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Coherent Potential Approximation
The coherent potential approximation (or CPA) is a method, in physics, of finding the Green's function of an effective medium. It is a useful concept in understanding how sound waves scatter in a material which displays spatial inhomogeneity. One version of the CPA is an extension to random materials of the muffin-tin approximation, used to calculate electronic band structure in solids. A variational implementation of the muffin-tin approximation to crystalline solids using Green's functions was suggested by Korringa and by Kohn and Rostoker, and is often referred to as the KKR method KKR & Co. Inc., also known as Kohlberg Kravis Roberts & Co., is an American global investment company that manages multiple alternative asset classes, including private equity, energy, infrastructure, real estate, credit, and, through its strateg .... For random materials, the theory is applied by the introduction of an ordered lattice of effective potentials to replace the varying potentials in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential operator, then * the Green's function G is the solution of the equation \operatorname G = \delta, where \delta is Dirac's delta function; * the solution of the initial-value problem \operatorname y = f is the convolution (G \ast f). Through the superposition principle, given a linear ordinary differential equation (ODE), \operatorname y = f, one can first solve \operatorname G = \delta_s, for each , and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of . Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound Waves
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges. Acoustics Acoustics is the interdisciplinary science that deals with the study of mechanical waves in gasses, liquids, and solids including vibration, sound, ultrasound, and infrasound. A scientist who works in the field of acoustics is an ''acoustician'', while someone working in the field of acoustical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Muffin-tin Approximation
The muffin-tin approximation is a shape approximation of the potential well in a crystal lattice. It is most commonly employed in quantum mechanical simulations of the electronic band structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method (APW) is a method which uses muffin-tin approximation. It is a method to approximate the energy states of an electron in a crystal lattice. The basic approximation lies in the potential in which the potential is assumed to be spherically symmetric in the muffin-tin region and constant in the interstitial region. Wave functions (the augmented plane waves) are constructed by matching solutions of the Schrödinger equation within each sphere with plane-wave solutions in the interstitial region, and linear combinations of these wave functions are then determined by the variational method. Many modern electronic structure methods employ the approximation. Among them APW method, the linear muffin-tin orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Band Structure
In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called ''band gaps'' or ''forbidden bands''). Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.). Why bands and band gaps occur The electrons of a single, isolated atom occupy atomic orbitals each of which has a discrete energy level. When two or more atoms join together to form a molecule, their atomic orbitals overlap and hybridize. Similarly, if a large number ''N'' of identical atoms come ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Korringa
Jan Korringa (31 March 1915 – 9 October 2015) was a Dutch American theoretical physicist, specializing in theoretical condensed matter physics. He also contributed to the KKR Method. Education and career Korringa received his undergraduate degree from the Delft University of Technology. In 1937, Korringa went to Leiden University, Netherlands, to pursue graduate studies. Due to the closure of Leiden University, Korringa returned to Delft University of Technology. In 1942, he gave a Doctor of Philosophy from Delft University of Technology and published his thesis, ''Onderzoekingen op het gebied algebraïsche optiek'' (''Essays in the area of science optics''). In 1946, Korringa became an associate professor at the University of Leiden. He was a protégé of Hendrik Kramers, who had been the first protégé of Niels Bohr; a large influence on his interest in quantum mechanics. In 1952, Korringa went to the United States and accepted a full professorship at Ohio State Universi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Kohn
Walter Kohn (; March 9, 1923 – April 19, 2016) was an Austrian-American theoretical physicist and theoretical chemist. He was awarded, with John Pople, the Nobel Prize in Chemistry in 1998. The award recognized their contributions to the understandings of the electronic properties of materials. In particular, Kohn played the leading role in the development of density functional theory, which made it possible to calculate quantum mechanical electronic structure by equations involving the electronic density (rather than the many-body wavefunction). This computational simplification led to more accurate calculations on complex systems as well as many new insights, and it has become an essential tool for materials science, condensed-phase physics, and the chemical physics of atoms and molecules. Early years in Canada Kohn arrived in England as part of the Kindertransport rescue operation immediately after the annexation of Austria by Hitler. He was from a Jewish family, and has wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norman Rostoker
Norman Rostoker (August 16, 1925 – December 25, 2014) was a Canadian plasma physicist known for being a pioneer in developing clean plasma-based fusion energy. He co-founded TAE Technologies (formerly known as Tri Alpha Energy) in 1998 and held 27 U.S. Patents on plasma-based fusion accelerators. The Korringa–Kohn–Rostoker method, a theory in solid-state physics, is named after him. Early life and career Rostoker studied at the University of Toronto, where he received his master's degree in physics in 1947, and received his doctorate in 1950 at the Carnegie Institute of Technology, where he did research from 1948. From 1953 to 1956, he was at the Armor Research Foundation and from 1956 to 1967 at General Atomics in San Diego, from 1965 as manager for fusion and plasma physics projects. He was also a professor at the University of California, San Diego from 1962 to 1965. From 1967, he was an IBM Professor of Engineering at Cornell University, where he headed the Facu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KKR Method
KKR & Co. Inc., also known as Kohlberg Kravis Roberts & Co., is an American global investment company that manages multiple alternative asset classes, including private equity, energy, infrastructure, real estate, credit, and, through its strategic partners, hedge funds. , the firm had completed more than 650 private equity investments in portfolio companies with approximately $675 billion of total enterprise value. , assets under management ("AUM") and fee paying assets under management ("FPAUM") were $471 billion and $357 billion, respectively. The firm was founded in 1976 by Jerome Kohlberg Jr., and cousins Henry Kravis and George R. Roberts, all of whom had previously worked together at Bear Stearns, where they completed some of the earliest leveraged buyout transactions. Since its founding, KKR has completed a number of transactions, including the 1989 leveraged buyout of RJR Nabisco, which was the largest buyout in history to that point, as well as the 2007 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer (publisher)
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRC Press
The CRC Press, LLC is an American publishing group that specializes in producing technical books. Many of their books relate to engineering, science and mathematics. Their scope also includes books on business, forensics and information technology. CRC Press is now a division of Taylor & Francis, itself a subsidiary of Informa. History The CRC Press was founded as the Chemical Rubber Company (CRC) in 1903 by brothers Arthur, Leo and Emanuel Friedman in Cleveland, Ohio, based on an earlier enterprise by Arthur, who had begun selling rubber laboratory aprons in 1900. The company gradually expanded to include sales of laboratory equipment to chemists. In 1913 the CRC offered a short (116-page) manual called the ''Rubber Handbook'' as an incentive for any purchase of a dozen aprons. Since then the ''Rubber Handbook'' has evolved into the CRC's flagship book, the '' CRC Handbook of Chemistry and Physics''. In 1964, Chemical Rubber decided to focus on its publishing ventures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Well-known products include the ''Methods in Enzymology'' series and encyclopedias such as ''The International Encyclopedia of Public Health'' and the ''Encyclopedia of Neuroscience''. See also * Akademische Verlagsgesellschaft (AVG) — the German predecessor, founded in 1906 by Leo Jolowicz (1868–1940), the father of Walter Jolowicz Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
