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

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
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.8K
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...
1.8K
Protein Diffusion in the Membrane01:24

Protein Diffusion in the Membrane

6.2K
Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
6.2K
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
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
Area Problem01:26

Area Problem

240
Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
240

You might also read

Related Articles

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

Sort by
Same author

Evolution Equations on Co-evolving Graphs: Long-Time Behaviour and the Graph-Continuity Equation.

Journal of nonlinear science·2026
Same author

Supramolecular chemistry in solution and solid-gas interfaces: synthesis and photophysical properties of monocolor and bicolor fluorescent sensors for barium tagging in neutrinoless double beta decay.

RSC applied interfaces·2024
Same author

Synthesis of Fluorescent Pyrrolo[1,2-<i>a</i>]pyrimidines from Fischer Carbene Complexes as Building Blocks.

The Journal of organic chemistry·2023
Same author

Singular boundary behaviour and large solutions for fractional elliptic equations.

Journal of the London Mathematical Society·2023
Same author

Evolution of a structured cell population endowed with plasticity of traits under constraints on and between the traits.

Journal of mathematical biology·2022
Same author

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical, Photophysical and Electrochemical Evaluation.

Chemistry (Weinheim an der Bergstrasse, Germany)·2022

Related Experiment Video

Updated: Apr 5, 2026

Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes
10:43

Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes

Published on: July 19, 2022

3.0K

Some free boundary problems involving non-local diffusion and aggregation.

José Antonio Carrillo1, Juan Luis Vázquez2

  • 1Department of Mathematics, Imperial College London, London SW7 2AZ, UK juanluis.vazquez@uam.es.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 12, 2015
PubMed
Summary
This summary is machine-generated.

This study explores evolution processes using degenerate parabolic equations, focusing on anomalous diffusion and aggregation effects. Research advances understanding of long-range effects and complex equilibria in diffusion theory.

Keywords:
aggregationinteraction energynon-local diffusionobstacle problems

More Related Videos

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

8.6K
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

10.8K

Related Experiment Videos

Last Updated: Apr 5, 2026

Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes
10:43

Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes

Published on: July 19, 2022

3.0K
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

8.6K
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

10.8K

Area of Science:

  • Mathematical Physics
  • Partial Differential Equations
  • Diffusion Theory

Background:

  • Degenerate parabolic equations are crucial for modeling diffusion processes.
  • Recent advancements focus on anomalous diffusion and aggregation phenomena.
  • Free boundaries present significant challenges in these models.

Purpose of the Study:

  • To present recent progress in the study of evolution processes governed by degenerate parabolic equations.
  • To investigate models incorporating anomalous diffusion with long-range effects.
  • To analyze the interplay between diffusion and aggregation leading to complex equilibria.

Main Methods:

  • Utilizing fractional operators and kernels with large tails to model anomalous diffusion.
  • Developing mathematical frameworks for degenerate parabolic equations with free boundaries.
  • Analyzing long-term behaviors and equilibria in combined diffusion-aggregation systems.

Main Results:

  • Demonstrated progress in understanding evolution processes with free boundaries.
  • Characterized anomalous diffusion through fractional operators and large-tail kernels.
  • Identified delicate long-term equilibria arising from diffusion-aggregation effects.

Conclusions:

  • The study advances the understanding of complex diffusion phenomena.
  • New insights into modeling anomalous diffusion and aggregation are provided.
  • Further research is needed to fully describe the emergent long-term equilibria.