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arXiv · 1803.10848

Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

Maximilian Schäfer·Wayan Wicke·Rudolf Rabenstein·Robert Schober
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Abstract

This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or magnetism. The dynamics of the diffusion process are modeled by multi-dimensional transfer functions in a spatio-temporal frequency domain. Realistic boundary conditions are incorporated by the design of a feedback loop. The result is a discrete-time semi-analytical model for the particle concentration in the channel. The model is validated by comparison to particle-based simulations. These numerical experiments reveal that the particle concentration of the proposed semi-analytical model and the particle-based model are in excellent agreement. The analytical form of the proposed solution provides several benefits over purely numerical models, e.g. high flexibility, existence of low run-time algorithms, extendability to several kinds of boundary conditions, and analytical connection to parameters from communication theory.

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Maximilian Schäfer, Wayan Wicke, Rudolf Rabenstein, Robert Schober. 2018-03-28. Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force. https://arxiv.org/abs/1803.10848

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