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On the distribution of free path lengths for the periodic Lorentz gas II

François Golse; Bernt Wennberg — 2000

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On the distribution of free path lengths for the periodic Lorentz gas II

François Golse; Bernt Wennberg — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

Consider the domain $Z_{ϵ} = {x \in ℝ^{n}; d i s t (x, ϵ ℤ^{n}) > ϵ^{γ}}$ and let the free path length be defined as $τ_{ϵ} (x, v) = inf {t > 0; x - t v \in Z_{ϵ}} .$ In the Boltzmann-Grad scaling corresponding to $γ = \frac{n}{n - 1}$ , it is shown that the limiting distribution $φ_{ϵ}$ of $τ_{ϵ}$ is bounded from below by an expression of the form , for some . A numerical study seems to indicate that asymptotically for large , $φ_{ϵ} \sim C / t$ . This is an extension of a previous work [J. Bourgain , (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate to describe the...

Modelling of peripheral fluid accumulation after a crystalloid bolus in female volunteers. A mathematical study.

Rodhe, Peter; Drobin, Dan; Hahn, Robert G.; Wennberg, Bernt; Lindahl, Christina; Sjöstrand, Fredrik; Svensen, Christer H. — 2010

Computational & Mathematical Methods in Medicine

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Currently displaying 1 – 3 of 3

On the distribution of free path lengths for the periodic Lorentz gas II

On the distribution of free path lengths for the periodic Lorentz gas II

Modelling of peripheral fluid accumulation after a crystalloid bolus in female volunteers. A mathematical study.