Search results for "Symplectic integrator"
showing 4 items of 4 documents
Multiple time step integrators and momentum conservation
1997
Abstract By use of the standard Liouville operator formalism, we derive a new symplectic multiple time step integrator for Hamiltonian systems with disparate masses, which, in contrast to previous algorithms, conserves the total momentum exactly, and is only moderately slower. The new scheme is tested numerically by application to Molecular Dynamics simulations of a polymer melt whose monomers have different masses, and compared to earlier algorithms.
High Field Polarization Response in Ferroelectrics: Current Solutions and Challenges
2006
Polarization response including ergodicity breaking and the divergence of relaxation time is reproduced for model Hamiltonians of growing complexity. Systematic derivation of the dynamical equations and its solutions is based on the Fokker-Planck and imaginary time Schrödinger equation techniques with subsequent symplectic integration. Test solutions are addressed to finite size and spatially extended problems with microscopically interpretation of the model parameters as a challenge.
Stochastic Dynamics of Ferroelectric Polarization
2008
This study is addressed to the conceptual and technical problems emerging for ferroelectric systems out of thermodynamic equilibrium. The theoretical setup includes a lattice of interacting cells, each cell obeying regular dynamics determined by Ginzburg-Landau model Hamiltonians whereas relaxation toward minimum energy state is reproduced by thermal environment. Representative examples include polarization response of a single lattice cell, birth of a domain as triggered by the ergodicity breaking, and the effect of nonlocal electroelastic interaction all evidenced combining the Fokker-Planck, imaginary time Schrodinger and symplectic integration techniques.
Theory and modeling of polarization switching in ferroelectrics
2005
Abstract Kinetics of polarization response in ferroelectrics is reproduced within Langevin, Fokker–Planck and imaginary time Schrodinger equation techniques for energy functionals of growing complexity modeling an assembly of coarse grained particles with attractive first neighbor interaction. Symplectic integration based numerical approach captures dynamic hysteresis, polarization switching, and spatially extended stationary polarization. Solution of relevant nonstationary problem is adapted to large scale parallel computing.