[ { "key": "HIRTWBR3", "version": 421, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/HIRTWBR3", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/HIRTWBR3", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "lastModifiedByUser": { "id": 49057, "username": "mucha", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/mucha", "type": "text/html" } } }, "creatorSummary": "Shi et al.", "parsedDate": "2010-09-24", "numChildren": 1 }, "data": { "key": "HIRTWBR3", "version": 421, "itemType": "presentation", "title": "Network analysis for electrical properties of sheared nano-rod dispersions", "creators": [ { "creatorType": "presenter", "firstName": "F.", "lastName": "Shi" }, { "creatorType": "presenter", "firstName": "S.", "lastName": "Wang" }, { "creatorType": "presenter", "firstName": "X.", "lastName": "Zheng" }, { "creatorType": "presenter", "firstName": "R.", "lastName": "Zhou" }, { "creatorType": "presenter", "firstName": "P.", "lastName": "Mucha" }, { "creatorType": "presenter", "firstName": "M.G.", "lastName": "Forest" } ], "abstractNote": "The first goal of this paper is to build a tight connection between two previously disjoint subjects: on one hand, complex networks, their graph representations, and graph anal-ysis, and on the other hand, electrical properties of composite materials consisting of conducting rods or fibers dispersed in a poorly conducting matrix with at least one per-colating path in the particle phase. This connection yields a new network analysis tool for experimental or numerical databases of a 3D rod or fiber dispersion. The novel appli-cation is for flow generated nano-rod and nano-fiber composites where particle number density overwhelms existing software and non-equilibrium, anisotropic distributions violate assumptions based on percolation threshold scaling behavior. The second goal of this pa-per is to apply this network analysis tool to the dimensional percolation phase diagram of sheared nano-rod dispersions [Zheng et. al. 2007]. The result is a statistical description of electrical properties appropriate to and consistent with statistical mechanics of nano-rod ensembles. The network analysis yields averaged conductance as well as local current and voltage distributions within the rod phase per realization. \n\nNetwork Analysis for Electrical Properties of Sheared Nano-Rod Dispersions (PDF Download Available). Available from: https://www.researchgate.net/publication/268266351_Network_Analysis_for_Electrical_Properties_of_Sheared_Nano-Rod_Dispersions [accessed Feb 26, 2016].", "presentationType": "", "date": "September 24-26, 2010", "meetingName": "Cha Cha Days", "place": "College of Charleston", "series": "", "sessionTitle": "", "DOI": "", "citationKey": "", "url": "", "accessDate": "", "shortTitle": "", "language": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-02-26T22:08:39Z", "dateModified": "2016-03-03T16:02:30Z" } }, { "key": "V2ATGD96", "version": 421, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/V2ATGD96", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/V2ATGD96", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "lastModifiedByUser": { "id": 49057, "username": "mucha", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/mucha", "type": "text/html" } } }, "creatorSummary": "Heroy et al.", "parsedDate": "2015-05-16", "numChildren": 0 }, "data": { "key": "V2ATGD96", "version": 421, "itemType": "presentation", "title": "Network Representations of Mechanical Percolation", "creators": [ { "creatorType": "presenter", "firstName": "S.", "lastName": "Heroy" }, { "creatorType": "presenter", "firstName": "D.", "lastName": "Taylor" }, { "creatorType": "presenter", "firstName": "F.", "lastName": "Shi" }, { "creatorType": "presenter", "firstName": "P.", "lastName": "Mucha" }, { "creatorType": "presenter", "firstName": "M.G.", "lastName": "Forest" } ], "abstractNote": "", "presentationType": "", "date": "May 16-17, 2015", "meetingName": "SIAM Workshop on Network Science (NS15)", "place": "Snowbird, Utah", "series": "", "sessionTitle": "", "DOI": "", "citationKey": "", "url": "", "accessDate": "", "shortTitle": "", "language": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-02-27T14:33:19Z", "dateModified": "2016-03-03T16:02:13Z" } }, { "key": "6IPFWBZJ", "version": 421, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/6IPFWBZJ", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/6IPFWBZJ", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "lastModifiedByUser": { "id": 49057, "username": "mucha", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/mucha", "type": "text/html" } } }, "creatorSummary": "Heroy et al.", "parsedDate": "2016-01-07", "numChildren": 1 }, "data": { "key": "6IPFWBZJ", "version": 421, "itemType": "presentation", "title": "Network Representations of Mechanical Percolation", "creators": [ { "creatorType": "presenter", "firstName": "S.", "lastName": "Heroy" }, { "creatorType": "presenter", "firstName": "D.", "lastName": "Taylor" }, { "creatorType": "presenter", "firstName": "F.", "lastName": "Shi" }, { "creatorType": "presenter", "firstName": "P.", "lastName": "Mucha" }, { "creatorType": "presenter", "firstName": "M.G.", "lastName": "Forest" } ], "abstractNote": "Nanoscopic to microscopic particles of high aspect ratio are routinely incorporated into polymeric host materials to enhance attributes such as electrical or thermal conductivity, charge storage, and mechanical properties. Experimentally, such composite materials typically exhibit a nonlinear response with respect to the density of filaments or rods: the property gain scales linearly with rod density at low densities, then increases dramatically as rod density approaches and exceeds a critical threshold. For conductivity, this sharp transition with conducting rods in a poorly conducting polymer is understood as a contact percolation phase transition within the rod network. A sharp rise in mechanical stability, however, occurs at volume fractions well above the contact percolation threshold. This so-called mechanical percolation phenomenon has been experimentally characterized in many rod composites, but the underlying physical mechanism remains a subject of intense interest, motivating different approaches including effective medium theory, mean-field micromechanics models, and for nanoscale rods, incorporation of the interfacial domain (interphase) between the rod and host polymer. Here we explore the underlying network structures within the rod phase that generalize contact percolation to rigidity percolation, one potential source of mechanical percolation.\nThe underlying method we employ involves simulating uniformly distributed rod distributions, and then use the topology and geometry of the resulting contacts between rods to determine the size and number of rigid clusters within the dispersion. \nOne of these methods is an adaptation of the rigidity pebble game, developed by DJ Jacobs and MF Thorpe. This is a purely topological algorithm, which tracks how degrees of freedom in the form of ‘pebbles’ are bound by increasing rod contacts. While we believe this method produces exact results in two dimensions, it does not readily extend to spatial rod dispersions. \nAnother approach is to treat the rods as collections of stiff springs, joined at rod intersection points. We then perturb the locations of these points and observe the behavior of the system as we relax the spring system, using nonlinear optimization techniques to minimize the system energy. In a rigid cluster, the distances between contact points should return to their original lengths after relaxation. However, in a flimsy cluster, only the distances adjacent points (those along the same rod) are preserved after relaxation. This method is more computationally expensive, but can be more easily extended to three dimensions.\nFinally, we employ an iterative graph compression algorithm, wherein we identify simple 2D rigid structures by a set of axioms and shrink these to single points. Then, we use the same axioms to identify and compress rigid structures in this reduced network, proceeding until no more rigid structures can be identified by these axioms. In the future, we look to establish axioms for rigidity in our spatial rod network, as this algorithm is much more efficient than the spring relaxation method.\nWith these approaches, we explore the dynamics of rigidity with respect to increasing rod density. Our results are currently limited to two dimensions, but our eventual goal is to provide a mechanistic explanation for the spatial mechanical percolation observed in real materials.", "presentationType": "", "date": "January 7-10, 2016", "meetingName": "Dynamics Days", "place": "Durham, NC", "series": "", "sessionTitle": "", "DOI": "", "citationKey": "", "url": "", "accessDate": "", "shortTitle": "", "language": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-02-26T22:13:36Z", "dateModified": "2016-03-03T16:01:44Z" } }, { "key": "4X2F5R6V", "version": 420, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/4X2F5R6V", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/4X2F5R6V", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "lastModifiedByUser": { "id": 49057, "username": "mucha", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/mucha", "type": "text/html" } } }, "creatorSummary": "AréValo et al.", "parsedDate": "2009", "numChildren": 1 }, "data": { "key": "4X2F5R6V", "version": 420, "itemType": "journalArticle", "title": "Topological Properties of the Contact Network of Granular Materials", "creators": [ { "creatorType": "author", "firstName": "Roberto", "lastName": "AréValo" }, { "creatorType": "author", "firstName": "Iker", "lastName": "Zuriguel" }, { "creatorType": "author", "firstName": "Diego", "lastName": "Maza" } ], "abstractNote": "", "publicationTitle": "International Journal of Bifurcation and Chaos", "publisher": "", "place": "", "date": "02/2009", "volume": "19", "issue": "02", "section": "", "partNumber": "", "partTitle": "", "pages": "695-702", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1142/S0218127409023056", "citationKey": "", "url": "http://www.worldscientific.com/doi/abs/10.1142/S0218127409023056", "accessDate": "2016-02-25T18:40:04Z", "PMID": "", "PMCID": "", "ISSN": "0218-1274, 1793-6551", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-02-25T18:40:04Z", "dateModified": "2016-03-03T15:50:29Z" } }, { "key": "QBXTEJ32", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/QBXTEJ32", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/QBXTEJ32", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "creatorSummary": "Vitelli et al.", "parsedDate": "2010-02-03", "numChildren": 0 }, "data": { "key": "QBXTEJ32", "version": 419, "itemType": "journalArticle", "title": "Heat transport in model jammed solids", "creators": [ { "creatorType": "author", "firstName": "Vincenzo", "lastName": "Vitelli" }, { "creatorType": "author", "firstName": "Ning", "lastName": "Xu" }, { "creatorType": "author", "firstName": "Matthieu", "lastName": "Wyart" }, { "creatorType": "author", "firstName": "Andrea J.", "lastName": "Liu" }, { "creatorType": "author", "firstName": "Sidney R.", "lastName": "Nagel" } ], "abstractNote": "", "publicationTitle": "Physical Review E", "publisher": "", "place": "", "date": "2010-2-3", "volume": "81", "issue": "2", "section": "", "partNumber": "", "partTitle": "", "pages": "", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1103/PhysRevE.81.021301", "citationKey": "", "url": "http://link.aps.org/doi/10.1103/PhysRevE.81.021301", "accessDate": "2016-03-02T05:20:54Z", "PMID": "", "PMCID": "", "ISSN": "1539-3755, 1550-2376", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-03-02T05:20:54Z", "dateModified": "2016-03-02T05:20:54Z" } }, { "key": "XHZSS278", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/XHZSS278", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/XHZSS278", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "creatorSummary": "O'Hern et al.", "parsedDate": "2002-01-31", "numChildren": 0 }, "data": { "key": "XHZSS278", "version": 419, "itemType": "journalArticle", "title": "Random Packings of Frictionless Particles", "creators": [ { "creatorType": "author", "firstName": "Corey S.", "lastName": "O'Hern" }, { "creatorType": "author", "firstName": "Stephen A.", "lastName": "Langer" }, { "creatorType": "author", "firstName": "Andrea J.", "lastName": "Liu" }, { "creatorType": "author", "firstName": "Sidney R.", "lastName": "Nagel" } ], "abstractNote": "", "publicationTitle": "Physical Review Letters", "publisher": "", "place": "", "date": "2002-1-31", "volume": "88", "issue": "7", "section": "", "partNumber": "", "partTitle": "", "pages": "", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1103/PhysRevLett.88.075507", "citationKey": "", "url": "http://link.aps.org/doi/10.1103/PhysRevLett.88.075507", "accessDate": "2016-03-02T05:20:13Z", "PMID": "", "PMCID": "", "ISSN": "0031-9007, 1079-7114", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-03-02T05:20:13Z", "dateModified": "2016-03-02T05:20:13Z" } }, { "key": "995NKQFU", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/995NKQFU", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/995NKQFU", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "creatorSummary": "Chen et al.", "parsedDate": "2014-02-25", "numChildren": 0 }, "data": { "key": "995NKQFU", "version": 419, "itemType": "journalArticle", "title": "Complexity in Surfaces of Densest Packings for Families of Polyhedra", "creators": [ { "creatorType": "author", "firstName": "Elizabeth R.", "lastName": "Chen" }, { "creatorType": "author", "firstName": "Daphne", "lastName": "Klotsa" }, { "creatorType": "author", "firstName": "Michael", "lastName": "Engel" }, { "creatorType": "author", "firstName": "Pablo F.", "lastName": "Damasceno" }, { "creatorType": "author", "firstName": "Sharon C.", "lastName": "Glotzer" } ], "abstractNote": "", "publicationTitle": "Physical Review X", "publisher": "", "place": "", "date": "2014-2-25", "volume": "4", "issue": "1", "section": "", "partNumber": "", "partTitle": "", "pages": "", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1103/PhysRevX.4.011024", "citationKey": "", "url": "http://link.aps.org/doi/10.1103/PhysRevX.4.011024", "accessDate": "2016-03-02T05:19:17Z", "PMID": "", "PMCID": "", "ISSN": "2160-3308", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-03-02T05:19:17Z", "dateModified": "2016-03-02T05:19:17Z" } }, { "key": "7GT7NAWN", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": 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"2013-1-20", "volume": "12", "issue": "4", "section": "", "partNumber": "", "partTitle": "", "pages": "326-331", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1038/nmat3543", "citationKey": "", "url": "http://www.nature.com/doifinder/10.1038/nmat3543", "accessDate": "2016-03-02T05:18:49Z", "PMID": "", "PMCID": "", "ISSN": "1476-1122, 1476-4660", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-03-02T05:18:49Z", "dateModified": "2016-03-02T05:18:49Z" } }, { "key": "PJRQIRGV", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/PJRQIRGV", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/PJRQIRGV", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1950974, "username": "samuelheroy", "name": "", "links": { "alternate": { "href": "https://www.zotero.org/samuelheroy", "type": "text/html" } } }, "creatorSummary": "Wang and Pan", "parsedDate": "2008-12-20", "numChildren": 0 }, "data": { "key": "PJRQIRGV", "version": 419, "itemType": "journalArticle", "title": "Predictions of effective physical properties of complex multiphase materials", "creators": [ { "creatorType": "author", "firstName": "M", "lastName": "Wang" }, { "creatorType": "author", "firstName": "N", "lastName": "Pan" } ], "abstractNote": "", "publicationTitle": "Materials Science and Engineering: R: Reports", "publisher": "", "place": "", "date": "2008-12-20", "volume": "63", "issue": "1", "section": "", "partNumber": "", "partTitle": "", "pages": "1-30", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1016/j.mser.2008.07.001", "citationKey": "", "url": "http://linkinghub.elsevier.com/retrieve/pii/S0927796X08000673", "accessDate": "2016-03-02T05:18:11Z", "PMID": "", "PMCID": "", "ISSN": "0927796X", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "CrossRef", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "EGXFJQ5E" ], "relations": {}, "dateAdded": "2016-03-02T05:18:11Z", "dateModified": "2016-03-02T05:18:11Z" } }, { "key": "Q7P4MTH4", "version": 419, "library": { "type": "group", "id": 267635, "name": "mechanicalpercolationunc", "links": { "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/267635/items/Q7P4MTH4", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/mechanicalpercolationunc/items/Q7P4MTH4", "type": 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