Related papers: On the Classification Scheme for Phenomenological …
Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the…
By the use of Perron-Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result…
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also…
Stochastic growth processes give rise to diverse intricate structures everywhere and across all scales in nature. Despite the seemingly unrelated complex phenomena at their origin, the Laplacian growth theory has succeeded in unifying their…
Economic growth and the growth of human population in the past 2,000,000 years are extensively examined. Data are found to be in a clear contradiction of the currently accepted explanations of the mechanism of growth, which revolve around…
The theory of growth kinetics developed previously is extended to the asymmetric case of off-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter $M$, the average global value of the…
A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth…
We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems arise from variational problems in plasticity with power…
The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent…
Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth…
In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $m$ mutations is an exponential function of $m$ but with a rate that depends only on the set of rules and not the size of…
We consider a stochastic Laplacian growth problem in the framework of normal random matrices. In the large $N$ limit the support of eigenvalues of random matrices is a planar domain with a sharp boundary which evolves under a change in the…
It is a central prediction of renormalisation group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and not on the specific choice of lattice. We investigate the…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
The paper considers a particular family of set--valued stochastic processes modeling birth--and--growth processes. The proposed setting allows us to investigate the nucleation and the growth processes. A decomposition theorem is established…
In this work, some phenomenological models, those that are based only on the population information (macroscopic level), are deduced in an intuitive way. These models, as for instance Verhulst, Gompertz and Bertalanffy models, are posted in…
This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present…
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
This article answers the question of V.M. Buchstaber about the growth function of a particular $n$-valued group. This question is closely related to discrete integrable systems. In this paper, we will find a formula for the growth function…