Related papers: Structural Evolution of Granular Systems: Theory
Steady state dynamics of clustering, long range order, and inelastic collapse are experimentally observed in vertically shaken granular monolayers. At large vibration amplitudes, particle correlations show only short range order like…
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…
A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation-selection process, four distinct phases of self-organization were unveiled. First, the…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
Kato's theory on the construction of strongly continuous evolution systems associated with hyperbolic equations is applied to the linear equation describing an age-structured population that is subject to time-dependent diffusion. The…
Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
A general scheme, which includes constructions of coarse-grained (CG) models, weighted ensemble dynamics (WED) simulations and cluster analyses (CA) of stable states, is presented to detect dynamical and thermodynamical properties in…
Globular clusters are stellar dynamical systems which evolve on stellar evolutionary and both internal and external dynamical timescales. Quantitative comparison of cluster properties with realistic evolutionary dynamical models is becoming…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
We examine two basic assumptions of kinetic theory-- binary collisions and molecular chaos-- using numerical simulations of sheared granular materials. We investigate a wide range of densities and restitution coefficients and demonstrate…
We argue that a number of recent experimental and numerical observations point to an ongoing cooperative stress-structure self-organisation (SO) in quasi-static granular dynamics. These observations include: a) detail-insensitive collapses…
Cells adapt to different conditions by altering a vast number of components, which is measurable using transcriptome analysis. Given that a cell undergoing steady growth is constrained to sustain each of its internal components, the…
A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…
We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…