![]() In typical fashion for Christian theologians of the era (and for many still today), Daneau positions the Jewish Diaspora as a necessary precursor for Christian evangelism. It also appears several times in the Christian New Testament, which was originally written in Greek, in reference to the apostles spreading the gospel.ĭiaspora makes its English debut in the closing years of the sixteenth century, in a 1594 translation of Lambert Daneau’s A Fruitfull Commentarie Upon the Twelve Small Prophets. It appears multiple times in the Septuagint, a second-to-third century BCE Greek translation of the Hebrew Bible. The word comes from the Hellenistic Greek διασπορά ( δια- “across” + σπορά “sowing”). The word has been subsequently applied to other ethnic groups scattered outside their homelands, and even to any group that has dispersed. The Diaspora, with capital letters, is that of Jews throughout the ancient world, which began with the destruction of the First Temple in 586 BCE. ![]() doi: 10.A diaspora is a dispersal of people or the collection of places where such people are dispersed. "Higher order Laue zone effects in electron diffraction and their use in lattice parameter determination". Water wave mechanics for engineers and scientists. The universality of the Kramers–Kronig relations (1926–27) became apparent with subsequent papers on the dispersion relation's connection to causality in the scattering theory of all types of waves and particles. ĭispersion of waves on water was studied by Pierre-Simon Laplace in 1776. Isaac Newton studied refraction in prisms but failed to recognize the material dependence of the dispersion relation, dismissing the work of another researcher whose measurement of a prism's dispersion did not match Newton's own. This dynamical effect has found application in the precise measurement of lattice parameters, beam energy, and more recently for the electronics industry: lattice strain. With high-energy (e.g., 200 keV, 32 fJ) electrons in a transmission electron microscope, the energy dependence of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns allows one, in effect, to directly image cross-sections of a crystal's three-dimensional dispersion surface. The others are optical phonons, since they can be excited by electromagnetic radiation. For most systems, the phonons can be categorized into two main types: those whose bands become zero at the center of the Brillouin zone are called acoustic phonons, since they correspond to classical sound in the limit of long wavelengths. The dispersion relation of phonons is also non-trivial and important, being directly related to the acoustic and thermal properties of a material. Phonons are to sound waves in a solid what photons are to light: they are the quanta that carry it. Properties of the band structure define whether the material is an insulator, semiconductor or conductor.įurther information: Phonon § Dispersion relation The collection of all possible energies and momenta is known as the band structure of a material. The periodicity of crystals means that many levels of energy are possible for a given momentum and that some energies might not be available at any momentum. In the study of solids, the study of the dispersion relation of electrons is of paramount importance. ![]() The speed of a plane wave, v is a constant that depends on the string. Main articles: Dispersion (optics), Dispersion (water waves), and Acoustic dispersionĭispersion occurs when sinusoidal waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency dependence of wave propagation and attenuation.ĭispersion may be caused either by geometric boundary conditions ( waveguides, shallow water) or by interaction of the waves with the transmitting medium. Given the dispersion relation, one can calculate the phase velocity and group velocity of waves in the medium, as a function of frequency. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.
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