First‐order stochastic cellular automata simulations of the lindemann mechanism

Abstract

The Lindemann mechanism explains how apparent unimolecular chemical reactions arise from bimolecular collisions. In this mechanism an ingredient M activates reactants A through collisions, and the resulting activated species A * can either decay to products P or be deactivated back to A, again via collisions with M. A first-order stochastic cellular automata model described previously [Seybold, Kier, and Cheng, J Chem Inf Comput Sci 1997, 37, 386] has been modified to simulate this mechanism. It is demonstrated that this model accurately reflects the salient features of the Lindemann mechanism, including the normal second-order kinetic behavior at low [M] and apparent first-order kinetics at high [M]. At low [M] the mechanism is equivalent to a rate-limited sequential process, whereas at high [M] it becomes a preequilibrium with leakage to products. The model also allows an examination of the validity of the steady-state approximation normally employed in a deterministic analysis of this mechanism, and it is seen that this approximation is not well justified under reasonable conditions.

Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19

“…Thirdly, we assume that susceptible and infected cells can both ‘signal’ for cytokine recruitment [ 5 , 6 ] after detecting free virus (process F in figure 2 ); the infected cell signal may be smaller or even repress the susceptible cell's signals. This cell signalling mechanism is represented by rate-limited kinetics [ 19 ], which assumes a sigmoidal Hill-like reaction term [ 20 ], multiplied by the amount of signalling cells present (see § 2.1 for further details). Fourthly, we assume that susceptible cells can also directly recruit (local) immune cells, bypassing the cytokine pathway, via rate-limited kinetics (process G in figure 2 ).…”

Persistence of a pandemic in the presence of susceptibility and infectivity distributions in a population: Mathematical model

“…Cellular automata is a popular technique to study physical processes like chemical reactions, wildfire propagation, traffic dynamics, phase transitions, pattern formation etc. [22][23][24][25][26][27][28][29] This technique has also been used to study the progress of epidemics. [30][31][32][33][34][35][36] We perform KMC-CA simulations of the present model with several parameters and factors that mimic the spread of an infectious disease into a population of susceptible individuals.…”

A Lattice Gas Automata Model for the Coupled Heat Transfer and Chemical Reaction of Gas Flow Around and Through a Porous Circular Cylinder

“…Following the steps illustrated by Wang et al [23], a porous two-dimensional cylinder can be generated with a set of three construction parameters, including (i) growing phase (fluid) distribution probability, C d , which decides initial number of fluid seeds in the system; (ii) directional growth probability of fluid, D i , which is considered the same for all directions in this work; and (iii) fluid volume fraction P. Figure 7 presents the inner morphology of the porous circular cylinders of diameter D = 100 (lattice unit) resulted from different combinations of construction parameters, where shaded area is solid phase and the rest to be pores. As can be seen in Figure 7a-d, the solid phase disappears homogenously with increasing porosity, leading to larger pore sizes; and for Figure 7e-h, more agglomeration of solid phase, i.e., less surface area and bigger pore size, appeared for larger directional growth probability; on the contrary, for Figure 7i-l, more homogenous structure as well as smaller pore size of porous media can be obtained as the distribution probability increases, as a result, more react-able surface area is generated.…”

“…Following the steps illustrated by Wang et al [23], a porous two-dimensional cylinder can be generated with a set of three construction parameters, including (i) growing phase (fluid) distribution probability, Cd, which decides initial number of fluid seeds in the system; (ii) directional growth probability of fluid, Di, which is considered the same for all directions in this work; and (iii) fluid volume fraction P. …”

“…More detailed microscopic interaction among particles or between particles and walls can be obtained when using LGA. Thus, various investigations on flow past obstacles or reaction using lattice gas automata have been carried out, such as flow over cylinders or plat plate [11][12][13], reaction and diffusion systems [14][15][16], first order reactions [17], motivation phenomena of atom and molecule [18,19], kinetically and thermodynamically controlled reactions [20][21][22], and Lindemann theory [23,24]. However, investigations on flow, heat transfer and chemical reaction around a porous cylinder using LGA were rarely reported.…”