The Effective Geometry Monte Carlo Algorithm: Applications to Molecular Communication

TL;DR

This paper introduces the Effective Geometry Monte Carlo (EG-MC) algorithm to improve the accuracy of diffusion simulations by modifying receiver geometry, achieving precise results with minimal computational cost.

Contribution

The paper presents a novel EG-MC algorithm that corrects biases in diffusion simulations through geometric modifications, applicable to molecular communication and potentially other physics fields.

Findings

EG-MC accurately simulates impulse responses of spherical receivers.

The algorithm reduces systematic biases with minimal computational overhead.

Constraints on the free parameter demonstrate the method's robustness.

Abstract

In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry of the receiver. We motivate our approach in a 1D toy model and then apply our findings to a spherical absorbing receiver in a 3D unbounded environment. We show that with minimal computational cost, the impulse response of this receiver can be precisely simulated using EG-MC. Afterwards, we demonstrate the accuracy of our simulations and give tight constraints on the single free parameter in EG-MC. Finally, we comment on the range of applicability of our results. While we present the EG-MC algorithm for the specific case of molecular diffusion, we believe that analogous methods with effective geometry manipulations can be utilized to approach a variety of problems in other branches of physics such as condensed matter physics and cosmological large scale structure simulations.