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Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid is investigated. The system is separable in ellipsoidal coordinates. A smooth description of the motion is given…
Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting…
We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel-Stewart formulation.…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…
This paper investigates a deterministic variant of the Saltzman-Maasch model for Pleistocene glacial cycles, formulated as a three-dimensional dynamical system with cubic feedback in the atmospheric carbon dioxide equation. After reducing…
We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The…
Taylor-Couette flow between rotating cylinders is a classical problem in fluid mechanics and has been extensively studied in the case of two concentric circular cylinders. There have been relatively small number of studies in complex-shaped…
A two-dimensional inviscid incompressible fluid is governed by simple rules. Yet, to characterise its long-time behaviour is a knotty problem. The fluid evolves according to Euler's equations: a non-linear Hamiltonian system with infinitely…
At high Reynolds number, the interaction between two vortex tubes leads to intense velocity gradients, which are at the heart of fluid turbulence. This vorticity amplification comes about through two different instability mechanisms of the…
Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which…
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first…
The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable…
We consider the problem of a slender rod slipping along a rough surface. Painlev\'e \cite{Painleve1895, Painleve1905a,Painleve1905b} showed that the governing rigid body equations for this problem can exhibit multiple solutions (the {\it…
We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from…