Related papers: Slow chaos in surface flows
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
Effective field theory descriptions of surface waves on flowing fluids have tended to assume that the flow is irrotational, but this assumption is often impractical due to boundary layer friction and flow recirculation. Here we develop an…
In this paper it is proved that near a compact, invariant, proper subset of a continuous flow on a compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. This result shows…
We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the $n$--dimensional flat torus. More precisely, we show that if…
The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to…
This article presents results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz…
We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a…
Particle motion is considered in incompressible two-dimensional flows consisting of a steady background gyre on which an unsteady wave-like perturbation is superimposed. A dynamical systems point of view that exploits the action--angle…
The abstract hyperbolic sets are introduced. Continuous and differentiable mappings as well as rate of convergence and transversal manifolds are not under discussion, and the symbolic dynamics paradigm is realized in a new way. Our…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
We prove that the limit hypersurfaces of converging curvature flows are stable, if the initial velocity has a weak sign, and give a survey of the existence and regularity results.
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.…
This paper investigates the nature of the development of vortex shedding for two-dimensional unsteady flow of an incompressible fluid at the rear stagnation point.
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of…
We report electron microscopy observations of the surface plastic flow in polishing of rough metal surfaces with a controlled spherical asperity structure. We show that asperity--abrasive sliding contacts exhibit viscous behavior, where the…