Related papers: Cluster expansion for a dilute hard sphere gas dyn…

Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), DSMC (Direct Simulation Monte Carlo), SPH (Smoothed Particle Hydrodynamics), PIC…

Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in unsupervised way the microscopic dynamical events occurring in…

We present a phenomenological model of the dynamics of buoyant bubbles in the atmosphere of a cluster of galaxies. The derived equations describe velocity, size, mass, temperature and density of the buoyant bubbles as functions of time…

Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric…

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…

This paper reviews the measurements of galaxy correlations at high redshifts, and discusses how these may be understood in models of hierarchical gravitational collapse. The clustering of galaxies at redshift one is much weaker than at…

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function…

The BBGKY hierarchy of equations for a particle interacting with ideal gas is analyzed in terms of irreducible many-particle correlations between gas atoms and the particle's motion. The transition to the hard-sphere interaction is…

In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single…

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…

We present new diagnostic metrics to probe the dynamical state of galaxy clusters. These novel metrics rely on the computation of the power spectra of the matter and gas distributions and their cross-correlation derived from cluster…

We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary.…

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…

Clusters of galaxies, the largest collapsed structures in the Universe, are located at the intersection of extended filaments of baryons and dark matter. Cosmological accretion onto clusters through large scale filaments adds material at…

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only,…

We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which…

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…

We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of…

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…