相关论文: Universality in stochastic exponential growth

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…

We uncover a universal scaling law governing the dispersion of collective attention and identify its underlying stochastic criticality. By analysing large-scale ensembles of Wikipedia page views, we find that the variance of logarithmic…

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…

The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative…

In the framework of a 1D cyclic competition model, the Rock-Paper-Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled…

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…

When a system is brought to a metastable state, nuclei of the equilibrium phase form and grow. This is the well-known nucleation and growth of first-order phase transitions. Near a critical point of a continuous phase transition, critical…

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…

In exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of…

We model the growth of a cell population by a piecewise deterministic Markov branching tree. Each cell splits into two offsprings at a division rate $B(x)$ that depends on its size $x$. The size of each cell grows exponentially in time, at…

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion…

Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…

We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several…

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…

Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well documented to much more tightly than traditionally assumed,…

Investigation of protein self-assembly processes is important for the understanding of the growth processes of functional proteins as well as disease-causing amyloids. Inside cells, intrinsic molecular fluctuations are so high that they…

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…

To maintain a constant cell size, dividing cells have to coordinate cell cycle events with cell growth. This coordination has for long been supposed to rely on the existence of size thresholds determining cell cycle progression [1]. In…

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…