Molecular dynamics equilibrium

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

Equilibrium molecular dynamics simulations have been performed to obtain the solution of the time correlation function (Table 14). ... 

Nonequilibrium molecular dynamics simulations provide another approach for viscosity predictions. This approach as well as equilibrium molecular dynamics was reviewed. 

Control in Non-Equilibrium-Molecular-Dynamics Simulations of the Shear Flow of Dense Liquids. 

Skoulidas AI, Sholl DS (2001) Direct tests of the darken approximation for molecular diffusion in zeolites using equilibrium molecular dynamics. J. Phys. Chem. B. 105 3151-3154... 

The static and dynamic properties of polymer-layered silicate nanocomposites are discussed, in the context of polymers in confined spaces and polymer brushes. A wide range of experimental techniques as applied to these systems are reviewed, and the salient results from these are compared with a mean field thermodynamic model and non-equilibrium molecular dynamics simulations. 

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

P. J. Daivis and D. J. Evans, Transport Coefficients of Liquid Butane near the Boiling Point by Equilibrium Molecular Dynamics, J. Chem. Phys. 

In a somewhat similar paper, diffusion through a 2D porous solid modeled by a regular array of hard disks was evaluated [65] using non-equilibrium molecular dynamics. It was found that Pick s law is not obeyed in this system unless one takes different diffusion constants for different regions in the flow system. Other non-equilibrium molecular dynamics simulations of diffusion for gases within a membrane have been presented [66]. The membrane was modeled as a randomly... 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

Equilibrium molecular dynamics uses the Green-Kubo relationship between the heat current autocorrelation function and the thermal conductivity [66] to obtain the thermal conductivity as ... 

Silicon thin film thermal conductivities are predicted using equilibrium molecular dynamics and the Grccn-Kubo relation. Periodic boundary conditions are applied in the direetions parallel to the thin film surfaees (Fig. 5). Atoms near the surfaces of the thin film are subjeeted to the above-described repulsive potential in addition to the Stillinger-Weber potential [75]. Simulations were also performed adding to each surface four layers of atoms kept frozen at their crystallographic positions, in order to eompare the dependence of the predieted thermal eonduetivities on the surface boundary eonditions. We found that the thermal eonduetivities obtained using frozen atoms or the repulsive potential are identical within the statistical deviations, exeept for the in-plane thermal eonduetivity of films with thickness less than 10 nm [79]. Therefore, in the present study, we present only the predietions obtained with the repulsive potential. 

We begin this chapter by making it clear that equilibrium molecular dynamics techniques are important. The methodology of dynamics, per se, has... 

One easy extension of equilibrium molecular dynamics is the computation of the properties of condensed matter systems in the presence of external fields. Many experiments are done by applying an external field, whether it be an electric field, heat gradient, or some type of flow. Usually, the experimentalist waits some time for the system under investigation to reach a steady state in the presence of the applied field. Measurements are then performed to deduce structural or dynamical information. Performing this task on a computer is what is commonly known as nonequilibrium molecular dynamics (NEMD). It is nonequilibrium in the sense that, in the presence of an external field, the system at the steady state will be in a state of lower entropy. Upon removing the external field, the system will return to the state of maximum entropy or the equilibrium state. 

Equilibrium molecular dynamics was put on a firm theoretical ground with Andersen s seminal paper on extended system dynamics (to be discussed in great detail later). NEMD found its first success in this area with the advent of the so-called DOLL s (not an acronym) algorithm by Hoover and coworkers. ... 

An immediate use for this conserved quantity is obvious it can (and should) be used to check the NEMD code for algorithmic and programming errors. It is also possible to use the conserved energy in obtaining a knowledge of the phase space. The approach proceeds in the same fashion as presented in the section on equilibrium molecular dynamics. Let F denote the full phase space of the variables, p , q,, ri,, I. We now make the assumption of equal a priori probability for each of the microstates F with energy H. This assumption has traditionally been applied to equilibrium systems only. In the isolated system we consider, this assumption is the most obvious one to make. Thus, one can write the phase space distribution function /(F) as... 

R0sjorde et al studied the phase transition in a pure fluid using non-equilibrium molecular dynamics simulations (NEMD). The NEMD method solves Newton s equations of motion for several thousand particles in an imaginary box see Hafskjold for a review. The particles interacted with a Lennard-Jones-type pair... 

The use of non-Hamiltonian dynamical systems has a long history in mechanics [8] and they have recently been used to study a wide variety of problems in molecular dynamics (MD). In equilibrium molecular dynamics we can exploit non-Hamiltonian systems in order to generate statistical ensembles other than the standard microcanonical ensemble NVE) that is generated by traditional Hamiltonian dynamics. These ensembles, such as the canonical (NVT) and isothermal-isobaric (NPT) ensembles, are much better than the microcanonical ensemble for representing the actual conditions under which experiments are carried out. 

D.J. Evans, W.G. Hoover, B.H. Failor, B. Moran, and A.J.C. Ladd (1983) Non-equilibrium molecular dynamics via Gauss s principle of least constraint. Phys. 

Non-equilibrium molecular dynamics Natural population analysis... 

However, for polymers with low degree of crystallization it was assessed that the melting point was depressed at high shear stresses (4). Shear Induced melting has been theoretically predicted from non-equilibrium molecular dynamic simulations (5,... 

Non-Equilibrium Molecular Dynamics Studies of Shock and Detonation Processes in Energetic Materials... 

Non-Equilibrium Molecular Dynamics (NEMD) Shockwave Simulations... 

The earliest efforts to develop non-equilibrium molecular dynamics (NEMD) methods used special boundary conditions and/or external fields to induce non-equilibrium behavior in the system. Important contributions to this development include those of Lees and Edwards [72], Gosling et al. [73], Hoover and Ashurst [74] and Ciccotti and Jacucci... 

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