Three Waves of Chemical Dynamics

@article{Gorban2015ThreeWO,
  title={Three Waves of Chemical Dynamics},
  author={Alexander N. Gorban and Gregory S. Yablonsky},
  journal={Mathematical Modelling of Natural Phenomena},
  year={2015},
  volume={10},
  pages={1-5}
}
Three epochs in development of chemical dynamics are presented. We try to un- derstand the modern research programs in the light of classical works. 
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24 Citations
Background Citations
8
Methods Citations
1

24 Citations

Stationary Distributions and Condensation in Autocatalytic Reaction Networks
We investigate a broad family of stochastically modeled reaction networks by looking at their stationary distributions. Most known results on stationary distributions assume weak reversibility and ...
Kinetics of Heterogeneous Self-Propagating High-Temperature Reactions
In this chapter, we present an overview of experimental techniques utilized and kinetic data collected for exothermic self-sustained noncatalytic heterogeneous reactions. The data focuses on five…
Some Recent Advances in Energetic Variational Approaches
In this paper, we summarize some recent advances related to the energetic variational approach (EnVarA), a general variational framework of building thermodynamically consistent models for complex…
Two Formalisms of Stochastization of One-Step Models
TLDR
In the article the authors briefly describe these formalisms: combinatorial (state vectors) and operator (occupation numbers) with an emphasis on their practical application.
Nonequilibrium Thermodynamics in Biochemical Systems and Its Application
TLDR
The history and current development of nonequilibrium thermodynamics, especially that in biochemical systems, are introduced and the development of stochastic thermodynamics is introduced, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation.
Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
Stationary distributions and condensation in autocatalytic CRN.
We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions…
Diagram Representation for the Stochastization of Single-Step Processes
TLDR
A diagram technique is proposed, which allows to unify getting master equation for the system under study, and the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model is demonstrated.
Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner System
TLDR
This work makes automatic computations on n−site phosphorylations and biomodels from the Biomodels repository using the grobcov library of the computer algebra system Singular to approach the binomiality problem using Comprehensive Gröbner systems.
Kinetics of SHS reactions: A review
  • A. Mukasyan, C. Shuck
  • Materials Science
    International Journal of Self-Propagating High-Temperature Synthesis
  • 2017
The current state of chemical kinetics for self-propagating high-temperature non-catalytic reactions has been reviewed for results over the past 50 years. Five different characterization techniques…
...
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References

SHOWING 1-10 OF 56 REFERENCES
On the H-theorem for polyatomic gases
The H-theorem for a classical gas of polyatomic molecules of arbitrarily complex structure is examined. A simple use of time reversal invariance of the equations of dynamics is used to circumvent the…
Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System
TLDR
This work deals with patterns in a thin layer of solution, in which cerium ions catalyse the oxidation of analogues of malonic acid by bromate by oscillations in the solution colour.
Tropicalization and tropical equilibration of chemical reactions
TLDR
Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale and these equilibrations find a natural formulation in tropical analysis and can be used for model reduction.
Kinetic models of catalytic reactions
Thermodynamic function analogue for reactions proceeding without interaction of various substances
The CSP method for simplifying kinetics
The Computational Singular Perturbation (CSP) method of simplified kinetics modeling is presented with emphasis on its comparative merits versus conventional methodologies. A new “refinement”…
Invariant Manifolds for Physical and Chemical Kinetics
Introduction.- The Source of Examples.- Invariance Equation in the Differential Form.- Film Extension of the Dynamics: Slowness as Stability.- Entropy, Quasi-Equilibrium and Projector Field.- Newton…
Robust Lyapunov Functions for Reaction Networks: An Uncertain System Framework
We present a framework to transform the problem of finding a Lyapunov function of a Chemical Reaction Network (CRN) in concentration coordinates with arbitrary monotone kinetics into finding a common…
Robust Lyapunov functions for Complex Reaction Networks: An uncertain system framework
We present a framework to transform the problem of finding a Lyapunov function for a Complex Reaction Network (CRN) in concentration coordinates with arbitrary monotone kinetics into finding a common…
The Dynamical Theory of Gases
MORE than eleven years have elapsed since the first edition of this work was-reviewed in NATURE (April 27, 1905). Most of the pioneers of the attempted rigorous mathematical theory hav passed away,…
...
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