Jean Bragard

Bénard–Marangoni convection: planforms and related theoretical predictions

A derivation is given of the amplitude equations governing pattern formation in surface tension gradient-driven B enard{Marangoni convection. The amplitude equations are obtained from the continuity, the Navier{Stokes and the Fourier equations in the Boussinesq approximation neglecting surface deformation and buoyancy. The system is a shallow liquid layer heated from below, conned below by a rigid plane and above with a free surface whose surface tension linearly depends on temperature. The amplitude equations of the convective modes are equations of the Ginzburg{Landau type with resonant advective non-variational terms. Generally, and in agreement with experiment, above threshold solutions of the equations correspond to an hexagonal convective structure in which the fluid rises in the centre of the cells. We also analytically study the dynamics of pattern formation leading not only to hexagons but also to squares or rolls depending on the various dimensionless parameters like Prandtl number, and the Marangoni and Biot numbers at the boundaries. We show that a transition from an hexagonal structure to a square pattern is possible. We also determine conditions for alternating, oscillatory transition between hexagons and rolls. Moreover, we also show that as the system of these amplitude equations is non-variational the asymptotic behaviour (t!1) may not correspond to a steady convective pattern. Finally, we have determined the Eckhaus band for hexagonal patterns and we show that the non-variational terms in the amplitude equations enlarge this band of allowable modes. The analytical results have been checked by numerical integration of the amplitude equations in a square container. Like in experiments, numerics shows the emergence of dierent hexagons, squares and rolls according to values given to the parameters of the system.

Modeling the effector - regulatory T cell cross-regulation reveals the intrinsic character of relapses in Multiple Sclerosis

BackgroundThe relapsing-remitting dynamics is a hallmark of autoimmune diseases such as Multiple Sclerosis (MS). Although current understanding of both cellular and molecular mechanisms involved in the pathogenesis of autoimmune diseases is significant, how their activity generates this prototypical dynamics is not understood yet. In order to gain insight about the mechanisms that drive these relapsing-remitting dynamics, we developed a computational model using such biological knowledge. We hypothesized that the relapsing dynamics in autoimmunity can arise through the failure in the mechanisms controlling cross-regulation between regulatory and effector T cells with the interplay of stochastic events (e.g. failure in central tolerance, activation by pathogens) that are able to trigger the immune system.ResultsThe model represents five concepts: central tolerance (T-cell generation by the thymus), T-cell activation, T-cell memory, cross-regulation (negative feedback) between regulatory and effector T-cells and tissue damage. We enriched the model with reversible and irreversible tissue damage, which aims to provide a comprehensible link between autoimmune activity and clinical relapses and active lesions in the magnetic resonances studies in patients with Multiple Sclerosis. Our analysis shows that the weakness in this negative feedback between effector and regulatory T-cells, allows the immune system to generate the characteristic relapsing-remitting dynamics of autoimmune diseases, without the need of additional environmental triggers. The simulations show that the timing at which relapses appear is highly unpredictable. We also introduced targeted perturbations into the model that mimicked immunotherapies that modulate effector and regulatory populations. The effects of such therapies happened to be highly dependent on the timing and/or dose, and on the underlying dynamic of the immune system.ConclusionThe relapsing dynamic in MS derives from the emergent properties of the immune system operating in a pathological state, a fact that has implications for predicting disease course and developing new therapies for MS.

Chaos suppression through asymmetric coupling.

We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.

Characterization of the Chaotic Magnetic Particle Dynamics

In this paper, we study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a time-dependent magnetic field using the Landau-Lifshitz equation. In particular, we study the case when the magnetic field is homogeneous with a fixed direction perpendicular to the anisotropy direction and consists of a constant and a time-periodic part. We characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and by bifurcation diagrams. We focus on the dependence of the largest Lyapunov exponent on the magnitude and frequency of the applied magnetic field as well as on the anisotropy parameter of the particle. We find rather complicated landscape of sometimes closely intermingled chaotic and nonchaotic areas in parameter space with rather fuzzy boundaries in-between. For actual experiments that means the system can exhibit multiple transitions between regular and chaotic behavior.

On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing.

CONTROL AND SYNCHRONIZATION OF SPACE EXTENDED DYNAMICAL SYSTEMS

We discuss the issues of controlling and synchronizing continuous space extended systems in the case of two bidirectionally coupled fields, each one obeying one-dimensional CGL. When the two equations are identical, control and synchronization are achieved by means of a finite number of local tiny perturbations, selected by an adaptive technique. We address the problem of the minimum number of local perturbations needed to realize control and synchronization. When the two equations are nonidentical, we show how to induce the appearance of different kinds of synchronized states, depending on the difference in the uncoupled dynamical regimes of the considered fields. Finally, we discuss the role of space-time defects in mediating the process leading to perfect synchronization between the two systems.

Dissipative dynamics of an open Bose Einstein condensate

As an atomic Bose Einstein condensate BEC is coupled to a source of uncondensed atoms at the same temperature and

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols.

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

Non-Linear Marangoni Convection in a Layer of Finite Depth

Non-linear thermal convection driven by surface tension in a thin layer of fluid heated from below is studied. The present analysis, based on the amplitude method, amplifies previous results obtained by other authors. The thin fluid layer is modelized by means of a finite-depth layer instead of a semi-infinite one, as proposed by Scanlon and Segel. The main differences with Scanlon and Segel analysis are emphasized.