Related papers: Explicit exponential convergence to equilibrium fo…
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global…
In two preceding papers we have shown that, when reaction networks are well-removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically-stabilized integration schemes that rival standard…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by…
In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In…
We introduce an extension of the concept of renormalised solutions for entropy-dissipating reaction-diffusion systems due to J. Fischer (Arch. Ration. Mech. Anal. 218, 2015) to systems coupled by nonlinear interface conditions. For this…
It is shown that two reacting cosmological fluids, each of them perfect on its own, which exchange energy and momentum without preserving particle numbers, give rise to an entropy producing `reactive' bulk stress of the system as a whole,…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
We consider a chemical reaction network governed by mass action kinetics and composed of N different species which can reversibly form heterodimers. A fast iterative algorithm is introduced to compute the equilibrium concentrations of such…
We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with…
We show that solutions of the chemical reaction-diffusion system associated to $A+B\rightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which…
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available…