Related papers: Slender Phoretic Loops and Knots
We show that strong bow shocks are turbulent and non-universal near the head, but asymptote to a universal steady, self-similar, and analytically solvable flow in the downstream. The turbulence is essentially 3D, and has been confirmed by a…
In this paper we give a simple and short proof of asymptotic stability of soliton for discrete nonlinear Schr\"odinger equation near anti-continuous limit. Our novel insight is that the analysis of linearized operator, usually…
We extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS with a short range linear potential obtained by the author in a previous paper. Now we drop the potential and allow moving solitons.…
The potential flow of an incompressible inviscid heavy fluid over a light one is considered. The integral version of the method of matched asymptotic expansion is applied to the construction of the solution over long intervals of time. The…
We consider a 2D model of an autophoretic particle in which the particle has a circular shape and emits/absorbs a solute that diffuses and is advected by the suspending fluid. Beyond a certain emission/absorption rate (characterized by a…
Accretion flows with pressure gradients permit the existence of standing waves which may be responsible for observed quasi-periodic oscillations (QPO's) in X-ray binaries. We present a comprehensive treatment of the linear modes of a…
Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations…
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations…
The goal of this paper is to study global dynamics of $C^\infty$-smooth slow-fast systems on the $2$-torus of class $C^\infty$ using geometric singular perturbation theory and the notion of slow divergence integral. Given any…
In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability…
The goal of this paper is to describe in mathematical terms the effect on the ocean circulation of a random stationary wind stress at the surface of the ocean. In order to avoid singular behaviour, non-resonance hypotheses are introduced,…
We provide a detailed description of solutions of Curve Shortening in $\R^n$ that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic…
We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms…
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…
We study the two-dimensional motion of a self-propelling asymmetric bent rod. By employing slender body theory and the Lorentz reciprocal theorem, we determine particle trajectories for different geometric configurations and arbitrary…
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the…
We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and…
We present a novel phenomenological theory describing how topological constraints in prime-knot ring polymers induce collective (cooperative) modes of motion. In low-complexity knots, chain segments can move quasi-independently. However, as…
We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical…
For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavior of these twisted Alexander polynomials evaluated at unit…