What's the molecular statics and what's the difference between molecular statics and molecular dynamics? In general, molecular statics can be used to simulate what?
FYI:
Article A STATIC ANALOG OF MOLECULAR DYNAMICS METHOD FOR CRYSTALS
Traditionally, molecular statics (MS) methods are based on various iterative energy minimization algorithms, such as first-order steepest descents or conjugate gradient and second-order Newton-Raphson or Quasi-Newton’s. By definition, the former methods require evaluation of the first derivatives of energy, while the latter ones require both first and second derivatives. Recently an algorithm proposed by Telitchev and Vinogradov allows the finding of lattice equilibrium by treating it as a truss system with nonlinear elements and variable connectivity between them. The forces are defined by the first derivatives and the iterative process of finding the equilibrium state is based on solving a nonlinear system of algebraic equations. In all of the above approaches the equilibrium state is found by solving a coupled system of equations.
In contrast, in molecular dynamics (MD) the atoms move independently of each other during each time step and thus the equilibrium state is found by solving a decoupled system of equations. Specifically, the motion of each atom is governed by the resultant force acting on it from the neighboring ones. The Newton’s equation of motion for each atom is solved numerically during a time step, which is chosen in such a way as to preserve the total Hamiltonian of the system and the time step is usually measured in femtoseconds. The latter places a severe limitation on the timescale of processes which can be simulated, including crystal fracture, dislocation formation and propagation, etc. For relatively short time scales, the MD method allows simulations of billions of atoms by using massively parallel computers and efficient multiresolution algorithms [Rountree et al. (2002)]. While the MD methods allow simulations of large systems they are limited to time scales of the order of nanoseconds. The MS methods are not constrained by the time scales but they are constrained by the size of the system they are able to simulate since these systems are always coupled (leaving aside the fact that the MS method effectively works in the realm of zero temperature, 0◦K).
"The starting point for the Molecular Dynamics (MD) method is a well-defined microscopic description of a physical system. The system can be a few- or many-body system. The description may be a Hamiltonian, Lagrangian or expressed directly in Newton's equations of motion. The molecular dynamics method, as the name suggests, calculates properties using the equations of motion, and one obtains the static as well as the dynamic properties of a system".. [1]. You can find a simple and detailed description of this method in [1,2].
The purpose of the Molecular Statics method is the simulation of the atomic structure in the vicinity of defects at zero temperature. You can find a explicit description of the method in [3,4].
We developed a new version of the Molecular Statics method [5,6] for calculating the diffusion characteristics of point defects, specifically, parameters describing the effect of pressure on diffusion in metals (the formation and migration volumes). A significant feature of this model is a self consistent procedure of calculating the atomic structure in the vicinity of a defect and parameters that determine displacements of atoms in the elastic medium surrounding the computational cell.
1. D.W. Heermann, Computer simulation methods in Theoretical Physics, Second Edition, Springer Verlag, 1990.
2. Richard LeSar, Introduction to Computational Materials Science: Fundamentals to Applications. Cambridge University Press, 2013, 427с
3. R. Johnson, and E. Brown, Point defects in copper. Phys. Rev., 1962. 127(2): p. 446-454.
4. R. Johnson, Interstitials and Vacancies in a-Iron. Phys. Rev. A, 1964. 134(5): p. 1329–1336.
5. I. Valikova and A. Nazarov, Simulation of characteristics determining pressure effects on the concentration and diffusivity of vacancies in BCC metals: A new approach. The Physics of Metals and Metallography, 2008. 105(6): p. 544-552.
6. I.V. Valikova, A.V. Nazarov, Simulation of Characteristics Determining Pressure Effects on Self-diffusion in BCC and FCC Metals, Phys. Metals. and Metallography, Vol. 109, No. 3, pp. 220–226 (2010).
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