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Parallel computing for mobilities in periodic geometries.

Martin Magill1, Andrew M Nagel1, Hendrick W de Haan1

  • 1Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St N, Oshawa, Ontario L1H7K4, Canada.

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Summary
This summary is machine-generated.

We explored two methods for calculating molecular mobility in periodic systems using particle simulations. The mean first-passage time method offers a faster alternative to the standard drift velocity approach, especially with modern hardware.

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Area of Science:

  • Computational physics
  • Molecular dynamics
  • Transport phenomena

Background:

  • Calculating effective molecular mobility in periodic systems is crucial for understanding transport phenomena.
  • Particle-based simulations are widely used but can be computationally intensive.
  • Existing methods for mobility calculation have limitations in efficiency and applicability.

Purpose of the Study:

  • To compare two formulations for calculating effective molecular mobility: standard drift velocity and mean first-passage time.
  • To derive the equivalence between these formulations under generalized conditions.
  • To assess the computational efficiency and performance of each method, particularly for parallel computing.

Main Methods:

  • Theoretical derivation of the equivalence between mobility formulations using the Markov property.
  • Approximate theoretical analysis of computational costs for particle simulations.
  • Numerical investigation using a slit-well device model for nanoparticle transport.
  • Comparison of convergence rates and performance across different Péclet numbers.

Main Results:

  • The equivalence of drift velocity and first-passage time mobility formulations is established under the Markov property at period crossings.
  • Theoretical analysis suggests first-passage time methods are better suited for parallel hardware.
  • Numerical simulations confirm that first-passage time formulation converges faster at moderate to high Péclet numbers.
  • The first-passage time method demonstrates potential for an order of magnitude speedup on GPU hardware.

Conclusions:

  • The mean first-passage time method provides a computationally advantageous alternative for calculating effective molecular mobilities in periodic systems.
  • This method shows significant performance gains, especially for systems with moderate to high Péclet numbers, when utilizing parallel computing resources.
  • The findings suggest a more efficient approach for simulating biomolecular transport in complex, periodic environments.