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Elements of Continuum Mechanics
Published in Clement Kleinstreuer, Biofluid Dynamics, 2016
According to statistical physics, physical quantities are represented by averages over configurations distributed according to a certain statistical ensemble. A trajectory obtained by molecular dynamics (see Eq. (5.2.2)) provides such a set of configurations. Therefore, a measurement of a physical quantity by simulation is simply obtained as an arithmetic average of the various instantaneous values assumed by that quantity during the numerical MD simulation run. Statistical physics is the link between the microscopic behavior and thermodynamics. In the limit of very long simulation times (and high N-values), one could expect the phase-space to be fully sampled, and in that limit this averaging process would yield the thermodynamic properties. In practice, the runs are always of finite length, and one should exert caution to estimate when the sampling may be good (i.e., the “system at equilibrium”) or not. In this way, MD simulations can be used to measure thermodynamic properties and therefore evaluate, say, the phase diagram of a specific material. Beyond this “traditional” use, MD is nowadays also used for other purposes, such as studies of nonequilibrium processes, and as an efficient tool for optimization of structures overcoming local energy minima, e.g., simulated annealing.
Machine learning and molecular dynamics based models to predict the temperature dependent elastic properties of silver nanowires
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2023
S. K. Joshi, Sanjeev K. Singh, Santosh Dubey
Through microscopic simulations, the MD approach allows us to investigate a system’s macroscopic characteristics. The Maxwell distribution is used to assign atomic movements and starting velocities at a given temperature T. So that the computation may be completed in a suitable amount of time, it is necessary to choose the number of particles time step, total time, and simulation size duration. As the simulation progresses, the system’s thermodynamic characteristics, such as pressure, volume, temperature, and total energy, change. Different methods of simulation can be used, including taking into account various ensemble kinds. A statistical ensemble is made up of all conceivable system states that are within certain bounds, such as a particular temperature or molecular concentration. Different statistical ensembles are utilized depending on the target application. The probability density of each statistical ensemble, or the likelihood that each system state will occur in the collection, serves as a defining characteristic of the ensemble. Recently, MD has been used extensively for the study of tensile [19–26] and melting properties [21, 27–34] of the nanowires of Cu, Ni, Sn, Ti and Au, etc.