Hard congestion limit of the dissipative Aw–Rascle system

In this study, we analyse the famous Aw–Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the momentum equation which vanishes when the density is zero. The resulting system of PDEs can be used to model traffic or suspension flows in one dimension with the maximal packing constraint taken into account. After proving the global existence of smooth solutions, we study the so-called 'hard congestion limit', and show the convergence of a subsequence of solutions towards a weak solution of a hybrid free-congested system. This is also illustrated numerically using a numerical scheme proposed for the model studied. In the context of suspension flows, this limit can be seen as the transition from a suspension regime, driven by lubrication forces, towards a granular regime, driven by the contacts between the grains

Congestion in a macroscopic model of self-driven particles modeling gregariousness

International audienceWe analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a one-dimensional Riemann problem and introduce a perturbation problem which regularizes the compressible-incompressible transition. Specific difficulties related to the non-conservativity of the problem are discussed

Detection of Complex Fractionated Atrial Electrograms (CFAE)using Recurrence Quantification Analysis.

International audienceAtrial fibrillation (AF) is the most common cardiac arrhythmia but its proarrhythmic substrate remains unclear. Reentrant electrical activity in the atria may be responsible for AF maintenance. Over the last decade, different catheter ablation strategies targeting the electrical substrate of the left atrium have been developed in order to treat AF. Complex Fractionated Atrial Electrograms (CFAE) recorded in the atria may represent not only reentry mechanisms, but also a large variety of bystander electrical wave fronts. In order to identify CFAE involved in AF maintenance as a potential target for AF ablation, we have developed an algorithm based on nonlinear data analysis using Recurrence Quantification Analysis (RQA). RQA features make it possible to quantify hidden structures in a signal and offer clear representations of different CFAE types. Five RQA features were used to qualify CFAE areas previously tagged by a trained electrophysiologist. Data from these analyzes were used by two classifiers to detect CFAE periods in a signal. While a single feature is not sufficient to properly detect CFAE periods, the set of five RQA features combined with a classifier were highly reliable for CFAE detection

PLoS ONE

e11457

BioMedical Engineering Online

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