Related papers: The flow of two falling balls mixes rapidly
We establish an improved criterion for rapid mixing of hyperbolic flows by weakening the requirement on the temporal distance function from positive box dimension to the existence of two values whose ratio is Diophantine. We also…
We introduce a flow in the space of constant width bodies in three-dimensional Euclidean space that simultaneously increases the volume and decreases the circumradius of the shape as time increases. Starting from any initial constant width…
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…
We present an extensive experimental study of birefringence and velocity-gradient components for a series of high molecular weight, flexible, entangled polystyrene solutions subjected to transient start-up flows in a co-rotating two-mill to…
The coupling between mass transfer and hydrodynamic phenomena in two-phase flow is not necessarily straightforward due to the different effects that can be encountered. The treatment of such coupling is complex and requires particular…
We study a slow-fast system with two slow and one fast variables. We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighbourhood of the fold. We derive a normal form for…
We report on quasi-two-dimensional granular systems in which either one or two large balls is fluidized by an upflow of air in the presence of a background of several hundred smaller beads. A single large ball is observed to propel…
We study the mixing properties of a scalar $\rho$ advected by a certain incompressible velocity field $u$ on the two dimensional unit ball, which is a stationary radial solution of the Euler equation. The scalar $\rho$ solves the continuity…
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…
This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincar\'e…
In this article, we give explicit conditions for compact group extensions of hyperbolic flows (including geodesic flows on negatively curved manifolds) to exhibit quantifiable rates of mixing (or decay of correlations) with respect to the…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a…
The fluid ball conjecture states that a static perfect fluid space-time is spherically symmetric. In this paper we construct a Robinson's divergence formula for the static perfect fluid space-time. Inspired by this conjecture, a rigidity…
We study in this work the dynamics of a collection of identical hollow spheres (ping-pong balls) that rest on a horizontal metallic grid. Fluidization is achieved by means of a turbulent air current coming from below. The upflow is adjusted…
In this paper, we study mixing rates for $\mathbb{T}^{d}$-extensions of hyperbolic flows. Given three closed orbits with their holonomies, we can relate them to a point in $\mathbb{R}^{d+1}$. We prove that the extension flow enjoys rapid…
We study enhancement of diffusive mixing by fast incompressible time-periodic flows. The class of relaxation-enhancing flows that are especially efficient in speeding up mixing has been introduced in [2]. The relaxation-enhancing property…
We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls…
We show that the entry and return times for dynamic balls (Bowen balls) is exponential for systems that have an $\alpha$-mixing invariant measure with certain regularities. We also show that systems modeled by Young's tower has exponential…
The evolution of suspension drops sedimenting under gravity in a viscous fluid close to a vertical wall was studied experimentally and numerically with the use of the point-force model, in the Stokes flow regime. The fluid inside and…