Related papers: Universality in stochastic exponential growth
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
This paper analyzes a stochastic logistic difference equation under the assumption that the population distribution follows a normal distribution. Our focus is on the mathematical relationship between the average growth rate and a newly…
Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size control mechanisms that act on a timescale of one generation. Such mechanisms lead to…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
Stochastic aspects of chemical reaction models related to the Soai reactions as well as to the homochirality in life are studied analytically and numerically by the use of the master equation and random walk model. For systems with a…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
The variability in cell size of an isogenic population of Escherichia coli has been widely reported in experiment. The probability density function (PDF) of cell lengths has been variously described by exponential and lognormal functions.…
Hierarchical decays of $N$ matter species to radiation may balance against Hubble expansion to yield stasis, a new phase of cosmological evolution with constant matter and radiation abundances. We analyze stasis with various machine…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape…
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged…
Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…
We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum…
Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in…
Periodic reversals of the direction of motion in systems of self-propelled rod shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize their swarming rate. In this paper, a connection is found…
A hypothesis of singleness of the growth equation for biological objects on different organizational levels and dimensional analysis are used in order to substantiate Schmalhausen's model of ontogenetic growth (the mass of a growing…
Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…
We study further the recently introduced [Ranguelov et al., Comptes Rendus de l'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystal growth over wide range of model parameters. The basic assumption of the model is that…
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
We analyze a size-structured branching process in which individual cells grow exponentially according to a Feller square-root process and divide under general size-control mechanisms. We obtain exact expressions for the asymptotic…
A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are…