Related papers: On Singular Vortex Patches, II: Long-time dynamics
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
Domain wall networks have attracted renewed interest, particularly in relation to the dynamics of network collapse. Accurately describing this process is challenging and typically requires large scale numerical simulations. Here we adopt a…
We report on self-assemblies formed from spherical patchy particles interacting by a long-range attraction through a patch region in a two-dimensional system. We performed Monte Carlo simulations to find stable structures in a system with…
Superfluidity and superconductivity are remarkable manifestations of quantum coherence at a macroscopic scale. The dynamics of superfluids has dominated the study of these systems for decades now, but a comprehensive theoretical framework…
It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. In this paper, we study Euler vortex…
We are concerned with the dynamics of one fold symmetric patches for the two-dimensional aggregation equation associated to the Newtonian potential. We reformulate a suitable graph model and prove a local well-posedness result in…
Using molecular dynamics simulations we study the slow dynamics of a hard sphere fluid confined in a disordered porous matrix. The presence of both discontinuous and continuous glass transitions as well as the complex interplay between…
We consider logarithmic spiral vortex sheets consisting of two branches. Based on some simple assumptions that appear true by numerical computations, we fully classify their long-time behavior and asymptotics, where in all cases each branch…
The {\it two-fold singularity} has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that…
It is well known that the Euler vortex patch in $\mathbb{R}^{2}$ will remain regular if it is regular enough initially. In bounded domains, the regularity theory for patch solutions is less complete. We study here the Euler vortex patch in…
We study the dynamics of the front separating a spatio-temporally chaotic region from a stable steady region using a simple model applicable to periodically forced systems. In particular, we investigate both the coarsening of the front…
A recent analysis has revealed singular but physically relevant 2D localized vortex states with density ~ 1/r^{4/3} at r --> 0 and a convergent total norm, which are maintained by the interplay of the potential of the attraction to the…
A comprehensive analytical theory for nonlinear excitations related to horizontal (longitudinal, acoustic mode) as well as vertical (transverse, optical mode) motion of charged dust grains in a dust crystal is presented. Different types of…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
This paper deals with the existence of $N$ vortex patches located at the vertex of a regular polygon with $N$ sides that rotate around the center of the polygon at a constant angular velocity. That is done for Euler and (SQG)$_\beta$…
Thermodynamic stability of composite vortex in a two-component superconductor is investigated by the Ginzburg-Landau theory. The predicted nature of these vortices has recently attracted much attention. Here we consider axially symmetric…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
We critically discuss the application of the Wertheim's theory to classes of complex associating fluids that can be today engineered in the laboratory as patchy colloids and to the prediction of their peculiar gas-liquid phase diagrams. Our…
Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle…
The experimental investigation of spontaneously created vortices is of utmost importance for the understanding of quantum phase transitions towards a superfluid phase, especially for two dimensional systems that are expected to be governed…