidalgo</second-name>
<first-names>R</first-names>
</au>
<au><second-name>Zuriguel</second-name>
<first-names>I</first-names>
</au>
<au><second-name>Maza</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Pagonabarraga</second-name>
<first-names>I</first-names>
</au>
</authors>
<year>2010</year>
<jnl-title>J. Stat. Mech.</jnl-title>
<art-number type="jstat">P06025</art-number>
<crossref><cr_doi>http://dx.doi.org/10.1088/1742-5468/2010/06/P06025</cr_doi>
<cr_issn type="print"></cr_issn>
<cr_issn type="electronic">1742-5468</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib11" num="11"><authors><au><second-name>Limon Duparcmeur</second-name>
<first-names>Y</first-names>
</au>
<au><second-name>Troadec</second-name>
<first-names>J P</first-names>
</au>
<au><second-name>Gervois</second-name>
<first-names>A</first-names>
</au>
</authors>
<year>1997</year>
<jnl-title>J. Physique</jnl-title>
<part>I</part>
<volume>7</volume>
<pages>1181</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1051/jp1:1997115</cr_doi>
<cr_issn type="print">1155-4304</cr_issn>
<cr_issn type="electronic">1286-4862</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib12" num="12"><authors><au><second-name>Ammi</second-name>
<first-names>M</first-names>
</au>
<au><second-name>Bideau</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Troadec</second-name>
<first-names>J P</first-names>
</au>
</authors>
<year>1987</year>
<jnl-title>J. Phys. D: Appl. Phys.</jnl-title>
<volume>20</volume>
<pages>424</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1088/0022-3727/20/4/005</cr_doi>
<cr_issn type="print">00223727</cr_issn>
<cr_issn type="electronic"></cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib13" num="13"><authors><au><second-name>Radin</second-name>
<first-names>C</first-names>
</au>
</authors>
<year>2008</year>
<jnl-title>J. Stat. Phys.</jnl-title>
<volume>131</volume>
<pages>567</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1007/s10955-008-9523-1</cr_doi>
<cr_issn type="print">0022-4715</cr_issn>
<cr_issn type="electronic">1572-9613</cr_issn>
</crossref>
</journal-ref>
<misc-ref id="jstat378273bib14" num="14"><authors><au><second-name>Aristoff</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Radin</second-name>
<first-names>C</first-names>
</au>
</authors>
<year>2009</year>
<misc-text>arXiv:<arxiv url="0909.2608">0909.2608</arxiv>
</misc-text>
</misc-ref>
<misc-ref id="jstat378273bib15" num="15"><authors><au><second-name>Jin</second-name>
<first-names>Y</first-names>
</au>
<au><second-name>Makse</second-name>
<first-names>H A</first-names>
</au>
</authors>
<year>2010</year>
<misc-text>arXiv:<arxiv url="1001.5287">1001.5287</arxiv>
</misc-text>
</misc-ref>
<journal-ref id="jstat378273bib16" num="16"><authors><au><second-name>Vidales</second-name>
<first-names>A M</first-names>
</au>
<au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
<au><second-name>Ippolito</second-name>
<first-names>I</first-names>
</au>
</authors>
<year>2008</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>77</volume>
<pages>051305</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.77.051305</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib17" num="17"><authors><au><second-name>Vidales</second-name>
<first-names>A M</first-names>
</au>
<au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
<au><second-name>Ippolito</second-name>
<first-names>I</first-names>
</au>
</authors>
<year>2009</year>
<jnl-title>Gran. Matter</jnl-title>
<volume>11</volume>
<pages>53</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1007/s10035-008-0119-x</cr_doi>
<cr_issn type="print">1434-5021</cr_issn>
<cr_issn type="electronic">1434-7636</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib18" num="18"><authors><au><second-name>Dijksman</second-name>
<first-names>J A</first-names>
</au>
<au><second-name>van Hecke</second-name>
<first-names>M</first-names>
</au>
</authors>
<year>2009</year>
<jnl-title>Europhys. Lett.</jnl-title>
<volume>88</volume>
<pages>44001</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1209/0295-5075/88/44001</cr_doi>
<cr_issn type="print">0295-5075</cr_issn>
<cr_issn type="electronic">1286-4854</cr_issn>
</crossref>
</journal-ref>
<misc-ref id="jstat378273bib19" num="19"><misc-text>Box2D Physics Engine <webref url="http://www.box2d.org">www.box2d.org</webref>
</misc-text>
</misc-ref>
<misc-ref id="jstat378273bib20" num="20"><authors><au><second-name>Catto</second-name>
<first-names>E</first-names>
</au>
</authors>
<misc-text>Iterative dynamics with temporal coherence, 2005, available at
 <webref url="http://box2d.googlecode.com/files/GDC2005_ErinCatto.zip">http://box2d.googlecode.com/files/GDC2005_ErinCatto.zip</webref> (retrived on October
 2010)</misc-text>
</misc-ref>
<journal-ref id="jstat378273bib21" num="21"><authors><au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
<au><second-name>Valluzzi</second-name>
<first-names>M G</first-names>
</au>
<au><second-name>Valluzzi</second-name>
<first-names>L G</first-names>
</au>
</authors>
<year>2006</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>73</volume>
<pages>051302</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.73.051302</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib22" num="22"><authors><au><second-name>Arévalo</second-name>
<first-names>R</first-names>
</au>
<au><second-name>Maza</second-name>
<first-names>D</first-names>
</au>
<au><second-name>Pugnaloni</second-name>
<first-names>L A</first-names>
</au>
</authors>
<year>2006</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>74</volume>
<pages>021303</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.74.021303</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<misc-ref id="jstat378273bib23" num="23"><authors><au><second-name>Shattuck</second-name>
<first-names>M D</first-names>
</au>
</authors>
<year>2006</year>
<misc-text>arXiv:<arxiv url="cond-mat/0610839">cond-mat/0610839</arxiv>
</misc-text>
</misc-ref>
<journal-ref id="jstat378273bib24" num="24"><authors><au><second-name>Edwards</second-name>
<first-names>S F</first-names>
</au>
<au><second-name>Oakeshott</second-name>
<first-names>R B S</first-names>
</au>
</authors>
<year>1989</year>
<jnl-title>Physica</jnl-title>
<part>A</part>
<volume>157</volume>
<pages>1080</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1016/0378-4371(89)90034-4</cr_doi>
<cr_issn type="print">03784371</cr_issn>
<cr_issn type="electronic"></cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib25" num="25"><authors><au><second-name>McNamara</second-name>
<first-names>S</first-names>
</au>
<au><second-name>Richard</second-name>
<first-names>P</first-names>
</au>
<au><second-name>Kiesgen de Richter</second-name>
<first-names>S</first-names>
</au>
<au><second-name>Le Car</second-name>
<first-names>G</first-names>
</au>
<au><second-name>Delannay</second-name>
<first-names>R</first-names>
</au>
</authors>
<year>2009</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>80</volume>
<pages>031301</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.80.031301</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib26" num="26"><authors><au><second-name>Schröter</second-name>
<first-names>M</first-names>
</au>
<au><second-name>Goldman</second-name>
<first-names>D I</first-names>
</au>
<au><second-name>Swinney</second-name>
<first-names>H L</first-names>
</au>
</authors>
<year>2005</year>
<jnl-title>Phys. Rev.</jnl-title>
<part>E</part>
<volume>71</volume>
<pages>030301</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1103/PhysRevE.71.030301</cr_doi>
<cr_issn type="print">1539-3755</cr_issn>
<cr_issn type="electronic">1550-2376</cr_issn>
</crossref>
</journal-ref>
<journal-ref id="jstat378273bib27" num="27"><authors><au><second-name>Blumenfeld</second-name>
<first-names>R</first-names>
</au>
<au><second-name>Edwards</second-name>
<first-names>S F</first-names>
</au>
</authors>
<year>2009</year>
<jnl-title>J. Phys. Chem.</jnl-title>
<part>B</part>
<volume>113</volume>
<pages>3981</pages> 
 <crossref><cr_doi>http://dx.doi.org/10.1021/jp809768y</cr_doi>
<cr_issn type="print">1520-6106</cr_issn>
<cr_issn type="electronic">1520-5207</cr_issn>
</crossref>
</journal-ref>
</reference-list>
</references>
</back>
</article>
</istex:document>
</istex:metadataXml>
<mods version="3.6"><titleInfo><title>Steady state of tapped granular polygons</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Steady state of tapped granular polygons</title>
</titleInfo>
<titleInfo type="alternative"><title>Steady state of tapped granular polygons</title>
</titleInfo>
<name type="personal"><namePart type="given">Carlos M</namePart>
<namePart type="family">Carlevaro</namePart>
<affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</affiliation>
<affiliation>Universidad Tecnolgica Nacional-FRBA, UDB Fsica, Mozart 2300, C1407IVT Buenos Aires, Argentina</affiliation>
<affiliation>E-mail:manuel@iflysib.unlp.edu.ar</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">Luis A</namePart>
<namePart type="family">Pugnaloni</namePart>
<affiliation>Instituto de Fsica de Lquidos y Sistemas Biolgicos (CONICET La Plata, UNLP), Casilla de Correo 565, 1900, La Plata, Argentina</affiliation>
<affiliation>E-mail:luis@iflysib.unlp.edu.ar</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="article">paper</genre>
<genre>paper</genre>
<originInfo><publisher>Institute of Physics Publishing</publisher>
<dateIssued encoding="w3cdtf">2011</dateIssued>
<copyrightDate encoding="w3cdtf">2011</copyrightDate>
</originInfo>
<language><languageTerm type="code" authority="iso639-2b">eng</languageTerm>
<languageTerm type="code" authority="rfc3066">en</languageTerm>
</language>
<physicalDescription><internetMediaType>text/html</internetMediaType>
<note type="production">Printed in the UK</note>
</physicalDescription>
<abstract>The steady state packing fraction of a tapped granular bed is studied for different grainshapes via a discrete element method. Grains are monosized regular polygons, fromtriangles to icosagons. Comparisons with disc packings show that the steady state packingfraction as a function of the tapping intensity presents the same general trends inpolygon packings. However, better packing fractions are obtained, as expected, forshapes that can tessellate the plane (triangles, squares and hexagons). In addition,we find a sharp transition for packings of polygons with more than 13 verticessignaled by a discontinuity in the packing fraction at a particular tapping intensity.Density fluctuations for most shapes are consistent with recent experimentalfindings in disc packing; however, a peculiar behavior is found for triangles andsquares.</abstract>
<subject><genre>Keywords</genre>
<topic></topic>
<topic></topic>
</subject>
<relatedItem type="host"><titleInfo><title>Journal of Statistical Mechanics: Theory and Experiment</title>
</titleInfo>
<titleInfo type="abbreviated"><title>J. Stat. Mech.</title>
</titleInfo>
<identifier type="ISSN">1742-5468</identifier>
<identifier type="eISSN">1742-5468</identifier>
<identifier type="publisherID">JSTAT</identifier>
<identifier type="CODEN">JSMTC6</identifier>
<identifier type="URL">stacks.iop.org/JSTAT</identifier>
<part><date>2011</date>
<detail type="volume"><caption>vol.</caption>
<number>2011</number>
</detail>
<detail type="issue"><caption>no.</caption>
<number>01</number>
</detail>
<extent unit="pages"><start>1</start>
<end>10</end>
<total>10</total>
</extent>
</part>
</relatedItem>
<identifier type="istex">FAC215E8152A70950D6B8B0D60534B5912395D59</identifier>
<identifier type="DOI">10.1088/1742-5468/2011/01/P01007</identifier>
<identifier type="arXivPPT">1010.3907</identifier>
<identifier type="PII">S1742-5468(11)78273-5</identifier>
<identifier type="articleID">378273</identifier>
<identifier type="articleNumber">P01007</identifier>
<accessCondition type="use and reproduction" contentType="copyright">IOP Publishing Ltd</accessCondition>
<recordInfo><recordContentSource>IOP Publishing Ltd</recordContentSource>
<recordOrigin>IOP</recordOrigin>
</recordInfo>
</mods>
</metadata>
<serie></serie>
</istex>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Musique/explor/MozartV1/Data/Istex/Corpus

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000B89 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000B89 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Musique
   |area=    MozartV1
   |flux=    Istex
   |étape=   Corpus
   |type=    RBID
   |clé=     ISTEX:FAC215E8152A70950D6B8B0D60534B5912395D59
   |texte=   Steady state of tapped granular polygons
}}

This area was generated with Dilib version V0.6.20.
Data generation: Sun Apr 10 15:06:14 2016. Site generation: Tue Feb 7 15:40:35 2023

	Serveur d'exploration sur Mozart
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur Mozart

Steady state of tapped granular polygons

Steady state of tapped granular polygons

Source :

Abstract

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri