Related papers: Ideal mixture approximation of cluster size distri…
Particle systems interacting with a soft repulsion, at thermal equilibrium and under some circumstances, are known to form cluster crystals, i.e. periodic arrangements of particle aggregates. We study here how these states are modified by…
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partition of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
We explore the constraints on globular cluster formation provided by the observed conditions in starbursts where globulars are currently forming, and by the observed properties of young and old globular clusters. We note that the pressure…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice.…
To study the interplay of jamming, cluster formation, and motility-induced phase separation in the zero temperature limit in two dimensions, we consider a simple model system consisting of a bidisperse mixture of disks that are only subject…
A statistical model for the calculation of the ionisation-cluster size distribution in nanodosimetry is proposed. It is based on a canonical ensemble and derives from the well-known nuclear droplet model. The model especially can be applied…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
We investigate the approach to stable and metastable equilibrium in Ising models using a cluster representation. The distribution of nucleation times is determined using the Metropolis algorithm and the corresponding $\phi^{4}$ model using…
We developed a new physical model to predict macroscopic properties of inorganic molten systems using a realistic description of inter-atomic interactions. Unlike the conventional approach, which tends to overestimate viscosity by several…
The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…
The isothermal dynamical evolution of a clumpy and turbulent molecular cloud region and its fragmentation into a protostellar cluster is investigated numerically. The effect of different initial density and velocity distributions, generated…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
We calculate density profiles for self-gravitating clusters of an ideal Bose-Einstein gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. Our study includes clusters with planar symmetry in…
On the basis of microscopic statistical mechanics of simple liquids the orientational interaction between clusters consisting of a particle and its nearest neighbors is estimated. It is shown that there are ranges of density and temperature…
Dissipation in granular media leads to interesting phenomena as there are cluster formation and crystallization in non-equilibrium dynamical states. The freely cooling system is examined concerning the energy decay and the cluster evolution…