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Modeling of State-to-State Oxygen Kinetics behind Reflected Shock Waves
AbstractIn this paper, we study a coupled problem of gas dynamics, vibrational relaxation, and dissociation in the flow of oxygen behind reflected...
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Regression Models for Calculating State-to-State Coefficients of the Rate of Vibrational Energy Exchanges
AbstractThe paper proposes an effective algorithm for solving problems of nonequilibrium gas dynamics taking into account detailed state-to-state...
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A Machine Learning Approach To Calculating the Non-Equilibrium Diffusion Coefficients in the State-To-State Solution of the Navier–Stokes Equations
AbstractThis work considers the application of machine learning methods for approximate determination of diffusion coefficients that are part of...
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Mathematical Modeling and Polarimetry of the Thermal Stressed State of a Partially Transparent Solid Subjected to the Action of Thermal Radiation
By using the method of modulation polarimetry and the developed model of thermomechanics of partially transparent solids, we study the kinetics and...
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Optimization of CO2 Vibrational Kinetics Modeling in the Full State-to-State Approach
AbstractNumerical modeling of nonequilibrium state-to-state carbon dioxide kinetics is a challenging time-consuming computational task that involves...
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Neural-Network-Based Approach to the Description of Vibrational Kinetics of Carbon Dioxide
AbstractThe nonequilibrium vibrational kinetics of carbon dioxide is modeled taking into account complex mechanisms of relaxation and energy...
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Dimensional Dependence of Binding Kinetics
In the context of protein–protein binding, the dissociation constant is used to describe the affinity between two proteins. For protein–protein...
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Nonlinear Differential Equations: Application to Chemical Kinetics
The laws governing chemical kinetics can be written as systems of ordinary differential equations (ODE). In the case of complex reactions with...
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Convex Representation of Metabolic Networks with Michaelis–Menten Kinetics
Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is...
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Nonclassical Riemann solver with prescribed kinetics—The hyperbolic regime
This chapter serves as an example of how a kinetic relation can be used to implement Lax’s shock inequalities. Specifically, we consider a model from...
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Analytical solution of phosphate kinetics for hemodialysis
Chronic kidney diseases imply an ongoing need to remove toxins, with hemodialysis as the preferred treatment modality. We derive analytical...
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Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles
AbstractThe aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration...
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Analysis of dim-light responses in rod and cone photoreceptors with altered calcium kinetics
Rod and cone photoreceptors in the retina of vertebrates are the primary sensory neurons underlying vision. They convert light into an electrical...
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Interpreting models of infectious diseases in terms of integral input-to-state stability
This paper aims to develop a system-theoretic approach to ordinary differential equations which deterministically describe dynamics of prevalence of...
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Data-Driven Approach for Modeling Coagulation Kinetics
Two approaches for the data-driven modeling of aggregation kinetics, described by Smoluchowski equations, are analyzed for binary and ternary...
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The Michaelis–Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation
We demonstrate that the Michaelis–Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate...
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Some Remarks About the Well-Posedness of Lifshitz–Slyozov’s Equations with Nucleation Kinetics
The Lifshitz–Slyozov model is a nonlocal transport equation that can describe certain types of phase transitions in terms of the temporal evolution...
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Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel
The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic...
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Single-Molecule Enzymology and Driven Biochemical Kinetics with Chemostat
The new millennium has witnessed a resurgence of interest in the theory of enzyme kinetics due to several developments in biochemical research: The...
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Identifiability analysis for models of the translation kinetics after mRNA transfection
Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants,...
