Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

460
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
460
Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

1.4K
Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
1.4K
Linearization and Approximation01:26

Linearization and Approximation

233
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
233
Equations of Wave Motion01:02

Equations of Wave Motion

5.6K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
5.6K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

502
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
502
Convergence of Fourier Series01:21

Convergence of Fourier Series

623
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
623

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reversal of rocuronium-induced fixed pupillary dilation by sugammadex in ICU patients with COVID-19.

British journal of anaesthesia·2024
Same author

A case of <i>Flavonifractor plautii</i> blood stream infection in a severe burn patient and a review of the literature.

Acta clinica Belgica·2021
Same author

First-order synchronization transition in a large population of strongly coupled relaxation oscillators.

Science advances·2020
Same author

Transition from spiral wave chimeras to phase cluster states.

Scientific reports·2020
Same author

Active poroelastic two-phase model for the motion of physarum microplasmodia.

PloS one·2019
Same author

Directed adaptation of synchronization levels in oscillator communities.

Chaos (Woodbury, N.Y.)·2019
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: May 4, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K

Analytical approximations for spiral waves.

Jakob Löber1, Harald Engel1

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, EW 7-1, 10623 Berlin, Germany.

Chaos (Woodbury, N.Y.)
|January 7, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a non-perturbative analytical solution for spiral waves in excitable media. The derived equations accurately predict spiral wave behavior across various core sizes, improving upon existing models.

More Related Videos

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

5.3K
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

9.8K

Related Experiment Videos

Last Updated: May 4, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

10.3K
Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

5.3K
Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

9.8K

Area of Science:

  • Nonlinear dynamics
  • Mathematical modeling
  • Excitable media

Background:

  • Spiral waves are complex patterns observed in various biological and chemical systems.
  • Understanding their dynamics, particularly rotation frequency and core structure, is crucial for predicting system behavior.
  • Existing models often rely on perturbative approaches or extensive numerical simulations.

Purpose of the Study:

  • To develop a non-perturbative analytical method for solving kinematic equations of spiral waves.
  • To establish an accurate relationship between rotation frequency and core radius for free and pinned spiral waves.
  • To provide analytical approximations for spiral wave shapes.

Main Methods:

  • Derivation of an implicit analytical relation from the eikonal equation for wave fronts.
  • Comparison of analytical predictions with numerical solutions of the linear eikonal equation.
  • Development of an equivalent dependence for pinned spiral waves with Neumann boundary conditions.

Main Results:

  • The analytical predictions show good agreement with numerical solutions for free spiral waves across a range of core radii.
  • An improved Ω(R(+)) dependence is derived for spiral waves pinned to a circular defect.
  • Analytical approximations for the shapes of both free and pinned spiral waves are obtained.

Conclusions:

  • The non-perturbative approach provides a robust analytical framework for spiral wave dynamics.
  • The derived relations offer accurate predictions for rotation frequency and core radius.
  • Further investigation is needed to understand the model's limitations regarding medium excitability.