Related papers: Model for clustering of living species
The formation, movement and gluing of clusters can be described through a system of non local balance laws. Here, the well posedness of this system is obtained, as well as various stability estimates. Remarkably, qualitative properties of…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains…
Studying particle-laden flows is essential to understand diverse physical processes such as rain formation in clouds, pathogen transmission, and pollutant dispersal. Distinct clustering patterns are formed in such flows with particles of…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is…
The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study…
Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over…
Cooperation between micro-organisms give rise to novel phenomena like clustering, swarming in suspension. We study the collective behavior of the artificial swimmer called Taylor line at low Reynolds number using multi-particle collision…
When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This…
We investigate methods for modelling metabolism within populations of cells. Typically one represents the interaction of a cloned population of cells with their environment as though it were one large cell. The question is as to whether any…
Cooperation is ubiquitous across all levels of biological systems ranging from microbial communities to human societies. It, however, seemingly contradicts the evolutionary theory, since cooperators are exploited by free-riders and thus are…
Cluster synchronization is a phenomenon in which oscillators in a given network are partitioned into synchronous clusters. As recently shown, diverse cluster synchronization patterns can be found using network symmetry when the oscillators…
We analyze the cluster formation in a non-ergodic stochastic system as a result of counter-flow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a…
The colonisation of a soft passive material by motile cells such as bacteria is common in biology. The resulting colonies of the invading cells are often observed to exhibit intricate patterns whose morphology and dynamics can depend on a…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…