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Distribution in TLM models for diffusion (Part II: multi-dimensional treatment)

✍ Scribed by P. Chardaire; D. de Cogan

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 230 KB
Volume: 16
Category: Article
ISSN: 0894-3370
DOI: 10.1002/jnm.516

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✦ Synopsis

Abstract

The signals obtained at each time step of a transmission line matrix (TLM) simulation of Gaussian diffusion are analysed for two‐ and three‐dimensional cases. A combinatorial formula is derived to provide the signal magnitude at any spatial position and any time step after a single‐shot excitation in the two‐dimensional link‐line model. Formulae for the expectation and variance of the axial positions of a particle are determined for two‐ and three‐dimensional link‐line and link‐resistor models. A generalization of these formulae is proposed for higher dimensions, and an entirely numerical proving scheme is devised. Finally, we briefly compare the resulting variances and that of the underlying diffusion process. Copyright © 2003 John Wiley & Sons, Ltd.

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Distribution in TLM models for diffusion

Distribution in TLM models for diffusion (Part I: one-dimensional treatment)

✍ P. Chardaire; D. de Cogan 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 123 KB

## Abstract The signal obtained at each time step of a TLM simulation for one‐dimensional diffusion is analysed for single shot injections. A combinatorial formula is provided to predict the signal value at any given spatial positions. Formulas for expectation and variance are obtained using a tech