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

Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.9K
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...
1.9K
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

2.1K
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....
2.1K
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

1.2K
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...
1.2K
Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

1.4K
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.
1.4K
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

482
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
482
Improper Integrals: Discontinuous Integrands01:28

Improper Integrals: Discontinuous Integrands

165
Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
165

You might also read

Related Articles

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

Sort by
Same author

Nature's forms are frilly, flexible, and functional.

The European physical journal. E, Soft matter·2021
Same author

Buckling sheets open a door to understanding self-organization in soft matter.

Proceedings of the National Academy of Sciences of the United States of America·2019
See all related articles

Related Experiment Video

Updated: Apr 25, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.2K

Sharp interfaces in two-dimensional free boundary problems: interface calculation via matched conformal maps.

Stuart Kent1, Shankar C Venkataramani2

  • 1Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new multiscale conformal mapping method to accurately model free boundary problems in electromechanical systems. This approach overcomes limitations of single-scale methods, enabling better analysis of fluid interfaces with sharp corners.

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

7.8K
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

8.2K

Related Experiment Videos

Last Updated: Apr 25, 2026

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces
08:05

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Published on: September 9, 2022

2.2K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

7.8K
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

8.2K

Area of Science:

  • Applied Mathematics
  • Fluid Dynamics
  • Electromagnetics

Background:

  • Free boundary problems in two-fluid electromechanical systems are governed by electrostatic forces, gravity, and surface tension.
  • Sharp corners or singularities in the fluid interface impede traditional single-scale numerical conformal mapping methods due to node crowding.
  • Existing methods struggle to resolve both sharp and smooth regions of the boundary effectively.

Purpose of the Study:

  • To develop a novel multiscale conformal mapping method for analyzing free boundary problems in electromechanical systems.
  • To overcome the limitations of single-scale methods in resolving sharp interface features.
  • To enable accurate numerical simulations of systems with complex boundary geometries.

Main Methods:

  • Development of an adaptive, multiscale conformal mapping technique.
  • Exploitation of scale separation between sharp and smooth boundary regions.
  • Stitching of conformal maps computed on different scales to create a globally accurate solution.

Main Results:

  • Successfully implemented a multiscale conformal mapping method capable of handling boundary singularities.
  • Demonstrated the method's effectiveness in resolving poorly resolved regions common in single-scale approaches.
  • Validated the approach on a two-fluid electromechanical model problem.

Conclusions:

  • The proposed multiscale conformal mapping method provides a robust solution for free boundary problems with complex interface geometries.
  • This adaptive approach overcomes the crowding phenomenon, enabling accurate analysis of previously intractable electromechanical systems.
  • The method offers a significant advancement for numerical simulations in fluid dynamics and electromagnetics.