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1

Electronic Resource

Dynamics of aeolian sand ripples (2000)

Csahók, Z. ; Misbah, C. ; Rioual, F. ; [et al.]

Springer

The European physical journal 3 (2000), S. 71-86

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ISSN: 1292-895X

Keywords: PACS. 83.70.Fn Granular solids - 81.05.Rm Porous materials; granular materials - 47.20.-k Hydrodynamic stability

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: We analyze theoretically the dynamics of aeolian sand ripples. In order to put the study in the context, we first review existing models. This paper is a continuation of two previous papers (Z. Csahók et al., Physica D 128, 87 (1999); A. Valance et al., Eur. Phys. J. B 10, 543 (1999)), the first one is based on symmetries and the second on a hydrodynamical model. We show how the hydrodynamical model may be modified to recover the missing terms that are dictated by symmetries. The symmetry and conservation arguments are powerful in that the form of the equation is model-independent. We then present an extensive numerical and analytical analysis of the generic sand ripple equation. We find that at the initial stage the wavelength of the ripple is that corresponding to the linearly most dangerous mode. At later stages the profile undergoes a coarsening process leading to a significant increase of the wavelength. We find that including the next higher-order nonlinear term in the equation leads naturally to a saturation of the local slope. We analyze both analytically and numerically the coarsening stage, in terms of a dynamical exponent for the mean wavelength increase. We discuss some future lines of investigations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s101890070043

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2

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Vesicle propulsion in haptotaxis: A local model (2000)

Cantat, I. ; Misbah, C. ; Saito, Y.

Springer

The European physical journal 3 (2000), S. 403-412

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ISSN: 1292-895X

Keywords: PACS. 87.16.-b Subcellular structure and processes [:AND:] 87.19.-j Properties of higher organisms - 47.55.Dz Drops and bubbles

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted. The dynamical model is akin to the Rousse model for polymers. An invariant formulation is used to solve a dynamical model which includes a kind of dissipation due to bond breaking/restoring with the substrate. For a stationary situation where the vesicle acquires a constant drift velocity, we formulate the propulsion problem in terms of a nonlinear eigenvalue (the a priori unknown drift velocity) one of Barenblat-Zeldovitch type. A counting argument shows that the velocity belongs to a discrete set. For a relatively tense vesicle, we provide an analytical expression for the drift velocity as a function of relevant parameters. We find good agreement with the full numerical solution. Despite the oversimplification of the model it allows the identification of a relevant quantity, namely the adhesion length, which turns out to be crucial also in the nonlocal model in the presence of hydrodynamics, a situation on which we have recently reported (I. Cantat and C. Misbah, Phys. Rev. Lett. 83, 235 (1999)) and which constitutes the subject of a forthcoming extensive study.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s101890070011

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3

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Non-linear evolution of step meander during growth of a vicinal surface with no desorption (2000)

Gillet, F. ; Pierre-Louis, O. ; Misbah, C.

Springer

The European physical journal 18 (2000), S. 519-534

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ISSN: 1434-6036

Keywords: PACS. 05.70.Ln Nonequilibrium and irreversible thermodynamics - 68.35.Fx Diffusion; interface formation - 81.15.Aa Theory and models of film growth

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a multiscale analysis. We give the detailed derivation of the highly nonlinear evolution equation on which a brief account has been given [6]. Decomposing the model into driving and relaxational contributions, we give a profound explanation to the origin of the unusual divergent scaling of step meander (where F is the incoming atom flux). A careful numerical analysis indicates that a cellular structure arises where plateaus form, as opposed to spike-like structures reported erroneously in reference [6]. As a robust feature, the amplitude of these cells scales as t 1/2, regardless of the strength of the Ehrlich-Schwoebel effect, or the presence of line diffusion. A simple ansatz allows to describe analytically the asymptotic regime quantitatively. We show also how sub-dominant terms from multiscale analysis account for the loss of up-down symmetry of the cellular structure.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s100510070042

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4

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An advected-field method for deformable entities under flow (2002)

Biben, T. ; Misbah, C.

Springer

The European physical journal 29 (2002), S. 311-316

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ISSN: 1434-6036

Keywords: PACS. 87.16.Dg Membranes, bilayers, and vesicles – 47.55.Dz Drops and bubbles – 87.17.Jj Cell locomotion; chemotaxis and related directed motion

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: We study dynamics of a deformable entity (such as a vesicles under hydrodynamical constraints). We show how the problem can be solved by means of Green's functions associated with the Stokes equations. A gauge-field invariant formulation makes the study of dynamics efficient. However, this procedure has its short-coming. For example, if the fluids are not Newtonian, then no Green's function is available in general. We introduce a new approach, the advected field one, which opens a new avenue of applications. For example, non-Newtonian entities can be handled without additional deal. In addition problems like budding, droplet break-up in suspensions, can naturally be treated without additional complication. We exemplify the method on vesicles filled by a fluid having a viscosity contrast with the external fluid, and submitted to a shear flow. We show that beyond a viscosity contrast (the internal fluid being more viscous), the vesicle undergoes a tumbling bifurcation, which has a saddle-node nature. This bifurcation is known for blood cells. Indeed red cells either align in a shear flow or tumble according to whether haematocrit concentration is high or low.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1140/epjb/e2002-00307-6

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5

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Elastic interaction between defects in thin and 2D films (2003)

Peyla, P. ; Misbah, C.

Springer

The European physical journal 33 (2003), S. 233-247

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ISSN: 1434-6036

Keywords: PACS. 68.35.Gy Mechanical properties; surface strains – 68.55.-a Thin film structure and morphology

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: Elastic interactions between defects is investigated at the surface of thin layers, a question on which we have given a brief account [P. Peyla et al. Phys. Rev. Lett. 82, 787 (1999)]. Two isotropic defects do not interact in an unlimited medium, regardless of the spatial dimension, a result which can be shown on the basis of the Gauss theorem in electrostatics. Within isotropic elasticity theory, defects interact only (i) if they are, for example, at a surface (or at least if they feel a boundary), or if their action on the material is anisotropic (e.g. they create a non central force distribution, though the material elasticity is isotropic). It is known that two identical isotropic defects on the surface of a semi-infinite material repel each other. The repulsion law behaves as 1/r 3(r = defects separation). We first revisit the Lau-Kohn theory and extend it to anisotropic defects. Anisotropy is found to lead to attraction. We show that in thin films defects may either attract or repel each other depending on the local geometric force distribution caused by the defect. It is shown that the force distribution (or more precisely the forces configuration symmetry) fixes the exponent in the power law 1/r n (e.g. for a four-fold symmetry n = 4). We discuss the implication of this behaviour in various situations. We treat the interactions in terms of the symmetries associated with the defect. We argue that if the defects are isotropic, then their effective interaction in an unlimited 2D (or a thin film) medium arises from the induced interaction, which behaves as 1/r 4 for any defect symmetry. We shall also comment on the contribution to the interaction which arises from flexion of thin films.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1140/epjb/e2003-00162-y

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6

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Kinetics of shape equilibration for two dimensional islands (1999)

Jensen, P. ; Combe, N. ; Larralde, H. ; [et al.]

Springer

The European physical journal 11 (1999), S. 497-504

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ISSN: 1434-6036

Keywords: PACS. 05.70.Ln Nonequilibrium and irreversible thermodynamics - 82.65.Dp Thermodynamics of surfaces and interfaces - 68.55.-a Thin film structure and morphology

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract: We study the relaxation to equilibrium of two dimensional islands containing up to 20 000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets: this allows us to explain both the activation energy and the island size dependence of the equilibration time.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s100510050961

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7

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Large-amplitude behavior of the Grinfeld instability: a variational approach (2003)

Kohlert, P. ; Kassner, K. ; Misbah, C.

Springer

The European physical journal 35 (2003), S. 493-504

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ISSN: 1434-6036

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract. In previous work, we have performed amplitude expansions of the continuum equations for the Grinfeld instability and carried them to high orders. Nevertheless, the approach turned out to be restricted to relatively small amplitudes. In this article, we use a variational approach in terms of multi-cycloid curves instead. Besides its higher precision at given order, the method has the advantages of giving a transparent physical meaning to the appearance of cusp singularities and of not being restricted to interfaces representable as single-valued functions. Using a single cycloid as ansatz function, the entire calculation can be performed analytically, which gives a good qualitative overview of the system. Taking into account several but few cycloid modes, we obtain remarkably good quantitative agreement with previous numerical calculations. With a few more modes taken into consideration, we improve on the accuracy of those calculations. Our approach extends them to situations involving gravity effects. Results on the shape of steady-state solutions are presented at both large stresses and amplitudes. In addition, their stability is investigated.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1140/epjb/e2003-00302-5

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8

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Nonlinear evolution of directional solidification patterns (1994)

Kassner, K. ; Misbah, C. ; Valance, A. ; [et al.]

Springer

Theoretical and mathematical physics 99 (1994), S. 681-686

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ISSN: 1573-9333

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract We have studied directional solidification theoretically for high velocities, where a time-dependent description is essential. The model equations can be simplified into an asymptotically valid strongly nonlinear equation. This quasilocal approximation preserves the essential dynamic features of the system. Analyzing the dynamic evolution of an isotrope-nematic interface, we find, besides the usual parity-breaking solution (PB), avacillating-breathing (VB) mode, which is associated with spatial period-doubling. Both the PB and VB modes can be understood analytically, the former as the consequence of aq-2q interaction, the latter on the basis of a perturbative approach. As the relevant system parameter, a renormalized thermal gradient, is decreased, the VB mode becomes unstable with respect to parity breaking and acquires a lateral drift velocity. The interface motion is thenquasiperiodic. Further decrease of the thermal gradient drives the interface into achaotic state. We suggest that the quasiperiodicity scenario is generic for systems in which both an oscillatory and a parity-breaking instability exist. This expectation is supported by a study of amplitude equations for the same system, in which only the two most important modes have been retained.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01017052

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