Secondary bifurcations of hexagonal patterns in a nonlinear optical system: alkali metal vapor in a single-mirror

Damià Gomila1, Thorsten Ackemann, Edgar Grosse Westhoff

  • 1Institut Mediterrani d'Estudis Avançats, IMEDEA (CSIC-UIB), Campus Universitat Illes Balears, E-07071 Palma de Mallorca, Spain.

Related Concept Videos

VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons on Molecule Geometry
Hybridization of Atomic Orbitals I03:24

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...
Molecular Orbital Theory II03:51

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams
Electrophilic Addition to Alkynes: Halogenation02:38

Electrophilic Addition to Alkynes: Halogenation

Introduction
Halogenation is another class of electrophilic addition reactions where a halogen molecule gets added across a π bond. In alkynes, the presence of two π bonds allows for the addition of two equivalents of halogens (bromine or chlorine). The addition of the first halogen molecule forms a trans-dihaloalkene as the major product and the cis isomer as the minor product. Subsequent addition of the second equivalent yields the tetrahalide.
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...