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Related Experiment Video

Updated: Mar 7, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Wavenumber selection in coupled transport equations.

Arnd Scheel1, Angela Stevens2

  • 1School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN, 55455, USA. scheel@umn.edu.

Journal of Mathematical Biology
|February 23, 2017
PubMed
Summary
This summary is machine-generated.

Nonlinearity in tumbling rates creates diverse wave patterns in run-and-tumble dynamics. This study reveals a selection mechanism for wave numbers, potentially explaining myxobacteria colony patterns.

Keywords:
Balance lawsCoupled transport equationsInvasion frontsStanding waveTraveling waveWavenumber selection

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Area of Science:

  • Mathematical modeling
  • Theoretical physics
  • Biophysics

Background:

  • Run-and-tumble dynamics describe the movement of microorganisms like bacteria.
  • Pattern formation is crucial for understanding collective behaviors in biological systems.
  • Wavenumber selection is a key phenomenon in pattern formation.

Purpose of the Study:

  • To investigate wavenumber selection mechanisms in a minimal run-and-tumble model.
  • To identify how nonlinearity influences pattern formation.
  • To explore potential explanations for observed rippling patterns in myxobacteria.

Main Methods:

  • Development of a minimal mathematical model for run-and-tumble dynamics.
  • Analysis of the model to identify traveling- and standing-wave solutions.
  • Investigation of nonlinearity in tumbling rates as a driver for pattern selection.

Main Results:

  • Nonlinearity in tumbling rates leads to a wide range of spatio-temporal wave patterns.
  • A subtle selection mechanism for wavenumbers of periodic waves was identified.
  • The model predicts conditions that could generate observed rippling patterns.

Conclusions:

  • Nonlinear tumbling rates are essential for complex pattern formation in run-and-tumble systems.
  • The study provides a theoretical framework for understanding wavenumber selection.
  • Findings may offer insights into the collective behavior and colony dynamics of myxobacteria.