Related papers: Cross diffusion models in complex frameworks From …
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic model. In particular, we combine conservation of mass and…
The relativistic hydrodynamic model is applied to describe the expansion of the dense matter formed in relativistic heavy-ion collisions. The hydrodynamic expansion of the fluid, supplemented with the statistical emission of hadrons at…
Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…
We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension…
Cross-diffusion systems are formally derived from multispecies kinetic models in the diffusion limit. The first limit in the multispecies BGK model of Gross and Krook leads to a variant of the non-isothermal Maxwell-Stefan equations. The…
In this paper, we propose a kinetic model describing the collective motion by chemotaxis of two species in interaction emitting the same chemoattractant. Such model can be seen as a generalisation to several species of the Othmer-Dunbar-Alt…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
Starting from a dynamic tensor model about two second-order tensors, we derive the frame hydrodynamics for the biaxial nematic phase using the Hilbert expansion. The coefficients in the frame model are derived from those in the tensor…
The dynamics of particle transport under the influence of localised high energy anomalies (explosions) is a complicated phenomena dependent on many physical parameters of both the particle and the medium it resides in. Here we present a…
Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
In this paper we investigate the behavior of particles crossing a neat interface between two media. A Monte Carlo and analytical model, based on fractional derivatives, are presented and discussed in detail, together with a comparison.…
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented…
We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we…
We propose a kinetic Ising model to study phase separation driven by surface diffusion. This model is referred to as "Model S", and consists of the usual Kawasaki spin-exchange kinetics ("Model B") in conjunction with a kinetic constraint.…
Mobile microscopic bodies, such as motile cells, can be modelled phenomenologically as ``active particles'' which can move against external forces by depleting an internal energy depot. The microscopic mechanisms underlying such ``active''…
Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…