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Deriving Finite Sphere Packings

Natalie Arkus, Vinothan N. Manoharan, Michael P. Brenner
<span title="">2011</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hn6wut4eynat5my6xdfsebg7fm" style="color: black;">SIAM Journal on Discrete Mathematics</a> </i> &nbsp;
Here, we present an analytical method for deriving all packings of n spheres in R^3 satisfying minimal rigidity constraints (>= 3 contacts per sphere and >= 3n-6 total contacts).  ...  We derive such packings for n <= 10, and provide a preliminary set of maximal contact packings for 10 < n <= 20.  ...  We thank John Lee for consultations in coding, and for writing code that (i) converted the packing output to LaTeX format for appropriate display in Appendix B in [8] , and (ii) interfaced the packing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/100784424">doi:10.1137/100784424</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iz72hrny5rbpfkzktnhoxle7dy">fatcat:iz72hrny5rbpfkzktnhoxle7dy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190220034049/http://pdfs.semanticscholar.org/238f/89cb0c6234a8b62642ea6679f06773706b12.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/23/8f/238f89cb0c6234a8b62642ea6679f06773706b12.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/100784424"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Analytical Dancoff factor evaluations for reactor designs loaded with TRISO particle fuel

Wei Ji, Chao Liang, Elise N. Pusateri
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fbubbos3yzdy7kw53whrhfm23a" style="color: black;">Annals of Nuclear Energy</a> </i> &nbsp;
The new model is employed to derive analytical solutions of infinite medium, intra-fuel pebble and intra-fuel compact/pin Dancoff factors over a wide range of volume packing fractions of 2 of 29 TRISO  ...  To address this model deficiency, the dual-sphere model is proposed by deriving a new chord length distribution function between two fuel kernels that explicitly accounts for coating regions.  ...  In this paper, we will show the derivation of the new dual-sphere model and its applications to evaluating Dancoff factors of fuel particles that are randomly distributed in infinite and finite media.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.anucene.2013.09.025">doi:10.1016/j.anucene.2013.09.025</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qz4dnlrs3zfv7ojh6aekz6j2ji">fatcat:qz4dnlrs3zfv7ojh6aekz6j2ji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160509122913/http://neams.rpi.edu:80/jiw2/papers/2013_09_ANE_Dual%20Dancoff.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3a/39/3a39f593285835841e477c44dc96979a56ac77c4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.anucene.2013.09.025"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Quantization bounds on Grassmann manifolds of arbitrary dimensions and MIMO communications with feedback

Wei Dai, Youjian Liu, B. Rider
<span title="">2005</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lgc2un3ucjf3fgwb7o42q3s7d4" style="color: black;">GLOBECOM &#39;05. IEEE Global Telecommunications Conference, 2005.</a> </i> &nbsp;
Based on the volume formula, the Gilbert-Varshamov and Hamming bounds for sphere packings are obtained.  ...  As an application of the derived quantization bounds, the information rate of a Multiple-Input Multiple-Output (MIMO) system with finite-rate channel-state feedback is accurately quantified for arbitrary  ...  Besides the sphere packing bounds, the rate distortion tradeoff is also treated in [9] , where approximations to the distortion rate function are derived by the sphere packing bounds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/glocom.2005.1577892">doi:10.1109/glocom.2005.1577892</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/globecom/DaiLR05.html">dblp:conf/globecom/DaiLR05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ejnq3xhvjnbidl7k6zvujjyd3u">fatcat:ejnq3xhvjnbidl7k6zvujjyd3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060907134446/http://math.colorado.edu/~brider/quantization_globecom.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/60/b4/60b467ea026f7f23eb4830462568208c926d1872.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/glocom.2005.1577892"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Quantization Bounds on Grassmann Manifolds of Arbitrary Dimensions and MIMO Communications with Feedback [article]

Wei Dai, Youjian Liu, Brian Rider
<span title="2007-05-16">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Based on the volume formula, the Gilbert-Varshamov and Hamming bounds for sphere packings are obtained.  ...  As an application of the derived quantization bounds, the information rate of a Multiple-Input Multiple-Output (MIMO) system with finite-rate channel-state feedback is accurately quantified for arbitrary  ...  Besides the sphere packing bounds, the rate distortion tradeoff is also treated in [9] , where approximations to the distortion rate function are derived by the sphere packing bounds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0705.2272v1">arXiv:0705.2272v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qhcwbuwdenel3kqvvehnxuyyem">fatcat:qhcwbuwdenel3kqvvehnxuyyem</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0705.2272/0705.2272.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0705.2272v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Characterization of maximally random jammed sphere packings. II. Correlation functions and density fluctuations

Michael A. Klatt, Salvatore Torquato
<span title="2016-08-31">2016</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5pgnwkvlevhybgsbuc3q7fchx4" style="color: black;">Physical review. E</a> </i> &nbsp;
First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings.  ...  In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales.  ...  The explicit expressions for finite packings of hard spheres, which we have derived here, can help to efficiently compute σ 2 S (R).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.94.022152">doi:10.1103/physreve.94.022152</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/27627291">pmid:27627291</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/55q2b3tu5ndzthc4nwxexxohlu">fatcat:55q2b3tu5ndzthc4nwxexxohlu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302111410/http://pdfs.semanticscholar.org/a267/9182b6a591ade75e35a6799fd0fa8c3bb1c2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a2/67/a2679182b6a591ade75e35a6799fd0fa8c3bb1c2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.94.022152"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Application of the Chord Method to Obtain Analytical Expressions for Dancoff Factors in Stochastic Media

Wei Ji, William R. Martin
<span title="">2011</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nlpvtcxdsfe5hfbfcl4uyfhvem" style="color: black;">Nuclear science and engineering</a> </i> &nbsp;
media and semianalytically for a collection of finite media.  ...  for a range of configurations from infinite stochastic media to finite stochastic media, including multiple finite stochastic media in a background medium (e.g., a pebble bed core).  ...  For a finite cylinder, the analytical derivation of F~L!  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13182/nse10-73">doi:10.13182/nse10-73</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jpv462lmfzdajcc23ybmzv7tpe">fatcat:jpv462lmfzdajcc23ybmzv7tpe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808213903/http://neams.rpi.edu/jiw2/papers/2011_11_NSE.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/81/88/81883d6b05554ab056d6b43829a4c167439f966c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.13182/nse10-73"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Apollonian packings as physical fractals

Francesco Varrato, Giuseppe Foffi
<span title="2011-11-10">2011</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i7q5dvut3raxlm5na3nizmdb3e" style="color: black;">Molecular Physics</a> </i> &nbsp;
The Apollonian packings (APs) are fractals that result from a space-filling procedure with spheres.  ...  We discuss the finite size effects for finite intervals s∈[s_min,s_max] between the largest and the smallest sizes of the filling spheres.  ...  In particular we have derived the finite size correction to the distribution laws that characterize the Apollonian packing fractals.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00268976.2011.630598">doi:10.1080/00268976.2011.630598</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t6f3gdrhjjgm3jal36btbn32sm">fatcat:t6f3gdrhjjgm3jal36btbn32sm</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1111.5256/1111.5256.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/00268976.2011.630598"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

On the Information Rate of MIMO Systems with Finite Rate Channel State Feedback and Power On/Off Strategy [article]

Wei Dai, Youjian Liu, Brian Rider, Vincent K.N. Lau
<span title="2007-05-16">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper quantifies the information rate of multiple-input multiple-output (MIMO) systems with finite rate channel state feedback and power on/off strategy.  ...  Besides the sphere packing bounds, the rate distortion tradeoff is also treated in [9] , where approximations to the distortion rate function are derived by the sphere packing bounds.  ...  An explicit volume formula for a metric ball in the G n,p (L) is derived when the radius is sufficiently small. Based on the derived volume formula, the sphere packing bounds are obtained.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0705.2273v1">arXiv:0705.2273v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vz423co7nrf4pnqe4pbuf7bu4u">fatcat:vz423co7nrf4pnqe4pbuf7bu4u</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0705.2273/0705.2273.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0705.2273v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Subjamming transition in binary sphere mixtures

Ishan Prasad, Christian Santangelo, Gregory Grason
<span title="2017-11-20">2017</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5pgnwkvlevhybgsbuc3q7fchx4" style="color: black;">Physical review. E</a> </i> &nbsp;
We argue that the critical value of finite size asymmetry α_c ≃ 5.75 is consistent with the geometric criterion for the transmission of small sphere contacts between neighboring tetrahedrally close packed  ...  Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures.  ...  rich jammed packings will become truly singular (accompanied by discontinuities in structural measures or their derivatives) in the N → ∞ limit.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.96.052905">doi:10.1103/physreve.96.052905</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/29347783">pmid:29347783</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nyj25dnk3ngyllkfthrctq3iky">fatcat:nyj25dnk3ngyllkfthrctq3iky</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302172629/http://pdfs.semanticscholar.org/9f72/aa1726d1cc74ae80a3502ab2a3e3a54ab5b1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9f/72/9f72aa1726d1cc74ae80a3502ab2a3e3a54ab5b1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.96.052905"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Building Materials by Packing Spheres

Vinothan N. Manoharan, David J. Pine
<span title="">2004</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4blfynd4h5govevt4qdogct6wi" style="color: black;">MRS bulletin</a> </i> &nbsp;
But most monodisperse particles in this size range are spheres, and thus one problem in building new micrometer-scale ordered materials is controlling how spheres pack.  ...  In this article, we discuss how this problem can be approached by constructing and studying packings in the few-sphere limit.  ...  Finite Sphere Packings To illustrate the variability of finite packings, we consider a finite packing problem related to the "kissing problem" 13 in mathematics: how many identical spheres can touch a  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1557/mrs2004.34">doi:10.1557/mrs2004.34</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5uqk22wygrfzxbueefnr4ljgiy">fatcat:5uqk22wygrfzxbueefnr4ljgiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060921190517/http://www.chemengr.ucsb.edu/%7Eceweb/faculty/pine/papers_pdf/2004092mrsMano.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/fe/35fe7d39424eca735f1a7186d53b53e0d2e10037.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1557/mrs2004.34"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Packing fraction of geometric random packings of discretely sized particles

H. J. H. Brouwers
<span title="2011-10-24">2011</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nuk2stxzvvhf7ljciu325kj77m" style="color: black;">Physical Review E</a> </i> &nbsp;
Here the packing of discretely sized particles with finite size ratio u is analyzed and compared with empirical data concerning five ternary geometric random close packings of spheres with a size ratio  ...  and the packing of continuously sized particles.  ...  That Eq. (1) also holds for a finite number of interacting particles with finite size ratio is verified here. This is done by considering empirical ternary sphere packing results of Jeschar et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.84.042301">doi:10.1103/physreve.84.042301</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/22181207">pmid:22181207</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oggqiv2bofgypjv7gnafjaqioi">fatcat:oggqiv2bofgypjv7gnafjaqioi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811022434/http://josbrouwers.bwk.tue.nl/publications/Journal74.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/2b/cc2b66a183cb6a979dbb4251f7f7008a9a3e08ba.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.84.042301"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Characterization of maximally random jammed sphere packings. III. Transport and electromagnetic properties via correlation functions

Michael A. Klatt, Salvatore Torquato
<span title="2018-01-16">2018</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5pgnwkvlevhybgsbuc3q7fchx4" style="color: black;">Physical review. E</a> </i> &nbsp;
We compare the effective properties of the MRJ sphere packings to those of overlapping spheres, equilibrium hard-sphere packings, and lattices of hard spheres.  ...  In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral  ...  APPENDIX A: INTEGRATING CORRELATION FUNCTIONS DERIVED FROM FINITE SIMULATION BOXES In the second paper of this series, we derived explicit formulas for S 2 (r), F sv (r), and F ss (r) for finite packings  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.97.012118">doi:10.1103/physreve.97.012118</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/29448326">pmid:29448326</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yzki6ulokvddddyp4nxxe3qv74">fatcat:yzki6ulokvddddyp4nxxe3qv74</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190224042646/http://pdfs.semanticscholar.org/5298/33a570659291d7e15fca4acc220aae6cb949.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/52/98/529833a570659291d7e15fca4acc220aae6cb949.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.97.012118"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Scaling collapse at the jamming transition

Yoav Kallus
<span title="2016-01-11">2016</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5pgnwkvlevhybgsbuc3q7fchx4" style="color: black;">Physical review. E</a> </i> &nbsp;
We extract numerical estimates of the critical exponents, θ = 0.451 ± 0.006 and γ = 0.404 ± 0.004, that match the exponents observed in sphere packing systems.  ...  Our results supports the conjectured link with sphere jamming, provide more precise measurements of the critical exponents than previously reported, and shed light on the finite-size scaling behavior of  ...  The jamming ensemble corresponds to the random packing configurations of nonoverlapping hard spheres such that no improvement in the packing density is possible by local movement of the spheres.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreve.93.012902">doi:10.1103/physreve.93.012902</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26871138">pmid:26871138</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aozxz36ljjhatmbscmtxqnej7u">fatcat:aozxz36ljjhatmbscmtxqnej7u</a> </span>
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Page 1376 of Mathematical Reviews Vol. , Issue 87c [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Tamme’s problem: determine the maximal density of a packing of n congruent circles on a sphere.  ...  Tarnai, T. 87c:52026 Multisymmetric packing of equal circles on a sphere. Ann. Univ. Sci. Budapest. Eétvés Sect. Math. 27 (1984), 199-204 (1985).  ... 
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On Contact Numbers of Finite Lattice Sphere Packings and the Maximal Coordination of Monatomic Crystals [article]

Samuel Reid
<span title="2016-02-06">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in R^d and show that in R^3 this problem is equivalent to determining the maximal coordination  ...  In this paper we provide some initial remarks on applied discrete geometry through crystal chemistry, e.g., we focus on finite congruent lattice sphere packings, rather than finite congruent sphere packings  ...  Brenner at Harvard University provided various constructions of finite sphere packings with maximal contacts up to n = 20 spheres [3] , and in 2014, M.  ... 
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