Monte Carlo study of a kinetic lattice model with random diffusion of disorder

We report Monte Carlo results for a nonequilibrium Ising-like model in two and three dimensions. Nearest-neighbor interactions J change sign randomly with time due to competing kinetics. There follows a fast and random, i.e., spin-configuration-independent diffusion of Js, of the kind that takes place in dilute metallic alloys when magnetic ions diffuse. The system exhibits steady states of the ferromagnetic (antiferromagnetic) type when the probability p that J>0 is large (small) enough. No counterpart to the freezing phenomena found in quenched spin glasses occurs. We compare our results with existing mean-field and exact ones, and obtain information about critical behavior.

Stability of a nonequilibrium steady-state interface

We study the interfacial modes of a driven diffusive model under suitable nonequilibrium conditions leading to possible instability. The external field parallel to the interface, which sets up a steady-state parallel flux, enhances the growth or decay rates of the interfacial modes. More dramatically, asymmetry in the model can introduce an oscillatory component into the interfacial dispersion relation. In certain circumstances, the applied field behaves as a singular perturbation.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Asymptotic flocking dynamics for the kinetic Cucker-Smale model

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.

Model-independent bounds for the potential and kinetic energy of liquid 4He at zero temperature

Using the experimental values of the chemical potentials of liquid 4He and of a 3He impurity in liquid 4He, we derive a model-independent lower (upper) bound to the kinetic (potential) energy per particle at zero temperature. The values of the bounds at the experimental saturation density are 13.42 K for the kinetic energy and -20.59 K for the potential energy. All the theoretical calculations based on the Lennard-Jones potential violate the upper-bound condition for the potential energy.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Covariant description of kinetic freeze-out through a finite spacelike layer

The problem of freeze-out (FO) in relativistic heavy-ion reactions is addressed. We develop and analyze an idealized one-dimensional model of FO in a finite layer, based on the covariant FO probability. The resulting post FO phase-space distributions are discussed for different FO probabilities and layer thicknesses.

Interfacial growth in driven diffusive systems

We have studied the growth of interfaces in driven diffusive systems well below the critical temperature by means of Monte Carlo simulations. We consider the region beyond the linear regime and of large values of the external field which has not been explored before. The simulations support the existence of interfacial traveling waves when asymmetry is introduced in the model, a result previously predicted by a linear-stability analysis. Furthermore, the generalization of the Gibbs-Thomson relation is discussed. The results provide evidence that the external field is a stabilizing effect which can be considered as effectively increasing the surface tension.

Side-branch growth in two-dimensional dendrits. Part II: Phase-field model

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Evidence of a critical time in constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.

Aggregation of liposomes induced by calcium: A structural and kinetic study

In this work, the calcium-induced aggregation of phosphatidylserine liposomes is probed by means of the analysis of the kinetics of such process as well as the aggregate morphology. This novel characterization of liposome aggregation involves the use of static and dynamic light-scattering techniques to obtain kinetic exponents and fractal dimensions. For salt concentrations larger than 5 mM, a diffusion-limited aggregation regime is observed and the Brownian kernel properly describes the time evolution of the diffusion coefficient. For slow kinetics, a slightly modified multiple contact kernel is required. In any case, a time evolution model based on the numerical resolution of Smoluchowski's equation is proposed in order to establish a theoretical description for the aggregating system. Such a model provides an alternative procedure to determine the dimerization constant, which might supply valuable information about interaction mechanisms between phospholipid vesicles.

Exploring the rate-limiting steps in visual phototransduction recovery by bottom-up kinetic modeling

Phototransduction in vertebrate photoreceptor cells represents a paradigm of signaling pathways mediated by G-protein-coupled receptors (GPCRs), which share common modules linking the initiation of the cascade to the final response of the cell. In this work, we focused on the recovery phase of the visual photoresponse, which is comprised of several interacting mechanisms. We employed current biochemical knowledge to investigate the response mechanisms of a comprehensive model of the visual phototransduction pathway. In particular, we have improved the model by implementing a more detailed representation of the recoverin (Rec)-mediated calcium feedback on rhodopsin kinase and including a dynamic arrestin (Arr) oligomerization mechanism. The model was successfully employed to investigate the rate limiting steps in the recovery of the rod photoreceptor cell after illumination. Simulation of experimental conditions in which the expression levels of rhodospin kinase (RK), of the regulator of the G-protein signaling (RGS), of Arr and of Rec were altered individually or in combination revealed severe kinetic constraints to the dynamics of the overall network. Our simulations confirm that RGS-mediated effector shutdown is the rate-limiting step in the recovery of the photoreceptor and show that the dynamic formation and dissociation of Arr homodimers and homotetramers at different light intensities significantly affect the timing of rhodopsin shutdown. The transition of Arr from its oligomeric storage forms to its monomeric form serves to temper its availability in the functional state. Our results may explain the puzzling evidence that overexpressing RK does not influence the saturation time of rod cells at bright light stimuli. The approach presented here could be extended to the study of other GPCR signaling pathways.

A simple model to describe the thixotropic behavior of paints.

We propose a simple rheological model to describe the thixotropic behavior of paints, since the classical hysteresis area, which is usually used, is not enough to evaluate thixotropy. The model is based on the assumption that viscosity is a direct measure of the structural level of the paint. The model depends on two equations: the Cross-Carreau equation to describe the equilibrium viscosity and a second order kinetic equation to express the time dependence of viscosity. Two characteristic thixotropic times are differentiated: one for the net structure breakdown, which is defined as a power law function of shear rate, and an other for the net structure buildup, which is not dependent on the shear rate. The knowledge of both kinetic processes can be used to improve the quality and applicability of paints. Five representative commercial protective marine paints are tested. They are based on chlorinated rubber, acrylic, alkyd, vinyl, and epoxy resins. The temperature dependence of the rheological behavior is also studied with the temperature ranging from 5 ºC to 35 ºC. It is found that the paints exhibit both shear thinning and thixotropic behavior. The model fits satisfactorily the thixotropy of the studied paints. It is also able to predict the thixotropy dependence on temperature. Both viscosity and the degree of thixotropy increase as the temperature decreases.

Horizontal Grid Size Selection and its Influence on Mesoscale Model Simulations

The use of two-dimensional spectral analysis applied to terrain heights in order to determine characteristic terrain spatial scales and its subsequent use for the objective definition of an adequate grid size required to resolve terrain forcing are presented in this paper. In order to illustrate the influence of grid size, atmospheric flow in a complex terrain area of the Spanish east coast is simulated by the Regional Atmospheric Modeling System (RAMS) mesoscale numerical model using different horizontal grid resolutions. In this area, a grid size of 2 km is required to account for 95% of terrain variance. Comparison among results of the different simulations shows that, although the main wind behavior does not change dramatically, some small-scale features appear when using a resolution of 2 km or finer. Horizontal flow pattern differences are significant both in the nighttime, when terrain forcing is more relevant, and in the daytime, when thermal forcing is dominant. Vertical structures also are investigated, and results show that vertical advection is influenced highly by the horizontal grid size during the daytime period. The turbulent kinetic energy and potential temperature vertical cross sections show substantial differences in the structure of the planetary boundary layer for each model configuration