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Sinuosity
Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the end points of the curve. This dimensionless quantity can also be rephrased as the "actual path length" divided by the "shortest path length" of a curve. The value ranges from 1 (case of straight line) to infinity (case of a closed loop, where the shortest path length is zero or for an infinitely-long actual path). Interpretation The curve must be continuous (no jump) between the two ends. The sinuosity value is really significant when the line is continuously differentiable (no angular point). The distance between both ends can also be evaluated by a plurality of segments according to a broken line passing through the successive inflection points (sinuosity of order 2). The calculation of the sinuosity is valid in a 3-dimensional space (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinuosity
Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the end points of the curve. This dimensionless quantity can also be rephrased as the "actual path length" divided by the "shortest path length" of a curve. The value ranges from 1 (case of straight line) to infinity (case of a closed loop, where the shortest path length is zero or for an infinitely-long actual path). Interpretation The curve must be continuous (no jump) between the two ends. The sinuosity value is really significant when the line is continuously differentiable (no angular point). The distance between both ends can also be evaluated by a plurality of segments according to a broken line passing through the successive inflection points (sinuosity of order 2). The calculation of the sinuosity is valid in a 3-dimensional space (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meander
A meander is one of a series of regular sinuous curves in the channel of a river or other watercourse. It is produced as a watercourse erodes the sediments of an outer, concave bank ( cut bank) and deposits sediments on an inner, convex bank which is typically a point bar. The result of this coupled erosion and sedimentation is the formation of a sinuous course as the channel migrates back and forth across the axis of a floodplain. The zone within which a meandering stream periodically shifts its channel is known as a meander belt. It typically ranges from 15 to 18 times the width of the channel. Over time, meanders migrate downstream, sometimes in such a short time as to create civil engineering challenges for local municipalities attempting to maintain stable roads and bridges.Neuendorf, K.K.E., J.P. Mehl Jr., and J.A. Jackson, J.A., eds. (2005) ''Glossary of Geology'' (5th ed.). Alexandria, Virginia, American Geological Institute. 779 pp. Charlton, R., 2007. ''Fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometrical Continuity
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surfa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curves
A curve is a geometrical object in mathematics. Curve(s) may also refer to: Arts, entertainment, and media Music * Curve (band), an English alternative rock music group * ''Curve'' (album), a 2012 album by Our Lady Peace * "Curve" (song), a 2017 song by Gucci Mane featuring The Weeknd * ''Curve'', a 2001 album by Doc Walker * "Curve", a song by John Petrucci from '' Suspended Animation'', 2005 * "Curve", a song by Cam'ron from the album '' Crime Pays'', 2009 Periodicals * ''Curve'' (design magazine), an industrial design magazine * ''Curve'' (magazine), a U.S. lesbian magazine Other uses in arts, entertainment, and media * ''Curve'' (film), a 2015 film * BBC Two 'Curve' idents, various animations based around a curve motif Brands and enterprises *Curve (payment card), a payment card that aggregates multiple payment cards * Curve (theatre), a theatre in Leicester, United Kingdom * Curve, fragrance by Liz Claiborne * BlackBerry Curve, a series of phones from Researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rivers
A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows into the ground and becomes dry at the end of its course without reaching another body of water. Small rivers can be referred to using names such as creek, brook, rivulet, and rill. There are no official definitions for the generic term river as applied to geographic features, although in some countries or communities a stream is defined by its size. Many names for small rivers are specific to geographic location; examples are "run" in some parts of the United States, " burn" in Scotland and northeast England, and "beck" in northern England. Sometimes a river is defined as being larger than a creek, but not always: the language is vague. Rivers are part of the water cycle. Water generally collects in a river from precipitation through a drainage basin from surface runoff and other sources such as groundwater recharge, springs, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxbow Lake
An oxbow lake is a U-shaped lake or pool that forms when a wide meander of a river is cut off, creating a free-standing body of water. In South Texas, oxbows left by the Rio Grande are called '' resacas''. In Australia, oxbow lakes are called billabongs. The word "oxbow" can also refer to a U-shaped bend in a river or stream, whether or not it is cut off from the main stream. Geology An oxbow lake forms when a meandering river erodes through the neck of one of its meanders. This takes place because meanders tend to grow and become more curved over time. The river then follows a shorter course that bypasses the meander. The entrances to the abandoned meander eventually silt up, forming an oxbow lake. Because oxbow lakes are stillwater lakes, with no current flowing through them, the entire lake gradually silts up, becoming a bog or swamp and then evaporating completely. When a river reaches a low-lying plain, often in its final course to the sea or a lake, it meanders w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Guardian
''The Guardian'' is a British daily newspaper. It was founded in 1821 as ''The Manchester Guardian'', and changed its name in 1959. Along with its sister papers ''The Observer'' and ''The Guardian Weekly'', ''The Guardian'' is part of the Guardian Media Group, owned by the Scott Trust Limited, Scott Trust. The trust was created in 1936 to "secure the financial and editorial independence of ''The Guardian'' in perpetuity and to safeguard the journalistic freedom and liberal values of ''The Guardian'' free from commercial or political interference". The trust was converted into a limited company in 2008, with a constitution written so as to maintain for ''The Guardian'' the same protections as were built into the structure of the Scott Trust by its creators. Profits are reinvested in journalism rather than distributed to owners or shareholders. It is considered a newspaper of record in the UK. The editor-in-chief Katharine Viner succeeded Alan Rusbridger in 2015. Since 2018, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature'' cover the full r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-organization
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization occurs in many physical, chemical, biological, robotic, and cognitive systems. Examples of self-organization include crystallization, thermal convection of fluids, chemical oscillation, animal swarming, neural circuits, and black mark ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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