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arXiv · 1809.06438

The Effective Geometry Monte Carlo Algorithm: Applications to Molecular Communication

Fatih Dinc·Leander Thiele·Bayram Cevdet Akdeniz
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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.

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Fatih Dinc, Leander Thiele, Bayram Cevdet Akdeniz. 2018-09-17. The Effective Geometry Monte Carlo Algorithm: Applications to Molecular Communication. https://doi.org/10.1016/j.physleta.2019.05.029

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