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Plummer Model
The Plummer model or Plummer sphere is a density law that was first used by H. C. Plummer to fit observations of globular clusters. It is now often used as toy model in N-body simulations of stellar systems. Description of the model The Plummer 3-dimensional density profile is given by : \rho_P(r) = \frac \left(1 + \frac\right)^, where ''M_0'' is the total mass of the cluster, and ''a'' is the Plummer radius, a scale parameter that sets the size of the cluster core. The corresponding potential is : \Phi_P(r) = -\frac, where ''G'' is Newton's gravitational constant. The velocity dispersion is : \sigma_P^2(r) = \frac. The distribution function is : f(\vec, \vec) = \frac \frac (-E(\vec, \vec))^, if E < 0, and otherwise, where is the .
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Henry Crozier Keating Plummer
Henry Crozier Keating Plummer FRS FRAS (24 October 1875 – 30 September 1946) was an English astronomer. Early years and education Born in Oxford, Plummer was the son of William Edward Plummer (1849–1928) and nephew of the distinguished astronomer John Isaac Plummer (1845-1925). He gained his education at St. Edward's School and then Hertford College at Oxford University. After studies in physics, he became a lecturer at Owen's College, Manchester, instructing in mathematics. Career In 1900, he became an assistant at the Radcliffe Observatory, Oxford, where his father had served previously. He remained there for most of the next twelve years, spending one year at Lick Observatory as a Research Fellow. In 1912, he was appointed to the position of Andrews Professor of Astronomy at Trinity College, Dublin, which carried with it the title of Royal Astronomer of Ireland. He was the last holder of both positions. He was the director of the Dunsink Observatory from 1912 to 1920 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star Clusters
Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clustered groups of stars, generally containing fewer than a few hundred members, and are often very young. Open clusters become disrupted over time by the gravitational influence of giant molecular clouds as they move through the galaxy, but cluster members will continue to move in broadly the same direction through space even though they are no longer gravitationally bound; they are then known as a stellar association, sometimes also referred to as a ''moving group''. Star clusters visible to the naked eye include the Pleiades, Hyades, and 47 Tucanae. Open cluster Open clusters are very different from globular clusters. Unlike the spherically distributed globulars, they are confined to the galactic plane, and are almost always foun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Units
''N''-body units are a completely self-contained system of units used for ''N''-body simulations of self-gravitating systems in astrophysics. In this system, the base physical units are chosen so that the total mass, ''M'', the gravitational constant, ''G'', and the virial radius, ''R'', are normalized. The underlying assumption is that the system of ''N'' objects (stars) satisfies the virial theorem In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. .... The consequence of standard ''N''-body units is that the velocity dispersion of the system, ''v'', is \scriptstyle \frac\sqrt and that the dynamical or crossing time, ''t'', is \scriptstyle 2\sqrt . The use of standard ''N''-body units was advocated by Michel Hénon in 1971. Early adopters of this system of units included H. Cohn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Function
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients , , , and are complex numbers, and the variable takes real values, and a\neq 0. In other words, it is both a polynomial function of degree three, and a real function. In particular, the domain and the codomain are the set of the real numbers. Setting produces a cubic equation of the form :ax^3+bx^2+cx+d=0, whose solutions are called roots of the function. A cubic function has either one or three real roots (which may not be distinct); all odd-degree polynomials have at least one real root. The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point. Up to an affine transformation, there are only t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Function
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients , , , and are complex numbers, and the variable takes real values, and a\neq 0. In other words, it is both a polynomial function of degree three, and a real function. In particular, the domain and the codomain are the set of the real numbers. Setting produces a cubic equation of the form :ax^3+bx^2+cx+d=0, whose solutions are called roots of the function. A cubic function has either one or three real roots (which may not be distinct); all odd-degree polynomials have at least one real root. The graph of a cubic function always has a single inflection point. It may have two critical points, a local minimum and a local maximum. Otherwise, a cubic function is monotonic. The graph of a cubic function is symmetric with respect to its inflection point; that is, it is invariant under a rotation of a half turn around this point. Up to an affine transformation, there are only thre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Relative Angular Momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. " Specific" in this context indicates angular momentum per unit mass. The SI unit for specific relative angular momentum is square meter per second. Definition The specific relative angular momentum is defined as the cross product of the relative position vector \mathbf and the relative velocity vector \mathbf . \mathbf = \mathbf\times \mathbf = \frac where \mathbf is the angular momentum vector, defined as \mathbf \times m \mathbf. The \mathbf vector is always perpendicular to the instantane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virial Theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by potential forces, with that of the total potential energy of the system. Mathematically, the theorem states \left\langle T \right\rangle = -\frac12\,\sum_^N \bigl\langle \mathbf_k \cdot \mathbf_k \bigr\rangle where is the total kinetic energy of the particles, represents the force on the th particle, which is located at position , and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from ''vis'', the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870. The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herwig Dejonghe
Herwig is both a masculine German given name and a surname. Notable people with the name include: Given name: *Herwig Ahrendsen (born 1948), German handball player *Herwig Dirnböck (born 1935), Austrian sprint canoeist *Herwig Drechsel (born 1973), Austrian footballer *Herwig Görgemanns (born 1931), German classical scholar *Herwig Kircher (born 1955), Austrian footballer *Herwig Kogelnik (born 1932), Austrian electrical engineer *Herwig Mitteregger (born 1953), Austrian musician *Herwig Reiter (born 1941), Austrian composer *Herwig Schopper (born 1924), German physicist *Herwig van Staa (born 1942), Austrian politician *Herwig Wolfram (born 1934), Austrian historian Surname: *Bob Herwig (1914–1974), American football player * Conrad Herwig (born 1959), American jazz trombonist *Holger Herwig (born 1941), German-Canadian historian *Malte Herwig (born 1972), German writer, journalist and literary critic *Walther Herwig Walther Herwig (February 25, 1838, Bad Arolsen, Waldeck â ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Globular Cluster
A globular cluster is a spheroidal conglomeration of stars. Globular clusters are bound together by gravity, with a higher concentration of stars towards their centers. They can contain anywhere from tens of thousands to many millions of member stars. Their name is derived from Latin (small sphere). Globular clusters are occasionally known simply as "globulars". Although one globular cluster, Omega Centauri, was observed in antiquity and long thought to be a star, recognition of the clusters' true nature came with the advent of telescopes in the 17th century. In early telescopic observations globular clusters appeared as fuzzy blobs, leading French astronomer Charles Messier to include many of them in his catalog of astronomical objects that he thought could be mistaken for comets. Using larger telescopes, 18th-century astronomers recognized that globular clusters are groups of many individual stars. Early in the 20th century the distribution of globular clusters in the sky w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Energy
Specific energy or massic energy is energy per unit mass. It is also sometimes called gravimetric energy density, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, stored heat and other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties. The SI unit for specific energy is the joule per kilogram (J/kg). Other units still in use in some contexts are the kilocalorie per gram (Cal/g or kcal/g), mostly in food-related topics, watt hours per kilogram in the field of batteries, and the Imperial unit BTU per pound (Btu/lb), in some engineering and applied technical fields. Kenneth E. Heselton (2004)"Boiler Operator's Handbook" Fairmont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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