Related papers: Dynamics of closed singularities
In this paper, we study the properties of nondegenerate cylindrical singularities of mean curvature flow. We prove they are isolated in spacetime and provide a complete description of the geometry and topology change of the flow passing…
In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
We analyze the dynamics of concentrated polymer solutions modeled by a 2D Smoluchowski equation. We describe the long time behavior of the polymer suspensions in a fluid. When the flow influence is neglected the equation has a gradient…
We consider the patterns formed by small rod-like objects advected by a random flow in two dimensions. An exact solution indicates that their direction field is non-singular. However, we find from simulations that the direction field of the…
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for $d$-dimensional flows, $d=2$ or $3$, the free-surface of a viscous water wave, modeled by the…
A two-layer quasi-geostrophic flow is quite insulated from the surrounding fluid, while the layers interact each other by means of the modulation of the interface between them and of the turbulence affecting the layers in the proximity of…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
The recently proposed definition of complexity for static and spherically symmetric self--gravitating systems [1], is extended to the fully dynamic situation. In this latter case we have to consider not only the complexity factor of the…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior meaning sensitiveness to initial…
We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we formulate a precise conjectural…
We explore some qualitative dynamics in the neighborhood of the $3-dimensional$ two-fold symmetric singularity. We study the existence of an one-parameter family of regular (pseudo) periodic orbits of such systems near a reversible two-fold…
The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional…
In this paper we study the singularity formation for two nonlocal 1D active scalar equations, focusing on the hyperbolic flow scenario. Those 1D equations can be regarded as simplified models of some 2D fluid equations.
In this fluid dynamics video we show how a drop of water freezes into a singular shape when deposited on a cold surface. The process of solidification can be observed very clearly due to the change in refraction when water turns into ice.…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
Oscillating shape motion of a freely falling water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two dimensional surfaces in gravity and apply it to analyze shape dynamics of freely…