Related papers: The exchange-driven growth model: basic properties…
Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This paper proposed a longitudinal higher-order diagnostic classification modeling approach for measuring…
An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by…
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We propose a new type of diffuse interface model describing the evolution of a tumor mass under the effects of a chemical substance (e.g., a nutrient or a drug). The process is described by utilizing the variables $\varphi$, an order…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
We investigate transient clustering dynamics in nonlocal aggregation-diffusion systems from an energetic perspective. Starting from a stochastic interacting particle system, we study the associated macroscopic McKean-Vlasov equation on the…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
We introduce a generalized version of the Kac ring model in which particles are of two types, black and white. Black particles modify the environment through which all particles move, thereby inducing indirect and potentially long-range…
The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved…
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to…
We study an agent-based model of evolution of wealth distribution in a macro-economic system. The evolution is driven by multiplicative stochastic fluctuations governed by the law of proportionate growth and interactions between agents. We…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
The molecular dynamics and Monte Carlo studies of the thermal stability of C20, C36, and C60 fullerenes and the methane molecule are reported. It has been shown that the heat transfer between the atomic cluster and the external heat…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they…
We propose a continuous-time stock-flow consistent model for inventory dynamics in an economy with firms, banks, and households. On the supply side, firms decide on production based on adaptive expectations for sales demand and a desired…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…