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Domain Walls
A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with polynomial potentials. Unstable domain walls can also appear if spontaneously broken discrete symmetry is approximate and there is a false vacuum. A domain (hyper volume) is extended in three spatial dimensions and one time dimension. A domain wall is the boundary between two neighboring domains. Thus a domain wall is extended in two spatial dimensions and one time dimension. Important examples are: *Domain wall (magnetism), an interface separating magnetic domains * Kink (materials science), a type of dislocation in a crystal *Domain wall (optics), for domain walls in optics *Domain wall (string theory), a theoretical 2-dimensional singularity Besides these important cases similar solitons appear in wide spectrum of the models. Here are oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Soliton
In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons do not decay, dissipate, disperse or evaporate in the way that ordinary waves (or solutions or structures) might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult. Overview The original soliton was observed in the 19th century, as a solitary water wave in a barge canal. It was eventually explained by noting that the K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Symmetry
In mathematics and geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called ''reflections'' or ''interchanges''. In mathematics and theoretical physics, a discrete symmetry is a symmetry under the transformations of a discrete group—e.g. a topological group with a discrete topology whose elements form a finite or a countable set. One of the most prominent discrete symmetries in physics is parity symmetry. It manifests itself in various elementary physical quantum systems, such as quantum harmonic oscillator, electron orbitals of Hydrogen-like atoms by forcing wavefunctions to be even or odd. This in turn gives rise to selection rules In physics and chemistry, a selection rule, or transition r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine-Gordon Model
The sine-Gordon equation is a second-order nonlinear partial differential equation for a function \varphi dependent on two variables typically denoted x and t, involving the wave operator and the sine of \varphi. It was originally introduced by in the course of study of surfaces of constant negative curvature as the Gauss–Codazzi equation for surfaces of constant Gaussian curvature −1 in 3-dimensional space. The equation was rediscovered by in their study of crystal dislocations known as the Frenkel–Kontorova model. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions, and is an example of an integrable PDE. Among well-known integrable PDEs, the sine-Gordon equation is the only ''relativistic'' system due to its Lorentz invariance. Realizations of the sine-Gordon equation Differential geometry This is the first derivation of the equation, by Bour (1862). There are two equivalent forms of the sine-Gordon equation. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Vacuum
In quantum field theory, a false vacuum is a hypothetical vacuum state that is locally stable but does not occupy the most stable possible ground state. In this condition it is called metastable. It may last for a very long time in this state, but could eventually decay to the more stable one, an event known as false vacuum decay. The most common suggestion of how such a decay might happen in our universe is called bubble nucleation – if a small region of the universe by chance reached a more stable vacuum, this "bubble" (also called "bounce") would spread. A false vacuum exists at a local minimum of energy and is therefore not completely stable, in contrast to a true vacuum, which exists at a global minimum and is stable. Definition of true vs. false vacuum A vacuum is defined as a space with as little energy in it as possible. Despite the name, the vacuum still has quantum fields. A true vacuum is stable because it is at a global minimum of energy, and is commonly a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Wall (magnetism)
In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. A domain wall is a gradual reorientation of individual moments across a finite distance. The domain wall thickness depends on the anisotropy of the material, but on average spans across around 100–150 atoms. Properties The energy of a domain wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is usually expressed as energy per unit wall area. The width of the domain wall varies due to the two opposing energies that create it: the magnetocrystalline anisotropy energy and the exchange energy (J_), both of which tend to be as low as possible so as to be in a more favorable energetic state. The anisotropy energy is lowest when the individual magnetic moments are aligned with the crystal lattice axes thus reducing the width o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kink (materials Science)
Kinks are deviations of a dislocation defect along its glide plane. In edge dislocations, the constant glide plane allows short regions of the dislocation to turn, converting into screw dislocations and producing kinks. Screw dislocations have rotatable glide planes, thus kinks that are generated along screw dislocations act as an anchor for the glide plane. Kinks differ from jogs in that kinks are strictly parallel to the glide plane, while jogs shift away from the glide plane. Energy Pure-edge and screw dislocations are conceptually straight in order to minimize its length, and through it, the strain energy of the system. Low-angle mixed dislocations, on the other hand, can be thought of as primarily edge dislocation with screw kinks in a stair-case structure (or vice versa), switching between straight pure-edge and pure-screw dislocation segments. In reality, kinks are not sharp transitions. Both the total length of the dislocation and the kink angle are dependent on the fre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as ''glide'' or Slip (materials science), slip. The crystalline order is restored on either side of a ''glide dislocation'' but the atoms on one side have moved by one position. The crystalline order is not fully restored with a ''partial dislocation''. A dislocation defines the boundary between ''slipped'' and ''unslipped'' regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plasticity (physics), Plastic deformation of a material occurs by the creation and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Wall (optics)
A domain wall is a term used in physics which can have similar meanings in optics, magnetism, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken. As of 2009, a phase-locked dark-dark vector soliton was observed only in fiber lasers of positive dispersion while a phase-locked dark-bright vector soliton was obtained in fiber lasers of either positive or negative dispersion. Numerical simulations confirmed the experimental observations, and further showed that the observed vector solitons are the two types of phase-locked polarization domain-wall solitons theoretically predicted. Another novel type of domain wall soliton is the vector dark domain wall, consisting of stable localized structures separating the two orthogonal linear polarization eigenstates of the laser emission, with a dark structure that is visible only when the total laser emission is measured.H. Zhang, D. Y. Ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain Wall (string Theory)
In string theory, a domain wall is a theoretical (d−1)-dimensional singularity. A domain wall is meant to represent an object of codimension one embedded into space (a defect in space localized in one spatial dimension). For example, D8-branes are domain walls in type II string theory. In M-theory, the existence of Horava–Witten domain walls, "ends of the world" that carry an E8 gauge theory, is important for various relations between superstring theory and M-theory. If domain walls exist, their interactions are hypothesized to emit gravitational waves that would be detectable by LIGO and similar experiments. See also * Topological defect * Cosmic string *Membrane (M-theory) *Gravitational singularity A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by defini ... References Hypo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmic Microwave Background Radiation
The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost isotropic, uniform and is not associated with any star, galaxy, or other astronomical object, object. This glow is strongest in the microwave region of the electromagnetic spectrum. The accidental Discovery of cosmic microwave background radiation, discovery of the CMB in 1965 by American radio astronomers Arno Allan Penzias and Robert Woodrow Wilson was the culmination of work initiated in the 1940s. The CMB is landmark evidence of the Big Bang scientific theory, theory for the origin of the universe. In the Big Bang cosmological models, during the earliest periods, the universe was filled with an Opacity (optics), opaque fog of dense, hot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Model
The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated some success in providing experimental predictions, it leaves some physics be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braneworld
Brane cosmology refers to several theories in particle physics and cosmology related to string theory, superstring theory and M-theory. Brane and bulk The central idea is that the visible, four-dimensional spacetime is restricted to a brane inside a higher-dimensional space, called the "bulk" (also known as "hyperspace"). If the additional dimensions are compact, then the observed universe contains the extra dimension, and then no reference to the bulk is appropriate. In the bulk model, at least some of the extra dimensions are extensive (possibly infinite), and other branes may be moving through this bulk. Interactions with the bulk, and possibly with other branes, can influence our brane and thus introduce effects not seen in more standard cosmological models. Why gravity is weak and the cosmological constant is small Some versions of brane cosmology, based on the large extra dimension idea, can explain the weakness of gravity relative to the other fundamental forces of natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
