Related papers: Two-dimensional individual clustering model

The nonlocal nonlinear aggregation equation in one space dimension is investigated. In the so-called attractive case smooth solutions blow up in finite time, so that weak measure solutions are introduced. The velocity involved in the…

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $\alpha =D/J$ between anisotropy $D$ and exchange $J$ the…

We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

In this paper we perform systematic investigation of all possible exponential solutions in Einstein-Gauss-Bonnet gravity with the spatial section being a product of two subspaces. We describe a scheme which always allow to find solution for…

We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…

This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…

In cancer research, clustering techniques are widely used for exploratory analyses and dimensionality reduction, playing a critical role in the identification of novel cancer subtypes, often with direct implications for patient management.…

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…

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…

We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with…

We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for…

I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…

We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…

We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…

We reconsider the problem of local persistence in directed site percolation. We present improved estimates of the persistence exponent in all dimensions from 1+1 to 7+1, obtained by new algorithms and by improved implementations of existing…

To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the…

We investigate the presence of non-topological solutions of the Q-ball type in (1, 1) spacetime dimensions. The model engenders the global U(1) symmetry and is of the k-field type, since it contains a new term, of the fourth-order power in…