The Method of Fictitious Negative Sources to Model Diffusive Channels With Absorbing Boundaries

IF 2.4 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Pub Date : 2024-09-02 DOI:10.1109/TMBMC.2024.3453808

Fardad Vakilipoor;Abdulhamid N. M. Ansari;Luca Barletta;Gian Guido Gentili;Maurizio Magarini

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Abstract

This paper presents an approach to address the diffusion equation in scenarios involving multiple absorbing boundary conditions, commonly found in diffusive molecular communication (MC) channels. Instead of using multiple mirror images of the source, fictitious sources with time-varying release rates are introduced to replace the boundaries. This transformation enables the calculation of the expected cumulative number of absorbed particles (CNAP) by multiple absorbing boundaries with finite volume. To compute the expected CNAP, the concept of barycenter, which represents the spatial mean of particles the receiver absorbs is introduced. Substituting absorbing objects with their barycenters leads to model the CNAP in scenarios with convex geometry of absorbers. In a one-dimensional (1D) space, the proposed approach yields the same expression as the method of images for describing the expected CNAP by an absorber. However, in three-dimensional (3D) space, where using the method of images is challenging or even impossible, the proposed approach enables substituting the objects with fictitious sources and compute the expected CNAP. In 1D, an extension of this approach to the case in which one boundary exhibits an absorption characteristic while the other has zero-flux characteristic is demonstrated. This research direction is valuable for modeling channels where not all objects are particle receptors.

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用虚构负源法模拟有吸收边界的扩散通道

本文提出了一种在涉及多个吸收边界条件的情况下处理扩散方程的方法，这种情况通常出现在扩散分子通讯（MC）通道中。该方法不使用多个源的镜像，而是引入具有时变释放率的虚构源来替代边界。通过这种转换，可以计算出具有有限体积的多个吸收边界的预期累积吸收粒子数（CNAP）。为了计算预期累积吸收粒子数，引入了 "原心 "的概念，它代表了接收器吸收粒子的空间平均值。用吸收物体的原心代替吸收物体，就能在吸收体具有凸几何形状的情况下建立 CNAP 模型。在一维（1D）空间中，所提出的方法与图像法描述吸收体预期 CNAP 的表达式相同。然而，在三维（3D）空间中，使用图像方法具有挑战性，甚至是不可能的，而所提出的方法可以用虚构源代替物体，并计算预期的 CNAP。在一维空间中，这种方法扩展到了一个边界显示吸收特性而另一个边界显示零流量特性的情况。这一研究方向对于模拟并非所有物体都是粒子受体的通道非常有价值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications Mathematics-Modeling and Simulation

CiteScore

3.90

自引率

13.60%

发文量

期刊介绍： As a result of recent advances in MEMS/NEMS and systems biology, as well as the emergence of synthetic bacteria and lab/process-on-a-chip techniques, it is now possible to design chemical “circuits”, custom organisms, micro/nanoscale swarms of devices, and a host of other new systems. This success opens up a new frontier for interdisciplinary communications techniques using chemistry, biology, and other principles that have not been considered in the communications literature. The IEEE Transactions on Molecular, Biological, and Multi-Scale Communications (T-MBMSC) is devoted to the principles, design, and analysis of communication systems that use physics beyond classical electromagnetism. This includes molecular, quantum, and other physical, chemical and biological techniques; as well as new communication techniques at small scales or across multiple scales (e.g., nano to micro to macro; note that strictly nanoscale systems, 1-100 nm, are outside the scope of this journal). Original research articles on one or more of the following topics are within scope: mathematical modeling, information/communication and network theoretic analysis, standardization and industrial applications, and analytical or experimental studies on communication processes or networks in biology. Contributions on related topics may also be considered for publication. Contributions from researchers outside the IEEE’s typical audience are encouraged.