Anomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson’s approach.

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Autor(es): dc.creatorCruz, Cláudio Nassif da-
Autor(es): dc.creatorSilva, P. R.-
Data de aceite: dc.date.accessioned2025-08-21T15:21:57Z-
Data de disponibilização: dc.date.available2025-08-21T15:21:57Z-
Data de envio: dc.date.issued2014-08-25-
Data de envio: dc.date.issued2014-08-25-
Data de envio: dc.date.issued2003-
Fonte completa do material: dc.identifierhttp://www.repositorio.ufop.br/handle/123456789/3592-
Fonte completa do material: dc.identifierhttps://doi.org/10.1016/j.physa.2003.11.019-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1011987-
Descrição: dc.descriptionInspired by models for A+A→A(0) reactions with non-Brownian diffusion, we suggest a possible analytical explanation for the phenomena of anomalous coalescence of bubbles found in one-dimension (1d) by Josserand and Rica through numerical work [Phys. Rev. Letters 78 (1997) 1215]. The explanation firstly requires an exponent γ, which is sometimes used to describe anomalous diffusion. Here it displays an explicit dependence on the dimensionality (γ=γ(d)=4/d for d⩽2). So we have dc=2, coinciding with the upper critical dimension of A+A→A(0) reactions (Mod. Phys. Lett. B 13 (1999) 829; Mod. Phys. Lett. B 15(26) (2001) 1205) with Brownian diffusion condition (γ=2). Thus anomalous coalescence emerges, only below the critical dimension (d<2). We show that the typical size of the structures (bubbles) grows as R(t)∼t1/4 in 1d. An alternative explanation could also be thought as a diffusion constant D which depends on the average concentration (〈n〉), namely D=D0〈n〉α. It is introduced into an effective action for A+A→A(0) reactions. Therefore we are also able to reproduce the anomalous behavior for n(t) and R(t) in 1d, being α=0 for d⩾2 (mean field behavior) and α=2(2−d)/d2 for d⩽2.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Direitos: dc.rightsO Periódico Physica A: Statistical Mechanics and its Applications concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3304700907426.-
Palavras-chave: dc.subjectThompson's approach-
Palavras-chave: dc.subjectAnomalous coalescence-
Palavras-chave: dc.subjectNonlinear Schrödinger equation-
Título: dc.titleAnomalous coalescence from a nonlinear Schroedinger equation with a quintic term: interpretation through Thompson’s approach.-
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