Related papers: Finite- and Infinite-Time Cluster Formation for Al…
In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the variational wave equations as those in [18]. The system posses…
The search of finite-time singularity solutions of Euler equations is considered for the case of an incompressible and inviscid fluid. Under the assumption that a finite-time blow-up solution may be spatially anisotropic as time goes by…
In a Newtonian system with localized interactions the whole set of particles is naturally decomposed into dynamical clusters, defined as finite groups of particles having an influence on each other's trajectory during a given interval of…
We have examined the spatial distribution of substructure in clusters of galaxies using Einstein X-ray observations. Subclusters are found to have a markedly anisotropic distribution that reflects the surrounding matter distribution on…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
The equilibrium size distribution function of clusters (nanoparticles) in the system of finite number of molecules (atoms) in finite closed volume with constant total energy (isolated system) is found using methods of statistical…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
In this paper we investigate analytically the formation of finite time singularities in the three dimensional incompressible Euler equations under the model of Gibbon, Fokas, and Doering for vorticity stretching within a bounded cylindrical…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
The universe's large-scale structure forms a vast, interconnected network of filaments, sheets, and voids known as the cosmic web. For decades, astronomers have observed that the orientations of neighboring galaxy clusters within these…
We consider a nonlinear Schr{\"o}dinger equation set in the whole space with a single power of interaction and an external source. We first establish existence and uniqueness of the solutions and then show, in low space dimension, that the…
A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity ($\Scri{}^+$)…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
Using the APM cluster data we investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned…
Inertial particles in turbulence form clusters, which strongly affect particle collisions and transport properties. Clustering models based on statistically stationary turbulence implicitly assume the instantaneous-equilibrium approximation…
We address the question whether a singularity in a three-dimensional incompressible inviscid fluid flow can occur in finite time. Analytical considerations and numerical simulations suggest high-symmetry flows being a promising candidate…
We propose a novel end-to-end neural network architecture that, once trained, directly outputs a probabilistic clustering of a batch of input examples in one pass. It estimates a distribution over the number of clusters $k$, and for each $1…
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems,…
This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers…