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Dispersion relation - Wikipedia, the free encyclopedia The relation between the energy of a system and its corresponding momentum is known as its dispersion relation. For electromagnetic waves, the energy is proportional to the frequency of the wave and the momentum to the wavenumber. In the study of solids, the study of the dispersion relation of electrons is of paramount importance. www.wikipedia.org /wiki/Dispersion_relation   (386 words)

Dispersion relation [Oulu]   (Site not responding. Last check: 2007-10-22) All the information about the propagation of a given plasma wave mode is contained in the appropriate dispersion relation, which relates the angular frequency w to the wave number k (magnitude of the propagation vector k). When using the more complicated plasma theories, the resulting dispersion relations can be diffucult to interpretate. Dispersion relation w(k) for the transverse wave propagating in an isotropic cold electron plasma. www.oulu.fi /~spaceweb/textbook/disprel.html   (415 words)

2pPAb6. Dispersion relation influence on rise times of sonic boom propagation through turbulence.   (Site not responding. Last check: 2007-10-22) Dispersion relation influence on rise times of sonic boom propagation through turbulence. Recent work suggests the ``average'' turbulence contribution to rise times is accounted for by an extra term in the propagation equation, evolving from an extra term in the dispersion relation k=((omega)/c)+F((omega)), where c is spatially averaged, and, for mechanical turbulence, F((omega)) depends on turbulent energy dissipation rate (epsilon) per unit fluid mass. The discrepancy with the 1971 prediction that the rise time scales as (epsilon)[sup 4/7]c[sup -19/7]x[sup 11/7] is discussed, such being consistent with an (omega)[sup 7/11] term in the dispersion relation. www.auditory.org /asamtgs/asa96ind/2pPAb/2pPAb6.html   (178 words)

Articles - Photon   (Site not responding. Last check: 2007-10-22) The associated dispersion relation for photons is a relation between frequency, f, and wavelength, λ. Matter excitations have a non-linear dispersion relation; that is, their momentum is not proportional to their energy. (The propagation speed is the derivative of the dispersion relation with respect to momentum.) This is the formal reason why light is slower in media (such as glass) than in vacuum. www.candlesa.com /articles/Photon   (1575 words)

Citebase - Pion dispersion relation at finite density and temperature Authors: Ayala, A. Amore, P. Aranda, A. We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature. The dispersion relation is described in terms of a density and temperature dependent mass and an index of refraction which is also temperature, density as well as momentum dependent. We study the behavior of the pion dispersion relation in a pion medium at finite density and temperature, introducing a chemical potential to describe the finite pion number density. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-ph/0207081   (1167 words)

Tailus Industries Aerospace > Dispersion Relation   (Site not responding. Last check: 2007-10-22) Noun, Science, Physics (Plasma, Fusion Or Energy Research): For a given wave, the dispersion relation relates the temporal frequency of a wave (w, or omega) to its wavenumber k and other physical quantities characteristic of the system. Dispersion relations can be quite simple (e.g., w = k * c for light; c being the speed of light), and they can also be quite complex, with interesting mathematical structure. The dispersion relation and its mathematical structure provide important information about the wave, including the phase and group velocities. www.aero.tailus.com /glossary/d/i/s/persion-relation/index.html   (124 words)

Dispersion Relation of the LETG+HRC-S   (Site not responding. Last check: 2007-10-22) The dispersion relation of the LETG+HRC-S is currently known to approximately a few parts in 10000, across the entire LETG+HRC-S wavelength range. The dispersion relation shows that the RMS decreases to 0.009 Å once the correction is applied. Although we have certainly made progress on characterizing the dispersion relation non-linearities along the detector, there still remain vast regions of the detector for which we do not have sufficient data to map out the wavelength distortions. cxc.harvard.edu /cal/Letg/Hrc_disp   (1409 words)

The dispersion relation Therefore, an equation that describes the vertical slowness as a function of the horizontal one, the dispersion relation, is a key equation for imaging such data. To obtain the dispersion relation for orthorhombic anisotropy we must first derive the Christoffel equation for such media. Note that the vertical velocity appears only once in equation (17) and thus the vertical-time based dispersion relation, like in the case of VTI media, become vertical velocity independent. sepwww.stanford.edu /public/docs/sep98/tariq2/paper_html/node3.html   (342 words)

Validation of the Linear Dispersion Relation Using Field Observations - Storming Media Although the main objective of the team's efforts was to quantify the accuracy and efficiency of each method, a secondary task was to identify possible error sources resulting from the use of the dispersion relation under field conditions. For water depths outside the surf zone region, the results indicate that the linear dispersion relation was highly accurate, with average depth estimation errors on the order of 6% of the observed depth. Correlations between the magnitude of the depth error and measured wave amplitudes suggest the importance of wave amplitude in the calculation of shallow water phase speeds, and correspondingly in the use of the dispersion relation in the surf zone region. www.stormingmedia.us /60/6099/A609933.html   (325 words)

Dispersion Dispersion is the manner in which the frequency and the wave number are related in a medium. Light waves have a linear dispersion in a vacuum but in water they have a nonlinear dispersion. This nonlinear dispersion can cause a white light spectrum to be changed into a rainbow. webphysics.davidson.edu /faculty/dmb/bernstein/qmwave/section2d.html   (294 words)

Strangeway: Applicability of Relativistic Dispersion for AKR - Ring Distribution At present we shall not include any temperature in the particle distribution functions as we are primarily interested in elucidating some of the more general characteristics of the dispersion relation for a weakly relativistic plasma.       The last dispersion surface plotted in Figure 1 corresponds to the Z mode and is shown in the lower left-hand corner of the figure. The parts of the dispersion surfaces corresponding to the unstable modes are the regions for which different dispersion surfaces are colocated. www-ssc.igpp.ucla.edu /~strange/AKR_86/akr86_2.html   (1501 words)

Citebase - Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole The quantum correction to the entanglement entropy of the event horizon is plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. We argue that modified dispersion relation is a generic feature of string theory, and this boundedness nature of the dispersion relation is a general consequence of the existence of a minimal distance in string theory. The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:hep-th/0312136   (874 words)

SINUM Volume 42 Issue 2   (Site not responding. Last check: 2007-10-22) The dispersive properties of high order finite element schemes are analyzed in the setting of the Helmholtz equation, and an explicit form of the discrete dispersion relation is obtained for elements of arbitrary order. It is shown that the numerical dispersion displays three different types of behavior, depending on the size of the order of the method relative to the mesh-size and the wave number. Quantitative estimates are obtained for the behavior and rates of decay of the dispersion error in the differing regimes. dx.doi.org /10.1137/S0036142903423460   (227 words)

CiteULike: Bogoliubov dispersion relation for a 'photon fluid': Is this a superfluid?   (Site not responding. Last check: 2007-10-22) CiteULike: Bogoliubov dispersion relation for a 'photon fluid': Is this a superfluid? Bogoliubov dispersion relation for a 'photon fluid': Is this a superfluid? This implies the existence of a Bogoliubov dispersion relation for the low-lying elementary excitations of the photon fluid, and in particular, that sound waves exist for long-wavelength, low-frequency disturbances of this fluid. www.citeulike.org /user/mankei/article/262225   (253 words)

No Title So, as we try a naive extension of Schrodinger's equation to a relativistic dispersion relation, we must be prepared to have the very foundations of quantum mechanics shaken. We found that we had to introduce matrices to obtain a linear dispersion relation: particularly, we found the dispersion relation Given such matrices, we used the canonical commutation relations to impose this linear relativistic dispersion relation on the wave function in position space, obtaining the Dirac equation. www.physics.emory.edu /faculty/benson/380-96/notes/24/24.html   (553 words)

Local dispersion relation   (Site not responding. Last check: 2007-10-22) (11.19)), a local dispersion relation is obtained by elimination of all primed quantities, and is the cubic Indeed, what the correct non-axisymmetric local dispersion relation is is a matter of some controversy. Such waves are tightly wound, and it is appropriate to use the quadratic local dispersion relation Eq. astron.berkeley.edu /~jrg/ay202/node154.html   (279 words)

Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations   (Site not responding. Last check: 2007-10-22) A dispersion relation for the scattering of a KleinGordon particle by a fixed static interaction is derived. The dispersion relation is valid only for momentum transfers less than a givenn limit determined by the behavior of the interaction at large distances. The dependence of this limit on the mass spectrum is discussed, and it is found that if the system admits sufficiently exation falls even in the case of forward scattering. www.osti.gov /energycitations/product.biblio.jsp?osti_id=4258077   (151 words)

Decay of metastable patterns for the Rosensweig instability: revisiting the dispersion relation   (Site not responding. Last check: 2007-10-22) Decay of metastable patterns for the Rosensweig instability: revisiting the dispersion relation The decay of metastable patterns in the form of magnetic liquid ridges is studied in the frame of a linear stability analysis where the ridges are the most unstable linear pattern of the Rosensweig instability. The analysis of the corresponding dispersion relation reveals that different sets of solutions exist. www.mpipks-dresden.mpg.de /~adlange/mhd03.html   (98 words)

Strangeway: Wave Dispersion, Ray Propagation, and AKR - Section 2       In this paper we are principally interested in the modifications of wave dispersion due to relativistic effects and in the dependence of the wave instabilities on the parameters which describe the plasma. However, the main thrust of the present work is to indicate those properties of the modified wave dispersion which may be of significance for the generation of AKR. However, the auroral electron distribution function usually displays considerable structure, and whether or not the wave dispersion for such a plasma results in fluidlike or resonant instabilities is not easily determined. igpp.ucla.edu /~strange/AKR_85/akr85_2.html   (967 words)

3aPAb5 Omega-to-the-one-third term in dispersion relation for acoustic   (Site not responding. Last check: 2007-10-22) The author's earlier formulation of pulse propagation through turbulence required a somewhat ad hoc separation of the effects of large scale and small scale turbulence with the selection of a cut-off turbulent wave number k[inf c] that separates the two regimes. A neater-cleaner formulation proceeds with the premise that the frequency dispersion of pulses is caused by that part of the turbulence spectrum which lies in the inertial range originally predicted by Kolmogoroff. The dispersion is typically small, but has an accumulative effect that leads to a sizable pulse distortion over large propagation distances. www.auditory.org /asamtgs/asa95stl/3aPAb/3aPAb5.html   (217 words)

NEA-0850: ECIS-03, Coupled Channel, Statistical Model, Schroedinger and Dirac Equation, Dispersion Relation - In ECIS03 the dispersion relation as described by "C. PHYS A528 (1991) 253", is added to the real potencial, (it is a generalisation of the dispersion relation as described in "MAHAUX, C. and SARTOR, R., Nucl. If there is more than one equation related to the ground state the whole calculation must be repeated. The efficiency of the method is proportional to the ratio of the total number of equations to the number of those related to the ground state. www.nea.fr /abs/html/nea-0850.html   (786 words)

IngentaConnect Dispersion relation of surface plasmons near photonic band gaps: ...   (Site not responding. Last check: 2007-10-22) Dispersion relation of surface plasmons near photonic band gaps: Influence of the interaction with light Our main purpose is to investigate the case where the band gap width is larger than the energy distance between the SP dispersion curve for a flat surface and the light line. We introduce a physical model of the interaction of light waves with SPs and derive an analytical expression for the SP wave vector near band gaps based on the coupled-mode approach involving three interacting modes (two of them are SP modes and one is a light mode). www.ingentaconnect.com /content/tandf/tmop/2001/00000048/00000010/art00006   (242 words)

Strangeway: Applicability of Relativistic Dispersion for AKR - Figure Captions An unstable mode is present where two stable modes coalesce, and the corresponding growth rates are shown by the contour plot. Solutions of the approximate shell dispersion relation (10) for equal temperature distributions. The plasma parameters together with the corresponding solutions of the shell dispersion relation for k = 0 are given as headers to each phase space density plot. www-ssc.igpp.ucla.edu /~strange/AKR_86/akr86_figcaps.html   (333 words)

Strangeway: Applicability of Relativistic Dispersion for AKR - Title   (Site not responding. Last check: 2007-10-22) Two different types of dispersion relation are employed for the purpose of studying the wave dispersion. Using this dispersion relation, we find that for sufficiently low densities, the most unstable mode is a "trapped" mode that is decoupled from the freely propagating R-X mode found in a cold plasma. Since the dispersion relation neglects the effects of temperature, we also study wave dispersion using a spherically symmetric Dory-Guest-Harris (DGH) distribution. igpp.ucla.edu /~strange/AKR_86/akr86_abstract.html   (316 words)

EPG419: Dispersion Relation Approach to the X-Ray Edge Problem   (Site not responding. Last check: 2007-10-22) Dispersion Relation Approach to the X-Ray Edge Problem We present a dispersion relation formulation of the open-line amplitude for the x-ray edge problem within the contact potential model. Using both multiple-scattering and determinant techniques, we find that to a very good approximation the many-body effects can be described within a single-particle transition-rate expression using a renormalized matrix element. physics.nist.gov /Divisions/Div841/Gp3/Pubs/abstract/epg419.html   (163 words)

[91.07] The Magnesium-Velocity Dispersion Relation for Early-type Galaxies   (Site not responding. Last check: 2007-10-22) [91.07] The Magnesium-Velocity Dispersion Relation for Early-type Galaxies Data for magnesium absorption feature indices and velocity dispersion for about 2000 early type galaxies is analyzed. Mg-index strength as a function of lookback time is indistinguishable from passive evolution of a monolithic collapse in our simulations, and we suggest that Mg zero-point is not a good test of galaxy evolution. www.aas.org /publications/baas/v35n5/aas203/1089.htm   (208 words)

Properties of lower hybrid solitary structures: A comparison between space observations, a laboratory experiment, and ... The laboratory measurements of electromagnetic fluctuations localized in a plasma density gradient are new and interesting. Furthermore, significant discrepancies between the predictions of the cold homogeneous plasma dispersion relation and the laboratory observations are presented. We speculate that these discrepancies arise because plasma density gradients, essential to description of the laboratory experiment, are neglected in the cold homogeneous plasma dispersion relation. www.agu.org /pubs/crossref/2004/2002JA009673.shtml   (362 words)

[2.03] Dispersion Relation and the Associated Instabilities Occurring in the Plumes   (Site not responding. Last check: 2007-10-22) This numerical result is compared with the recently derived analytical result obtained from the dispersion relations which govern the MHD shear instabilities. These analytical results suggest that there exist two more dispersion relations apart from the two known relations which have been used over the past few years for compressible fluid or plasma studies. These dispersion relations in their incompressible limit exactly reduce to the relations studied elsewhere. www.aas.org /publications/baas/v32n2/spd2000/190.htm   (294 words)

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