Modeling 3-D diffusion using queueing networks

Vahraz Honary, Marissa Nitz, Beata J. Wysocki, Tadeusz A. Wysocki

Research output: Contribution to journalArticle

Abstract

The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick's law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski's approach.

Original languageEnglish (US)
Pages (from-to)17-23
Number of pages7
JournalBioSystems
Volume179
DOIs
StatePublished - May 2019

Fingerprint

Queueing networks
3D Modeling
Queueing Networks
Albert Einstein
Kolmogorov-Smirnov Test
Diffusion Model
Fick's laws
Standard deviation
3D
Brownian motion
Brownian movement
Partial differential equation
Nonparametric Statistics
Numerical Methods
Molecules
Partial differential equations
Numerical methods
Simulation
Model

Keywords

  • 3-D simulation
  • Brownian motion
  • Diffusion
  • Queuing networks

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics

Cite this

Modeling 3-D diffusion using queueing networks. / Honary, Vahraz; Nitz, Marissa; Wysocki, Beata J.; Wysocki, Tadeusz A.

In: BioSystems, Vol. 179, 05.2019, p. 17-23.

Research output: Contribution to journalArticle

Honary, Vahraz ; Nitz, Marissa ; Wysocki, Beata J. ; Wysocki, Tadeusz A. / Modeling 3-D diffusion using queueing networks. In: BioSystems. 2019 ; Vol. 179. pp. 17-23.
@article{425296818c1d455bac859e01caef5f81,
title = "Modeling 3-D diffusion using queueing networks",
abstract = "The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick's law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski's approach.",
keywords = "3-D simulation, Brownian motion, Diffusion, Queuing networks",
author = "Vahraz Honary and Marissa Nitz and Wysocki, {Beata J.} and Wysocki, {Tadeusz A.}",
year = "2019",
month = "5",
doi = "10.1016/j.biosystems.2018.12.006",
language = "English (US)",
volume = "179",
pages = "17--23",
journal = "BioSystems",
issn = "0303-2647",
publisher = "Elsevier Ireland Ltd",

}

TY - JOUR

T1 - Modeling 3-D diffusion using queueing networks

AU - Honary, Vahraz

AU - Nitz, Marissa

AU - Wysocki, Beata J.

AU - Wysocki, Tadeusz A.

PY - 2019/5

Y1 - 2019/5

N2 - The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick's law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski's approach.

AB - The objective of this paper is to propose and then validate a new method for simulating molecular diffusion in a 3-D environment. Diffusion governing principles of Brownian motion have been discovered by Einstein and Smoluchowski. In a classical approach, diffusion is modeled using partial differential equations. However, solving those, even using numerical methods is usually time consuming, particularly in the case of an inhomogeneous environment. In this paper, we propose to use queueing networks to model diffusion of molecules as governed by Fick's law. The proposed model has been validated using the Kolmogorov-Smirnov test to compare results obtained from a simulation with theoretical standard deviations resulting from Einstein-Smoluchowski's approach.

KW - 3-D simulation

KW - Brownian motion

KW - Diffusion

KW - Queuing networks

UR - http://www.scopus.com/inward/record.url?scp=85061923950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061923950&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2018.12.006

DO - 10.1016/j.biosystems.2018.12.006

M3 - Article

C2 - 30594592

AN - SCOPUS:85061923950

VL - 179

SP - 17

EP - 23

JO - BioSystems

JF - BioSystems

SN - 0303-2647

ER -