Stéphane Metens

Stability and decay rates of nonisotropic attractive Bose-Einstein condensates

Nonisotropic attractive Bose-Einstein condensates are investigated numerically with Newton and inverse Arnoldi methods. The stationary solutions of the Gross-Pitaevskii equation and their linear stability are computed. Bifurcation diagrams are calculated and used to find the condensate decay rates corresponding to macroscopic quantum tunneling, two-three-body inelastic collisions, and thermally induced collapse. Isotropic and nonisotropic condensates are compared. The effect of anisotropy on the bifurcation diagram and the decay rates is discussed. Spontaneous isotropization of the condensates is found to occur. The influence of isotropization on the decay rates is characterized near the critical point.

Chemomechanical Instabilities in Responsive Materials

From Sustained Oscillations to Stationary Reaction-Diffusion Patterns P. De Kepper et al.- Mechanochemical Instabilities in Active Gels R. Yoshida.- An Excursion in Theoretical Non Linear Chemistry: From Oscillations to Turing Patterns P. Borckmans and S. Metens.- Chemomechanics: Oscillatory Dynamics in Chemoresponsive Gels: J. Boissonade and P. De Kepper.- Structural Approaches on the Toughness in Double Network Hydrogels T. Tominaga et al.- Chemomechanical Dynamics of Responsive Gels S. Metens et al.- Autonomous Rhythmic Drug Delivery Systems Based on Chemical and Biochemomechanical Oscillators R.A. Siegel.- Structure Formation and Nonlinear Dynamics in Polyelectrolyte Responsive Gels A.R. Khokhov et al.- Nonlinear Chemical Dynamics in Synthetic Polymer Systems J.A. Pojman Sr.- Internal Stress as a Link Between Macroscale and Mesoscale Mechanics K. Sekimoto.- On Some Passive and Active Motion in Biology C. Misbah.

Spatio-temporal behaviors of a clock reaction in an open gel reactor

The concentration profiles along the feeding direction of a one side fed gel reactor are analyzed for the iodate-arsenous acid reaction. Multiplicity of inhomogeneous stationary solutions is derived. It is also shown that such profiles may undergo oscillatory bifurcations under long range activation conditions. The bifurcation diagram is analyzed using a Galerkin approximation, the asymptotic validity of which is discussed.

Pattern formation and spatial self-entrainment in bistable chemical systems

We describe the formation of spatial structures generated by diffusive instabilities in bistable systems. The coupling between the different spatial modes emanating from the two homogeneous steady states can then give rise to self-parametric instabilities favoring the occurrence of resonant rhombic or quasiperiodic structures such as superlattices or quasicrystalline patterns.

Chemomechanical Dynamics of Responsive Gels

In this contribution we present a formalism to describe the spatio-temporalevolution of a responsive gel submitted to some autocatalytic chemical reaction. This theory is based on an hydrodynamical multi-diffusional approach of a gel, which is plunged in a chemically active mixture. Emergent volume self-oscillation dynamics of the gel result from the nonlinear coupling of the elastic deformation, the chemical kinetics and the transport phenomenon, that take place in the system. We apply our formalism to the case of the Belouzov-Zhabotinsky oscillatory chemical reaction, for which Yoshida et al. (see in this volume) have obtained many experimental results. In particular we discuss some possible coupling between the gel and the chemical reaction.

An excursion in theoretical non linear chemistry: from oscillations to Turing patterns

Some basic principles of theoretical nonlinear chemistry are introduced to explain an origin of temporal oscillations and spatial bistability, that have both been used in other chapters in conjunction with gels sensitive to such chemical behavior. Because the use of inert gels played such importance in their experimental discovery, elements of the theory of Turing stationary spatial periodic patterns are also discussed.

Mechano-chemical dynamics of active gels: interplay between spatial bistability and volume variations

Abstract The mechano-chemical dynamics of a spherical bead of gel immersed in an autocatalytic bistable chemical reaction are examined. The spheres exhibit autonomous volume self-oscillation dynamics. We present a multi-diffusional approach to a hydrodynamic theory of gels, and also evolution equations incorporating chemical processes.

An excursion in theoretical non linear chemistry: From oscillations to turing patterns

Some basic principles of theoretical nonlinear chemistry are introduced to explain an origin of temporal oscillations and spatial bistability, that have both been used in other chapters in conjunction with gels sensitive to such chemical behavior. Because the use of inert gels played such importance in their experimental discovery, elements of the theory of Turing stationary spatial periodic patterns are also discussed.