Related papers: Modeling Chemical Reactors I: Quiescent Reactors
Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enable a wide range of…
In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular…
In this paper, we develop a method to generate the Lyapunov function for stability analysis for chemical reaction networks. Based on the Chemical Master Equation, we derive the Lyapunov Function partial differential equations (PDEs), whose…
A chemical reaction mechanism (CRM) is a sequence of molecular-level events involving bond-breaking/forming processes, generating transient intermediates along the reaction pathway as reactants transform into products. Understanding such…
Reaction barriers are a crucial ingredient for first principles based computational retro-synthesis efforts as well as for comprehensive reactivity assessments throughout chemical compound space. While extensive databases of experimental…
Diffusion in heterogeneous energy and diffusivity landscapes is widespread in biological systems. However, solving the Langevin equation in such environments introduces ambiguity due to the interpretation parameter $\alpha$, which depends…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The inter-reaction times are exponentially distributed under the assumption that the system is well mixed. We…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
Chemical clock reactions are characterised by a relatively long induction period followed by a rapid `switchover' during which the concentration of a \emph{clock chemical} rises rapidly. In addition to their interest in chemistry education,…
The interaction of a quantized electromagnetic field in a cavity with a set of two-level atoms inside can be described with algebraic Hamiltonians of increasing complexity, from the Rabi to the Dicke models. Their algebraic character…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus extend previous results to the case of time-space dependent…
To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction-diffusion master equations or deterministic, macroscopic reaction-diffusion system. The connection between these two models is not…
We propose a concise stochastic mechanics framework for chemical reaction systems that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating…
We analyze the Gray-Scott reaction--diffusion system on $\Omega\subset\mathbb{R}^n$ ($n\ge 1$) with mixed diffusion combining local and nonlocal operators. Using semigroup methods and duality estimates, we prove global existence of…
In this paper we develop a theoretical framework which allows us to study excitations of the nucleon. Assuming an effective two-body interaction as a model for low-energy QCD, we derive a relativistic TDHF equation for a many-body system of…
In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…
The tensor-RPA approach developed previously in part I is applied to the Nambu-Jona-Lasinio (NJL) model. As a first step we investigate the structure of Dirac-Hartree-Fock solutions for a rotationally and isospin invariant ground-state…
We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for…