Related papers: Structural evolution of granular systems: Theory
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model ``dust'', provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is…
Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are…
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
The subject of this paper is the evolution of the concept of information processing in regular structures based on multi-level processing in nested cellular automata. The essence of the proposed model is a discrete space-time containing…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
The dynamical behavior of two types of non-equilibrium systems is discussed: $(a)$ two-dimensional cellular structures, and $(b)$ living polymers. Simple models governing their evolution are introduced and steady state distributions (cell…
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
One of the main properties of biological systems is modularity, which manifests itself at all levels of their organization, starting with the level of molecular genetics, ending with the level of whole organisms and their communities. In a…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
We present here a system of self-propelled particles that follow a very simple motion law in continuous space in a deterministic and asynchronous way. This system of particles is capable of producing, depending on the particle density in…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
Stress transmission in planar open-cell cellular solids is analysed using a recent theory developed for marginally rigid granular assemblies. This is made possible by constructing a one-to-one mapping between the two systems. General…
A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the…