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Topological Fluid Dynamics
Topological ideas are relevant to fluid dynamics (including magnetohydrodynamics) at the kinematic level, since any fluid flow involves continuous deformation of any transported scalar or vector field. Problems of stirring and mixing are particularly susceptible to topological techniques. Thus, for example, the Thurston–Nielsen classification has been fruitfully applied to the problem of stirring in two-dimensions by any number of stirrers following a time-periodic 'stirring protocol' (Boyland, Aref & Stremler 2000). Other studies are concerned with flows having chaotic particle paths, and associated exponential rates of mixing (Ottino 1989). At the dynamic level, the fact that vortex lines are transported by any flow governed by the classical Euler equations implies conservation of any vortical structure within the flow. Such structures are characterised at least in part by the helicity of certain sub-regions of the flow field, a topological invariant of the equations. Helicity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buoyancy
Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus, the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained by Archimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the Displacement (fluid), displaced fluid. For this reason, an object with average density greater than the surrounding fluid tends to sink because its weight is greater than the weight of the fluid it displaces. If the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renzo L
Renzo, the diminutive of Lorenzo, is an Italian masculine given name and a surname. Given name Notable people named Renzo include the following: * Renzo Alverà (1933–2005), Italian bobsledder *Renzo Arbore (born 1937), Italian TV host, showman, singer, musician, film actor, and film director *Renzo Barbieri (1940–2007), Italian author and editor of Italian comics *Renzo Caldara (born 1943), Italian bobsledder *Renzo Cesana (1907–1970), Italian-American actor, writer, composer, and songwriter * Renzo Cramerotti (born 1947), Italian male javelin thrower * Renzo Dalmazzo (1886–?), Italian lieutenant general *Renzo De Felice (1929–1996), Italian historian *Renzo De Vecchi (1894–1967), Italian football player and coach * Renzo "Larry" Di Ianni (born 1948), Italian-Canadian politician * Renzo Fenci (1914–1999), Italian-American sculptor based in Southern California. *Renzo Furlan (born 1970), Italian tennis player * Renzo Gobbo (born 1961), Italian association foot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Parker
Eugene Newman Parker (June 10, 1927 – March 15, 2022) was an American solar and plasma physicist. In the 1950s he proposed the existence of the solar wind and that the magnetic field in the outer Solar System would be in the shape of a Parker spiral, predictions that were later confirmed by spacecraft measurements. In 1987, Parker proposed the existence of nanoflares, a leading candidate to explain the coronal heating problem. Parker obtained his PhD from Caltech and spent four years as a postdoctoral researcher at the University of Utah. He joined University of Chicago in 1955 and spent the rest of his career there, holding positions in the physics department, the astronomy and astrophysics department, and the Enrico Fermi Institute. Parker was elected to the National Academy of Sciences in 1967. In 2017, NASA named its Parker Solar Probe in his honor, the first NASA spacecraft named after a living person. Biography Parker was born in Houghton, Michigan to Glenn and H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Moffatt
Henry Keith Moffatt, FRS FRSE (born 12 April 1935) is a British mathematician with research interests in the field of fluid dynamics, particularly magnetohydrodynamics and the theory of turbulence. He was Professor of Mathematical Physics at the University of Cambridge from 1980 to 2002. Early life and education Moffatt was born on 12 April 1935 to Emmeline Marchant and Frederick Henry Moffatt''.'' He was schooled at George Watson's College, Edinburgh, going on to study Mathematical Sciences at the University of Edinburgh, graduating in 1957. He then went to Trinity College, Cambridge, where he studied mathematics and, 1959, he was a Wrangler. In 1960, he was awarded a Smith's Prize while preparing his PhD. He received his PhD in 1962; his dissertation, ''Magnetohydrodynamic Turbulence'', was supervised by George Batchelor. Career After completing his PhD, Moffatt joined the staff of the Mathematics Faculty at the University of Cambridge as an Assistant Lecturer and became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hassan Aref
Hassan Aref (Arabic: حسن عارف), (28 September 1950 – 9 September 2011) was the Reynolds Metals Professor in the Department of Engineering Science and Mechanics at Virginia Tech, and the Niels Bohr Visiting Professor at the Technical University of Denmark. Education He was educated at the University of Copenhagen Niels Bohr Institute, graduating in 1975 with a cand. scient degree in Physics and Mathematics. Subsequently he received a PhD degree in Physics from Cornell University in 1980. Career Academia and research Prior to joining Virginia Tech as Dean of Engineering in 2003-2005 Aref was Head of the Department of Theoretical and Applied Mechanics at University of Illinois at Urbana-Champaign for a decade from 1992-2003. Before that he was on the faculty of University of California, San Diego, split between the Department of Applied Mechanics and Engineering Science and the Institute of Geophysics and Planetary Physics 1985-1992. Simultaneously, he was Chief Scient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Khesin
Boris Aronovich Khesin (in Russian: Борис Аронович Хесин, born in 1964) is a Russian and Canadian mathematician working on infinite-dimensional Lie groups, Poisson geometry and hydrodynamics. He has held positions at the University of California, Berkeley, Yale University, and currently is a professor at the University of Toronto. Khesin obtained his Ph.D. from Moscow State University in 1990 under the supervision of Vladimir Arnold (Thesis: ''Normal forms and versal deformations of evolution differential equations''). From 1990 to 1992 he was Morrey Assistant Professor at the University of California at Berkeley and from 1992 to 1996 Assistant Professor at Yale University. In 1997/98 and in 2012 he worked at the Institute for Advanced Study. In 1996 he became Associate Professor and in 2002 Professor at the University of Toronto. He is an editor of the Complete Works of Vladimir Arnold. Honors and awards In 1997 he was awarded the Aisenstadt Prize The André ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Arnold
Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to several areas, including geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem. His first main result was the solution of Hilbert's thirteenth problem in 1957 when he was 19. He co-founded three new branches of mathematics: topological Galois theory (with his student Askold Khovanskii), symplectic topology and KAM theory. Arnold was also a populariser of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as '' Mathematical Methods of Clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reeb Graph
A Reeb graphY. Shinagawa, T.L. Kunii, and Y.L. Kergosien, 1991. Surface coding based on Morse theory. IEEE Computer Graphics and Applications, 11(5), pp.66-78 (named after Georges Reeb by René Thom) is a mathematics, mathematical object reflecting the evolution of the level sets of a real-valued function (mathematics), function on a differentiable manifold, manifold. A similar concept was introduced by Georgy Adelson-Velsky, G.M. Adelson-Velskii and Alexander Kronrod, A.S. Kronrod and applied to analysis of Hilbert's thirteenth problem. Proposed by G. Reeb as a tool in Morse theory, Reeb graphs are the natural tool to study multivalued functional relationships between 2D scalar fields \psi, \lambda, and \phi arising from the conditions \nabla \psi = \lambda \nabla \phi and \lambda \neq 0, because these relationships are single-valued when restricted to a region associated with an individual edge of the Reeb graph. This general principle was first used to study Neutral density#Spat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contour Line
A contour line (also isoline, isopleth, isoquant or isarithm) of a Function of several real variables, function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a cross-section (geometry)#Definition, plane section of the graph of a function of two variables, three-dimensional graph of the function f(x,y) parallel to the (x,y)-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines. The gradient of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivalued Function
In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in its range for at least one point in its domain. It is a set-valued function with additional properties depending on context; some authors do not distinguish between set-valued functions and multifunctions, but English Wikipedia currently does, having a separate article for each. A ''multivalued function'' of sets ''f : X → Y'' is a subset : \Gamma_f\ \subseteq \ X\times Y. Write ''f(x)'' for the set of those ''y'' ∈ ''Y'' with (''x,y'') ∈ ''Γf''. If ''f'' is an ordinary function, it is a multivalued function by taking its graph : \Gamma_f\ =\ \. They are called single-valued functions to distinguish them. Motivation The term multivalued function originated in complex analysis, from analytic continuation. It often occurs that one knows the value of a complex analytic function f(z) in some neighbourhood of a point z=a. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Density
The neutral density ( \gamma^n\, ) or empirical neutral density is a density variable used in oceanography, introduced in 1997 by David R. Jackett and Trevor McDougall.Jackett, David R., Trevor J. McDougall, 1997: A Neutral Density Variable for the World's Oceans. J. Phys. Oceanogr., 27, 237–263 It is a function of the three state variables (salinity, temperature, and pressure) and the geographical location (longitude and latitude). It has the typical units of density (M/V). Isosurfaces of \gamma^n\, form “neutral density surfaces”, which are closely aligned with the "neutral tangent plane". It is widely believed, although this has yet to be rigorously proven, that the flow in the deep ocean is almost entirely aligned with the neutral tangent plane, and strong lateral mixing occurs along this plane ("epineutral mixing") vs weak mixing across this plane ("dianeutral mixing"). These surfaces are widely used in water mass analyses. Neutral density is a density variable that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
