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This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime…

Analysis of PDEs · Mathematics 2025-10-21 Madi Yerlanov , Nancy Rodriguez

Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are…

Statistical Mechanics · Physics 2009-10-31 Haye Hinrichsen

We analyze semilinear reaction-diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation…

Analysis of PDEs · Mathematics 2023-05-04 Chunyou Sun , Bao Quoc Tang , Juan Yang

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…

Analysis of PDEs · Mathematics 2026-03-24 Brocchieri Elisabetta , Soresina Cinzia

Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…

Soft Condensed Matter · Physics 2022-01-20 Clara del Junco , André Estevez-Torres , Ananyo Maitra

We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to…

Statistical Mechanics · Physics 2009-11-10 S. Lubeck , P. C. Heger

Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…

Pattern Formation and Solitons · Physics 2014-07-17 Anton S. Zadorin , Yannick Rondelez , Jean-Christophe Galas , André Estevez-Torres

Certain systems with slow driving and avalanche-like dissipation events are naturally close to a critical point when the ratio of two energy scales is large. The first energy scale is the threshold above which an avalanche is triggered, the…

Statistical Mechanics · Physics 2015-06-25 Barbara Drossel

Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size…

Soft Condensed Matter · Physics 2009-11-11 Santanu Sinha , Vimal Kishore , S. B. Santra

Temporal autocorrelation functions for avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical simulations show that they decay as power laws with two distinct regimes separated by a time scale which…

Condensed Matter · Physics 2009-10-30 Stefan Boettcher , Maya Paczuski

We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the…

Analysis of PDEs · Mathematics 2020-12-07 Artur Stephan

The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description -…

Statistical Mechanics · Physics 2015-03-13 Juan A. Bonachela , Miguel A. Munoz

In a recent paper, de Freitas et al. [Phys. Rev. E 61, 6330 (2000)] presented simulational results for the critical exponents of the two-species reaction-diffusion system A + B -> 2B and B -> A in dimension d = 1. In particular, the…

Statistical Mechanics · Physics 2009-10-31 Hans-Karl Janssen

Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…

Disordered Systems and Neural Networks · Physics 2010-11-10 A. Wolff , I. Lohmar , J. Krug , Y. Frank , O. Biham

We obtain evidence that the dynamics of glassy systems below the glass transition is characterized by self-organized criticality. Using molecular dynamics simulations of a model glass-former we identify clusters of cooperatively jumping…

Disordered Systems and Neural Networks · Physics 2015-06-25 Katharina Vollmayr-Lee , Elizabeth A. Baker

Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally…

Statistical Mechanics · Physics 2026-05-14 Kartik Chhajed , P. K. Mohanty

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove…

Analysis of PDEs · Mathematics 2017-11-16 José A. Carrillo , Simone Fagioli , Filippo Santambrogio , Markus Schmidtchen

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…

Statistical Mechanics · Physics 2015-05-13 S. D. da Cunha , Ronaldo R. Vidigal , L. R. da Silva , Ronald Dickman

Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the…

Statistical Mechanics · Physics 2009-10-31 K. Oerding , H. K. Janssen

We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of…

Probability · Mathematics 2026-05-27 Dionysis Milesis , Michael Salins