Biomedical subjects

Chaouqi Misbah

Publications and source records attributed to Chaouqi Misbah.

7 recordsLinked to original sources

PubMed2006

Nonlinear dynamics in one dimension: a criterion for coarsening and its temporal law.

We develop a general criterion about coarsening for some classes of nonlinear evolution equations describing one-dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process takes place and the one where the wavelength is fixed in the course of time. An intermediate scenario may occur, namely "interrupted coarsening." The power of the criterion on which a brief account has been given [Politi and Misbah, Phys. Rev. Lett. 92, 090601 (2004)], and which we extend here to more general equations, lies in the fact that the statement about the occurrence of coarsening, or selection of a length scale, can be made by only inspecting the behavior of the branch of steady state periodic solutions. The criterion states that coarsening occurs if lambda'(A)>0 while a length scale selection prevails if lambda'(A)<0, where lambda is the wavelength of the pattern and A is the amplitude of the profile (prime refers to differentiation). This criterion is established thanks to the analysis of the phase diffusion equation of the pattern. We connect the phase diffusion coefficient D(lambda) (which carries a kinetic information) to lambda'(A), which refers to a pure steady state property. The relationship between kinetics and the behavior of the branch of steady state solutions is established fully analytically. Another important and new result which emerges here is that the exploitation of the phase diffusion coefficient enables us to determine in a rather straightforward manner the dynamical coarsening exponent. Our calculation, based on the idea that |D(lambda)| approximately lambda2/t, is exemplified on several nonlinear equations, showing that the exact exponent is captured. We are not aware of another method that so systematically provides the coarsening exponent. Contrary to many situations where the one-dimensional character has proven essential for the derivation of the coarsening exponent, this idea can be used, in principle, at any dimension. Some speculations about the extension of the present results are outlined.

Journal Article↗

PubMed2006

Vacillating breathing and tumbling of vesicles under shear flow.

The dynamics of vesicles under a shear flow are analyzed analytically in the small deformation regime. We derive two coupled nonlinear equations which describe the vesicle orientation in the flow and its shape evolution. A new type of motion is found, namely, a "vacillating-breathing" mode: the vesicle orientation undergoes an oscillation around the flow direction, while the shape executes breathing dynamics. This solution coexists with tumbling. Moreover, we provide an explicit expression for the tumbling threshold. A rheological law for a dilute vesicle suspension is outlined.

Cell Physiological Phenomena↗

PubMed2005

Phase-field approach to three-dimensional vesicle dynamics.

We extend our recent phase-field [T. Biben and C. Misbah, Phys. Rev. E 67, 031908 (2003)] approach to 3D vesicle dynamics. Unlike the boundary-integral formulations, based on the use of the Oseen tensor in the small Reynolds number limit, this method offers several important flexibilities. First, there is no need to track the membrane position; rather this is automatically encoded in dynamics of the phase field to which we assign a finite width representing the membrane extent. Secondly, this method allows naturally for any topology change, like vesicle budding, for example. Thirdly, any non-Newtonian constitutive law, that is generically nonlinear, can be naturally accounted for, a fact which is precluded by the boundary integral formulation. The phase-field approach raises, however, a complication due to the local membrane incompressibility, which, unlike usual interfacial problems, imposes a nontrivial constraint on the membrane. This problem is solved by introducing dynamics of a tension field. The first purpose of this paper is to show how to write adequately the advected-field model for 3D vesicles. We shall then perform a singular expansion of the phase field equation to show that they reduce, in the limit of a vanishing membrane extent, to the sharp boundary equations. Then, we present some results obtained by the phase-field model. We consider two examples; (i) kinetics towards equilibrium shapes and (ii) tanktreading and tumbling. We find a very good agreement between the two methods. We also discuss briefly how effects, such as the membrane shear elasticity and stretching elasticity, and the relative sliding of monolayers, can be accounted for in the phase-field approach.

Computer Simulation↗

PubMed2005

Irreversible aggregation of interacting particles in one dimension.

We present a study of the aggregation of interacting particles in one dimension. This situation, for example, applies to atoms trapped along linear defects at the surface of a crystal. Simulations are performed with two lattice models. In the first model, the borders of atoms and islands interact in a vectorial manner via force monopoles. In the second model, each atom carries a dipole. These two models lead to qualitatively similar but quantitatively different behaviors. In both cases, the final average island size S(f) does not depend on the interactions in the limits of very low and very high coverages. For intermediate coverages, S(f) exhibits an asymmetric behavior as a function of the interaction strength: while it saturates for attractive interactions, it decreases for repulsive interactions. A class of mean-field models is designed, which allows one to retrieve the interaction dependence on the coverage dependence of the average island size with a good accuracy.

Journal Article↗

PubMed2004

When does coarsening occur in the dynamics of one-dimensional fronts?

Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period lambda of the steady-state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidence for the growth equation of a stepped crystal surface.

Journal Article↗

PubMed2003

Pattern selection in biaxially stressed solids.

We analyze the morphological instability of the surface of a solid which is subject to a biaxial stress. The stability calculation reveals a new favored pattern: a diamond morphology. This occurs if the stress is tensile in one direction and compressive in the orthogonal one and the ratio exceeds a certain value. A nonlinear analysis shows that the bifurcation is subcritical and hints to a nontrivial competition between tilted stripes and diamonds. This study opens a new line of inquiries in the field of stress-induced pattern selection.

Journal Article↗

PubMed2002

Amplitude equations for systems with long-range interactions.

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.

Journal Article↗