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We present a method for performing atomistic spin dynamic simulations. A comprehensive summary of all pertinent details for performing the simulations such as equations of motions, models for including temperature, methods of extracting…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applications, where focus on data leads to novel outcomes, rather than the a priori tendencies of applied analysis which imposes constructs on the…
A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations with monotone operators in a Hilbert space is studied in this paper. An a posteriori stopping rule, based on a discrepancy-type principle is proposed…
We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients.…
The pressure-induced structural transition in fcc C$_{60}$ fullerene by shock compression and rapid quenching is investigated by a semi-empirical tight-binding molecular dynamics simulation, adopting a constant-pressure scheme and a method…
We present a first principles molecular dynamics approach that is based on time-reversible ex- tended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field…
Quantum mechanical equations of motion are strictly linear in state descriptors, such as wavefunctions and density matrices, but equations describing chemical kinetics and hydrodynamics may be non-linear in concentrations. This…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
Chemical reactions can be modelled via diffusion processes conditioned to make a transition between specified molecular configurations representing the state of the system before and after the chemical reaction. In particular the model of…
This Feature Article presents an overview of the current status of Ring Polymer Molecular Dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical…
We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and…
The diffusion, "explosion" and "evaporation" of dimers and the subsequent coalescence are treated in a formal way by identifying and solving the differential equations deduced from the respective behaviors of dimers in the different cases.…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We simulate the compression of a two-component Lennard-Jones liquid at a variety of constant temperatures using a molecular dynamics algorithm in an isobaric-isothermal ensemble. The viscosity of the liquid increases with pressure,…
We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited…
Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting…
We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville von-Neumann…