{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:16Z","timestamp":1760147536920,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,11]],"date-time":"2023-02-11T00:00:00Z","timestamp":1676073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional diffusion parameter and for the medium size.<\/jats:p>","DOI":"10.3390\/axioms12020191","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T02:14:11Z","timestamp":1676254451000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bidimensional Deterministic Model for Diffusion and Settling of Particles"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0493-2265","authenticated-orcid":false,"given":"Stephanie Esmeralda","family":"Vel\u00e1zquez P\u00e9rez","sequence":"first","affiliation":[{"name":"Departamento F\u00edsico-Matem\u00e1ticas, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Ni\u00f1o Artillero s\/n. Zona Universitaria Poniente, San Luis Potos\u00ed 78290, Mexico"},{"name":"Facultad de Ciencias, Universidad Aut\u00f3noma de San Luis Potos\u00ed, Av. Parque Chapultepec 1570, Privadas del Pedregal, San Luis Potos\u00ed 78295, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1098-1610","authenticated-orcid":false,"given":"Eric","family":"Campos-Cant\u00f3n","sequence":"additional","affiliation":[{"name":"Division of Control and Dynamical Systems, Instituto Potosino de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica A. C., Camino a la Presa San Jos\u00e9 2055, Col. Lomas 4 Secci\u00f3n, San Luis Potos\u00ed 78216, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Huerta Cuellar","sequence":"additional","affiliation":[{"name":"Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique D\u00edaz de Le\u00f3n 1144, Paseos de la Monta\u00f1a, Lagos de Moreno 47460, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor Eduardo","family":"Gilardi Vel\u00e1zquez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Panamericana, Josemar\u00eda Escriv\u00e1 de Balaguer 101, Aguascalientes 20290, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,11]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Brown, R. (1828). 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