Related papers: Phase separation in random cluster models III: cir…
Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring,…
We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the model is supercritical:…
We study stability of multivariable control-affine nonlinear systems under sparsification of feedback controllers. Sparsification in our context refers to the scheduling of the individual control inputs one at a time in rapid periodic…
Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan[2010] introduced a deterministic condition for clustering datasets. They showed that this single deterministic condition…
We numerically study the phase diagram and critical properties of the two-dimensional disordered O(n) loop model by using the transfer matrix and the worm Monte Carlo methods. The renormalization group flow is extracted from the landscape…
The phase transition of the even offspringed branching and annihilating random walk is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing to reach zero branching rate a phase transition can be seen for…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site it reaches outside the cluster. We assume that the increment…
The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…
In the standard paradigm for cosmological structure formation, clustering develops from initially random-phase (Gaussian) density fluctuations in the early Universe by a process of gravitational instability. The later, non-linear stages of…
Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of…
Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hove's theorem is to consider an interparticle potential that is…
After fifty years of lattice gauge theories (LGTs), the nature of the transition between their topological phases (confinement/deconfinement) remains challenging due to the absence of a local order parameter. In this work, we conduct a…
This Article presents a nonequilibrium thermodynamic theory for the mean-field precipitation, aggregation and pattern formation of colloidal clusters. A variable gradient energy coefficient and the arrest of particle diffusion upon…
Fast Radio Bursts (FRBs) are millisecond-duration radio transients of extragalactic origin. Classifying repeating FRBs is essential for understanding their emission mechanisms, but remains challenging due to their short durations, high…
We consider the Random-Cluster model on $\mathbb{Z}^d$ with interactions of infinite range of the form $J_x = \psi(x)\mathsf{e}^{-\rho(x)}$ with $\rho$ a norm on $\mathbb{Z}^d$ and $\psi$ a subexponential correction. We first provide an…
Self-sustained oscillations, limit cycles, are a fundamental phenomenon unique to nonlinear dynamic systems of high-dimensional phase space. They enable understanding of a wide range of cyclic processes in natural, social and engineering…
It is found experimentally that the coexistence region of a vapor-liquid system or a binary mixture is substantially narrowed when the fluid is confined in a aerogel with a high degree of porosity (e.g. of the order of 95% to 99%). A…
We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…
We study in this paper the sine-Gordon model using functional Renormalization Group (fRG) at Local Potential Approximation (LPA) using different RG schemes. In $d=2$, using Wegner-Houghton RG we demonstrate that the location of the phase…