相关论文: Ising, Schelling and Self-Organising Segregation
The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform disorder is investigated by intensive Monte Carlo simulations. Taking into account finite-time corrections to scaling, simple ageing behaviour is…
Phase separation plays an role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The…
The axial next-nearest-neighbor Ising model is studied in two dimensions at finite temperature using the density matrix renormalization group. The model exhibits phase transition of the second-order between the antiphase in low temperature…
The research of one-dimensional Ising model with the different number of neighbors and the different sign of the exchange integral were performed. Magnetization shows the transition from disorder to order (in finite systems) only at…
The dynamics of an asymmetric kinetic Ising model is studied. Two schemes for improving the existing mean-field description are proposed. In the first scheme, we derive the formulas for instantaneous magnetization, equal-time correlation,…
The phenomena of radial and axial segregation in a horizontal rotating cylinder containing a mixture of granular particles of two different species have been modeled using discrete particle simulation. Space-time plots and detailed imagery…
We investigate a model for randomly layered magnets, viz. a three-dimensional Ising model with planar defects. The magnetic phase transition in this system is smeared because static long-range order can develop on isolated rare spatial…
We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered…
We present a theoretical model for predicting the phase behavior of polymer solutions in which phase separation competes with oligomerization. Specifically, we consider scenarios in which the assembly of polymer chains into stoichiometric…
Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in…
We study chemical oscillators in the presence of phase separation. By imposing timescale separation between slow reactions and fast diffusion, we define a dynamics at phase equilibrium for the relevant degrees of freedom. We demonstrate…
Thermal quenching has been used to find metastable materials such as hard steels and metallic glasses. More recently, quenching-based phase control has been applied to correlated electron systems that exhibit metal--insulator, magnetic or…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
We study mixtures of self-propelled and passive rod-like particles in two dimensions using Brownian dynamics simulations. The simulations demonstrate that the two species spontaneously segregate to generate a rich array of dynamical domain…
In this work, we employed the Ising model to identify phase transitions in a magnetic system where the degree distribution of the network follows a power-law and the connections are assortatively mixed. In the Ising model, the spins assume…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
We introduce and theoretically investigate a minimal particle-based model for a new class of active matter where particles exhibit directional, volume-conserving division in confinement while interacting sterically, mimicking cells in early…
We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
In the present article we consider the Schelling model, an agent-based model describing a segregation dynamics when we have a cohabitation of two social groups. As for several social models, the behaviour of the Schelling model was analyzed…