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Atomic-Scale Simulation of Tribological and Related Phenomena
Published in Bharat Bhushan, Handbook of Micro/Nano Tribology, 2020
Judith A. Harrison, Steven J. Stuart, Donald W. Brenner
A more-sophisticated approach to maintaining a given temperature is through Langevin dynamics. Originally used to describe Brownian motion, this method has found widespread use in MD simulations. In this approach, additional terms are added to the equations of motion, corresponding to a frictional term and a random force (Schneider and Stoll, 1978; Hoover, 1986; Kremer and Grest, 1990). The equations of motion (see Equation 11.1) are given by ma=F=mξv+R(t), where F are the forces due to the interatomic potential, the quantities m and v are the particle mass and velocity, respectively, ξ is a friction coefficient, and R(t) represents a random “white noise” force. The friction kernel is defined in terms of a memory function in formal applications; kernels developed for harmonic solids have been used successfully in MD simulations (Adelman and Doll, 1976; Adelman, 1980; Tully, 1980).
Magnetic Skyrmions on Discrete Lattices
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Elena Y. Vedmedenko, Roland Wiesendanger
The continuum theory of micromagnetism is very successful for the description of low-temperature chiral systems, where temperature fluctuations do not play a significant role. For skyrmionic systems on discrete lattices, however, fluctuations are particularly important, because their strength depends on the interplay between the lattice symmetry and the symmetry of interactions. The effect of the lattice becomes pronounced at temperatures that are close to the Curie temperature. To take the temperature effects into account, atomistic simulations such as Langevin dynamics or Monte-Carlo simulations are required. Most of the temperature-dependent phase diagrams from the discrete systems stem from Monte-Carlo simulations. The energy terms for the atomistic simulations exhibit certain differences with respect to Equations 10.8 through 10.14 and will be discussed in Section 10.4.
Molecular Description of Heterophase Polymerization
Published in Hugo Hernandez, Klaus Tauer, Heterophase Polymerization, 2021
The numerical solution to Langevin’s equation for Brownian motion (Eq. 1.24) is known as Langevin Dynamics simulation. If the system is assumed to relax completely, the solution to the equations of motion corresponds to the method of Brownian Dynamics (BD) simulation. There are several techniques for the numerical solution to Brownian motion [20]. One of the most representative methods is the Monte Carlo random flight (MCRF) algorithm [21, 22]. A flowchart for the MCRF algorithm for BD simulation is presented in Fig. 1.5.
Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect
Published in Molecular Physics, 2018
Satoshi Nakagawa, Isman Kurniawan, Koichi Kodama, Muhammad Saleh Arwansyah, Kazutomo Kawaguchi, Hidemi Nagao
In this paper, we present a novel CG model extended from our previous CG model to investigate the interaction of Cytf-Pc complex from the viewpoint of the molecular crowding effects [18] of the hydrophobic interaction arising from water molecules. In the present CG model, we use the concept of the molecular crowding effect, that is, the hydrophobic interaction decreases around the contacting area of the complex crowded with many hydrophobic particles. Some force field parameters for CG particles for hydrophobic amino acid residues used in the CG model are presented. Some physical properties such as the structure of the complex, the binding site, and the reaction rate are estimated by the Langevin dynamics simulation. We discuss some structures of Cytf–Pc complex obtained by the present CG model in relation to the molecular crowding effect.