Related papers: The phase transition in random catalytic sets

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…

This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure,…

Autocatalysis, the ability of a chemical system to make more of itself, is a crucial feature in metabolism and is speculated to have played a decisive role in the origin of life. Nevertheless, how autocatalytic systems behave far from…

Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…

A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory,…

We identify a new universality class of phase transitions that emerges in non-normal systems, extending the classical framework beyond eigenvalue instabilities. Unlike traditional critical phenomena, where transitions occur when eigenvalues…

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and…

External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…

In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…

The continuous phase transition, indicated by the macroscopic order parameter and the occurrence of the spontaneous symmetry breaking, is well illustrated based on the Ginzburg-Landau's paradigm. In systems described by one order parameter,…

We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

An exactly solvable reaction-diffusion model consisting of first-class particles in the presence of a single second-class particle is introduced on a one-dimensional lattice with periodic boundary condition. The number of first-class…

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…

Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of…

This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…