Dynamical equations for the period vectors in a periodic system under constant external stress1

@article{Liu2015DynamicalEF,
  title={Dynamical equations for the period vectors in a periodic system under constant external stress1},
  author={Gang Liu},
  journal={Canadian Journal of Physics},
  year={2015},
  volume={93},
  pages={974-978}
}
  • Gang Liu
  • Published 16 September 2002
  • Physics
  • Canadian Journal of Physics
The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The… 

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References

SHOWING 1-10 OF 42 REFERENCES
Metric tensor as the dynamical variable for variable-cell-shape molecular dynamics
We propose a variable-cell-shape molecular dynamics algorithm where the dynamical variables associated with the cell are the six independent dot products between the vectors defining the cell instead
New equations of motion for molecular dynamics systems that change shape
TLDR
This work constructs some new equations of motion of the Parrinello–Rahman family which are more practically useful than their antecedents for studies of systems whose computational cells may undergo extensive changes in shape, especially for Studies of yield and flow under an applied stress.
Molecular dynamics equations of motion for systems varying in shape and size
A unified derivation of the molecular dynamics equations of motion for systems with changing shape and size is presented. Ambiguities in the choice of the kinetic energy of the molecular dynamics
Molecular dynamics simulations at constant pressure and/or temperature
In the molecular dynamics simulation method for fluids, the equations of motion for a collection of particles in a fixed volume are solved numerically. The energy, volume, and number of particles are
Introduction to the mechanics of a continuous medium
This textbook offers a unified presentation of the concepts and general principles common to all branches of solid and fluid mechanics. It deals with: vectors and tensors, stress, strain and
Unified approach for molecular dynamics and density-functional theory.
TLDR
The approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems, and permits the application of density-functional theory to much larger systems than previously feasible.
Computer Simulation of Liquids
Introduction Statistical mechanics Molecular dynamics Monte Carlo methods Some tricks of the trade How to analyse the results Advanced simulation techniques Non-equilibrium molecular dynamics
Crystal structure and pair potentials: A molecular-dynamics study
With use of a Lagrangian which allows for the variation of the shape and size of the periodically repeating molecular-dynamics cell, it is shown that different pair potentials lead to different
Structural Phase Transformations via First-Principles Simulation
We present a new simulation scheme for structural phase transitions via first-principles molecular dynamics. The method is obtained by combining the Car-Parrinello method for ab initio simulation
...
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