Related papers: Hamiltonian Maps and Transport in Structured Fluid…
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…
Nontwist area-preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist…
Advective trapping occurs when solute enters low velocity zones in heterogeneous porous media. Classical local modeling approaches combine the impact of slow advection and diffusion into a hydrodynamic dispersion coefficient and many…
Hamiltonian flows on compact surfaces are characterized, and the topological invariants of such flows with finitely many singular points are constructed from the viewpoints of integrable systems, fluid mechanics, and dynamical systems.…
Irreversible transport is generally attributed to vorticity, nonlinear forcing, or explicit symmetry breaking. We show that it can arise even in strictly time-periodic and locally irrotational flows through a purely geometric mechanism. By…
We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle…
The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a…
Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal…
Some non-Gaussian aspects of chaotic transport are investigated for a general class of two-dimensional area-preserving maps. Kurtosis, in particular, is calculated from the diffusion and the Burnett coefficients, which are obtained…
Visualization of turbulent flows is a powerful tool to help understand the turbulence dynamics and induced transport. However, it does not provide a quantitative description of the observed structures. In this paper, an approach to…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
We consider steady gravity-driven flow of a thin layer of viscous fluid over a curved substrate. The substrate has topographical variations (`bumps') on a large scale compared to the layer thickness. Using lubrication theory, we find the…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…