1 / 8

Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential

Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential. V. Gotcheva, Yanting Wang, Albert Wang and S. Teitel University of Rochester. Lattice gas dynamics for driven steady states. Particles can hop over energy barriers in a single bound! Can greatly speed

nathan
Download Presentation

Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Continuous Time Monte Carlo and Driven Vortices in a Periodic Potential V. Gotcheva, Yanting Wang, Albert Wang and S. Teitel University of Rochester Lattice gas dynamics for driven steady states. Particles can hop over energy barriers in a single bound! Can greatly speed up simulation time as compared to continuum molecular dynamics.

  2. integer charge on site i of a periodic square LxL grid f uniform background charge 2D Lattice Coulomb gas integer charges on a compensating uniform background charge neutrality fixes Nc particles logarithmic interactions periodic boundary conditions

  3. Continuous time Monte Carlo dynamics Uniform applied force F For a single particle move of displacement Drthe energy difference for the move, including work done by F, is Define the rate to move a particle at site i a unit spacing in direction a, Rates satisfy local detailed balance. Probability to make the above move is, Sample the distribution Piato decide which move to make, and then update the simulation clock by

  4. Periodic grid of lattice gas represents the minima of a periodic potential with energy barriers Eb. Algorithm describes thermal activation over energy barriers when DU < Eb. Use particle densityf = 1/25 F = 0 ground state charge configuration is a 5x5 square lattice real space k-space Compute structure function Real space correlation function

  5. Large drive F = 0.10 in x direction T = 0.004 L = 50 S(k) after 6000 passes S(k) after 107 passes S(k) after 6x107 passes C(r) corresponding to (c) Long time steady state is smectic with flow of particles in periodically spaced channels; channels are out of phase with each other.

  6. Low drive F = 0.04 in x direction T = 0.004 L = 75 Coexisting liquid and solid phases, as in a 1st order transition. F liquid solid

  7. C(r) liquid C(r) solid F Solid consists of particles moving in channels parallel to F. Channels are separated by 3 grid spacings. Particles within each channel are separated by 81/3 grid spacings on average. This is different than both the ground state or the high drive smectic! The liquid has long ranged 6-fold orientational order! Local 6-fold clusters prefer to lock into the grid direction transverse to the driving force.

  8. moving solid is transversely pinned

More Related