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Clement Sire

Publications and source records attributed to Clement Sire.

24 records · Page 2Linked to original sources
arXiv1997

Smoluchowski's equation for cluster exogenous growth

We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with $ds/dt=As^β$. A physical example, dropwise condensation is provided, and its collision kernel K is derived. In the general case, the gelation criterion is determined. Exact solutions are found and scaling solutions are investigated. Finally we show how these results apply to nucleation of discs on a plane

cond-mat.stat-mech↗
arXiv1997

Nontrivial Polydispersity Exponents in Aggregation Models

We consider the scaling solutions of Smoluchowski's equation of irreversible aggregation, for a non gelling collision kernel. The scaling mass distribution f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now, only be computed by numerical simulations. We develop here new general methods to obtain exact bounds and good approximations of $τ$. For the specific kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R is the particle radius), perturbative and nonperturbative expansions are derived. For a general kernel, we find exact inequalities for tau and develop a variational approximation which is used to carry out the first systematic study of tau(d,D) for KdD. The agreement is excellent both with the expansions we derived and with existing numerical values. Finally, we discuss a possible application to 2d decaying turbulence.

cond-mat.stat-mech↗
arXiv1996

Nontrivial Exponent for Simple Diffusion

The diffusion equation \partial_tϕ= \nabla^2ϕis considered, with initial condition ϕ( _x_ ,0) a gaussian random variable with zero mean. Using a simple approximate theory we show that the probability p_n(t_1,t_2) that ϕ( _x_ ,t) [for a given space point _x_ ] changes sign n times between t_1 and t_2 has the asymptotic form p_n(t_1,t_2) \sim [\ln(t_2/t_1)]^n(t_1/t_2)^{-θ}. The exponent θhas predicted values 0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with simulation results.

cond-mat↗
arXiv1995

Decaying Turbulence and the Dynamics of Diffusing Vortices with Conservation Laws

In this letter, I solve a model for the dynamics of vortices in a decaying two-dimensional turbulent fluid. The model describes their effective diffusion, and the merging of pairs of vortices of same vorticity sign, when they get too close. The merging process is characterized by the conservation of energy and of the quantity $Nr^n$, where $r$ is the mean vortex radius, and $N$ their number. $n=4$ corresponds to a constant peak vorticity, and $n=2$ to a constant kurtosis. I found the scaling laws for various physical quantities ($r$, enstrophy, kurtosis...), and for instance, it is shown that $N\sim (t/\ln(t))^{-\frac{2n}{3n-4}}$ for $n>2$, and $N\sim t^{-2}$ for $n=2$, in good agreement with extensive numerical simulations. I also discuss some recent experiments in view of these results.

cond-mat↗
arXiv1995

Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization

We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high temperature disordered phase to zero temperature. The time dependent two-point correlation functions of the order parameter field satisfy dynamic scaling with a length scale $L(t)\sim t^{1/2}$. In particular, the autocorrelation function decays as $L(t)^{-λ(q)}$. We illustrate these properties by solving exactly the kinetic Potts model in $d=1$. We then analyze a Langevin equation of an appropriate field theory to compute these correlation functions for general $q$ and $d$. We establish a correspondence between the two-point correlations of the $q$-state Potts model and those of a kinetic Ising model evolving with a fixed magnetization $(2/q-1)$. The dynamics of this Ising model is solved exactly in the large q limit, and in the limit of a large number of components $n$ for the order parameter. For general $q$ and in any dimension, we introduce a Gaussian closure approximation and calculate within this approximation the scaling functions and the exponent $λ(q)$. These are in good agreement with the direct numerical simulations of the Potts model as well as the kinetic Ising model with fixed magnetization. We also discuss the existing and possible experimental realizations of these models.

cond-mat↗