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Technology Complex Fluids (INCT-FCx)","award":["001"],"award-info":[{"award-number":["001"]}]},{"name":"National Institute of Science and Technology Complex Fluids (INCT-FCx)","award":["301715\/2022\u20130"],"award-info":[{"award-number":["301715\/2022\u20130"]}]},{"name":"National Institute of Science and Technology Complex Fluids (INCT-FCx)","award":["303533\/2021-8"],"award-info":[{"award-number":["303533\/2021-8"]}]},{"name":"National Institute of Science and Technology Complex Fluids (INCT-FCx)","award":["304634\/2020\u20134"],"award-info":[{"award-number":["304634\/2020\u20134"]}]},{"name":"National Institute of Science and Technology Complex Fluids (INCT-FCx)","award":["465259\/2014\u20136"],"award-info":[{"award-number":["465259\/2014\u20136"]}]},{"name":"National Institute of Science and Technology Complex Fluids (INCT-FCx)","award":["FAPESP\u20142014\/50983-3"],"award-info":[{"award-number":["FAPESP\u20142014\/50983-3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which are nonlinear diffusion equations. We use analytical and numerical calculations to obtain and interpret the probability distribution of the position of the particles and the mean square displacement. These results are further compared and shown to agree with the results of numerical simulations. Our findings show that a system of this kind exhibits non-Gaussian distributions, transient anomalous diffusion (subdiffusion and superdiffusion), and stationary states that simultaneously depend on the nonlinearity and resetting rate.<\/jats:p>","DOI":"10.3390\/e25121647","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T04:28:31Z","timestamp":1702355311000},"page":"1647","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Results for Nonlinear Diffusion Equations with Stochastic Resetting"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3853-1790","authenticated-orcid":false,"given":"Ervin K.","family":"Lenzi","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil"},{"name":"National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4930-5262","authenticated-orcid":false,"given":"Rafael S.","family":"Zola","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Tecnol\u00f3gica Federal do Paran\u00e1, Apucarana 86812-460, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6158-3068","authenticated-orcid":false,"given":"Michely P.","family":"Rosseto","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5216-0578","authenticated-orcid":false,"given":"Renio S.","family":"Mendes","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maringa 87020-900, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9532-5195","authenticated-orcid":false,"given":"Haroldo V.","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maringa 87020-900, PR, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6875-1965","authenticated-orcid":false,"given":"Luciano R. da","family":"Silva","sequence":"additional","affiliation":[{"name":"National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil"},{"name":"Departamento de F\u00edsica, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7202-1386","authenticated-orcid":false,"given":"Luiz R.","family":"Evangelista","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maringa 87020-900, PR, Brazil"},{"name":"Istituto dei Sistemi Complessi (ISC\u2013CNR), Via dei Taurini, 19, 00185 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6634","DOI":"10.1103\/PhysRevE.57.6634","article-title":"Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model","volume":"57","author":"Borland","year":"1998","journal-title":"Phys. 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