Related papers: Stochastic growth equations on growing domains
Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations…
A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum…
We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p.…
The growth of correlation lengths in equilibrium glass-forming liquids near the glass transition is considered a critical finding in the quest to understand the physics of glass formation. These understandings helped us understand various…
Stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps, as in the etching model [1]. In this paper I modify the etching model to perform sequential, instead of random,…
Limited dispersal distance, whether associated with vegetative growth or localized reproduction, induces spatial clustering and, in turn, focuses ecological interactions at the neighborhood scale. In particular, most invasive plants are…
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…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
We summarize studies of growing lengths in different aging systems. The article is structured as follows. We recall the definition of a number of observables, typically correlations and susceptibilities, that give access to dynamic and…
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
The non-equilibrium dynamics of three paradigmatic models for two-dimensional systems with quenched disorder is studied with a focus on the existence and analysis of a growing length scale during aging at low temperatures: 1) The random…
Dynamics among central sources (hubs) providing a resource and large number of components enjoying and contributing to this resource describes many real life situations. Modeling, controlling, and balancing this dynamics is a general…
A simple theory, based on observations of snowflake distribution in a turbulent flow, is proposed to model the growth of inertial particles as a result of dynamic clustering at scales larger than the Kolmogorov length scale. Particles able…
We consider the speed of propagation of a {continuous-time continuous-space} branching random walk with the additional restriction that the birth rate at any spatial point cannot exceed $1$. The dispersion kernel is taken to have density…
We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual…
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and…