Related papers: Cluster expansions, trees, inversions and correlat…
Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the…
The infinite set of coupled integral nonlinear equations for correlation functions in the case of classical canonical ensemble is considered. Some kind of graph expansions of correlation functions in the density parameter are constructed.…
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…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
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)…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
Clustering is one of the mayor collective phenomena observed in active matter. We study the overdamped motion of interacting active Brownian particles in two dimensions. An instability in the pair correlation function causes the onset of…
It appears that the dynamical status of clusters and groups of galaxies is related to the large-scale structure of the Universe. A few interesting trends have been established: (1) The Cluster Substructure - Alignment Connection, by which…
We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n=4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this…
We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the…
Crystalline alloys and related mixed systems make up a large family of materials with high tunability which have been proposed as the solution to a large number of energy related materials design problems. Due to the presence of chemical…
We consider a binary system of small and large spheres of finite size in a continuous medium interacting via a non-negative potential. We work in the canonical ensemble and compute upper and lower bound for the free energy at finite and…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions.…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
Non-aligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods…
Using computer simulations, we validate a simple free energy model that can be analytically solved to predict the equilibrium size of self-limiting clusters of particles in the fluid state governed by a combination of short-range attractive…