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Pieter Kasteleyn
Pieter Willem "Piet" Kasteleyn (12 October 1924 – 16 January 1996) was a Dutch physicist famous for his contributions to the field of statistical mechanics. Biography Pieter Willem Kasteleyn was born in Leiden on 12 October 1924. After finishing high school in 1942, Kasteleyn briefly studied chemistry in Amsterdam. After the war, Leiden University reopened, where he undertook the study of physics and graduated in 1951. He defended his Ph.D. thesis working under S.R. de Groot in 1956. In 1963 Kasteleyn was nominated Full Professor at the Lorentz Institute of Theoretical Physics in Leiden. In 1979 he was elected a member of the Royal Netherlands Academy of Arts and Sciences. From 1981 to 1985 he acted as secretary of the Physics Section of the Academy. From 1978 to 1984 he was chairman of the Commission for Theoretical Physics of the Dutch National Physics Foundation. He retired in 1985. He died on 16 January 1996, after an unexpected and short illness. Research While inves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FKT Algorithm
The FKT algorithm, named after Fisher, Kasteleyn, and Temperley, counts the number of perfect matchings in a planar graph in polynomial time. This same task is #P-complete for general graphs. For matchings that are not required to be perfect, counting them remains #P-complete even for planar graphs. The key idea of the FKT algorithm is to convert the problem into a Pfaffian computation of a skew-symmetric matrix derived from a planar embedding of the graph. The Pfaffian of this matrix is then computed efficiently using standard determinant algorithms. History The problem of counting planar perfect matchings has its roots in statistical mechanics and chemistry, where the original question was: If diatomic molecules are adsorbed on a surface, forming a single layer, how many ways can they be arranged? The partition function is an important quantity that encodes the statistical properties of a system at equilibrium and can be used to answer the previous question. However, trying t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kasteleyn Transition
Pieter Willem "Piet" Kasteleyn (12 October 1924 – 16 January 1996) was a Dutch physicist famous for his contributions to the field of statistical mechanics. Biography Pieter Willem Kasteleyn was born in Leiden on 12 October 1924. After finishing high school in 1942, Kasteleyn briefly studied chemistry in Amsterdam. After the war, Leiden University reopened, where he undertook the study of physics and graduated in 1951. He defended his Ph.D. thesis working under S.R. de Groot in 1956. In 1963 Kasteleyn was nominated Full Professor at the Lorentz Institute of Theoretical Physics in Leiden. In 1979 he was elected a member of the Royal Netherlands Academy of Arts and Sciences. From 1981 to 1985 he acted as secretary of the Physics Section of the Academy. From 1978 to 1984 he was chairman of the Commission for Theoretical Physics of the Dutch National Physics Foundation. He retired in 1985. He died on 16 January 1996, after an unexpected and short illness. Research While investi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leiden
Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration with its suburbs Oegstgeest, Leiderdorp, Voorschoten and Zoeterwoude with 206,647 inhabitants. The Netherlands Central Bureau of Statistics (CBS) further includes Katwijk in the agglomeration which makes the total population of the Leiden urban agglomeration 270,879, and in the larger Leiden urban area also Teylingen, Noordwijk, and Noordwijkerhout are included with in total 348,868 inhabitants. Leiden is located on the Oude Rijn, at a distance of some from The Hague to its south and some from Amsterdam to its north. The recreational area of the Kaag Lakes (Kagerplassen) lies just to the northeast of Leiden. A university city since 1575, Leiden has been one of Europe's most prominent scientific centres for more than four centuries. Leide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Lattice
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as . It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group in IUC notation as , Coxeter notation as , and orbifold notation as . Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered square lattice.. They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard. Symmetry The square lattice's symmetry category is wallpaper group . A pattern with this lattice of translational symmetry cannot have more, but may have less symmetry than the lattice itself. An upright square lattice can be viewed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leiden University Alumni
Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration with its suburbs Oegstgeest, Leiderdorp, Voorschoten and Zoeterwoude with 206,647 inhabitants. The Statistics Netherlands, Netherlands Central Bureau of Statistics (CBS) further includes Katwijk in the agglomeration which makes the total population of the Leiden urban agglomeration 270,879, and in the larger Leiden urban area also Teylingen, Noordwijk, and Noordwijkerhout are included with in total 348,868 inhabitants. Leiden is located on the Oude Rijn (Utrecht and South Holland), Oude Rijn, at a distance of some from The Hague to its south and some from Amsterdam to its north. The recreational area of the Kaag Lakes (Kagerplassen) lies just to the northeast of Leiden. A University town, university city since 1575, Leiden has been one of Eu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1924 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1996 Deaths
File:1996 Events Collage.png, From left, clockwise: A bomb explodes at Centennial Olympic Park in Atlanta, set off by a radical anti-abortionist; The center fuel tank explodes on TWA Flight 800, causing the plane to crash and killing everyone on board; Eight people die in a blizzard on Mount Everest; Dolly the Sheep becomes the first mammal to have been cloned from an adult somatic cell; The Port Arthur Massacre occurs on Tasmania, and leads to major changes in Australia's gun laws; Macarena, sung by Los del Río and remixed by The Bayside Boys, becomes a major dance craze and cultural phenomenon; Ethiopian Airlines Flight 961 crash-ditches off of the Comoros Islands after the plane was hijacked; the 1996 Summer Olympics are held in Atlanta, marking the Centennial (100th Anniversary) of the modern Olympic Games., 300x300px, thumb rect 0 0 200 200 Centennial Olympic Park bombing rect 200 0 400 200 TWA FLight 800 rect 400 0 600 200 1996 Mount Everest disaster rect 0 200 30 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Cluster Model
In statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial structures, electrical networks, etc. It is also referred to as the RC model or sometimes the FK representation after its founders Cees Fortuin and Piet Kasteleyn. Definition Let G = (V,E) be a graph, and \omega: E \to \ be a bond configuration on the graph that maps each edge to a value of either 0 or 1. We say that a bond is ''closed'' on edge e\in E if \omega(e)=0, and open if \omega(e)=1. If we let A(\omega) = \ be the set of open bonds, then an open cluster is any connected component in A(\omega). Note that an open cluster can be a single vertex (if that vertex is not incident to any open bonds). Suppose an edge is open independently with probability p and closed otherwise, then this is just the standard Bernoulli percolation process. The prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domino Tiling
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares. Height functions For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the vertices of the grid. For instance, draw a chessboard, fix a node A_0 with height 0, then for any node there is a path from A_0 to it. On this path define the height of each node A_ (i.e. corners of the squares) to be the height of the previous node A_n plus one if the square on the right of the path from A_n to A_ is black, and minus one otherwise. More details can be found in . Thurston's height condition describes a test for determining whether a simply- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. This established the fields of statistical thermodynamics and statistical physics. The founding of the field of statistical mechanics is generally credited to three physicists: *Ludwig Boltzmann, who developed the fundamental interpretation of entropy in terms of a collection of microstates *James Clerk Maxwell, who developed models of probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Netherlands Academy Of Arts And Sciences
The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory and administrative functions it operates a number of research institutes and awards many prizes, including the Lorentz Medal in theoretical physics, the Dr Hendrik Muller Prize for Behavioural and Social Science and the Heineken Prizes. Main functions The academy advises the Dutch government on scientific matters. While its advice often pertains to genuine scientific concerns, it also counsels the government on such topics as policy on careers for researchers or the Netherlands' contribution to major international projects. The academy offers solicited and unsolicited advice to parliament, ministries, universities and research institutes, funding agencies and internationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
