The paper presents the premises and equations which are the basis of the mathematical n-order model, which contrarily to standard models based on the laws of chemical kinetics, i.e. 0-order and 1-order kinetics, enables categorization of the investigated process taking into account two parameters: the rate at which it occurs, and actual order, which it is distinguished by. Standard models, whic...

Kinetic Monte Carlo methods such as the Gillespie algorithm model chemical reactions as random walks in particle number space. The interreaction times are exponentially distributed under the assumption that the system is well mixed. We introduce an arbitrary interreaction time distribution, which may account for the impact of incomplete mixing on chemical reactions, and in general stochastic re...

Fast self sustained waves of chemical or phase transformations, observed in several contexts in condensed matter effectively result in “gasless detonation”. The phenomenon is modelled by coupling the reaction diffusion equation, describing chemical or phase transformations, and the wave equation, describing elastic perturbations. The coupling considered in this work involves (i) a dependence of...

A major portion of the computational effort in simulations by threedimensional (3-D) chemistry-transport models is consumed in chemical kinetics calculations which repeatedly solve coupled ordinary differential equations. To address this burden, this paper introduces a high-speed fully equivalent operational model (FEOM) for chemical kinetics calculations. The FEOM consists of a hierarchical co...

Spontaneous antispiral wave formation was observed during the simulation of typical reaction-diffusion systems using differential equations models. The equations for the FitzHugh-Nagumo (FHN), complex Ginzburg-Landau (CGL) and the two-variable Oregonator models were integrated using Runge-Kutta methods. It was found that antispiral waves can occur only near the Hopf bifurcation, i.e. the point ...

INTRODUCTION The increasing demand for diesel fuels has resulted in the use of greater percentage of cracked distillates having poor ignition properties. The ignition properties of diesel fuels can be rated in terms of their cetane number and diesel fuels having low cetane number may have poor ignition properties such as diesel knock, difficulties to start engines in the cold weather and so on....

Chemical kinetics modeling accounts for a significant portion of the computational time of atmospheric models. Effective application of multiple levels of heterogeneous parallelism can significantly reduce computational time, but implementation on emerging multi-core technologies can be prohibitively difficult. We introduce an approach for chemical kinetics modeling on multi-core SIMD architect...

We develop a preconditioned Bayesian regression method that enables sparse polynomial chaos representations of noisy outputs for stochastic chemical systems with uncertain reaction rates. The approach is based on the definition of an appropriate multiscale transformation of the state variables coupled with a Bayesian regression formalism. This enables efficient and robust recovery of both the t...