Entropy Production Of Entirely Diffusional Laplacian Transfer And The Possible Role Of Fragmentation Of The Boundaries

Abstract

The Entropy Production And The Variational Functional Of A Laplacian Diffusional Field Around The First Four Fractal Iterations Of A Linear Self-Similar Tree (Von Koch Curve) Is Studied Analytically And Detailed Predictions Are Stated. In A Next Stage, These Predictions Are Confronted With Results From Numerical Resolution Of The Laplace Equation By Means Of Finite Elements Computations. After A Brief Review Of The Existing Results, The Range Of Distances Near The Geometric Irregularity, The So-Called »Near Field», A Situation Never Studied In The Past, Is Treated Exhaustively. We Notice Here That In The Near Field, The Usual Notion Of The Active Zone Approximation Introduced By Sapoval Et Al. [M. Filoche And B. Sapoval, Transfer Across Random Versus Deterministic Fractal Interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos And R. Brizzi, Can One Hear The Shape Of An Electrode? I. Numerical Study Of The Active Zone In Laplacian Transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 Is Strictly Inapplicable. The Basic New Result Is That The Validity Of The Active-Zone Approximation Based On Irreversible Thermodynamics Is Confirmed In This Limit, And This Implies A New Interpretation Of This Notion For Laplacian Diffusional Fields.

Department(s)

Physics

Keywords and Phrases

Diffusion; Entropy Production; Fractals; Laplacian Fields; Near Field

International Standard Serial Number (ISSN)

0218-348X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 World Scientific Publishing, All rights reserved.

Publication Date

04 Sep 2015

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