Related papers: Quantitative analysis of self-organized patterns i…
Active matter generates order or patterns through nonequilibrium dynamics. An open research challenge is to determine how efficiently a nonequilibrium self-organising system can convert consumed energy into macroscopic order. We study an…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
The restructuring process of diagenesis in the sedimentary rocks is studied using a percolation type model. The cementation and dissolution processes are modeled by the culling of occupied sites in rarefied and growth of vacant sites in…
Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed…
Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion is typically modeled using gradients in chemical potential. However, chemical potential is derived for uniform pressure and…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based…
Sedentism was a decisive moment in the history of humankind. In a review article Kay and Kaplan quantified land use for early human settlements and found that sedentism and the emergence of farming go hand in hand. For these settlements two…
Using a simple lattice model for granular media, we present a scenario of self-organization that we term self-organized structuring where the steady state has several unusual features: (1) large scale space and/or time inhomogeneities and…
The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters size distributions is developed. It allows for full description of percolation transition…
A particular sequence of patterns, "$\text{gaps} \to \text{labyrinth} \to \text{spots}$," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the…
We study how changes in population size and fluctuating environmental conditions influence the establishment of seed banks in plants. Our model is a modification of the Wright-Fisher model with seed bank, introduced by Kaj, Krone and…
We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
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…
An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these…