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

Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

1.3K
Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
1.3K
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.6K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.6K
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

1.8K
When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity....
1.8K
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

778
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
778
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

922
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
922
Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

371
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
371

You might also read

Related Articles

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

Sort by
Same author

Smart strategies to navigate turbulent odor plumes reorienting to local wind.

ArXiv·2026
Same author

Spontaneous cortical vasodynamics form a multiscale propagation architecture in the awake brain.

bioRxiv : the preprint server for biology·2026
Same author

Rapid transcriptional response to a dynamic morphogen by time integration.

Current biology : CB·2026
Same author

Touch sensation: Convergent mechanical sensitivity between elephant and rat whiskers.

Current biology : CB·2026
Same author

Policy heterogeneity improves collective olfactory search in three-dimensional turbulence.

Physical review. E·2026
Same author

The neurovascular impulse response function differentially reflects intrinsic neuromodulation across cortical regions.

Nature neuroscience·2026

Related Experiment Video

Updated: Jan 12, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.0K

Defects, Parcellation, and Renormalized Negative Diffusivities in Nonhomogeneous Oscillatory Media.

Marie Sellier-Prono1, Massimo Cencini2, David Kleinfeld3,4

  • 1Sorbonne University, Ecole Normale Supérieure, Laboratoire de Physique, CNRS, PSL Research University, Paris 75005, France.

Physical Review Letters
|October 31, 2025
PubMed
Summary

Spatial nonhomogeneities synchronize oscillator clusters across frequency plateaus. Nonlinear effects and defects determine plateau amplitude or phase-locked states in this Ginzburg-Landau model.

More Related Videos

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.7K
Mechano-Node-Pore Sensing: A Rapid, Label-Free Platform for Multi-Parameter Single-Cell Viscoelastic Measurements
05:49

Mechano-Node-Pore Sensing: A Rapid, Label-Free Platform for Multi-Parameter Single-Cell Viscoelastic Measurements

Published on: December 2, 2022

3.1K

Related Experiment Videos

Last Updated: Jan 12, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.0K
Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Published on: September 8, 2016

10.7K
Mechano-Node-Pore Sensing: A Rapid, Label-Free Platform for Multi-Parameter Single-Cell Viscoelastic Measurements
05:49

Mechano-Node-Pore Sensing: A Rapid, Label-Free Platform for Multi-Parameter Single-Cell Viscoelastic Measurements

Published on: December 2, 2022

3.1K

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Spatial nonhomogeneities can induce synchronization in spatially extended oscillators.
  • Physiological rhythms often exhibit complex spatiotemporal dynamics and frequency gradients.

Purpose of the Study:

  • To fully characterize the phase diagram of a Ginzburg-Landau model with a frequency gradient.
  • To understand the formation and behavior of synchronized clusters and defects.

Main Methods:

  • Analysis of the Ginzburg-Landau model with a frequency gradient.
  • Mapping the linear spectrum to the non-Hermitian Bloch-Torrey equation.
  • Investigating nonlinear effects and saddle-node bifurcations.

Main Results:

  • Identified stable rest states for large gradients and diffusion.
  • Observed precursors of frequency plateaus growing from unstable complex eigenvalues.
  • Characterized defect formation via nonlinear diffusivity renormalization.
  • Determined scaling laws for defect number and length.

Conclusions:

  • Nonlinear effects dictate whether plateaus saturate or lock into a phase-locked state.
  • Defect dynamics are crucial for understanding synchronization patterns in heterogeneous oscillator systems.
  • The study provides a comprehensive phase diagram for frequency-gradient systems.