Algorithms for Brownian first-passage-time estimation

Area of Science:

• Computational physics
• Statistical mechanics

Background:

• Brownian motion is fundamental to understanding diffusion processes.
• Estimating first-passage times is crucial in various scientific fields.
• Existing methods like Langevin-based algorithms have limitations.

Purpose of the Study:

• To develop a novel algorithm for Brownian first-passage-time estimation.
• To assess the algorithm's accuracy and performance compared to existing methods.

Main Methods:

• Developed a class of algorithms operating in discrete space and continuous time.
• Derived a simple algorithm for exact mean first-passage time (MFPT) calculation in linear potentials.
• Numerically tested the algorithm on nonlinear potentials and higher spatial dimensions.

Main Results:

• The derived algorithm provides exact MFPTs for linear potentials, independent of lattice spacing.
• Numerical results indicate superior or competitive performance against Langevin-based estimates for nonlinear potentials and higher dimensions.

Conclusions:

• The new algorithm offers an accurate and efficient method for MFPT estimation.
• It presents a promising alternative to traditional simulation techniques for complex systems.