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Ion Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. Terminology The word ''flux'' comes from Latin: ''fluxus'' means "flow", and ''fluere'' is "to flow". As '' fluxion'', this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), defines ''fluxion'' as a central quantity and proceeds to derive the now well-known expressions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth". The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several inequivalent such formalizations that are all called ''surface'', sometimes with a qualifier such as algebraic surface, smooth surface or fractal surface. The concept of surface and its mathematical abstractions are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Theorem Of Calculus
The fundamental theorem of calculus is a theorem that links the concept of derivative, differentiating a function (mathematics), function (calculating its slopes, or rate of change at every point on its domain) with the concept of integral, integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be thought of as inverses of each other. The first part of the theorem, the first fundamental theorem of calculus, states that for a continuous function , an antiderivative or indefinite integral can be obtained as the integral of over an interval with a variable upper bound. Conversely, the second part of the theorem, the second fundamental theorem of calculus, states that the integral of a function over a fixed Interval (mathematics), interval is equal to the change of any antiderivative between the ends of the interval. This greatly simplifies the calculation of a definite integral pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Area
In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions. Every bounded surface in three dimensions can be associated with a unique area vector called its vector area. It is equal to the surface integral of the surface normal, and distinct from the usual ( scalar) surface area. Vector area can be seen as the three dimensional generalization of signed area in two dimensions. Definition For a finite planar surface of scalar area and unit normal , the vector area is defined as the unit normal scaled by the area: \mathbf = \hat \mathbfS For an orientable surface composed of a set of flat facet areas, the vector area of the surface is given by \mathbf = \sum_i \hat \mathbf_i S_i where is the unit normal vector to the area . For bounded, oriented curved surfaces that are sufficiently well-behaved, we can still define vector area. First, we split the su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface (mathematics)
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space. The exact definition of a surface may depend on the context. Typically, in algebraic geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological space of dimension two; this means that a moving point on a surface may move in two directions (it has two degrees of freedom). In other words, around almost every point, there is a '' coordinate patch'' on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two Euclidean vector, vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the Product (mathematics), products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weathervane
A wind vane, weather vane, or weathercock is an list of weather instruments, instrument used for showing the wind direction, direction of the wind. It is typically used as an architectural ornament to the highest point of a building. The word ''vane'' comes from the Old English word , meaning "flag". Although partly functional, wind vanes are generally decorative, often featuring the traditional chicken, cockerel design with letters indicating the points of the compass. Other common motifs include ships, arrows, and horses. Not all wind vanes have pointers. In a sufficiently strong wind, the head of the arrow or cockerel (or equivalent) will indicate the direction from which the wind is blowing. Wind vanes are also found on small wind turbines to keep the wind turbine pointing into the wind. History The oldest known textual references to weather vanes date from 1800-1600 BCE Babylon, where a fable called ''The Fable of the Willow'' describes people looking at a weather vane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abuse Of Notation
In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not entirely formally correct, but which might help simplify the exposition or suggest the correct intuition (while possibly minimizing errors and confusion at the same time). However, since the concept of formal/syntactical correctness depends on both time and context, certain notations in mathematics that are flagged as abuse in one context could be formally correct in one or more other contexts. Time-dependent abuses of notation may occur when novel notations are introduced to a theory some time before the theory is first formalized; these may be formally corrected by solidifying and/or otherwise improving the theory. ''Abuse of notation'' should be contrasted with ''misuse'' of notation, which does not have the presentational benefits of the former and should be avoided (such as the misuse of constants of integration). A related concept is abuse of language or abuse of termin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Field
In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical quantity (with units). In a physical context, scalar fields are required to be independent of the choice of reference frame. That is, any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory. Definition Mathematically, a scalar field on a region ''U'' is a real or complex-valued function or distribution on ''U''. The region ''U'' may be a set in some Euclidean space, Minkowski spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Quantity
A physical quantity (or simply quantity) is a property of a material or system that can be Quantification (science), quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ''numerical value'' and a ''unit of measurement''. For example, the physical quantity mass, symbol ''m'', can be quantified as ''m'n''kg, where ''n'' is the numerical value and kg is the unit symbol (for kilogram). Quantities that are vectors have, besides numerical value and unit, direction or orientation in space. Components Following ISO 80000-1, any value or Magnitude (mathematics), magnitude of a physical quantity is expressed as a comparison to a unit of that quantity. The ''value'' of a physical quantity ''Z'' is expressed as the product of a ''numerical value'' (a pure number) and a unit [''Z'']: :Z = \ \times [Z] For example, let Z be "2 metres"; then, \ = 2 is the numerical value and [Z] = \mathrm is the unit. Conversely, the nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Integral - Definition
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth". The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several inequivalent such formalizations that are all called ''surface'', sometimes with a qualifier such as algebraic surface, smooth surface or fractal surface. The concept of surface and its mathematical abstractions are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Flux Diagram
A general officer is an officer of high rank in the armies, and in some nations' air and space forces, marines or naval infantry. In some usages, the term "general officer" refers to a rank above colonel."general, adj. and n.". OED Online. March 2021. Oxford University Press. https://www.oed.com/view/Entry/77489?rskey=dCKrg4&result=1 (accessed May 11, 2021) The adjective ''general'' had been affixed to officer designations since the late medieval period to indicate relative superiority or an extended jurisdiction. French Revolutionary system Arab system Other variations Other nomenclatures for general officers include the titles and ranks: * Adjutant general * Commandant-general * Inspector general * General-in-chief * General of the Air Force (USAF only) * General of the Armies of the United States (of America), a title created for General John J. Pershing, and subsequently granted posthumously to George Washington and Ulysses S. Grant * (" general admiral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
