Related papers: Non Local Hyperbolic Dynamics of Clusters
Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…
This study presents an enhanced method for analyzing cluster dynamics, with a particular focus on tracking clusters' continuity over time using time-series data from molecular dynamics (MD) simulation. The proposed method was applied to…
We study transient sequential dynamics of evolving dynamical networks, i.e., those having active nodes and links and activity-dependent topology. We show that such networks can generate sequences of metastable cluster states where each…
We examine the hydrodynamics of a granular gas using numerical simulation. We demonstrate the appearance of shearing and clustering instabilities predicted by linear stability analysis, and show that their appearance is directly related to…
Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the…
We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily…
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain…
We analyze a simplistic model for run-and-tumble dynamics, motivated by observations of complex spatio-temporal patterns in colonies of myxobacteria. In our model, agents run with fixed speed either left or right, and agents turn with a…
Irreversible diffusion limited cluster aggregation (DLCA) of hard spheres was simulated using Brownian cluster dynamics. Bound spheres were allowed to move freely within a specified range, but no bond breaking was allowed. The structure and…
Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and…
We demonstrate that migration away from self-produced chemicals (chemorepulsion) generates a generic route to clustering and pattern formation among self-propelled colloids. The clustering instability can be caused either by anisotropic…
We present simulations of a hard disc system and analyze the time evolution of the dynamic heterogeneities. We characterize the time evolution of slow regions and slow particles individually. The motion of slow clusters turns out to be very…
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, solutions to initial data from a…
Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit a rich clustering dynamics. It can be argued that clusters are responsible for the distribution of (local) information…
This model describes cluster aggregation in a stirred colloidal solution Interacting clusters compete for growth in this 'winner-takes-all' model; for finite assemblies, the largest cluster always wins, i.e. there is a uniform sediment. In…
We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is…