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Equations Of State Calculations By Fast Computing Machines
"Equation of State Calculations by Fast Computing Machines" is a scholarly article published by Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller in the Journal of Chemical Physics in 1953. This paper proposed what became known as the Metropolis Monte Carlo algorithm, later generalized as the Metropolis–Hastings algorithm, which forms the basis for Monte Carlo statistical mechanics simulations of atomic and molecular systems. Development Some controversy exists with regard to credit for development of the algorithm. Prior to 2003, there was no detailed account of the algorithm's development. Then, shortly before his death, Marshall Rosenbluth attended a 2003 conference at LANL marking the 50th anniversary of the 1953 publication. At this conference, Rosenbluth described the algorithm and its development in a presentation titled "Genesis of the Monte Carlo Algorithm for Statistical Mechanics". Further historical clari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scholarly Article
Academic publishing is the subfield of publishing which distributes academic research and scholarship. Most academic work is published in academic journal articles, books or theses. The part of academic written output that is not formally published but merely printed up or posted on the Internet is often called "grey literature". Most scientific and scholarly journals, and many academic and scholarly books, though not all, are based on some form of peer review or editorial refereeing to qualify texts for publication. Peer review quality and selectivity standards vary greatly from journal to journal, publisher to publisher, and field to field. Most established academic disciplines have their own journals and other outlets for publication, although many academic journals are somewhat interdisciplinary, and publish work from several distinct fields or subfields. There is also a tendency for existing journals to divide into specialized sections as the field itself becomes more specia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and light. Energy is a Conservation law, conserved quantity—the law of conservation of energy states that energy can be Energy transformation, converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a Classical field theory, field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, the internal energy contained within a thermodynamic system, and rest energy associated with an object's rest mass. These are not mutual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William L
William is a masculine given name of Germanic origin. It became popular in England after the Norman conquest in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will or Wil, Wills, Willy, Willie, Bill, Billie, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie). Female forms include Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the German given name ''Wilhelm''. Both ultimately descend from Proto-Germanic ''*Wiljahelmaz'', with a direct cognate also in the Old Norse name ''Vilhjalmr'' and a West Germanic borrowing into Medieval Latin ''Willelmus''. The Proto-Germanic name is a compound of *''wiljô'' "will, wish, desire" and *''helmaz'' "helm, helmet".Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a Lemon (geometry), spindle torus (or ''self-crossing torus'' or ''self-intersecting torus''). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector In mathematics, a unit vector in a normed vector space is a Vector (mathematics and physics), vector (often a vector (geometry), spatial vector) of Norm (mathematics), length 1. A unit vector is often denoted by a lowercase letter with a circumfle ..., for example) does not necessarily have unit size, or even a particular size at all. Rather, the primitive cell is the closest analogy to a unit vector, since it has a determined size for a given lattice and is the basic building block from which larger cells are constructed. The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its unit cell, which is a section of the tiling (a parallelogra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Boundary Conditions
Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a ''unit cell''. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a ''world map'' of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (Compactification (mathematics), compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called ''images''. During the simulation, only the properties of the original simulation box need to be recorded and propaga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Alamos National Lab
Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development laboratories of the United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, in the American southwest. Best known for its central role in helping develop the first atomic bomb, LANL is one of the world's largest and most advanced scientific institutions. Los Alamos was established in 1943 as Project Y, a top-secret site for designing nuclear weapons under the Manhattan Project during World War II.The site was variously called Los Alamos Laboratory and Los Alamos Scientific Laboratory. Chosen for its remote yet relatively accessible location, it served as the main hub for conducting and coordinating nuclear research, bringing together some of the world's most famous scientists, among them numerous Nobel Prize winners. The town of Los Alamos, directly north of the lab, grew extensively through this period. After th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MANIAC
__NOTOC__ The MANIAC I (Mathematical Analyzer Numerical Integrator and Automatic Computer Model I) was an early computer built under the direction of Nicholas Metropolis at the Los Alamos Scientific Laboratory. It was based on the von Neumann architecture of the IAS, developed by John von Neumann. As with almost all computers of its era, it was a one-of-a-kind machine that could not exchange programs with other computers (even the several other machines based on the IAS). Metropolis chose the name MANIAC in the hope of stopping the rash of silly acronyms for machine names, although von Neumann may have suggested the name to him. The MANIAC weighed about . The first task assigned to the Los Alamos MANIAC was to perform more precise and extensive calculations of the thermonuclear process. In 1953, the MANIAC obtained the first equation of state calculated by modified Monte Carlo integration over configuration space. In 1956, MANIAC I became the first computer to defeat a human ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lennard-Jones Potential
In computational chemistry, molecular physics, and physical chemistry, the Lennard-Jones potential (also termed the LJ potential or 12-6 potential; named for John Lennard-Jones) is an intermolecular pair potential. Out of all the intermolecular potentials, the Lennard-Jones potential is probably the one that has been the most extensively studied. It is considered an archetype model for simple yet realistic intermolecular interactions. The Lennard-Jones potential is often used as a building block in molecular models (a.k.a. force fields) for more complex substances. Many studies of the idealized "Lennard-Jones substance" use the potential to understand the physical nature of matter. Overview The Lennard-Jones potential is a simple model that still manages to describe the essential features of interactions between simple atoms and molecules: Two interacting particles repel each other at very close distance, attract each other at moderate distance, and eventually stop intera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Sphere
Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") repulsion that atoms and spherical molecules experience at very close distances. Hard spheres systems are studied by analytical means, by molecular dynamics simulations, and by the experimental study of certain colloidal model systems. Beside being a model of theoretical significance, the hard-sphere system is used as a basis in the formulation of several modern, predictive Equations of State for real fluids through the SAFT approach, and models for transport properties in gases through Chapman-Enskog Theory. Formal definition Hard spheres of diameter \sigma are particles with the following pairwise interaction potential: V(\mathbf_1, \mathbf_2) = \begin 0 & \text \quad , \mathbf_1-\mathbf_2, \geq \sigma \\ \infty & \text \qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Though there are many equations of state, none accurately predicts properties of substances under all conditions. The quest for a universal equation of state has spanned three centuries. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit Of A Sequence
As the positive integer n becomes larger and larger, the value n\times \sin\left(\tfrac1\right) becomes arbitrarily close to 1. We say that "the limit of the sequence n \times \sin\left(\tfrac1\right) equals 1." In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the \lim symbol (e.g., \lim_a_n).Courant (1961), p. 29. If such a limit exists and is finite, the sequence is called convergent. A sequence that does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests. Limits can be defined in any metric space, metric or topological space, but are usually first encountered in the real numbers. History The Greek philosopher Zeno of Elea is famous for formulating Zeno's paradoxes, paradoxes that involve limiting processes. Leucippus, Democritus, Antiphon (person), Antiphon, Eudoxus of Cnidus, Eudoxus, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
