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Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems…
Using molecular dynamics simulations we study the temperature-density phase diagram of a simple model system of particles in two dimensions. In addition to translational degrees of freedom, each particle has two internal states and…
We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A + B \to S$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that concentration-dependent…
We introduce a rejection-free continuous-time kinetic Monte Carlo framework to study stochastic systems governed by multiple concurrent dynamical mechanisms. In this approach, the relative activity of each dynamical channel emerges…
We develop a phenomenological vector model of polar liquids capable to describe aqueous interactions of macroscopic bodies. It is shown that a strong, long-range and orientationally dependent interaction between macroscopic objects appears…
The equilibrium properties of the lattice fluid with the repulsion between the nearest neighbors on the two-level planar triangular lattice are investigated. The numerical results obtained from the analytical expressions are compared with…
We realize and study an attractively interacting two-dimensional Fermi liquid. Using momentum resolved photoemission spectroscopy, we measure the self-energy, determine the contact parameter of the short-range interaction potential, and…
We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We discuss 2D systems with Ising symmetry and competing interactions at different scales. In the framework of the Renormalization Group, we study the effect of relevant quartic interactions. In addition to the usual constant interaction…
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…
Evolutionary games between species are known to lead to intriguing spatio-temporal patterns in systems of diffusing agent. However, the role of inter-species interactions is hardly studied when agents are (self-)propelled, as is the case in…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
We study the repulsive polaron problem in a two-component two-dimensional system of fermionic atoms. We use two different interaction models: a short-range (hard-disk) potential and a dipolar potential. In our approach, all the atoms have…
Aggregation of like-charged polymers is widely observed in biological and soft matter systems. In many systems, bundles are formed when a short-range attraction of diverse physical origin like charge-bridging, hydrogen-bonding or…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
We analyzed pattern formation and identified different phases in a system of particles interacting through a non-monotonic short-range repulsive (r<r_c) and long-range attractive (r>r_c) potential, using molecular-dynamics simulations.…
We introduce a lattice spin model that mimics a system of interacting particle through a short range repulsive potential and a long range attractive power law decaying potential. We performed a detailed analysis of the general equilibrium…