Related papers: Optimal strategies for the growth of dual-seeded l…
In this paper, we develop a Markov decision process (MDP) formulation for the low--temperature metastable Ising model evolving according to Kawasaki dynamics in a finite box of the two--dimensional square lattice. We analyze how an external…
The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the…
The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
We use computer simulation to study the layer-by-layer growth of particle structures in a lattice gas, taking the number of incorporated vacancies as a measure of the quality of the grown structure. By exploiting a dynamic scaling relation…
We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling…
Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties…
This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff…
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for…
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are…
Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…
The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
The dynamical processes taking place on a network depend on its topology. Influencing the growth process of a network therefore has important implications on such dynamical processes. We formulate the problem of influencing the growth of a…