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The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
We introduce a modified molecular dynamics algorithm that allows one to freeze the dynamics of parts of a physical system, and thus concentrate the simulation effort on selected, central degrees of freedom. This freezing, in contrast to…
We describe a novel coarse-grained simulation method for modelling the dynamics of globular macromolecules, such as proteins. The macromolecule is treated as a continuum that is subject to thermal fluctuations. The model includes a…
A force-based optimization method is proposed to apply the first and second kind of Piola-Kirchhoff stresses in molecular statics simulation. This method is important for finite deformation problems in which the atomistic behavior can be…
We present a brief review on the Impulse Approximation method to study processes of scattering off composite particles. We first construct the model in a non-relativistic fashion that enables us to extend the model to a covariant Impulse…
Molecular dynamics simulations have been performed on pure liquid water, aqueous solutions of sodium chloride, and polymer solutions exposed to a strong external electric field with the goal to gain molecular insight into the structural…
The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the…
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
This paper proposes a finite-time Newton seeking control design for systems described by unknown multivariable static maps. The Newton seeking system has an averaged system that implements a Newton continuous-time algorithm. The averaged…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
In this paper we have explored computationally the solidification process of large nickel clusters. This process has the characteristic features of the first order phase transition occurring in a finite system. The focus of our research is…
A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size $N_t$ is fixed, the temperature $T$ is varied by changing $N_t$ at fixed…
An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is…