Application of inverse iteration to 2‐dimensional master equations

On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak

“…Examples of other treatments are also available. [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] We focus on the limiting low pressure rate constant k 0 . It is of particular interest partly because it describes the maximum effect of the collisions and partly because it is simpler to treat than the rate constant at higher pressures, where a solution of the complete master equation would have been necessary.…”

“…If a tagged A is followed in time in its progress to form AB, and if a tagged A in AB is followed in time in its progress to form A + B, beginning with an equilibrium concentrations of AB for the given A and B concentration, the sum of the tagged distribution functions at any energy E is equal to the equilibrium distribution at that E. Thus, to solve the problem, one can either begin with a tagged A or a tagged AB. To simplify the comparison with earlier work, [46][47][48][49][50] we begin with AB and use the result to calculate also the rate of recombination A + B → AB. We consider the reaction in the low pressure regime…”

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

“…While solving the diffusion version of the ME is clearly an approximation to the solution of the full ME, this approximation has proved useful. 6,7,16,[32][33][34][35] One of the keys to the scalability of the methods presented in the current work is the inversion of the diffusion approximation matrix. As described elsewhere, 6,7 rearranging the ordering of the energy grains within the state space p to bring grains of the same energy together results in a banded matrix with the bandwidth equal to the number of isomers being modeled, p. A banded matrix of this type can be factorized with computational effort scaling at O(np 2 ), a vast improvement over the O(n 3 ) standard solve as usually p Ӷn.…”

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

“…The 2DME includes a kernel for collisional energy transfer transitions that depends on both variables. Although such treatments were first demonstrated decades ago [39][40][41][42][43] and exist in improved forms today, [39][40][41][42][43][44][45][46] they require input parameters that involve extensive additional calculations. 47 Instead of an explicit 2DME, most practical ME calculations utilize various methods for reducing the 2DME to one dimension.…”