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

Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

467
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...
467
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

805
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
805
Curve Equations01:17

Curve Equations

115
Curves are essential geometric elements characterized by tangent distance, chord length, middle ordinate, and total arc length. These measurements are crucial in understanding a curve's geometric and spatial properties and are defined by the relationship between its radius and its central angle.The tangent distance (T) refers to the straight-line measurement from the intersection point of two tangents to either the start or end of the curve. This distance is influenced by the curve's radius (R)...
115
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

15.5K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
15.5K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

708
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...
708
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

164
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,...
164

You might also read

Related Articles

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

Sort by
Same author

A Spatiotemporal Perspective on Dynamical Computation in Neural Information Processing Systems.

ArXiv·2026
Same author

Geometric perspective of linear stability of q-states in finite Kuramoto networks on circulant graphs.

Physical review. E·2025
Same author

Spatially Selective Metal Nanoparticle Deposition via Cathodic Corrosion of an Ultramicroelectrode Surface Probe.

Langmuir : the ACS journal of surfaces and colloids·2025
Same author

The Role of Modality-specific Brain Regions in Statistical Learning: Insights from Intracranial Neural Entrainment.

Journal of cognitive neuroscience·2025
Same author

Developing and Testing an Online Portal for Virtual Navigation for Asian American Patients With Cancer: Pilot Feasibility Study.

JMIR cancer·2025
Same author

Electrochemical Liquid-Liquid-Solid Electrodeposition of Ge Nanowire Films with Low Reflectance for Light Management Coatings and High Mass-Loading for High Areal Capacity Li<sup>+</sup> Battery Anodes.

ACS applied materials & interfaces·2025

Related Experiment Video

Updated: Oct 20, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.1K

Algebraic approach to the Kuramoto model.

Lyle Muller1, Ján Mináč1, Tung T Nguyen1

  • 1Department of Mathematics, Western University, London, Ontario, Canada N6A 3K7.

Physical Review. E
|September 16, 2021
PubMed
Summary

Researchers developed a complex-valued matrix formulation for the Kuramoto model. This new approach offers an exact solution, providing analytical insights into nonlinear dynamics and synchronization phenomena.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Mathematical Physics

Background:

  • The Kuramoto model is a fundamental tool for studying synchronization in coupled oscillator systems.
  • Analyzing individual realizations of the Kuramoto model can be analytically challenging.

Purpose of the Study:

  • To introduce a novel complex-valued matrix formulation for the Kuramoto model with attractive sine coupling.
  • To derive an exact analytical solution for this complex-valued formulation.
  • To demonstrate the utility of higher-order number fields in analyzing nonlinear dynamics.

Main Methods:

  • Formulation of the Kuramoto model using complex-valued matrices.
  • Derivation of an exact analytical solution for the complex-valued model.
  • Analysis of the properties and implications of the complex-valued formulation.

More Related Videos

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.6K

Related Experiment Videos

Last Updated: Oct 20, 2025

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.1K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.6K

Main Results:

  • An exact solution for the complex-valued Kuramoto model was successfully derived.
  • The complex-valued formulation's argument accurately represents the original Kuramoto dynamics.
  • The study provides analytical insight into individual realizations of the model.

Conclusions:

  • The complex-valued formulation offers a tractable analytical approach to the Kuramoto model.
  • Reformulating nonlinear dynamics in higher-order number fields can yield powerful analytical tools.
  • This work opens new avenues for studying synchronization and complex systems.