49,718 research outputs found
Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent
Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics
Scaling analysis exploiting timescale separation has been one of the most
important techniques in the quantitative analysis of nonlinear dynamical
systems in mathematical and theoretical biology. In the case of enzyme
catalyzed reactions, it is often overlooked that the characteristic timescales
used for the scaling the rate equations are not ideal for determining when
concentrations and reaction rates reach their maximum values. In this work, we
first illustrate this point by considering the classic example of the
single-enzyme, single-substrate Michaelis--Menten reaction mechanism. We then
extend this analysis to a more complicated reaction mechanism, the auxiliary
enzyme reaction, in which a substrate is converted to product in two sequential
enzyme-catalyzed reactions. In this case, depending on the ordering of the
relevant timescales, several dynamic regimes can emerge. In addition to the
characteristic timescales for these regimes, we derive matching timescales that
determine (approximately) when the transitions from initial fast transient to
steady-state kinetics occurs. The approach presented here is applicable to a
wide range of singular perturbation problems in nonlinear dynamical systems.Comment: 35 pages, 11 figure
Mechanism Deduction from Noisy Chemical Reaction Networks
We introduce KiNetX, a fully automated meta-algorithm for the kinetic
analysis of complex chemical reaction networks derived from semi-accurate but
efficient electronic structure calculations. It is designed to (i) accelerate
the automated exploration of such networks, and (ii) cope with model-inherent
errors in electronic structure calculations on elementary reaction steps. We
developed and implemented KiNetX to possess three features. First, KiNetX
evaluates the kinetic relevance of every species in a (yet incomplete) reaction
network to confine the search for new elementary reaction steps only to those
species that are considered possibly relevant. Second, KiNetX identifies and
eliminates all kinetically irrelevant species and elementary reactions to
reduce a complex network graph to a comprehensible mechanism. Third, KiNetX
estimates the sensitivity of species concentrations toward changes in
individual rate constants (derived from relative free energies), which allows
us to systematically select the most efficient electronic structure model for
each elementary reaction given a predefined accuracy. The novelty of KiNetX
consists in the rigorous propagation of correlated free-energy uncertainty
through all steps of our kinetic analyis. To examine the performance of KiNetX,
we developed AutoNetGen. It semirandomly generates chemistry-mimicking reaction
networks by encoding chemical logic into their underlying graph structure.
AutoNetGen allows us to consider a vast number of distinct chemistry-like
scenarios and, hence, to discuss assess the importance of rigorous uncertainty
propagation in a statistical context. Our results reveal that KiNetX reliably
supports the deduction of product ratios, dominant reaction pathways, and
possibly other network properties from semi-accurate electronic structure data.Comment: 36 pages, 4 figures, 2 table
Mode transitions in a model reaction-diffusion system driven by domain growth and noise
Pattern formation in many biological systems takes place during growth of the underlying domain. We study a specific example of a reaction–diffusion (Turing) model in which peak splitting, driven by domain growth, generates a sequence of patterns. We have previously shown that the pattern sequences which are presented when the domain growth rate is sufficiently rapid exhibit a mode-doubling phenomenon. Such pattern sequences afford reliable selection of certain final patterns, thus addressing the robustness problem inherent of the Turing mechanism. At slower domain growth rates this regular mode doubling breaks down in the presence of small perturbations to the dynamics. In this paper we examine the breaking down of the mode doubling sequence and consider the implications of this behaviour in increasing the range of reliably selectable final patterns
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