Related papers: Phase-space geometry of mass-conserving reaction-d…
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such…
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…
This short review covers a wide selection of topics from a multidisciplinary area of dynamics of nonequilibrium systems in physics, chemistry, biology. Theoretical models of colloid particle and protein deposition and adhesion at surfaces,…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
This paper studies a bulk-surface reaction-diffusion system for cell polarization in two-dimensional domains. The model describes the formation of localized patterns through the wave-pinning mechanism, while explicitly incorporating the…
Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical for numerous applications, including the computation of chemical reaction rates and transport of objects in the solar system. Many…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…
We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is…
This article presents a multi-physics methodology for the numerical simulation of physical systems that involve the non-linear interaction of multi-phase reactive fluids and elastoplastic solids, inducing high strain-rates and high…