{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T04:46:45Z","timestamp":1776746805536,"version":"3.51.2"},"reference-count":36,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T00:00:00Z","timestamp":1541721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"LabEx Tec 21","award":["ANR-11-LABX-0030"],"award-info":[{"award-number":["ANR-11-LABX-0030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see \u201cexperimental validation of a nonextensive scaling law in confined granular media\u201d). Basically, the pdf of grain displacements has clear nonextensive (q-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales\u2014the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the q-statistics with the shear increment. This analysis has shown a singular behavior of q at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the q-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.<\/jats:p>","DOI":"10.3390\/e20110862","type":"journal-article","created":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T03:27:31Z","timestamp":1542079651000},"page":"862","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics"],"prefix":"10.3390","volume":"20","author":[{"given":"L\u00e9o","family":"Viallon-Galinier","sequence":"first","affiliation":[{"name":"Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institute of Engineering Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8633-0793","authenticated-orcid":false,"given":"Ga\u00ebl","family":"Combe","sequence":"additional","affiliation":[{"name":"Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institute of Engineering Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8897-5499","authenticated-orcid":false,"given":"Vincent","family":"Richefeu","sequence":"additional","affiliation":[{"name":"Univ. Grenoble Alpes, CNRS, Grenoble-INP, Institute of Engineering Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7614-2721","authenticated-orcid":false,"given":"Allbens","family":"Picardi Faria Atman","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica and National Institute of Science and Technology for Complex Systems, CEFET-MG, Belo Horizonte CEP 30510-000, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,9]]},"reference":[{"key":"ref_1","unstructured":"Tolman, R. (1979). The Principles of Statistical Mechanics, Dover Publications."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s00032-008-0087-y","article-title":"On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics","volume":"76","author":"Umarov","year":"2008","journal-title":"Milan J. 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