Biomedical subjects

C Misbah

Publications and source records attributed to C Misbah.

At least 19 recordsLinked to original sources

PubMed2006

Birth and morphological evolution of step bunches under electromigration.

We analyze the dynamics of electromigration-induced step bunching in the absence of desorption. We show that, even when the instability occurs at long wavelength, hinting to a smooth morphology, the surface suddenly splits into bunches escorted with wide terraces, in agreement with several observations. As the size of the bunches increases, a nonstandard regime is exhibited, namely, the bunches do not match tangentially to the facet, as would the classical Pokrosvky-Talapov shape dictate. This Letter presents a complete scenario of evolution of bunches from their birth up to their ultimate stage.

Journal Article↗

PubMed2005

Fluctuations and instability of a biological membrane induced by interaction with macromolecules.

This paper studies the dynamics and fluctuations of a phospholipidic membrane in the presence of a diffusion field of foreign molecules, such as polymers, proteins, etc., which have the ability to adsorb on, and to desorb from, the membrane. We develop a model that includes, besides hydrodynamics, molecular diffusion in the surrounding fluid and lateral diffusion (i.e., diffusion along the membrane) as well as the kinetics of attachment and detachment to and from the membrane. This model is exploited here for the case of a free membrane which is globally at equilibrium while the nonequilibrium part will be presented in the future. We show that if the coupling between the membrane and the molecules is strong enough, the flat membrane can suffer a morphological instability. The numerical calculation in the nonlinear regime reveals budding, and an initial stage of spontaneous vesicle emission. When the condition of stability is satisfied we show how kinetic fluctuations lead to a rich variety of dynamical behaviors expressing the dominant dissipation mechanisms. We show that in the limit of well separated length scales related to the physical mechanisms that enter into play, the width of the membrane fluctuations exhibits various dynamical scalings with universal scaling exponents. It is shown that the usual behavior with time w approximately t(1/3) is altered in various time and length scales of interest. For example, we find that , w approximately t(1/4), w approximately t(1/2), and w approximately [t ln(t)](1/2), depending on which physical mechanism limits the membrane fluctuations on the time scale under consideration. The experimental study of the fluctuation spectrum can be viewed as a precious tool in order to have access to the underlying microscopic physical mechanisms.

Biopolymers↗

PubMed2004

Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces.

We report on peculiar behaviors due to anisotropic terrace diffusion on step meandering on a vicinal surface. We find that anisotropy triggers tilted ripples. In addition, if the fast diffusion direction is perpendicular to the steps, the instability is moderate and coarsening is absent, while in the opposite case the instability is promoted, and interrupted coarsening may be observed. Strong enough anisotropy restabilizes the step for almost all step orientations. These findings point to the nontrivial effect of anisotropy and open promising lines of inquiries in the design of surface architectures.

Journal Article↗

PubMed2004

Analytical analysis of a vesicle tumbling under a shear flow.

Vesicles under a shear flow exhibit a tank-treading motion of their membrane, while their long axis points with an angle <pi/4 with respect to the shear stress if the viscosity contrast between the interior and the exterior is not large enough. Above a certain viscosity contrast, the vesicle undergoes a tumbling bifurcation, a bifurcation which is known for red blood cells. We have recently presented the full numerical analysis of this transition. In this paper, we introduce an analytical model that has the advantage of being both simple enough and capturing the essential features found numerically. The model is based on general considerations and does not resort to the explicit computation of the full hydrodynamic field inside and outside the vesicle.

Computer Simulation↗

PubMed2004

Steady to unsteady dynamics of a vesicle in a flow.

We investigate the dynamics of a vesicle in a shear flow on the basis of the newly proposed advected field (AF) method [T. Biben and C. Misbah, Eur. Phys. J. E 67, 031908 (2003)]. We also solve the same problem with the boundary integral formulation for the sake of comparison. We find that the AF results presented previously overestimated the tumbling threshold due to the finite size of the membrane, inherent to the AF model. A comparison between the two methods shows that only in the sharp interface limit (extrapolating the results to a vanishing width) the AF method leads to accurate quantitative results. We extensively investigate the tank-treading to tumbling transition, and compare our numerical results to the theory of Keller and Skalak which assumes a fixed ellipsoidal shape for the vesicle. We show that this theory describes correctly the two regimes, at least in two dimensions, even for the quite elongated non-convex shapes corresponding to red blood cells (and therefore far from ellipsoidal), This theory is, however, not fully quantitative. Finally we investigate the effect of a confinement on the tank-treading to tumbling transition, and show that the tumbling regime becomes unfavorable in a capillary vessel, which should have strong effects on blood rheology in confined geometries.

Computer Simulation↗

PubMed2003

Interrupted coarsening of anisotropic step meander.

We report on the effect of anisotropy on the step meandering instability on vicinal surfaces during molecular beam epitaxy growth. A scenario of interrupted coarsening is found: the lateral length scale of the structure first significantly increases with time and then freezes at a larger length scale. The wavelength selection mechanism results from a nontrivial nonlinear effect of anisotropy. Anisotropy also leads to solutions which drift sideways, resulting from the loss of the back-front symmetry of the meander and the nonvariational character of dynamics.

Journal Article↗

PubMed2003

Tumbling of vesicles under shear flow within an advected-field approach.

We study dynamics of vesicles with a viscosity contrast between the interior and exterior, and subjected to a linear shear flow. It is shown that the vesicle, which assumes a steady orientation with respect to the shear flow for r identical with eta(in)/eta(out) or=r(c). Tumbling occurs as a saddle-node bifurcation. We present analytical and numerical results. We develop a powerful method, the advected-field approach. This method allows one to treat several different phenomena with great flexibility.

Biophysical Phenomena↗

PubMed2003

Vesicles in haptotaxis with hydrodynamical dissipation.

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a "droplet" with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions.

Adsorption↗

PubMed2003

Sand ripple dynamics in the case of out-of-equilibrium aeolian regimes.

From a phenomenological hydrodynamical model, we analyze the aeolian sand ripple evolution in an out-of-equilibrium aeolian regime where erosion exceeds accretion (and vice versa). We find, in particular, that the ripple structure can be destroyed in favor of a flat sand bed. In the ripple regime we report on a new class of generic dynamics described by the Benney equation. This equation reveals either order or disorder depending on whether wave dispersion is strong or weak. In both cases, the average wavelength of the pattern is fixed in time. This markedly contrasts with the regime of equilibrium aeolian regime -reached when erosion balances deposition- where ripples undergo a coarsening process at long time (i.e., the wavelength increases indefinitely with time).

Journal Article↗

PubMed2002

Elastic interaction of point defects on biological membranes.

The interaction between inclusions mediated by biological membranes undulations is analyzed. The interaction law is interpreted in terms of symmetries associated with inclusions. We show, in particular, that for a C3 and C3v symmetries the interaction law falls as 1/r3. We show that for completely isotropic inclusions, the dominant interaction vanishes to all orders, and the first contribution stems from the induced interaction which behaves as 1/r4. The same law holds for any other symmetry which is higher than C4. We introduce a straightforward method to compute these interactions. We point out important differences with results in the literature and explain the discrepancies.

Journal Article↗

PubMed2001

Unstable step meandering with elastic interactions.

We report on theoretical investigations of the influence of step interactions due to elasticity on unstable step meandering during molecular beam homoepitaxy. It is shown that elasticity causes coarsening of the cellular structure of the meander found in a previous work. The time dependence of step roughness is found to be robust, behaving as t(1/2). The lateral length scale coarsening is shown to be sensitive to the underlying physical mechanisms. In particular, the typical length follows the law t(alpha), with alpha = 1/6 or 1/4 depending on whether line diffusion is negligibly small or not.

Journal Article↗

PubMed2001

Phase-field modeling of stress-induced instabilities.

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. Using a formulation that is independent of the state of reference chosen for the displacement field, we write down the elastic energy in an unambiguous fashion, thus obtaining an entire class of models. According to the choice of reference state, the particular model emerging from this class will become equivalent to one of the two independently constructed models on which brief accounts have been given recently [J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999); K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999)]. We show that our phase-field approach recovers the sharp-interface limit corresponding to the continuum model equations describing the Asaro-Tiller-Grinfeld instability. Moreover, we use our model to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by reproducing some known results and by comparison with a sharp-interface simulation. We then proceed to investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wave numbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion. In the absence of gravity, the end state of a laterally finite system is a single groove growing at constant velocity, as long as no secondary instabilities arise (that we have not been able to see with our code). With gravity, several grooves are possible, all of which are bound to stop eventually. A laterally infinite system approaches a scaling state in the absence of gravity and probably with gravity, too.

Journal Article↗

PubMed1999

Fractal growth of epitaxial surface clusters with elastic interaction.

The fractal growth of clusters adsorbed on crystal surfaces has been studied by Monte Carlo simulations. Elastic interactions between the atoms through the substrate have been included. Attractive and repulsive interaction potentials 1/r(3) have been used, including a varying cutoff for the range of interaction. As an important result we find that there exists a crossover radius beyond which the fractal dimension of the cluster corresponds to the fractal dimension of conventional two-dimensional diffusion limited aggregation. The crossover radius itself and the properties of the cluster inside that radius depend sensitively on the details of the interaction. The results have been analyzed by a scaling theory. Furthermore, we have implemented a multigrid scheme which allows for very efficient simulation of a large number of mobile atoms with long-range interaction on the surface.

Journal Article↗

PubMed1996