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

Cláudio Nassif and P.R. Silva

Physica A: Statistical Mechanics and its Applications, 2004, vol. 334, issue 3, 335-342

Abstract: Inspired 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.

Keywords: Thompson's approach; Anomalous coalescence; Nonlinear Schrödinger equation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:334:y:2004:i:3:p:335-342

DOI: 10.1016/j.physa.2003.11.019

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