We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscop...

Kinetics Monte Carlo simulation has been done for solving Master equation about dynamics of intracellular viral reaction kinetics. Scaling relationship between equilibrium time and initial population of template has been founded as power low, ( ) b eq time f N aN  , where N , ( ) eq time f N are the number of initial population of template species , equilibrium time, a = 274.2, b = 0.1378 resp...

We extend Karma and Rappel’s improved asymptotic analysis of the phase field model to different diffusivities in solid and liquid. We consider both second-order “classical” asymptotics, in which the interface thickness is taken much smaller than the capillary length, and the new “isothermal” asymptotics, in which the two lengths are considered comparable. In the first case, if the phase field m...

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-...

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...

This article is concerned with the asymptotic accuracy of the Computational Singular Perturbation (CSP) method developed by Lam and Goussis [The CSP method for simplifying kinetics, Int. J. Chem. Kin. 26 (1994) 461–486] to reduce the dimensionality of a system of chemical kinetics equations. The method, which is generally applicable to multiple-time scale problems arising in a broad array of sc...

Statistical copolymers of norbornene (NBE) with cyclopentene (CP) were prepared by ring-opening metathesis polymerization, employing the 1st-generation Grubbs' catalyst, in the presence or absence of triphenylphosphine, PPh₃. The reactivity ratios were estimated using the Finemann-Ross, inverted Finemann-Ross, and Kelen-Tüdos graphical methods, along with the computer program COPOINT, which eva...

Interfacial charge transfer is widely assumed to obey the Butler-Volmer kinetics. For certain liquid-solid interfaces, the Marcus-Hush-Chidsey theory is more accurate and predictive, but it has not been applied to porous electrodes. Here we report a simple method to extract the charge transfer rates in carbon-coated LiFePO4 porous electrodes from chronoamperometry experiments, obtaining curved ...

Special voltage-clamp pulse protocols are given that make differential predictions for the kinetics of models based on a simple sequential, simple cyclic, and an aggregation scheme. Detailed kinetic time-courses for the discriminating pulse protocols are numerically derived from the differential equation system that describes the aggregation model.

With the advances in measurement technology for molecular biology, predictive mathematical models of cellular processes come in reach. A large fraction of such models addresses the kinetics of interaction between biomolecules such as proteins, transcription factors, genes, and messenger RNA. In contrast to classical chemical kinetics – utilizing the reaction-rate equation – the small volume of ...