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In this short note we sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations…
We develop tools from computational algebraic geometry for the study of steady state features of autonomous polynomial dynamical systems via elimination of variables. In particular, we obtain nontrivial bounds for the steady state…
Chemical theories involving thermodynamical equilibrium states invariably utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo mechanical coherence is first made, and…
Rate-independent systems allow for solutions with jumps that need additional modeling. Here we suggest a formulation that arises as limit of viscous regularization of the solutions in the extended state space. Hence, our parametrized metric…
Network models are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of these systems are generally nonlinear, suggesting that…
Predicting enzyme-substrate interactions has long been a fundamental problem in biochemistry and metabolic engineering. While existing methods could leverage databases of expert-curated enzyme-substrate pairs for models to learn from known…
In this article we focus on kinetic equations for gas mixtures since in applications one often has to deal with mixtures instead of a single gas. In particular we consider an approximation of the Boltzmann equation, the…
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
We present a real-time path integral theory for the rate of electron transfer reactions. Using graph theoretic techniques, the dynamics is expressed in a formally exact way as a set of integral equations. With a simple approximation for the…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
Enzyme kinetics is very often characterised by the irreversible Michaelis-Menten (MM) equation. However, in open chemical reaction networks such as metabolic pathways, this approach can lead to significant kinetic and thermodynamic…
We propose a new model for making generalizable and diverse retrosynthetic reaction predictions. Given a target compound, the task is to predict the likely chemical reactants to produce the target. This generative task can be framed as a…
Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For…
The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits,…
The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle dimeters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement…
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in…
A kind of fluid dynamic description for the collective movement of pedestrians is developed on the basis of a Boltzmann-like gaskinetic model. The differences between these pedestrian specific equations and those for ordinary fluids are…