Related papers: Percolation and depinning transitions in cut-and-p…
A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
We study the asymptotic macroscopic properties of the mixed majority-minority game, modeling a population in which two types of heterogeneous adaptive agents, namely ``fundamentalists'' driven by differentiation and ``trend-followers''…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…
We introduce two three sided adaptative systems as toy models to mimic the exchange of commodities between buyers and sellers. These models are simple extensions of the minority game, exhibiting similar behaviour as well as some new…
Models for the microstructure evolution during hot rolling are reviewed. The basic macroscopic phenomena related to recrystallization are summarized. Constitutive models based on semi empirical equations are compared to more sophisticated…
We introduce a toy model, which represents a simplified version of the problem of the depinning transition in the limit of strong disorder. This toy model can be formulated as a simple renormalization transformation for the probability…
The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks…
We propose a model for evolution aiming to reproduce statistical features of fossil data, in particular the distributions of extinction events, the distribution of species per genus and the distribution of lifetimes, all of which are known…
We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection…
In this study, we employ analytical and numerical techniques to examine a phase transition model with moving boundaries. The model displays two relevant spatial scales pointing out to a macroscopic phase and a microscopic phase, interacting…