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

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.3K
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

1.7K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.7K
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

515
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
515
Limits to Natural Selection01:38

Limits to Natural Selection

31.5K
Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.
31.5K
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

134
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
134
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

121
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
121

You might also read

Related Articles

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

Sort by
Same author

On the dynamics of point vortices for the two-dimensional Euler equation with <i>L</i><sup></sup> vorticity.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

Insights into capacity-constrained optimal transport.

Proceedings of the National Academy of Sciences of the United States of America·2013
Same author

Phase transitions and symmetry breaking in singular diffusion.

Proceedings of the National Academy of Sciences of the United States of America·2003
Same journal

Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics.

Archive for rational mechanics and analysis·2026
Same journal

An Inverse Signorini Obstacle Problem.

Archive for rational mechanics and analysis·2026
Same journal

Global Results for Weakly Dispersive KP-II Equations on the Cylinder.

Archive for rational mechanics and analysis·2026
Same journal

Finite Time Blow-Up for the Hypodissipative Navier Stokes Equations with a Force in <math><mrow><msubsup><mi>L</mi> <mi>t</mi> <mn>1</mn></msubsup> <msubsup><mi>C</mi> <mi>x</mi> <mrow><mn>1</mn> <mo>,</mo> <mi>ϵ</mi></mrow></msubsup> <mo>∩</mo> <msubsup><mi>L</mi> <mi>t</mi> <mi>∞</mi></msubsup> <msubsup><mi>L</mi> <mi>x</mi> <mn>2</mn></msubsup></mrow></math>.

Archive for rational mechanics and analysis·2026
Same journal

Separation of Time Scales in Weakly Interacting Diffusions.

Archive for rational mechanics and analysis·2026
Same journal

Long-Time Dynamics for the Kelvin-Helmholtz Equations Close to Circular Vortex Sheets.

Archive for rational mechanics and analysis·2026
See all related articles

Related Experiment Video

Updated: Aug 8, 2025

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

8.6K

Asymptotics Near Extinction for Nonlinear Fast Diffusion on a Bounded Domain.

Beomjun Choi1, Robert J McCann2, Christian Seis3

  • 1Department of Mathematics, POSTECH, Pohang, Gyeongbuk South Korea.

Archive for Rational Mechanics and Analysis
|March 2, 2023
PubMed
Summary
This summary is machine-generated.

Fast diffusion equations with vanishing boundary conditions lead to finite-time extinction. This study quantifies convergence rates, revealing exponential or algebraic speeds depending on non-integrable zero modes, confirming a long-standing conjecture.

More Related Videos

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.8K
From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

11.5K

Related Experiment Videos

Last Updated: Aug 8, 2025

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

8.6K
Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.8K
From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope
15:10

From Fast Fluorescence Imaging to Molecular Diffusion Law on Live Cell Membranes in a Commercial Microscope

Published on: October 9, 2014

11.5K

Area of Science:

  • Partial Differential Equations
  • Mathematical Physics
  • Nonlinear Dynamics

Background:

  • Fast diffusion equations on bounded domains with vanishing boundary trace exhibit finite-time extinction.
  • The vanishing profile is determined by the initial data, but convergence rates are not fully understood.

Purpose of the Study:

  • To quantify the rate of convergence to the vanishing profile in rescaled variables, uniformly in relative error.
  • To analyze the influence of non-integrable zero modes on the convergence rate.
  • To refine and confirm existing conjectures regarding nonlinear dynamics and eigenmode approximation.

Main Methods:

  • Analysis of Sobolev-subcritical fast diffusion equations.
  • Rescaling of variables to study convergence rates.
  • Investigation of spectral properties and zero modes.
  • Development of a new, simpler analytical approach.

Main Results:

  • Convergence rates are either exponentially fast (linked to spectral gap) or algebraically slow (in the presence of non-integrable zero modes).
  • Nonlinear dynamics are well-approximated by exponentially decaying eigenmodes up to twice the spectral gap.
  • A new method accommodates zero modes, improving on prior results.

Conclusions:

  • The study provides a comprehensive understanding of extinction dynamics in fast diffusion.
  • It confirms and refines a 1980 conjecture by Berryman and Holland.
  • The developed approach offers a more robust analysis, particularly in cases with non-isolated vanishing profiles.