Related papers: The discrete generalized exchange-driven system
We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two…
Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
We study statistical characterization of the many-body states in the exactly solvable model with internal degree of freedom in more than one dimension. The model exhibits the Mott metal-insulator transition. It is shown that the ground…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove…
Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE)…
We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single…
We study a statistical model consisting of $N$ basic units which interact with each other by exchanging a physical entity, according to a given microscopic random law, depending on a parameter $\lambda$. We focus on the equilibrium or…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…
We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings' models, and replace it by a less…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed…
Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models…
The construction of coarse-grained descriptions of a system's kinetics is well established in biophysics. One prominent example is Markov state models in protein folding dynamics. In this paper, we develop a coarse-grained, discrete state…
Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on…