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Macro- and Microcomputational Materials Mechanics
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
Another way to keep a constant temperature is the Berendsen method [27]. In this method, the simulated system is contacted with a heat bath that has an expected temperature. Acting as a heat source, the heat bath absorbs heat from, or releases heat to, the system. For each simulation step, the velocities are rescaled so that the rate of temperature change is proportional to the temperature difference between the heat bath and the system () dT(t)dt=1τTbath-T(t),
Thermodynamics from Lagrangian theory and its applications to nanosize particle systems
Published in Molecular Physics, 2021
Eduardo Hernández-Huerta, Ruben Santamaria, Tomás Rocha-Rinza
The temperature T = 300 K and viscosity coefficient ps of the heat-bath fluid are defined before starting the simulations. The molecular model with 64 confined water molecules and a spherical container consisting of 240 carbon atoms is employed. The simulations demand average simulation times of 200 ps, with an integration step of 1 fs. The mechanical temperature (which may play the role of a thermometer temperature) is corroborated with the statistical temperature of the heat bath. The averages of the physical variables are calculated in 50 ps intervals. Some plots of the cluster density for the four subvolumes of the spherical container were obtained to check the isotropic and homogeneity aspects of the molecular system (Figure 2). The average densities turn out to be approximately 1.0 g/mL, thus showing the isotropic and homogeneity features of the molecular system. The RDF, also shown in that figure, shows that the nanometric system preserves the pattern observed in bulk water, where the prominent peak between 2.8–2.9 Å corresponds to the first hydration shell [33, 34]. The model using a finite number of water molecules shows to be similar to the macroscopic water bulk.
Dynamic magnetic properties of a hexagonal Ising nanowire system with higher-spin
Published in Phase Transitions, 2020
We considered a hexagonal Ising nanowire (HIN) system with spin-2 particles as illustrated in Figure 1, in which the red and blue spheres illustrate spin-2 particles at the core and shell surface, respectively. Each spin is joined to the two nearest-neighbor magnetic atoms on the below and above sections along the HIN. The Hamiltonian describing HIN model takes the following form:in Equation (1), <ii′>, <ij> and <jj′> stand for the summations over all pairs of neighboring spins at the core, between shell surface, core, shell, respectively. JC, JS and J1 are the exchange interaction parameters for the core–core, shell–shell and core–shell, respectively. D stands for crystal-field. H = H0cos(wt) is the frequency dependence of an external magnetic field and H0, w are the amplitude and the frequency of magnetic field. The HIN model is in contact with the heat bath at TA that is an absolute temperature.
Accurate configurational and kinetic statistics in discrete-time Langevin systems
Published in Molecular Physics, 2019
Lucas Frese Grønbech Jensen, Niels Grønbech-Jensen
Many methods for controlling the temperature of a simulated system (thermostats) have been developed, and most of them fall into two major categories: Deterministic (e.g. Nosé-Hoover [19,20]) and stochastic (Langevin) thermostats [8,21–25]. The deterministic approach includes additional degrees of freedom, which act as an energy reservoir and thereby mimic a thermal heat bath. A requirement for such method is that the temperature of a simulated system can be reliably measured in order for the method to interact properly with the heat-bath. The stochastic approach is to directly simulate the Langevin equation Equation (10), which does not include additional degrees of freedom, but instead interacts with a heat-bath through the fluctuation-dissipation balance for . Since discrete-time tends to distort the conjugated relationship between the positional coordinate and its corresponding momentum (see, e.g. Appendix in Ref. [16] and the Appendix in this paper), a common problem for all methods is that kinetic and configurational measures of temperature disagree, which is a concern for both the integrity of a simulation and the extraction of self-consistent information, which may depend on configurational as well as kinetic sampling. It is therefore imperative to understand how to properly define a kinetic measure consistent with the statistics of the trajectory.