From massively parallel algorithms and fluctuating time horizons to nonequilibrium surface growth

Area of Science:

• Computational physics
• Parallel algorithms
• Discrete-event simulation

Background:

• Discrete-event simulations are crucial for modeling complex systems.
• Massively parallel algorithms are needed for large-scale simulations.
• Understanding asymptotic scaling is key to algorithm efficiency.

Purpose of the Study:

• To investigate the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations.
• To determine if the algorithm exhibits scalable performance.

Main Methods:

• Analysis of asymptotic scaling properties.
• Modeling discrete events as Poisson arrivals.
• Utilizing Monte Carlo simulations.
• Employing a coarse-grained approximation.

Main Results:

• The simulated time horizon evolution resembles a nonequilibrium surface.
• The steady-state macroscopic landscape is governed by the Edwards-Wilkinson Hamiltonian.
• Algorithm efficiency correlates with the density of local minima on the surface.

Conclusions:

• The studied algorithm demonstrates asymptotic scalability.
• The findings provide theoretical underpinnings for the algorithm's efficiency in large-scale simulations.