Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Singularity Functions for Shear

Singularity Functions for Shear

In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...

Deflection of a Beam

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...

Standing Waves

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...

Wave Parameters

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...

Propagation of Waves

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

Singularity Functions for Bending Moment

Singularity Functions for Bending Moment

Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...

You might also read

Related Articles

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

Sort by

Same author

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 author

Quantum tunneling and its absence in deep wells and strong magnetic fields.

Proceedings of the National Academy of Sciences of the United States of America·2025

Same author

Dating app users: Differences between middle-aged men and women.

International journal of clinical and health psychology : IJCHP·2024

Same author

Attitudes towards the sexuality of adults with intellectual disabilities: Family, staff, community and student perspectives.

Journal of intellectual disabilities : JOID·2024

Same author

The relationship of stereotypes, social distance and sexuality knowledge with attitudes towards sexuality of people with mild intellectual disabilities.

Journal of applied research in intellectual disabilities : JARID·2024

Same author

Psychological and Psychosexual Adjustment in University Students as a Function of Sexual Activity and Relationship Type.

International journal of sexual health : official journal of the World Association for Sexual Health·2024

Search research articles

Related Experiment Video

Updated: May 26, 2026

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Splash singularity for water waves.

Angel Castro¹, Diego Córdoba, Charles L Fefferman

¹Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera, 13-15, Campus Cantoblanco, 28049 Madrid, Spain.

Proceedings of the National Academy of Sciences of the United States of America

|January 6, 2012

Summary

This summary is machine-generated.

Researchers proved that the interface smoothness for the 2D water-wave equation breaks down in finite time. Numerical evidence supports solutions collapsing into splash singularities, demonstrating finite-time breakdown for water waves.

More Related Videos

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Published on: August 27, 2013

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Related Experiment Videos

Last Updated: May 26, 2026

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Published on: August 27, 2013

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System

Published on: May 9, 2021

Area of Science:

Fluid dynamics
Nonlinear partial differential equations
Mathematical analysis

Background:

The two-dimensional (2D) water-wave equation models surface water dynamics.
Understanding the long-term behavior and potential singularities of these waves is crucial.
Previous studies have explored wave breaking, but finite-time breakdown of interface smoothness requires further investigation.

Purpose of the Study:

To investigate the breakdown of interface smoothness for the 2D water-wave equation with smooth initial data.
To demonstrate the existence of solutions that develop splash singularities in finite time.
To provide a stability result for such phenomena.

Main Methods:

Analytical techniques to prove the breakdown of interface smoothness.
Numerical simulations to support the existence of splash singularities.
Stability analysis of solutions exhibiting finite-time collapse.

Main Results:

Demonstrated finite-time breakdown of interface smoothness for the 2D water-wave equation.
Established the existence of solutions that evolve from smooth initial data to form splash singularities.
Provided numerical evidence consistent with theoretical predictions of wave collapse.

Conclusions:

The interface smoothness of solutions to the 2D water-wave equation is not guaranteed to be preserved indefinitely.
Splash singularities represent a physically relevant phenomenon of finite-time wave collapse.
The study contributes to a deeper understanding of nonlinear wave phenomena and their potential for singular behavior.