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

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

You might also read

Related Articles

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

Sort by

Same author

Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent statistics.

Physical review. E·2023

Same author

Superradiant Droplet Emission from Parametrically Excited Cavities.

Physical review letters·2023

Same author

Emergent order in hydrodynamic spin lattices.

Nature·2021

Same author

A guideline to limit indoor airborne transmission of COVID-19.

Proceedings of the National Academy of Sciences of the United States of America·2021

Same author

Classical pilot-wave dynamics: The free particle.

Chaos (Woodbury, N.Y.)·2021

Same author

Hydrodynamic quantum analogs.

Reports on progress in physics. Physical Society (Great Britain)·2020

Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026

Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026

Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026

Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026

Same journal

Data-driven soliton manifold approximations for dark and bright waves: Some prototypical 1D case examples.

Chaos (Woodbury, N.Y.)·2026

Same journal

Gap junction architecture and synchronization clusters in the thalamic reticular nuclei.

Chaos (Woodbury, N.Y.)·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Feb 4, 2026

Use of an Optical Trap for Study of Host-Pathogen Interactions for Dynamic Live Cell Imaging

Use of an Optical Trap for Study of Host-Pathogen Interactions for Dynamic Live Cell Imaging

Published on: July 28, 2011

Exploring orbital dynamics and trapping with a generalized pilot-wave framework.

Lucas D Tambasco¹, John W M Bush¹

¹Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Chaos (Woodbury, N.Y.)

|October 4, 2018

Summary

This summary is machine-generated.

Walking droplets exhibit stable, quantized circular orbits around a central well. At higher accelerations, these orbits can become unstable, leading to chaotic droplet motion.

More Related Videos

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

Published on: October 1, 2014

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

Related Experiment Videos

Last Updated: Feb 4, 2026

Use of an Optical Trap for Study of Host-Pathogen Interactions for Dynamic Live Cell Imaging

Use of an Optical Trap for Study of Host-Pathogen Interactions for Dynamic Live Cell Imaging

Published on: July 28, 2011

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

Published on: October 1, 2014

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses

Published on: May 9, 2021

Area of Science:

Fluid dynamics
Wave phenomena
Nonlinear dynamics

Background:

Walking droplets are macroscopic systems exhibiting wave-particle duality.
Faraday waves generated by a central well can trap droplets in quantized orbits.
Previous models explored droplet dynamics but lacked imposed potentials.

Purpose of the Study:

To investigate the effect of an imposed potential on walking droplet dynamics.
To analyze the stability of quantized orbits under varying conditions.
To explore the transition to chaos in droplet motion.

Main Methods:

Experimental study of walking droplets on a fluid bath with a central well.
Utilizing a stroboscopic model with an added potential to simulate droplet-wave interaction.
Analyzing droplet trajectories and probability distributions in different dynamic regimes.

Main Results:

Observed stable, quantized circular orbits with radii matching Faraday wave extrema.
Demonstrated orbit stability at low accelerations and instability leading to chaos at higher accelerations.
Showcased chaotic switching between orbits when drop inertia is dominated by pilot-wave force.

Conclusions:

Imposed potentials significantly influence walking droplet dynamics and orbit stability.
The Ruelle-Takens-Newhouse scenario describes the transition to chaos in this system.
The probability distribution of droplet position reflects underlying wavefield instabilities.