Signal transmission in chemical systems: Propagation of chemical waves through capillary tubes

A. Tóth, V. Gáspár, Kenneth Showalter

Research output: Contribution to journalArticle

112 Citations (Scopus)

Abstract

The propagation of chemical waves through narrow channels has been investigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are connected by precision-bore capillary tubes of different internal diameters. A wave initiated on one side of an otherwise impenetrable barrier enters and travels through the capillary tube, forming a hemisphere of excited solution at the exit. When the tube diameter is greater than a critical value, the excitation serves to initiate a circular wave in the second compartment; otherwise, the hemisphere collapses and no wave is initiated. Electrochemically generated periodic wave trains give rise to resonance patterns characterized by firing numbers 1/n, where n = 1,2, etc. is the number of waves entering the tube for every wave exiting. These firing numbers correspond to one branch of a Farey tree; higher periodic resonances in modeling calculations indicate that more fully developed Farey sequences may also occur. A one-dimensional mapping procedure is proposed to describe the appearance and ordering of the resonance patterns.

Original languageEnglish
Pages (from-to)522-531
Number of pages10
JournalJournal of Physical Chemistry
Volume98
Issue number2
Publication statusPublished - 1994

Fingerprint

Capillary tubes
capillary tubes
signal transmission
propagation
hemispheres
tubes
compartments
Wave propagation
travel
cavities
excitation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

Signal transmission in chemical systems : Propagation of chemical waves through capillary tubes. / Tóth, A.; Gáspár, V.; Showalter, Kenneth.

In: Journal of Physical Chemistry, Vol. 98, No. 2, 1994, p. 522-531.

Research output: Contribution to journalArticle

@article{9fb10878b6e34b17b1827df181557bdc,
title = "Signal transmission in chemical systems: Propagation of chemical waves through capillary tubes",
abstract = "The propagation of chemical waves through narrow channels has been investigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are connected by precision-bore capillary tubes of different internal diameters. A wave initiated on one side of an otherwise impenetrable barrier enters and travels through the capillary tube, forming a hemisphere of excited solution at the exit. When the tube diameter is greater than a critical value, the excitation serves to initiate a circular wave in the second compartment; otherwise, the hemisphere collapses and no wave is initiated. Electrochemically generated periodic wave trains give rise to resonance patterns characterized by firing numbers 1/n, where n = 1,2, etc. is the number of waves entering the tube for every wave exiting. These firing numbers correspond to one branch of a Farey tree; higher periodic resonances in modeling calculations indicate that more fully developed Farey sequences may also occur. A one-dimensional mapping procedure is proposed to describe the appearance and ordering of the resonance patterns.",
author = "A. T{\'o}th and V. G{\'a}sp{\'a}r and Kenneth Showalter",
year = "1994",
language = "English",
volume = "98",
pages = "522--531",
journal = "Journal of Physical Chemistry",
issn = "0022-3654",
publisher = "American Chemical Society",
number = "2",

}

TY - JOUR

T1 - Signal transmission in chemical systems

T2 - Propagation of chemical waves through capillary tubes

AU - Tóth, A.

AU - Gáspár, V.

AU - Showalter, Kenneth

PY - 1994

Y1 - 1994

N2 - The propagation of chemical waves through narrow channels has been investigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are connected by precision-bore capillary tubes of different internal diameters. A wave initiated on one side of an otherwise impenetrable barrier enters and travels through the capillary tube, forming a hemisphere of excited solution at the exit. When the tube diameter is greater than a critical value, the excitation serves to initiate a circular wave in the second compartment; otherwise, the hemisphere collapses and no wave is initiated. Electrochemically generated periodic wave trains give rise to resonance patterns characterized by firing numbers 1/n, where n = 1,2, etc. is the number of waves entering the tube for every wave exiting. These firing numbers correspond to one branch of a Farey tree; higher periodic resonances in modeling calculations indicate that more fully developed Farey sequences may also occur. A one-dimensional mapping procedure is proposed to describe the appearance and ordering of the resonance patterns.

AB - The propagation of chemical waves through narrow channels has been investigated. Thin layers of excitable Belousov-Zhabotinsky mixtures are connected by precision-bore capillary tubes of different internal diameters. A wave initiated on one side of an otherwise impenetrable barrier enters and travels through the capillary tube, forming a hemisphere of excited solution at the exit. When the tube diameter is greater than a critical value, the excitation serves to initiate a circular wave in the second compartment; otherwise, the hemisphere collapses and no wave is initiated. Electrochemically generated periodic wave trains give rise to resonance patterns characterized by firing numbers 1/n, where n = 1,2, etc. is the number of waves entering the tube for every wave exiting. These firing numbers correspond to one branch of a Farey tree; higher periodic resonances in modeling calculations indicate that more fully developed Farey sequences may also occur. A one-dimensional mapping procedure is proposed to describe the appearance and ordering of the resonance patterns.

UR - http://www.scopus.com/inward/record.url?scp=25844503764&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25844503764&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:25844503764

VL - 98

SP - 522

EP - 531

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

SN - 0022-3654

IS - 2

ER -