Related papers: Differential dissipativity analysis of reaction-di…
Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
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…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular…
The purpose of this paper is two-fold. First, to make clear (and de-mystify) the basic concepts of classical thermodynamics, and thus to enable the integration of thermodynamics within systems modeling and control. Second, to demonstrate…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We establish weak-strong uniqueness and stability properties of renormalised solutions to a class of energy-reaction-diffusion systems. The systems considered are motivated by thermodynamically consistent models, and their formal entropy…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical…
Contraction theory is a recently developed dynamic analysis and nonlinear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory to local and global stability analysis of…
Diffusion occurs in numerous physical systems throughout nature, drawing its generality from the universality of the central limit theorem. Around a century ago it was realized that an extension to this type of dynamics can be obtained in…
Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems.…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
From a simple analysis of particle orbits and fluid flows in presence or not of dissipation, some connections between apparently uncorrelated research areas are made. The main results point out for a deep relation between quantization of…