相关论文: Mathematical Theory of Exchange-driven Growth
We develop a mean-field theory of the growth, exchange and distribution (GED) model introduced by Kang et al. (preceding paper) that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity.…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are…
We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate r and clusters merge at a constant total rate 1, so that both the total number of clusters and the total mass steadily grow…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
Firm growth process in the developing economies is known to produce divergence in their growth path giving rise to bimodality in the size distribution. Similar bimodality has been observed in wealth distribution as well. Here, we introduce…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
The time-dependent kinetics of formation and evolution of nano-size atomic clusters is investigated and illustrated with the nucleation dynamics of ion-seed Ar$_n$H$^+$ particles. The rates of growth and degradation of Ar-atomic shells…
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter…
In exchange processes clusters composed of elementary building blocks, monomers, undergo binary exchange in which a monomer is transferred from one cluster to another. In assortative exchange only clusters with comparable masses participate…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of…
Mean-field control (MFC) problems aim to find the optimal policy to control massive populations of interacting agents. These problems are crucial in areas such as economics, physics, and biology. We consider the non-local setting, where the…
The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked particle is studied in detail on different time scales for {\em general} kicking potentials. It is shown that the asymptotic time behavior of a wave-packet MKE is…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
These notes are based on the lectures given in a mini-course at VIASM (Vietnam Institute for Advanced Study in Mathematics) 2025 Summer School. They give a brief account of the theory (with detailed proofs) for propagation governed by a…
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…