相关论文: A caustic terminating at an inflection point

We analytically derive an equation describing vesicle evolution in a fluid where some stationary flow is excited regarding that the vesicle shape is close to a sphere. A character of the evolution is governed by two dimensionless…

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at…

We observe and characterize the scattering of acoustic wave packets by a sunspot, in a regime where the wavelength is comparable to the size of the sunspot. Spatial maps of wave traveltimes and amplitudes are measured from the…

Estimating collision rates is of immense importance in particle-laden flows. An economical way of doing this is to directly identify incidences of caustics, or extreme clustering, by tracking particle velocity gradients in the neighborhoods…

In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the…

We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium…

The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…

We consider inviscid flow with isentropic coefficient greater than one. For flow along smooth infinite protruding corners we attempt to impose a nonzero limit for velocity at infinity at the upstream wall. We prove that the problem does not…

We study an abstract damped wave equation. We prove that the solution of the damped wave equation becomes closer to the solution of a heat type equation as time tend to infinity. As an application of our approach, we also study the…

We present new experimental results on the development of turbulent spots in channel flow. The internal structure of a turbulent spot is measured, with Time Resolved Stereoscopic Particle Image Velocimetry. We report the observation of…

Understanding topological phases of matter is essential for advancing both the fundamental theory and practical applications of condensed matter physics. Recently, a theoretical framework for a quantum Hall system with an expanding edge…

We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincar\'e dodecahedral space, when the scale factor is exponentially increasing. We prove the existence of a limit…

Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size. This sharp-edge streaming can be relatively intense, \textcolor{blue}{owing to the strongly focused inertial…

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a…

The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening, and eventual overturning of a wave. Using a self-similar description in two space dimensions, we show that the…

We consider an inner problem for whispering gallery high-frequency asymptotic mode's scattering by a boundary inflection. The related boundary-value problem for a Schr\"{o}dinger equation on a half-line with a potential linear in both space…

We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…

Matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase-space. The caustics separate regions with different number of streams and the volume elements change the parity by turning…

The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear cut instability mechanism, the spatio-temporal intermittent character and extremely long…

A light breeze rising over calm water initiates an intricate chain of events that culminates in a centimeters-deep turbulent shear layer capped by gravity-capillary ripples. At first, viscous stress accelerates a laminar wind-drift layer…