China
Africa
Explore chapters and articles related to this topic
Overview of Basic Numerical Methods and Parallel Computing
Published in Sourav Banerjee, Cara A.C. Leckey, Computational Nondestructive Evaluation Handbook, 2020
Sourav Banerjee, Cara A.C. Leckey
Verlet method or simply the velocity verlet integration scheme is frequently used in molecular dynamics simulation to solve the second-order Newton's equation, which involves force and acceleration. In Perielastodynamic simulation method for CNDE, similar set of equations are obtained as discussed in Chapter 11. Hence, solution of perielastodynamic approach requires solving equations similar to the molecular dynamic formulation. The equation of motion (or Newton's equation of motion) for a conservative multidegrees-of-freedom system with second-order ordinary differential equations can be written as Mx¨_=f_(x_)=−∇V(x_)
Lattice Monte Carlo Simulations of Micellar and Microemulsion Systems
Published in Promod Kumar, K. L. Mittal, Handbook of Microemulsion Science and Technology, 2018
Raj Rajagopalan, L. A. Rodriguez-Guadarrama, Sameer K. Talsania
The equations of motion can be solved numerically using the Verlet integration scheme [18]. Esselink et al. [16] use a time step of δt = 0.005 τ0, where τ0 = a(m/e)1/2 and m is the mass of the bead. The temperature is kept constant in the canonical ensemble by scaling the velocities every 200 time steps. The results discussed below correspond to a density p = 0.7σ-3, with the simulations done on a 30.4σ x 30.4σ x 60.8σ box (corresponding to 39,304 beads). The concentration of surfactant ranges from 0.75 to 3.0% by volume, with the remainder of the sites being assigned as solvent. Any two surfactants whose minimum separation distance is no more than 1.5σ are considered part of the same micelle.
Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids
Published in Molecular Physics, 2020
Biplab Kumar Mandal, Pankaj Mishra
In this section, we discuss our results of the DFT calculation of the isotropic fluid-triangular solid freezing transition and propose the corresponding phase diagram in the plane. In order to achieve this we require the solution of IET at much higher densities, close to the freezing transitions. However, as discussed in section II, HNC is known to quantitatively underestimate the PCF at the large densities investigated here. In order to test the reliability of HNC closure in the present system at higher density, we perform an elementary molecular dynamics (MD) simulation with 625 particles placed on a 2D square lattice. The box length and time were scaled in unit of σ and respectively. The total momentum was conserved by shifting the velocities of the particle. Velocity Verlet integration scheme was used to integrate Newton's equation of motion. The periodic boundary conditions were imposed in the usual fashion. The equilibrium condition was achieved by 10 time steps in NVE ensemble followed by another 10 runs to calculate the radial distribution function by [48], . Here represents ensemble average over different configurations.