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The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal gradients of sea surface temperature and salinity that are closely coordinated with the slowly varying envelope of the…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them.…

We present a description of granular dynamics based on the idea of differentiation between fluid and solid components. First, we construct a model of completely fluidized phase. Then we discuss a shear surface motion on the boundary of the…

In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas…

Granular materials are characterized by large collections of discrete particles of sizes larger than one micron, where the particle-particle interactions are significantly more important than the particle-fluid interactions. These flows can…

We analyze the nonlinear waves that propagate on a microtubule that is tethered at its minus end due to kinesin walking on it, as is seen during the fluid mixing caused by cytoplasmic streaming in Drosophila oocytes.The model we use assumes…

Spiral waves arise in many biological, chemical, and physiological systems. The kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane. For this model, there appeared some results in the…

In this paper we describe a method for modeling the dynamic behavior of splashing fluids. The model simulates the behavior of a fluid when objects impact or float on its surface. The forces generated by the objects create waves and splashes…

We numerically follow the response of density-enhanced slabs to impulsive, localized, transverse velocity perturbations by working in the framework of ideal magnetohydrodynamics (MHD). Both linear and nonlinear regimes are addressed. Kink…

We report on new patterns in high-speed flows of granular materials obtained by means of extensive numerical simulations. These patterns emerge from the destabilization of unidirectional flows upon increase of mass holdup and inclination…

We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by Helzel and Tzavaras in \cite{HT2015}. Here we restrict our…

Organisms often swim through density stratified fluids. In this Letter, we investigate the dynamics of small active particles swimming in density gradients and report theoretical evidence of taxis as a result of density stratification…

The seismic waves emitted during granular flows are generated by different sources: high frequencies by inter-particle shocks and low frequencies by global motion and large scale deformation. To unravel these different mechanisms, an…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…

Vertically vibrated rod-shaped granular materials confined to quasi-2D containers self organize into distinct patterns. We find, consistent with theory and simulation, a density dependent isotropic-nematic transition. Along the walls, rods…

We investigate steady granular surface flows in a rotating drum and demonstrate the existence of rigid clusters of grains embedded in the flowing layer. These clusters are fractal and their size is power-law distributed from the grain size…

Novel technological applications often involve fluid flows in the Knudsen regime in which the mean free path is comparable to the system size. We use molecular dynamics simulations to study the transition between the dilute gas and the…