Helicity (other)
Helicity may refer to: *Helicity (fluid mechanics), the extent to which corkscrew-like motion occurs *Helicity (particle physics), the projection of the spin onto the direction of momentum *Magnetic helicity, the extent to which a magnetic field "wraps around itself" * Circular dichroism, the differential absorption of left and right circularly polarized light * A form of axial chirality * A former name for inherent chirality See also *Helix A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, ...

Helicity (fluid Mechanics)
:''This page is about helicity in fluid dynamics. For helicity of magnetic fields, see magnetic helicity. For helicity in particle physics, see helicity (particle physics).'' In fluid dynamics, helicity is, under appropriate conditions, an invariant of the Euler equations of fluid flow, having a topological interpretation as a measure of linkage and/or knottedness of vortex lines in the flow. This was first proved by Jean-Jacques Moreau in 1961 and Moffatt derived it in 1969 without the knowledge of Moreau's paper. This helicity invariant is an extension of Woltjer's theorem for magnetic helicity. Let \mathbf(x,t) be the velocity field and \nabla\times\mathbf the corresponding vorticity field. Under the following three conditions, the vortex lines are transported with (or 'frozen in') the flow: (i) the fluid is inviscid; (ii) either the flow is incompressible (\nabla\cdot\mathbf = 0), or it is compressible with a barotropic relation p = p(\rho) between pressure p and density ...
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Helicity (particle Physics)
In physics, helicity is the projection of the spin onto the direction of momentum. Overview The angular momentum J is the sum of an orbital angular momentum L and a spin S. The relationship between orbital angular momentum L, the position operator r and the linear momentum (orbit part) p is :\mathbf = \mathbf\times\mathbf so L's component in the direction of p is zero. Thus, helicity is just the projection of the spin onto the direction of linear momentum. The helicity of a particle is positive (" right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite. Helicity is conserved. That is, the helicity commutes with the Hamiltonian, and thus, in the absence of external forces, is time-invariant. It is also rotationally invariant, in that a rotation applied to the system leaves the helicity unchanged. Helicity, however, is not Lorentz invariant; under the action of a Lorentz boost, the helicity may chang ...
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Magnetic Helicity
In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field. In ideal magnetohydrodynamics, magnetic helicity is conserved. When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred as an inverse transfer in Fourier space. This second property makes magnetic helicity special: three-dimensional turbulent flows tend to "destroy" structure, in the sense that large-scale vortices break-up in smaller and smaller ones (a process called "direct energy cascade", described by Lewis Fry Richardson and Andrey Nikolaevich Kolmogorov). At the smallest scales, the vortices are dissipated in heat through viscous effects. Through a sort of "inverse cascade of magnetic helicity", the opposite happens: small helical structures (with a non-zero magnetic helicity) lead to the formation of large-scale magnetic fields. This is for example visible in the heliospheric curren ...
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Axial Chirality
Axial may refer to: * one of the anatomical directions describing relationships in an animal body * In geometry: :* a geometric term of location :* an axis of rotation * In chemistry, referring to an axial bond * a type of modal frame, in music * axial-flow, a type of fan * the Axial age in China, India, etc. * Axial Seamount and submarine volcano off Oregon, USA * Axial, Colorado, a ghost town See also *Axiality (other) *Axis (other) An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis *Axis (mathematics), a designator for a Cartesian-coordinate ...

Inherent Chirality
In chemistry, inherent chirality is a property of asymmetry in molecules arising, not from a stereogenic or chiral center, but from a twisting of the molecule in 3-D space. The term was first coined by Volker Boehmer in a 1994 review, to describe the chirality of calixarenes arising from their non-planar structure in 3-D space. This phenomenon was described as resulting from "the absence of a place of symmetry or an inversion center in the molecule as a whole". Boehmer further explains this phenomenon by suggesting that if an inherently chiral calixarene macrocycle were opened up it would produce an "achiral linear molecule". There are two commonly used notations to describe a molecules inherent chirality: cR/cS (arising from the notation used for classically chiral compounds, with ''c'' denoting curvature) and P/M. Inherently chiral molecules, like their classically chiral counterparts, can be used in chiral host–guest chemistry, enantioselective synthesis, and other applicati ...
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