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Partial Differential Equations

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...

Standing Electromagnetic Waves

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the superposition principle, so do electromagnetic waves. The superposition of an incident wave and a reflected electromagnetic wave produces a standing wave analogous to the standing waves created on a stretched string.
Suppose a sheet of a perfect conductor is placed in the yz-plane, and a linearly polarized electromagnetic wave traveling in the...

Plane Electromagnetic Waves I

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
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Bessel Function of Order Zero

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A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...

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Propagation of Waves

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Related Experiment Video

Updated: Jun 23, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Ellipticity and pulse shape dependence of localised wavepackets.

A Patel, N Kylstra, P Knight

|April 28, 2009

Summary

Intense laser fields can stabilize atoms against ionization. This study examines how laser pulse properties like ellipticity and rise-time affect stabilized wavepackets in a model hydrogen atom.

Area of Science:

Atomic physics
Quantum mechanics
Strong-field laser physics

Background:

Atoms subjected to intense, high-frequency laser fields can resist ionization.
Understanding atomic stabilization mechanisms is crucial for controlling atomic behavior in extreme conditions.

Purpose of the Study:

Investigate the structure of stabilized wavepackets for a 2D model hydrogen atom.
Analyze the influence of laser pulse ellipticity and rise-time on wavepacket stability.
Compare computed wavepackets with Kramers-Henneberger (K-H) ground states.

Main Methods:

Numerical computation of wavepacket structures.
Simulation of a two-dimensional model hydrogen atom.
Systematic variation of laser pulse ellipticity and rise-time.

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Last Updated: Jun 23, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

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

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Published on: May 9, 2021

Quasi-light Storage for Optical Data Packets

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

Main Results:

Stabilized wavepackets exhibit distinct structures influenced by laser parameters.
Comparison with K-H states reveals similarities and differences in stabilization.
Laser pulse turn-on effects significantly alter wavepacket localization and ionization dynamics.

Conclusions:

Laser pulse ellipticity and rise-time are critical factors in achieving atomic stabilization.
The study provides insights into the dynamics of wavepacket formation and ionization under intense laser fields.
Findings contribute to the understanding of light-matter interactions in the strong-field regime.