相关论文: The phase transition in random catalytic sets

We derive an exact solution of an explicitly time-dependent multichannel model of quantum mechanical nonadiabatic transitions. In the limit N >>1, where N is the number of states, we find that the survival probability of the initially…

Phase transitions are fundamental features of statistical physics. While the well-studied continuous phase transitions are known to be controlled by external \textit{macroscopic} changes in the order parameter, the origin of abrupt…

Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…

We study the large deviations of additive quantities, such as energy or current, in stochastic processes with intermittent reset. Via a mapping from a discrete-time reset process to the Poland-Scheraga model for DNA denaturation, we derive…

A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…

The present note deals with a nonstandard systems of differential equations describing a two-species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion…

Motivated by the idea that criticality and universality of phase transitions might play a crucial role in achieving and sustaining learning and intelligent behaviour in biological and artificial networks, we analyse a theoretical and a…

The hallmark feature of polymorphic systems is their ability to assemble into many possible structures at the same thermodynamic state. Designer polymorphic materials can in principle be engineered via programmable self-assembly, but the…

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…

Phase transitions are a fundamental concept in science describing diverse phenomena ranging from, e.g., the freezing of water to Bose-Einstein condensation. While the concept is well-established in equilibrium, similarly fundamental…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…

We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…

Recently, we introduced [Physical Review E 100, 022303 (2019)] a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior. One important finding of our study was a…

Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…

Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…

We study theoretical limits of \emph{descending} phase retrieval algorithms. Utilizing \emph{Random duality theory} (RDT) we develop a generic program that allows statistical characterization of various algorithmic performance metrics.…

We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…