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The effective geometry Monte Carlo algorithm: Applications to molecular communication

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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Submitted on : Tuesday, December 17, 2019 - 4:13:54 PM
Last modification on : Saturday, July 9, 2022 - 4:02:03 AM
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Fatih Dinc, Leander Thiele, Bayram Cevdet Akdeniz. The effective geometry Monte Carlo algorithm: Applications to molecular communication. Modern Physics Letters A, World Scientific Publishing, 2019, 383, pp.2594 - 2603. ⟨10.1016/j.physleta.2019.05.029⟩. ⟨hal-02415980⟩



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