A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived. The governing master equation is formulated in a manner that explicitly separates the effects of network topology from other aspects, and the evolution equations for the first two moments are derived. We find the surprising, and apparent...

We present a model order reduction technique for parametrized nonlinear reaction-diffusion systems. In our approach we combine the reduced basis method — a computational framework for rapid evaluation of functional outputs associated with the solution of parametrized partial differential equations — with the empirical interpolation method — a tool to construct “affine” coefficient-function appr...

The approximate analytical solution of fractional order, nonlinear, reaction differential equations, namely the nonlinear diffusion equations, with a given initial condition, is obtained by using the homotopy analysis method. As a demonstration of a good mathematical model, the present article gives graphical presentations of the effect of the reaction terms on the solution profile for various ...

In 1917, Marian von Smoluchowski presented a simple mathematical description of diffusioncontrolled reactions on the scale of individual molecules. His model postulated that a reaction would occur when two reactants were sufficiently close and, more specifically, presented a succinct relationship between the relative proximity of two reactants at the moment of reaction and the macroscopic react...

Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numerical approximation of nonlinear reaction diffusion equations. High order methods are obtained by coupling ENO and WEN...

Gravitational radiation reaction forces and balance equations for energy and momenta are investigated to 3/2 post-Newtonian (1.5PN) order beyond the quadrupole approximation, corresponding to the 4PN order in the equations of motion of an isolated system. By matching a post-Newtonian solution for the gravitational field inside the system to a post-Minkowskian solution (obtained in a previous wo...

On the assumption that photosynthesis is a cyclic process and that irradiation by ultraviolet light does not change the reaction constants, the Blackman reaction is shown to be of first order.

We investigate Leifer and Milner RPO approach for deriving efficient (finitely branching) LTS’s and bisimilarities for π-calculus. To this aim, we work in a category of second-order term contexts and we apply a general pruning technique, which allows to simplify the set of transitions in the LTS obtained from the original RPO approach. The resulting LTS and bisimilarity provide an alternative p...