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

Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

586
Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures enhance...
586
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

4.1K
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...
4.1K
Surface Tension of Fluid01:22

Surface Tension of Fluid

2.0K
Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies...
2.0K
Transformation of Plane Stress01:18

Transformation of Plane Stress

877
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
877
Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

607
In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
607
Hydrostatic Pressure Force on a Curved Surface01:04

Hydrostatic Pressure Force on a Curved Surface

2.7K
Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...
2.7K

You might also read

Related Articles

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

Sort by
Same author

Parameter identification problems in the modelling of cell motility.

Journal of mathematical biology·2014
Same author

Modelling cell motility and chemotaxis with evolving surface finite elements.

Journal of the Royal Society, Interface·2012
Same journal

Inverse FIP effect plasma in the solar atmosphere: a synthesis of current understanding and new insights from AR 11967.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Signs of sulfur fractionation under high magnetic field strength.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

First ionization potential fractionation of sulfur observed with spectral imaging of the coronal environment.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Chromospheric dynamics and turbulence regulate the solar FIP effect.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Exploring the link between wave activity in the photospheric velocity driver and the FIP bias in the solar corona.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Radiative hydrodynamic simulations of first ionization potential fractionation in solar flares.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Apr 5, 2026

Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

7.0K

A Stefan problem on an evolving surface.

Amal Alphonse1, Charles M Elliott2

  • 1Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK a.c.alphonse@warwick.ac.uk.

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

This study addresses the Stefan problem on evolving surfaces, proving well-posedness for weak solutions with L(1) data. Novel function spaces and regularization techniques were developed for this complex mathematical challenge.

Keywords:
Stefan problemfree boundary problemsfunction spaces for evolving domainsparabolic equations on moving hypersurfaces

More Related Videos

Surrogate Model Development for Digital Experiments in Welding
09:17

Surrogate Model Development for Digital Experiments in Welding

Published on: March 28, 2025

2.1K
Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Published on: January 6, 2023

3.4K

Related Experiment Videos

Last Updated: Apr 5, 2026

Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

7.0K
Surrogate Model Development for Digital Experiments in Welding
09:17

Surrogate Model Development for Digital Experiments in Welding

Published on: March 28, 2025

2.1K
Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Published on: January 6, 2023

3.4K

Area of Science:

  • Partial Differential Equations
  • Geometric Analysis
  • Mathematical Physics

Background:

  • The Stefan problem models phase transitions, often involving evolving boundaries.
  • Analyzing these problems on dynamic surfaces presents significant mathematical challenges.

Purpose of the Study:

  • To establish the well-posedness of weak solutions for a Stefan problem on evolving hypersurfaces.
  • To extend existing solution methodologies to handle L(1) data, a more general case.

Main Methods:

  • Development of specialized function spaces tailored for evolving surfaces.
  • Application of regularization techniques to address nonlinearities.
  • Utilization of fixed-point theorems for existence proofs.
  • Employing duality methods to demonstrate continuous dependence.

Main Results:

  • Established well-posedness for weak solutions with L(1) data.
  • Successfully handled equations on evolving surfaces using novel function spaces.
  • Demonstrated existence of solutions for L(infinity) data via regularization.

Conclusions:

  • The developed framework provides a robust method for analyzing Stefan problems on evolving hypersurfaces.
  • The results extend the applicability of these models to a broader range of data conditions.