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We expand on two previous developments in the modeling of discrete-time Langevin systems. One is the well-documented Gr{o}nbech-Jensen Farago (GJF) thermostat, which has been demonstrated to give robust and accurate configurational sampling of the phase space. Another is the recent discovery that also kinetics can be accurately sampled for the GJF method. Through a complete investigation of all possible finite difference approximations to the velocity, we arrive at two main conclusions:~1) It is not possible to define a so-called on-site velocity such that kinetic temperature will be correct and independent of the time step, and~2) there exists a set of infinitely many possibilities for defining a two-point (leap-frog) velocity that measures kinetic energy correctly for linear systems in addition to the correct configurational statistics obtained from the GJF algorithm. We give explicit expressions for the possible definitions, and we incorporate these into convenient and practical algorithmic forms of the normal Verlet-type algorithms along with a set of suggested criteria for selecting a useful definition of velocity.
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grads moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the existence of its
Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decr
In light of the recently developed complete GJ set of single random variable stochastic, discrete-time St{o}rmer-Verlet algorithms for statistically accurate simulations of Langevin equations, we investigate two outstanding questions: 1) Are there an
To study epitaxial thin-film growth, a new model is introduced and extensive kinetic Monte Carlo simulations performed for a wide range of fluxes and temperatures. Varying the deposition conditions, a rich growth diagram is found. The model also repr
We expand on the previously published Gr{o}nbech-Jensen Farago (GJF) thermostat, which is a thermodynamically sound variation on the St{o}rmer-Verlet algorithm for simulating discrete-time Langevin equations. The GJF method has been demonstrated to g