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Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important…

We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…

A recombination reaction model for high-temperature chemical kinetics is derived from ab initio simulations data. A kinetic recombination rate model is derived using a recently developed ab initio state-specific dissociation model and the…

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a…

Enzyme-catalysed reactions involve two distinct timescales. There is a short timescale on which enzymes bind to substrate molecules to produce bound complexes, and a comparatively long timescale on which the complex is transformed into a…

In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…

Often a number of precipitation processes in steels and alloys occur simultaneously (they have the same origin in time) albeit at different rates. Consequently, isothermic transformations are accompanied, in this case, by the occurrence of…

We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main…

We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of the evolution are obscured when observing a statistical ensemble…

Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the…

By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…

Numerical hydrodynamics simulations of gases dominated by ideal, nondegenerate matter pressure and thermal radiation pressure in equilibrium entail finding the temperature as part of the evolution. Since the temperature is not typically a…

Single molecule spectroscopy aims at unveiling often hidden but potentially very important contributions of single entities to a system's ensemble response. Albeit contributing tremendously to our ever growing understanding of molecular…

We study transient thermal processes in infinite harmonic crystals with complex (polyatomic) lattice. Initially particles have zero displacements and random velocities such that distribution of temperature is spatially uniform. Initial…

The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…

A scarcity of known chemical kinetic parameters leads to the use of many reaction rate estimates, which are not always sufficiently accurate, in the construction of detailed kinetic models. To reduce the reliance on these estimates and…

In this work we study, at the single molecular level, the thermodynamic and dynamic characteristics of an enzymatic reaction comprising a rate limiting step. We investigate how the stability of the enzyme-state stationary probability…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Precise temperature measurements on systems of few ultracold atoms is of paramount importance in quantum technologies, but can be very resource-intensive. Here, we put forward an adaptive Bayesian framework that substantially boosts the…