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Related Concept Videos

Torsional Pendulum01:09

Torsional Pendulum

A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected.
As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
Simple Pendulum01:10

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily life, pendulums have many uses, such as in clocks, on a swing set, and on a sinker on a fishing line.
The period of a simple pendulum depends on two factors: its length and the acceleration due to gravity. The period is completely independent of any other factors, such as mass or maximum displacement. For small displacements, a pendulum is...
Physical Pendulum01:06

Physical Pendulum

When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
When dealing with complicated systems, the mass moment of inertia is an important parameter, as it describes the mass...
Magnetic Damping01:17

Magnetic Damping

Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit the...
Dynamics of Circular Motion01:30

Dynamics of Circular Motion

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
The Contractile Ring02:15

The Contractile Ring

Contractile rings are composed of microfilaments and are responsible for separating the daughter cells during cytokinesis. Contractile ring assembly proceeds along with other cell cycle events; however, very few mechanistic details are known about the timing and coordination of the contractile rings with the cell cycle.
A small GTPase, RhoA, controls the function and assembly of the contractile ring. RhoA belongs to the Ras superfamily of proteins. The activation of formins by RhoA promotes...

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The Assembly and Application of 'Shear Rings': A Novel Endothelial Model for Orbital, Unidirectional and Periodic Fluid Flow and Shear Stress
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Pinned scroll rings in an excitable system.

Zulma A Jiménez1, Bradley Marts, Oliver Steinbock

  • 1Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA.

Physical Review Letters
|August 8, 2009
PubMed
Summary

Three-dimensional spiral waves in chemical reactions can be stabilized by defects. This study shows how these waves are pinned, preventing collapse and revealing insights into wave dynamics.

Area of Science:

  • Chemical kinetics
  • Complex systems

Background:

  • Three-dimensional spiral waves are complex spatiotemporal patterns observed in various chemical and biological systems.
  • Understanding the stability and dynamics of these waves is crucial for comprehending phenomena like cardiac arrhythmias and pattern formation.

Purpose of the Study:

  • To investigate the pinning of three-dimensional spiral waves to unexcitable heterogeneities in the Belousov-Zhabotinsky reaction.
  • To determine the conditions under which heterogeneities can prevent the collapse of scroll rings.
  • To explore the relationship between wave filament structure, phase gradients, and the forced Burgers equation.

Main Methods:

  • Experimental observation of three-dimensional spiral waves in the Belousov-Zhabotinsky reaction.
  • Introduction of unexcitable heterogeneities to study wave pinning phenomena.

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  • Analysis of wave filament dynamics and phase gradients.
  • Comparison of experimental results with algebraic solutions of the forced Burgers equation.

    • Main Results:

    • Three-dimensional spiral waves are effectively pinned by unexcitable heterogeneities.
    • Pinning can stabilize scroll rings even when heterogeneities do not span the entire wave filament.
    • Frequency differences lead to stationary phase gradients in cases of incomplete pinning.
    • Observed twist patterns and frequencies align with solutions of the forced Burgers equation.

    Conclusions:

    • Unexcitable heterogeneities serve as crucial pinning sites for stabilizing three-dimensional spiral waves.
    • The study provides a framework for understanding scroll wave dynamics and phase coupling through the forced Burgers equation.
    • These findings offer insights into controlling complex wave phenomena in reaction-diffusion systems.