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Cone (other)
A cone is a basic geometrical shape. Cone may also refer to: Mathematics *Cone (category theory) *Cone (formal languages) * Cone (graph theory), a graph in which one vertex is adjacent to all others *Cone (linear algebra), a subset of vector space *Mapping cone (homological algebra) *Cone (topology) *Conic bundle, a concept in algebraic geometry *Conical surface, generated by a moving line with one fixed point *Projective cone, the union of all lines that intersect a projective subspace and an arbitrary subset of some other disjoint subspace Computing * Cone (software), a text-based e-mail and news client for Unix-like operating systems *Cone tracing, a derivative of the ray-tracing algorithm that replaces rays, which have no thickness, with cones *Second-order cone programming, a library of routines that implements a predictor corrector variant of the semidefinite programming algorithm Astronomy *Cone Nebula (also known as NGC 2264), an H II region in the constellation of Mono ...
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Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the ''lateral surface''; if the lateral surface is unbounded, it is a conical surface. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lin ...
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Cone Algorithm
In computational geometry, the cone algorithm is an algorithm for identifying the particles that are near the surface of an object composed of discrete particles. Its applications include computational surface science and computational nano science. The cone algorithm was first described in a publication about nanogold Colloidal gold is a sol or colloidal suspension of nanoparticles of gold in a fluid, usually water. The colloid is usually either wine-red coloured (for spherical particles less than 100  nm) or blue/purple (for larger spherical particl ... in 2005. The cone algorithm works well with clusters in condensed phases, including solid and liquid phases. It can handle the situations when one configuration includes multiple clusters or when holes exist inside clusters. It can also be applied to a cluster iteratively to identify multiple sub-surface layers. References * Yanting Wang, S. Teitel, and Christoph Dellago (2005)Melting of Icosahedral Gold Nanoclus ...
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Hertzian Cone
A Hertzian cone is the cone produced when an object passes through a solid, such as a bullet through glass. More technically, it is a cone of force that propagates through a brittle, amorphous, or cryptocrystalline solid material from a point of impact. This force eventually removes a full or partial cone in the material. This is the physical principle that explains the form and characteristics of the flakes removed from a core of tool stone during the process of lithic reduction. This phenomenon is named after the German physicist Heinrich Rudolf Hertz, who first described this type of wave-front propagation through various media. Although it might not be agreed by all, natural phenomena which have been grouped with the Hertzian cone phenomena include the crescentic " chatter marks" made on smoothed bedrock by glacial ice dragging along boulders at its base, the numerous crescentic impact marks sometimes seen on pebbles and cobbles, and the shatter cones found at bolide impac ...
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Helical Cone Beam Computed Tomography
X-ray computed tomography operates by using an X-ray generator that rotates around the object; X-ray detectors are positioned on the opposite side of the circle from the X-ray source. A visual representation of the raw data obtained is called a ''sinogram'', yet it is not sufficient for interpretation. Once the scan data has been acquired, the data must be processed using a form of tomographic reconstruction, which produces a series of cross-sectional images. In terms of mathematics, the raw data acquired by the scanner consists of multiple "projections" of the object being scanned. These projections are effectively the Radon transformation of the structure of the object. Reconstruction essentially involves solving the inverse Radon transformation. Structure In conventional CT machines, an X-ray tube and detector are physically rotated behind a circular shroud (see the image above right). An alternative, short lived design, known as electron beam tomography (EBT), used electrom ...
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Conical Scanning
Conical scanning is a system used in early radar units to improve their accuracy, as well as making it easier to steer the antenna properly to point at a target. Conical scanning is similar in concept to the earlier lobe switching concept used on some of the earliest radars, and many examples of lobe switching sets were modified in the field to conical scanning during World War II, notably the German Würzburg radar. Antenna guidance can be made entirely automatic, as in the American SCR-584. Potential failure modes and susceptibility to deception jamming led to the replacement of conical scan systems with monopulse radar sets. They are still used by the Deep Space Network for maintaining communications links to space probes. The spin-stabilized Pioneer 10 and Pioneer 11 probes used onboard conical scanning maneuvers to track Earth in its orbit. Concept A typical radar antenna commonly has a beam width of a few degrees. While this is adequate for locating the target in an earl ...
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Conical Pendulum
A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of swinging back and forth, the bob of a conical pendulum moves at a constant speed in a circle with the string (or rod) tracing out a cone. The conical pendulum was first studied by the English scientist Robert Hooke around 1660 as a model for the orbital motion of planets. In 1673 Dutch scientist Christiaan Huygens calculated its period, using his new concept of centrifugal force in his book ''Horologium Oscillatorium''. Later it was used as the timekeeping element in a few mechanical clocks and other clockwork timing devices. Uses During the 1800s, conical pendulums were used as the timekeeping element in a few clockwork timing mechanisms where a smooth motion was required, as opposed to the unavoidably jerky motion provided by ordinary pendulums. Two examples were mechanisms to turn the lenses of ...
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Conical Mill
A conical mill (or conical screen mill) is a machine used to reduce the size of material in a uniform manner. It is an alternative to the hammermill or other forms of grinding mills. As the name implies, the conical mill varies in diameter from where the feed enters to where the product exits. The conical mill operates by having the product being fed into the mill by gravity or vacuum. A rotating impeller forces the material outward to a conical screen surface, where it is sized and passed through the openings in the screen. Once finished, the product simply drops through the milling chamber to a receptacle underneath. Conical mills come in a variety of sizes from tabletop lab models to full-size high-capacity machines for use in processing large quantities of material, and the impeller and screen can be customized for each individual use. The machines can be used not only to reduce the size of particles, but also for deagglomeration, sieving, dispersion, and mixing. The applicat ...
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Conical Measure
A conical measure is a type of laboratory glassware which consists of a conical cup with a notch on the top to allow for the easy pouring of liquids, and graduated markings on the side to allow easy and accurate measurement of volumes of liquid. They may be made of plastic, glass, or borosilicate glass. The use of the conical measure usually dictates its construction material. Plastic conical measures, commonly referred to as measuring cups are used by patients to measure liquid medicaments for oral administration. Glass and borosilicate conical measures are commonly used when compounding by the pharmacy profession. Conical measures are the most commonly used item of glassware used in the preparation of extemporaneous medicaments. They are not as precise as graduated cylinders for measuring liquids, but make up for this in terms of easy pouring and ability to mix solutions within the measure itself. History During his experiments, Abū al-Rayhān al-Bīrūnī (973-1048) invented t ...
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Conical Intersection
In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenheimer approximation breaks down and the coupling between electronic and nuclear motion becomes important, allowing non-adiabatic processes to take place. The location and characterization of conical intersections are therefore essential to the understanding of a wide range of important phenomena governed by non-adiabatic events, such as photoisomerization, photosynthesis, vision and the photostability of DNA. The conical intersection involving the ground electronic state potential energy surface of the C6H3F3+ molecular ion is discussed in connection with the Jahn–Teller effect in Section 13.4.2 on pages 380-388 of the textbook by Bunker and Jensen. Conical inters ...
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Cone Penetrometer
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the ''lateral surface''; if the lateral surface is unbounded, it is a conical surface. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, ...
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Cone Penetration Test
The cone penetration or cone penetrometer test (CPT) is a method used to determine the geotechnical engineering properties of soils and delineating soil stratigraphy. It was initially developed in the 1950s at the Dutch Laboratory for Soil Mechanics in Delft to investigate soft soils. Based on this history it has also been called the "Dutch cone test". Today, the CPT is one of the most used and accepted soil methods for soil investigation worldwide. The test method consists of pushing an instrumented cone, with the tip facing down, into the ground at a controlled rate (controlled between 1.5 -2.5 cm/s accepted). The resolution of the CPT in delineating stratigraphic layers is related to the size of the cone tip, with typical cone tips having a cross-sectional area of either 10 or 15 cm², corresponding to diameters of 3.6 and 4.4 cm. A very early ultra-miniature 1 cm² subtraction penetrometer was developed and used on a US mobile ballistic missile launch sys ...
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Cone Of Depression
A cone of depression occurs in an aquifer when groundwater is pumped from a Water well, well. In an unconfined aquifer (water table), this is an actual depression of the water levels. In confined aquifers (Artesian aquifer, artesian), the cone of depression is a reduction in the pressure head surrounding the pumped well. When a well is pumped, the water level in the well is lowered. By lowering this water level, a gradient occurs between the water in the surrounding aquifer and the water in the well. Because water flows from high to low water levels or pressure, this gradient produces a flow from the surrounding aquifer into the well. As the water flows into the well, the water levels or pressure in the aquifer around the well decrease. The amount of this decline becomes less with distance from the well, resulting in a cone-shaped depression radiating away from the well. This, in appearance, is similar to the effect one sees when the plug is pulled from a bathtub. This conical-sha ...
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