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In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter in solids and some liquids. Designated a quasiparticle, it represents an excited state in the quantum mechanical quantization of the modes of vibrations of elastic structures of interacting particles. Phonons play a major role in many of the physical properties of condensed matter, such as thermal conductivity and electrical conductivity; the study of phonons is an important part of condensed matter physics. The concept of phonons was introduced in 1932 by Soviet physicist Igor Tamm; the name phonon comes from the Greek word φωνή, which translates to sound or voice because long-wavelength phonons give rise to sound. The name is analogous to the word photon. A phonon is the quantum mechanical description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency. In classical mechanics this designates a normal mode of vibration.

Normal modes are important because any arbitrary lattice vibration can be considered to be a superposition of these elementary vibration modes. While normal modes are wave-like phenomena in classical mechanics, phonons have particle-like properties too, in a way related to the wave–particle duality of quantum mechanics; the equations in this section do not use axioms of quantum mechanics but instead use relations for which there exists a direct correspondence in classical mechanics. For example: a rigid regular, crystalline lattice is composed of N particles; these particles may be molecules. N is a large number, say of the order of 1023, or on the order of Avogadro's number for a typical sample of a solid. Since the lattice is rigid, the atoms must be exerting forces on one another to keep each atom near its equilibrium position; these forces may be Van der Waals forces, covalent bonds, electrostatic attractions, others, all of which are due to the electric force. Magnetic and gravitational forces are negligible.

The forces between each pair of atoms may be characterized by a potential energy function V that depends on the distance of separation of the atoms. The potential energy of the entire lattice is the sum of all pairwise potential energies multiplied by a factor of 1/2 to compensate for double counting: 1 2 ∑ i ≠ j V where ri is the position of the ith atom, V is the potential energy between two atoms, it is difficult to solve this many-body problem explicitly in either classical or quantum mechanics. In order to simplify the task, two important approximations are imposed. First, the sum is only performed over neighboring atoms. Although the electric forces in real solids extend to infinity, this approximation is still valid because the fields produced by distant atoms are screened. Secondly, the potentials V are treated as harmonic potentials; this is permissible as long. Formally, this is accomplished by Taylor expanding V about its equilibrium value to quadratic order, giving V proportional to the displacement x2 and the elastic force proportional to x.

The error in ignoring higher order terms remains small if x remains close to the equilibrium position. The resulting lattice may be visualized as a system of balls connected by springs; the following figure shows a cubic lattice, a good model for many types of crystalline solid. Other lattices include a linear chain, a simple lattice which we will shortly use for modeling phonons; the potential energy of the lattice may now be written as ∑ 1 2 m ω 2 2. Here, ω is the natural frequency of the harmonic potentials, which are assumed to be the same since the lattice is regular. Ri is the position coordinate of the ith atom; the sum over nearest neighbors is denoted. Due to the connections between atoms, the displacement of one or more atoms from their equilibrium positions gives rise to a set of vibration waves propagating through the lattice. One such wave is shown in the figure to the right; the amplitude of the wave is given by the displacements of the atoms from their equilibrium positions. The wavelength λ is marked.

There is a minimum possible wavelength, given by twice the equilibrium separation a between atoms. Any wavelength shorter than this can be mapped onto a wavelength longer than 2a, due to the periodicity of the lattice; this can be thought as one consequence of Nyquist–Shannon sampling theorem, the lattice points are viewed as the "sampling points" of a continuous wave. Not every possible lattice vibration has frequency. However, the normal modes do possess well-defined frequencies. In order to simplify the analysis needed for a 3-dimensional lattice of atoms, it is convenient to model a 1-dimensional lattice or linear chain; this model is complex enough to display the salient features of phonons. The forces between the atoms are assumed to be linear and nearest-neigh

Toda-Kōen Station

Toda-kōen Station is a railway station on the Saikyō Line in Toda, Japan, operated by the East Japan Railway Company. Toda-Kōen Station is served by the Saikyō Line which runs between Ōsaki in Tokyo and Ōmiya in Saitama Prefecture; some trains continue northward to Kawagoe via the Kawagoe Line and southward to Shin-Kiba via the TWR Rinkai Line. The station is located 11.0 km north of Ikebukuro Station. The station identification colour is sky blue; the station consists of one elevated island platform serving two tracks, with the station building underneath. Additional passing tracks lie on either side of the station for non-stop rapid services; the tracks of the Tōhoku Shinkansen run adjacent to this station, on the west side. The station has a "Midori no Madoguchi" staffed ticket office. An arrangement of the Toda City song has been used as the departure melody for trains departing from the up platform since 1 August 2007. Toda-kōen Station opened on 30 September 1985. In fiscal 2014, the station was used by an average of 32,008 passengers daily.

The passenger figures for previous years are as shown below. Arakawa River Toda Park, after which the station is named Boat Race Toda boat racing circuit Toda Rowing Course Toda Chuo General Hospital National Route 17 List of railway stations in Japan Toda-Kōen Station information

South Presbyterian Church

South Presbyterian Church just referred to as South Church, is located along Broadway in Dobbs Ferry, New York, United States. Founded in 1820, it is in its second building, a stone Gothic Revival style structure dating to 1869. Members of the church have done much of the work on both buildings, the church itself is involved in the community; the main church building is the only known extant work of architect Julius Munckowitz. Two outbuildings, a manse and a house built by a former parishioner, were built around the same time and of similar materials but show traces of the Second Empire style, such as mansard roofs, they have changed little since they were first opened, despite the conversion of one into a day care center. All three were added to the National Register of Historic Places in 2000 as a well-preserved example of an urban Gothic Revival church; the property has three buildings: the church, a manse and the Second Empire-style house of Robert Wilde, an early congregant and owner of the property.

All three are considered contributing resources to the National Register listing. The church and Wilde's house are connected by a more modern wing, not; the church is rectangular with smaller narthex and an engaged bell tower. Its central section, faced with granite trimmed with limestone, is three bays wide by five deep. In addition to the non-contributing connecting wing, it has another one, polygonal in shape, original to the building although modified since then. South Presbyterian's exterior has lancet windows with wood tracery, limestone hoods and diamond-shaped bosses; the main entrance features Gothic-carved wood doors beneath a carved tympanum. The bell tower features a lancet window of its own, with four smaller tabernacle windows on its octagonal spire separated from the lower level by a wooden frieze. Inside, the church's sanctuary features a ribbed plaster ceiling and its original pews and wainscoting. Pew number 49 is marked with a brass plaque noting its use by Theodore Roosevelt while he was vacationing in Dobbs Ferry in summer 1871.

The second floor of the original wing has heavy molded plaster cornices. The Wilde House dates to 1870, it is a six-by-three-bay two-story granite structure with brick window trim and a convex mansard roof. The second-story windows are paired, separated by wood colonettes with stylized capitals. Polygonal bays flank a stone course separates the two main stories. A wood front porch has carved balusters, its interior has been modified for its present use as a day care center, but still retains original woodwork such as the banister on the stairway. The hearth of one of the fireplaces still has its original tiling; the manse built in 1869, is a granite building with a mansard roof, in its case a bracketed one topped by red slate. It is three bays square; the roof dormers have bargeboards with Gothic Revival detailing, as does the wooden porch in the rear. There is a one-story two-bay extension on the north side with a flat bracketed roof; some of its fenestration uses Gothic Revival detailing. A front bay window is surrounded with decorative wood carving, in the rear there is a lancet window in the middle of the second story.

As a congregation, South Presbyterian Church dates to 1820. At that time Dobbs Ferry was a small cluster of buildings around a junction on the Albany Post Road, there were no churches. On Sundays devout locals met in the largest building in town, the barn on Peter Van Brugh Livingston's estate, to attend services conducted by travelling Presbyterian or Methodist ministers. Three years the group formally incorporated as South Presbyterian Church, to distinguish themselves from a North Presbyterian Church in the nearby hamlet of Halls Corners. In August 1823, six congregants bought a 1-acre triangle of land at the present junction of Storm Street and Ashford Road; the small church built on the property was made of local timber and painted white in the style of New England rural churches. It was known as the Little White Church for years afterwards. Today it is gone and a Lutheran church stands on the site, but the original cemetery, known as the Little White Cemetery, remains. Two years in 1825, the church was received by the Presbytery of New York.

That body censured the church six years when discord broke out after Van Brugh Livingston, its original benefactor, tried to require that anyone joining the church sign a temperance pledge agreeing to abstain from distilled beverages. He resigned as an elder afterwards; the church continued to grow over the next few decades, by the 1860s it had 140 members. All agreed. James Wilde, one of the wealthier members and bought for the church the current property, closer to the center of the growing village, in 1864. Julius Munckowitz, an architect about whom little is known outside South Presbyterian Church save his early membership in the American Society of Architects and his tenure as supervising architect of the New York City Department of Public Parks, designed the church, the cornerstone was laid in 1868; as with the original church, construction was done by congregants using local materials. The granite was quarried and cut near the old church. Local firms did the carpentry and masonry. Individual members donated money or both.

When the new church was dedicated on the last Sunday in 1869, it had every modern convenience of the day, including gas lighting. The manse, begun that yearWilde had built the stone house as a retirement home, but never used it for that purpose, he inste

Wabanquot (Chippewa chief)

Wabanquot, Wah-bon-ah-quot, Wau-bon-a-quat or Wa-bon-o-quot was an Ojibwa chief. Wabanquot was born at Gull Lake, around 1830, he succeeded to the office of chief of the Ojibwa at the death of his father, one of the principal chiefs for the Gull Lake Band of Mississippi Chippewa. After the Dakota War of 1862, the Gull Lake Band was removed to the Leech Lake area. There, Wabanquot was considered by many to be the principal chief of the removed Mississippi bands of Chippewa, he was a signatory to the Treaty of Washington, in which on June 14, 1868, he led his band to the White Earth Indian Reservation, where he lived until his death 30 years later. Upon his supposed conversion to Christianity sometime in the 1870s, he adopted the name D. G. Wright after an Episcopalian benefactor, but he used his English name. — Wabanquot, 1874, in asking about a clergyman, an Indian Agent, who took property away from Indians without consent or consultation. Chief White Cloud State Monument, in Becker County, in Calvary Catholic Cemetery of the St. Benedict's Mission, a mile south of White Earth, honoring Chippewa Chief White Cloud, was established in 1909.

The monument inscription says:The United States Navy tug USS Wabanquot, in service from 1945 to 1976, was named for him. Department of the Navy Naval Historical Center Dictionary of American Naval Fighting Ships Wabanquot Treaty of Washington This article incorporates text from the public domain Dictionary of American Naval Fighting Ships

Marcel Pérès

Marcel Pérès is a French musicologist, choral director and singer, the founder of the early music group Ensemble Organum. He is an authority on pre-Gregorian chant. Pérès was born into an Algerian family of Spanish origin, repatriated to France, he grew up in Nice, where he was organist at the Anglican church. He trained in organ and composition at the Nice conservatoire, before continuing his studies in church music at the Royal School of Church Music and at English cathedrals, he worked for the National Film Board of Canada. In 1979 he returned to France where he studied medieval music under Michel Huglo at the École pratique des hautes études. In 1984 Peres became director of ARIMM, the Atelier pour la Recherche sur l’Interprétation des Musiques Médiévales with the support of the Fondation Royaumont, created by the Goüin family. In 1994 the Atelier became CERIMM, the Centre Européen pour la Recherche sur l'Interprétation des Musiques Médiévales. In 2001 Pérès and his group Ensemble Organum moved to Moissac where he founded CIRMA, the Centre itinérant de recherche sur les musiques anciennes.

He was musical director of Kaj Munk's play, Ordet, at the Festival d'Avignon in 2008. Pérès' compositions include Le Livre des morts égyptiens, written in 1979, Mysteria Apocalypsis. In 1990 he was awarded the Leonardo da Vinci Prize by the Italian government, Since 1996 he has been a Chevalier dans l'Ordre des Arts et des Lettres. In 2013 he received a title of Honorary Citizen of Jarosław. In 1982 Peres founded Ensemble Organum, a group specialising in "pre- and para-Gregorian" chant; the group has been based at three medieval monastic sites. Sénanque Abbey, an active Cistercian community. Royaumont Abbey, a former Cistercian monastery near Asnières-sur-Oise, run as a cultural centre. Moissac Abbey, a former Benedictine monastery CIRMA and Ensemble Organum

Nazas River

The Nazas River is a river located in northern Mexico, in territory of the states of Coahuila and Durango. It is part of the endorheic Bolsón de Mapimí, it is only 560 kilometres long, but irrigates an area of 71,906 square kilometres in the middle of the desert. The Nazas is nurtured by the San Juan, Potreritos, del Oro, Santiago, Tepehuanes and Peñón Blanco rivers; the river starts at the Sierra Madre Occidental. The aboriginal title for this stream is Tlahualilo, coming from the Nahuatl words tlalli meaning "fertile land" and ahualila, meaning "water for irrigation"; the Nazas took its name when the Spaniards, during the conquest of Mexico in the early 1500s, saw the original inhabitants on the shore of the river fishing with some artifacts similar to baskets, whose Spanish name is'nasa', for that reason it became known as the'river of nazas'. The Nazas watershed contains considerable desertic habitat, outside of the immediate riparian zone. A large variety of flora and fauna populate the Nazas Basin, with a variety of succulent native plants.

One of the widespread flora is the ocotillo. A number of freshwater fishes are found including Notropis nazas; the river acts as a geographic division between the cities of Gómez Palacio in Durango and Torreón in Coahuila. The city of Torreón is named after a tower, built in the area to monitor the water level of the Nazas from afar; the Nazas has served as one of the most important natural resources enabling development in the Laguna Region since the middle of the 19th century. All of its waters are locked in Francisco Zarco and Lázaro Cardenas dams, both located in Durango, which have reduced the once mighty flow of the river. However, Coahuila receives an annual share by mutual agreement between the state governments. Indeed, on its course, the Nazas fills smaller water bodies like the Palmito dam and the Santiaguillo lagoons; the river ends in the Caimán Lakes in the Tlahualilo region. The river was an important shooting location for the film The Wild Bunch. In the celebrated scene where a bridge is dynamited, the Nazas stands in for the Rio Grande.

There is an amateur annual kayak competition on the Nazas River between the cities of Rodeo and Lerdo in Durango. List of longest rivers of Mexico Hogan, C. Michael. 2009. Ocotillo, ed. N. Stromberg Meek, Seth Eugene Meek. 1904. The fresh-water fishes of Mexico north of the isthmus of Tehuantepec, 252 pages Wolfe, Mikael D. 2017. Watering the Revolution: An Environmental and Technological History of Agraria Reform in Mexico. Stanford: Stanford University Press. Río Nazas at Torreon government site