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

Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

3.7K
Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
3.7K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

590
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
590
Equations of Wave Motion01:02

Equations of Wave Motion

5.9K
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.
5.9K
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

4.1K
A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
4.1K
Deriving the Speed of Sound in a Liquid01:09

Deriving the Speed of Sound in a Liquid

566
As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
The speed of sound in fluids can be derived by considering a mechanical wave...
566
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.3K

You might also read

Related Articles

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

Sort by
Same author

Allee effects introduced by density dependent phenology.

Mathematical biosciences·2024
Same author

Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect.

Journal of mathematical biology·2024
Same author

Forced Traveling Waves in a Reaction-Diffusion Equation with Strong Allee Effect and Shifting Habitat.

Bulletin of mathematical biology·2023
Same author

Characterization of trial duration in traditional and emerging postural control measures.

Journal of biomechanics·2023
Same author

Can a barrier zone stop invasion of a population?

Journal of mathematical biology·2020
Same author

How Phenological Variation Affects Species Spreading Speeds.

Bulletin of mathematical biology·2018

Related Experiment Video

Updated: Aug 24, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K

Wave speed and critical patch size for integro-difference equations with a strong Allee effect.

Bingtuan Li1, Garrett Otto2

  • 1Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA. bing.li@louisville.edu.

Journal of Mathematical Biology
|October 22, 2022
PubMed
Summary

This study identifies conditions for wave speed in integro-difference equations with Allee effects. It establishes a critical patch size for habitat persistence, crucial for ecological modeling.

Keywords:
Allee effectCritical patch sizeEquilibriumIntegro-difference equationSpreading speedTraveling wave

More Related Videos

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.8K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° 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

11.7K

Related Experiment Videos

Last Updated: Aug 24, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K
Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.8K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° 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

11.7K

Area of Science:

  • Mathematical Biology
  • Ecological Modeling
  • Dynamical Systems

Background:

  • Integro-difference equations model population dynamics with spatial structure.
  • The Allee effect describes reduced per capita fitness at low population densities.
  • Habitat size and dispersal influence population persistence.

Purpose of the Study:

  • To determine conditions for the existence and positivity of wave speed in an integro-difference equation with a strong Allee effect.
  • To establish the existence of a critical patch size for population persistence in bounded habitats.
  • To analyze the relationship between wave speed, critical patch size, and Allee threshold.

Main Methods:

  • Analysis of integro-difference equations with strong Allee effects.
  • Derivation of simplified conditions for wave speed existence and positivity.
  • Development of an analytical integral formula for critical patch size using a Laplace dispersal kernel.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • Simplified conditions for wave speed existence and positivity were established for unbounded habitats.
  • The existence of a critical patch size was proven for bounded habitats.
  • A positive wave speed implies persistence above a critical habitat size; negative wave speed leads to extinction.
  • An analytical formula for critical patch size revealed multiple equilibrium solutions.

Conclusions:

  • Wave speed and critical patch size are key factors in determining population persistence in spatially structured environments with Allee effects.
  • The study provides a theoretical framework and numerical evidence for understanding ecological dynamics influenced by dispersal and density-dependent effects.
  • The findings are applicable to conservation biology and habitat management strategies.