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searching for Dispersion relation 85 found (201 total)

Energy–momentum relation (4,048 words) [view diff] exact match in snippet view article find links to article

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called

Surface plasmon (1,394 words) [view diff] exact match in snippet view article find links to article

the dispersion relation (relation between frequency and wavevector) is the same as in free space. At a higher frequency, the dispersion relation bends

Airy wave theory (5,453 words) [view diff] exact match in snippet view article find links to article

this reduces to the dispersion relation of surface gravity waves on water of finite depth h. In this case the dispersion relation allows for two modes:

Empty lattice approximation (1,092 words) [view diff] exact match in snippet view article find links to article

the periodicity of the dispersion relation and the division of k-space in Brillouin zones. The periodic energy dispersion relation is expressed as: E n

Rossby-gravity waves (841 words) [view diff] exact match in snippet view article find links to article

equatorially trapped Rossby wave) on a dispersion relation diagram ("w-k" diagram). At n = 0 on a dispersion relation diagram, the mixed Rossby-gravity waves

Abbe number (1,293 words) [view diff] exact match in snippet view article find links to article

system's chromaticity (such as in the design of apochromats), the full dispersion relation (refractive index as a function of wavelength) is used. An Abbe diagram

Two-stream instability (929 words) [view diff] exact match in snippet view article find links to article

^{2}}}+{\frac {1}{(\omega -kv_{0})^{2}}}\right],} which represents the dispersion relation for longitudinal waves, and represents a quartic equation in ω {\displaystyle

Stokes wave (8,189 words) [view diff] exact match in snippet view article find links to article

non-zero contribution to the dispersion relation comes from ω2 (see e.g. the sub-section "Third-order dispersion relation" above). For non-linear surface

Farley–Buneman instability (1,133 words) [view diff] exact match in snippet view article find links to article

of ionosphere by the use of electromagnetic pulses. To derive the dispersion relation below, we make the following assumptions. First, quasi-neutrality

Diffusive–thermal instability (705 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \omega } is the temporal growth rate of the disturbance, the dispersion relation ω ( k ) {\displaystyle \omega (k)} for one-reactant flames is given

Darrieus–Landau instability (1,202 words) [view diff] exact match in snippet view article find links to article

\omega } is the temporal growth rate of the disturbance, then the dispersion relation is given by ω S L k = σ 1 + σ ( 1 + σ 2 − 1 σ − 1 ) {\displaystyle

Spin-polarized electron energy loss spectroscopy (604 words) [view diff] exact match in snippet view article find links to article

spectroscopy or SPEELS is a technique mainly used to measure the dispersion relation of the collective excitations, over the whole Brillouin zone. Spin

Weyl semimetal (2,076 words) [view diff] exact match in snippet view article find links to article

particle in vacuum. In these materials, electrons have a linear dispersion relation, making them a solid-state analogue of relativistic massless particles

Plane wave expansion method (1,252 words) [view diff] exact match in snippet view article find links to article

crystal community as a method of solving for the band structure (dispersion relation) of specific photonic crystal geometries. PWE is traceable to the

Weibel instability (2,186 words) [view diff] exact match in snippet view article find links to article

}}(1+{\frac {k^{2}v_{b0}^{2}}{\omega ^{2}}})\mathbf {\hat {z}} } The dispersion relation can now be found from Maxwell's Equations: ∇ × E 1 = i ω B 1 {\displaystyle

Trochoidal wave (1,839 words) [view diff] exact match in snippet view article find links to article

the x {\displaystyle x} -direction. The phase speed satisfies the dispersion relation: c 2 = g k , {\displaystyle c^{2}={\frac {g}{k}},} which is independent

John S. Toll (565 words) [view diff] exact match in snippet view article find links to article

July 2011. Retrieved July 18, 2011. Toll, John Sampson (1952). The dispersion relation for light and its application to problems involving electron pairs

Zero sound (1,216 words) [view diff] exact match in snippet view article find links to article

{p}}')\nu ({\hat {p}}')} . This functional operator equation gives the dispersion relation for the zero sound waves with frequency ω {\displaystyle \omega }

Plasmon (3,168 words) [view diff] exact match in snippet view article find links to article

may also be observed in the X-ray emission spectra of metals. A dispersion relation for surface plasmons in the X-ray emission spectra of metals has

Inertial wave (1,113 words) [view diff] exact match in snippet view article find links to article

to have a frequency ω {\displaystyle \omega } that satisfies the dispersion relation ω = 2 k ^ ⋅ Ω → = 2 Ω cos ⁡ θ , {\displaystyle \omega =2{\hat {k}}\cdot

Plasmonics (2,989 words) [view diff] exact match in snippet view article find links to article

surface plasmon is necessary. The dispersion relation for the surface plasmon lies entirely below the dispersion relation for light, which means that for

Mild-slope equation (4,161 words) [view diff] exact match in snippet view article find links to article

group speed of the waves. The phase and group speed depend on the dispersion relation, and are derived from Airy wave theory as: ω 2 = g k tanh ( k h )

GNU Archimedes (1,157 words) [view diff] exact match in snippet view article find links to article

{qF(r)}{\hbar }}} where F is the electric field, E(k) is the energy dispersion relation, and k is the momentum wave vector. To solve the above equation,

QCD sum rules (397 words) [view diff] exact match in snippet view article find links to article

amplitudes. The result of the QCD calculation is then matched, via dispersion relation, to a sum over hadronic states. The sum rule obtained in this way

Superlattice (3,224 words) [view diff] exact match in snippet view article find links to article

dispersionless states, which are fully confined as well. In this case the dispersion relation E z ( k z ) {\displaystyle E_{z}(k_{z})} , periodic over 2 π / d

Equatorial Rossby wave (820 words) [view diff] exact match in snippet view article find links to article

Upon linearization, the primitive equations yield the following dispersion relation: ω = − β k / ( k 2 + ( 2 n + 1 ) β / c ) {\displaystyle \omega =-\beta

Goldstone boson (3,697 words) [view diff] exact match in snippet view article find links to article

bosons are also called gapless modes (i.e. states where the energy dispersion relation is like E ∝ p n {\displaystyle E\propto p^{n}} and is zero for p

Attenuation (2,645 words) [view diff] exact match in snippet view article find links to article

(1868). Link to paper S. Benjelloun and J. M. Ghidaglia, "On the dispersion relation for compressible Navier-Stokes Equations," Link to Archiv e-print

Heat transfer physics (9,679 words) [view diff] exact match in snippet view article find links to article

vector κp, and this relation is called the phonon dispersion relation. Thus, the phonon dispersion relation is determined by matrices M and D, which depend

Nearly free electron model (1,346 words) [view diff] exact match in snippet view article find links to article

Dispersion relation for the 2D nearly free electron model as a function of the underlying crystalline structure.

Ballistic conduction in single-walled carbon nanotubes (1,632 words) [view diff] exact match in snippet view article find links to article

on the wave vector in CNTs; c) Dispersion relation near the Fermi energy for a semiconducting CNT; d) Dispersion relation near the Fermi energy for a metallic

Free particle (1,888 words) [view diff] exact match in snippet view article find links to article

notion of group velocity is based on a linear approximation to the dispersion relation ω ( k ) {\displaystyle \omega (k)} near a particular value of k {\displaystyle

Einstein relation (kinetic theory) (1,938 words) [view diff] exact match in snippet view article

case for a proof of this relation). An example assuming a parabolic dispersion relation for the density of states and the Maxwell–Boltzmann statistics, which

Kondo insulator (561 words) [view diff] exact match in snippet view article find links to article

Dispersion relation of conduction band and localized states.

Refractometer (1,669 words) [view diff] exact match in snippet view article find links to article

of a given sample varies with wavelength for all materials. This dispersion relation is nonlinear and is characteristic for every material. In the visible

Stokes drift (2,212 words) [view diff] exact match in snippet view article find links to article

period may not be chosen arbitrarily, but must satisfy the deep-water dispersion relation: ω 2 = g k {\displaystyle \omega ^{2}=gk} with g the acceleration

Klein paradox (1,062 words) [view diff] exact match in snippet view article find links to article

Fig. 1 A depiction of the dispersion relation, the x-axis represents momentum while the y-axis represents energy.

Superstripes (2,313 words) [view diff] exact match in snippet view article find links to article

ground state in the first band. In this regime, the single particle dispersion relation can host a BEC in each minima. The result is that the BEC has 2 momentum

Surface states (4,112 words) [view diff] exact match in snippet view article find links to article

zone boundary k = ± π / a {\displaystyle k=\pm \pi /a} , where the dispersion relation will be parabolic, as shown in figure 4. At the Brillouin zone boundaries

Acoustic attenuation (1,612 words) [view diff] exact match in snippet view article find links to article

18682100602. Benjelloun, Saad; Ghidaglia, Jean-Michel (2020). "On the dispersion relation for compressible Navier-Stokes Equations". arXiv:2011.06394 [math

Photonic crystal (7,088 words) [view diff] exact match in snippet view article find links to article

essentially the gap between the air-line and the dielectric-line in the dispersion relation of the PBG system. To design photonic crystal systems, it is essential

Maffei 1 (1,788 words) [view diff] exact match in snippet view article find links to article

Maffei 1, which is based on the re-calibrated luminosity/velocity dispersion relation for the elliptical galaxies and the updated extinction, is 2.85 ±

Stokes's law of sound attenuation (821 words) [view diff] exact match in snippet view article find links to article

(1868). Link to paper S. Benjelloun and J. M. Ghidaglia, "On the dispersion relation for compressible Navier-Stokes Equations," Link to Archiv e-print

Nano-ARPES (3,647 words) [view diff] exact match in snippet view article find links to article

the ARPES technique, are traditionally shown as energy-momentum dispersion relation along the high symmetry directions of the irreducible Brillouin Zone

Liu Chen (physicist) (1,475 words) [view diff] exact match in snippet view article

jointly with Fulvio Zonca, and named as the general fishbone-like dispersion relation. In 2000, Chen and coworkers elucidated that drift wave turbulence

Radiation stress (3,158 words) [view diff] exact match in snippet view article find links to article

modulated short waves within the group. While, according to the dispersion relation, a long wave of this length should propagate at its own – higher

Monte Carlo methods for electron transport (5,007 words) [view diff] exact match in snippet view article find links to article

{qF(r)}{\hbar }}} where F is the electric field, E(k) is the energy dispersion relation, and k is the momentum wave vector. To solve the above equation,

Plasmonic nanolithography (1,200 words) [view diff] exact match in snippet view article find links to article

perpendicularly to the interface where the propagation occurs. The dispersion relation for SPPs permits the excitation of wavelengths shorter than the free-space

Long delayed echo (1,723 words) [view diff] exact match in snippet view article find links to article

oscillation at the difference frequency of the two signals satisfies the dispersion relation for electrostatic waves, such waves would exist and begin to propagate

Azimi Q models (465 words) [view diff] exact match in snippet view article find links to article

where a2 and a3 are constants. Now we can use the Krämers-Krönig dispersion relation and get a phase velocity: 1 c ( w ) = 1 c ∞ − 2 a 2 l n ( a 3 w )

Kramers–Kronig relations (2,910 words) [view diff] case mismatch in snippet view article find links to article

Numerical analytic continuation John S. Toll (1956). "Causality and the Dispersion Relation: Logical Foundations". Physical Review. 104 (6): 1760–1770. Bibcode:1956PhRv

Rainbow (9,112 words) [view diff] exact match in snippet view article find links to article

rainbow. For red light (wavelength 750nm, n = 1.330 based on the dispersion relation of water), the radius angle is 42.5°; for blue light (wavelength

Contact lithography (1,938 words) [view diff] exact match in snippet view article find links to article

50 and even 22 nm using wavelengths of 365 and 436 nm. The exotic dispersion relation of surface plasmon has led to the extremely short wavelength, which

Mattis–Bardeen theory (1,024 words) [view diff] exact match in snippet view article find links to article

gap 2Δ in the single-particle density of states arises, and the dispersion relation can be described like the one of a semiconductor with band gap 2Δ

Robert Weber (astronomer) (1,418 words) [view diff] case mismatch in snippet view article

Weber & P.E. Tannenwald, "Temperature Variation of the Spin-Wave Dispersion Relation." Journal of Applied Physics 37(3): 1058-1059. (1966) "Comparative

V. K. Samaranayake (1,241 words) [view diff] case mismatch in snippet view article find links to article

Lengths (with W.S. Woolcock) Nucl. Phys. B48 (1972) 205 – 224. Forward Dispersion Relation Constraints on the Pion-Nucleon P-Wave and D-Wave Scattering Lengths

Bethe ansatz (2,316 words) [view diff] exact match in snippet view article find links to article

obtain the correct spectrum of the Heisenberg antiferromagnet (spinon dispersion relation), showing that it differs from Anderson’s spin-wave theory predictions

Magnetohydrodynamics (5,241 words) [view diff] exact match in snippet view article find links to article

respect to the time independent or bulk field B0 will satisfy the dispersion relation ω k = v A cos ⁡ θ {\displaystyle {\frac {\omega }{k}}=v_{A}\cos \theta

Wave shoaling (1,262 words) [view diff] exact match in snippet view article find links to article

\lambda =2\pi /k} because the nondispersive shallow water limit of the dispersion relation for the wave phase speed, ω / k ≡ c = g h {\displaystyle \omega /k\equiv

Surface acoustic wave (4,065 words) [view diff] exact match in snippet view article find links to article

transitions. In graphene these transitions are the only way, as the linear dispersion relation of its electrons prevents momentum/energy conservation when it would

Wave power (6,023 words) [view diff] exact match in snippet view article find links to article

{\displaystyle P=E\,c_{g},} with cg the group velocity (m/s). Due to the dispersion relation for waves under gravity, the group velocity depends on the wavelength

Andromeda Galaxy (10,637 words) [view diff] exact match in snippet view article find links to article

galaxy was first based on interpreting its anomalous age-velocity dispersion relation, as well as the fact that 2 billion years ago, star formation throughout

Maxwell–Boltzmann distribution (5,683 words) [view diff] exact match in snippet view article find links to article

dE. Making use of the spherical symmetry of the energy-momentum dispersion relation E = | p | 2 2 m , {\displaystyle E={\tfrac {|{\textbf {p}}|^{2}}{2m}}

Speed of light (15,331 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-7503-0926-4. Toll, J. S. (1956). "Causality and the Dispersion Relation: Logical Foundations". Physical Review. 104 (6): 1760–1770. Bibcode:1956PhRv

Raman spectroscopy (9,829 words) [view diff] exact match in snippet view article find links to article

of the sample is known then detailed information about the phonon dispersion relation can also be gleaned from a single test. Optical tweezers Raman spectroscopy

Spoof surface plasmon (1,528 words) [view diff] exact match in snippet view article find links to article

that is stratified along the z-direction in Cartesian coordinates, dispersion relation for SPPs can be obtained from solving Maxwell's equations: k x =

Helium atom scattering (2,568 words) [view diff] case mismatch in snippet view article find links to article

R. Bruce; Toennies, J. Peter (1981-02-09). "Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering

Heinz Raether (680 words) [view diff] exact match in snippet view article find links to article

Physics of Thin Films. 9: 145–261. Raether, H. (15 July 1982). "Dispersion relation of surface plasmons on gold- and silver gratings". Optics Communications

Computational aeroacoustics (2,297 words) [view diff] no match in snippet view article find links to article

Society, Vol. A264, 1969, pp. 321-342 C. K. W. Tam, and J. C. Webb, "Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics"

Viacheslav Belyi (1,009 words) [view diff] case mismatch in snippet view article find links to article

Experiment, 06, P06001, 2009. V.V. Belyi, Fluctuation-Dissipation Dispersion Relation and Quality Factor for Slow Processes, Phys. Rev. E, V. 69, N1, p

Richard Allan Ferrell (1,628 words) [view diff] case mismatch in snippet view article find links to article

"Characteristic Energy Loss of Electrons Passing through Metal Foils. II. Dispersion Relation and Short Wavelength Cutoff for Plasma Oscillations". Physical Review

Hiroshi Suura (1,004 words) [view diff] case mismatch in snippet view article find links to article

1016/0003-4916(61)90151-8. (over 1900 citations) Suura, H.; Simmons, L. M. (1966). "Dispersion Relation for the Axial-Vector Vertex and a Sum Rule for the Axial-Vector Coupling-Constant

Scanning tunneling spectroscopy (3,641 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Delta E\approx 0.1\,\mathrm {eV} } . Assuming the dispersion relation for simple metals, it follows from the uncertainty relation Δ x Δ

Fermi's golden rule (3,906 words) [view diff] exact match in snippet view article find links to article

and wavevector q {\displaystyle {\textbf {q}}} , where the light dispersion relation is ω = ( c / n ) | q | {\displaystyle \omega =(c/n)\left|{\textbf

Green's function (many-body theory) (4,547 words) [view diff] exact match in snippet view article

_{\mathbf {k} }=\epsilon _{\mathbf {k} }-\mu } is the single-particle dispersion relation measured with respect to the chemical potential. The spectral density

Schamel equation (2,174 words) [view diff] exact match in snippet view article find links to article

V(ψ)=0{\displaystyle {\mathcal {V}}(\psi )=0}. This is a nonlinear dispersion relation (NDR) because it determines the phase velocity v0{\displaystyle v_{0}}

Silicon photonics (6,368 words) [view diff] exact match in snippet view article find links to article

result from this tight confinement substantially alter the optical dispersion relation. By selecting the waveguide geometry, it is possible to tailor the

Negative-index metamaterial (7,703 words) [view diff] exact match in snippet view article find links to article

propagation, which fits with theoretical predictions. Mathematically, the dispersion relation leads to a band with negative group velocity everywhere, and a bandwidth

Frenkel–Kontorova model (2,597 words) [view diff] exact match in snippet view article find links to article

\exp[i(\omega _{\text{ph}}(\kappa )t-\kappa n)]} with the phonon dispersion relation ω ph 2 ( κ ) = ω min 2 + 2 g ( 1 − cos ⁡ κ ) {\displaystyle \omega

Interfacial thermal resistance (2,843 words) [view diff] exact match in snippet view article find links to article

equations form the basis for both models. n is determined based on the dispersion relation for the materials (for example, the Debye model) and Bose–Einstein

Internal wave breaking (2,853 words) [view diff] exact match in snippet view article find links to article

frequency and ω {\displaystyle \omega } is the wave frequency in the dispersion relation that governs the propagation of internal waves in a continuously

Magnetorotational instability (4,620 words) [view diff] exact match in snippet view article find links to article

magnetic field in the vertical direction satisfies an equation ("dispersion relation") exactly analogous to equation 5, with the "spring constant" K =

Kelvin wake pattern (1,485 words) [view diff] exact match in snippet view article find links to article

boat or other object causing a wake. This pattern follows from the dispersion relation of deep water waves, which is often written as, ω = g k , {\displaystyle

Sound amplification by stimulated emission of radiation (7,513 words) [view diff] exact match in snippet view article find links to article

Dispersion relation ω=ω(k) for some waves corresponding to lattice vibrations in GaAs.

Peter Kelly Senecal (2,427 words) [view diff] exact match in snippet view article find links to article

and viscosity, determining a transition point for simplifying the dispersion relation and correctly forecasting spray characteristics for pressure-swirl