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 Differential Equations01:27

Linear Differential Equations

140
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
140
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.4K
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...
1.4K
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

513
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
513
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

5.1K
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....
5.1K
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1.1K
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

2.5K
Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations:...
2.5K

You might also read

Related Articles

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

Sort by
Same author

Heterogeneous model for superdiffusive movement of dense core vesicles in C. elegans.

Scientific reports·2025
Same author

Model for random internalization of nanoparticles by cells.

Physical review. E·2024
Same author

The role of kinesin-1 in neuronal dense core vesicle transport, locomotion and lifespan regulation in C. elegans.

Journal of cell science·2024
Same author

Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway.

Entropy (Basel, Switzerland)·2024
Same author

Population heterogeneity in the fractional master equation, ensemble self-reinforcement, and strong memory effects.

Physical review. E·2023
Same author

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells.

Scientific reports·2023

Related Experiment Video

Updated: Mar 24, 2026

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
09:17

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

11.3K

Single integrodifferential wave equation for a Lévy walk.

Sergei Fedotov1

  • 1School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review. E
|March 18, 2016
PubMed
Summary

We developed a new wave equation for classical one-dimensional Lévy walks, applicable at all times. This generalized equation describes anomalous diffusion and reaction-transport systems.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Classical random walks often use Markovian assumptions, limiting their applicability to complex systems.
  • Existing models like the telegraph equation are restricted to specific switching time distributions and long-time limits.

Purpose of the Study:

  • To derive a universal integrodifferential wave equation for classical one-dimensional Lévy walks with continuous paths.
  • To generalize existing persistent random walk models and explore non-Markovian dynamics.
  • To investigate wave propagation in reaction-transport systems with Lévy diffusion.

Main Methods:

  • Derivation of a single integrodifferential wave equation incorporating a classical wave operator and memory integrals.
  • Analysis of non-Markovian cases with gamma and power-law distributed random switching times.

More Related Videos

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

12.0K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K

Related Experiment Videos

Last Updated: Mar 24, 2026

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods
09:17

Experimental Investigation of the Flow Structure over a Delta Wing Via Flow Visualization Methods

Published on: April 23, 2018

11.3K
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

12.0K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
  • Implementation of a Kolmogorov-Petrovsky-Piskounov type nonlinear reaction term.

    • Main Results:

    • The derived equation is valid at all times and does not rely on large-scale approximations.
    • It generalizes the Cattaneo equation for persistent random walks with exponential switching times.
    • Asymptotic solutions were obtained for the strong anomalous diffusion case, and wave propagation in reaction-transport systems was analyzed.

    Conclusions:

    • The new wave equation provides a comprehensive framework for studying Lévy walks beyond traditional limitations.
    • This work advances the understanding of anomalous diffusion and reaction-transport phenomena.
    • The findings have implications for modeling complex systems exhibiting non-Markovian behavior.