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	Irrotational vector field Information
		In vector calculus, an irrotational or conservative vector field is a vector field whose curl is zero.
		In fluid mechanics, an irrotational field is practically synonymous with a lamellar field.
		The adjective "irrotational" implies that irrotational fluid flow (whose velocity field is irrotational) has no rotational component: the fluid does not move in circular or helical motions; it does not form vortices.
	www.bookrags.com /wiki/Irrotational_vector_field (179 words)

	Irrotational vector field (Site not responding. Last check: 2007-10-28)
		Category:Multivariate calculus In fluid mechanics, an irrotational vector field is a vector field whose curl is zero.
		An irrotational field is practically synonymous with a lamellar field.
		The adjective "irrotational" implies that irrotational fluid flow (whose velocity field is irrotational) has no rotational component: the fluid does not move in circular or helical motions; it does not form vortices.
	encyclopedia.codeboy.net /wikipedia/i/ir/irrotational_vector_field.html (206 words)

	PlanetMath: irrotational field
		is a vector field with differentiable real (or possibly complex) valued component functions.
		is called an irrotional vector field, or curl free field.
		This is version 6 of irrotational field, born on 2002-11-13, modified 2003-10-18.
	planetmath.org /encyclopedia/IrrotationalField.html (76 words)

	Vector calculus - Wikipedia, the free encyclopedia
		Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions.
		We consider vector fields, which associate a vector to every point in space, and scalar fields, which associate a scalar to every point in space.
		curl: measures a vector field's tendency to rotate about a point; the curl of a vector field is another vector field.
	en.wikipedia.org /wiki/Vector_calculus (251 words)

	Irrotational vector field - Wikipedia, the free encyclopedia
		In vector calculus, an irrotational or conservative vector field is a vector field whose curl is zero.
		In fluid mechanics, an irrotational field is practically synonymous with a lamellar field.
		From the zero curl definition of an irrotational field, it can be deduced, by means of Stokes' theorem, that the circulation of any closed loop in the field is zero:
	en.wikipedia.org /wiki/Irrotational_vector_field (212 words)

	Vector potential - Wikipedia, the free encyclopedia
		In vector calculus, a vector potential is a vector field whose curl is a given vector field.
		This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field.
		A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field.
	en.wikipedia.org /wiki/Vector_potential (247 words)

	[No title]
		in this case c the vector field (v,w) is computed on the entire sphere.
		c c c nt nt is the number of scalar and vector fields.
		c c c ************************************************************ c c output parameters c c c v,w two or three dimensional arrays (see input parameter nt) that c contain an irrotational vector field such that the gradient of c the scalar field** sf is (v,w).
	www.scd.ucar.edu /css/software/spherepack/gradgs.txt (946 words)

	Irrotational vector field -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-28)
		In (Study of the mechanics of fluids) fluid mechanics, an irrotational vector field is a (additional info and facts about vector field) vector field whose (American chemist who with Richard Smalley and Harold Kroto discovered fullerenes and opened a new branch of chemistry (born in 1933)) curl is zero.
		The adjective "irrotational" implies that irrotational fluid flow (whose velocity field is irrotational) has no rotational component: the fluid does not move in circular or helical motions; it does not form (additional info and facts about vortices) vortices.
		This lack of circulation means that irrotational field lines ((additional info and facts about streamline) streamlines of irrotational flow) do not form loops (or (additional info and facts about helices) helices).
	www.absoluteastronomy.com /encyclopedia/i/ir/irrotational_vector_field.htm (312 words)

	Irrotational vector field - TheBestLinks.com - Irrotational field, Curl, Fluid mechanics, Gradient, ... (Site not responding. Last check: 2007-10-28)
		Irrotational vector field - TheBestLinks.com - Irrotational field, Curl, Fluid mechanics, Gradient,...
		Irrotational field, Irrotational vector field, Curl, Fluid mechanics, Gradient...
		In fluid mechanics, an irrotational vector field is a vector field whose curl is zero.
	www.thebestlinks.com /Irrotational_field.html (274 words)

	[No title] (Site not responding. Last check: 2007-10-28)
		the vorticity of (v,w) is the zero scalar c field.
		c c c nt nt is the number of divergence and vector fields.
		c the curl or vorticity of (v,w) is the zero vector field.
	www.scd.ucar.edu /css/software/sound/idivgc.txt (1118 words)

	Robert Curl Information (Site not responding. Last check: 2007-10-28)
		In vector calculus, '''curl''' is a vector operator that shows a vector field's rate of rotation about a point.
		is the vector differential operator del, and ''F'' is the vector field the curl is being applied to.
		It states that the curl of an electric field is equal to the opposite of the rate of change of the magnetic flux density.
	www.echostatic.com /Robert_Curl.html (409 words)

	[No title]
		4 was initiated with the representation of an irrotational vector field E, this chapter began by focusing on the solenoidal character of the magnetic flux density.
		The boundary conditions obeyed by the vector potential at surfaces of discontinuity (containing surface currents) reflect the discontinuity in tangential H field and the continuity of the normal flux density.
		The homogeneous solution is both irrotational and solenoidal, so it is possible to use either the vector or the scalar potential to represent this part of the field everywhere.
	web.mit.edu /6.013_book/www/chapter8/8.7.html (896 words)

	Irrotational vector field (Site not responding. Last check: 2007-10-28)
		Since there is an identity of vector calculus which states that the curl of gradient is zero:
		The adjective "irrotational" implies that irrotational flow (whose velocity field is irrotational) has rotational component: the fluid does not move circular or helical motions; it does not vortices.
		This lack of circulation means that field lines (streamlines of irrotational flow) do not form (or helices).
	www.freeglossary.com /Irrotational (291 words)

	PowerPedia:Scalar field theory - PESWiki
		Scalar field theory (SWT) is a set of theories in a abstract model which posits that there is a basic mechanism that produces the electric field and the magnetic field.
		Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure.
		Vector fields are associate a vector to every point in space.
	www.peswiki.com /index.php/PowerPedia:Scalar_field_theory (4754 words)

	Active Contours, Deformable Models, and Gradient Vector Flow
		This field is computed as a spatial diffusion of the gradient of an edge map derived from the image.
		The GVF forces are used to drive the snake, modeled as a physical object having a resistance to both stretching and bending, towards the boundaries of the object.
		This is a gradient vector flow (GVF) field for a U-shaped object.
	iacl.ece.jhu.edu /projects/gvf (1914 words)

	Irrotational vector field - Term Explanation on IndexSuche.Com (Site not responding. Last check: 2007-10-28)
		Since there is an identity of vector_calculus which states that the curl of any gradient is zero: : \nabla \times \nabla \phi = 0 where ''φ'' is a scalar field, it follows that any irrotational field can be expressed as the gradient of a scalar_potential: : \mathbf{v} = \nabla \phi.
		An irrotational field is practically synonymous with a.
		From the zero curl definition of an irrotational field, it can be deduced, by means of Stokes'_theorem, that the circulation of any closed loop in the field is zero: : \oint_S \mathbf{v} \cdot \, d\mathbf{s} = \int \int_A \nabla \times \mathbf{v} \cdot d\mathbf{A} = 0 where ''A'' is the area enclosed by loop ''S''.
	www.indexsuche.com /Irrotational_vector_field.html (213 words)

	Curl.nb (Site not responding. Last check: 2007-10-28)
		The curl of this vector field is the zero vector.
		Thus the vector field is said to be irrotational.
		There is no nonzero vector for the flow of the vector field to rotate around.
	banach.millersville.edu /~bob/math261/Curl (80 words)

	Curl - Indopedia, the Indological knowledgebase (Site not responding. Last check: 2007-10-28)
		In vector calculus, curl is a vector operator that shows a vector field's tendency to rotate about a point.
		In a tornado the winds are rotating about the eye, and a vector field showing wind velocities would have a non-zero curl at the eye, and possibly elsewhere (see vorticity).
		In a vector field that describes the linear velocities of each individual part of a rotating disk, the curl will have a constant value on all parts of the disk.
	www.indopedia.org /Curl.html (479 words)

	[No title] (Site not responding. Last check: 2007-10-28)
		A vector field decomposition was recently applied to the bioelectromagnetic inverse problem to divide the primary current density into its solenoidal and irrotational parts [1].
		Condition a) reduces the solution space, excluding solenoidal vector fields that are not a gradient of a harmonic function.
		This is a reasonable restriction for a continuous vector field that is zero beyond the brain volume.
	www.neurologie.uni-duesseldorf.de /HBM99/cd/methods/2082.html (575 words)

	Inverse-square law (Site not responding. Last check: 2007-10-28)
		The density of flux lines is inversely proportional to the square of the distance from the source because the surface area of a sphere increases with the square of the radius.
		Thus the strength of the field is inversely proportional to the square of the distance from the source.
		For an irrotational vector field the law corresponds to the property that the divergence is zero outside the source.
	www.tocatch.info /en/Inverse-square_law.htm (595 words)

	[No title] (Site not responding. Last check: 2007-10-28)
		Provide an introduction to vector calculus and vector fields, with particular interest in conservative and irrotational vector fields.
		state what a conservative vector field is, what a potential function is, and be able to calculate a potential function for a conservative vector field.
		state what an irrotational vector field is and the relationship between conservative and irrotational vector fields.
	www.aero.gla.ac.uk /UGrad/courses2004-5/Year2/AIMathemAE2X.doc (249 words)

	8.2 What Does Curl Signify? Why is it Important? (Site not responding. Last check: 2007-10-28)
		Line integrals of vector fields along paths are path dependent when the field is not irrotational, that is when the curl is non-zero.
		The difference of the "circulation" integral of a vector field along two paths with the same endpoints can be described as the integral on the closed path obtained by going up one and down the other.
		A vector field that is the curl of another is divergence free: its divergence vanishes, which means its arrows have no sources or sinks, and consist only of swirls.
	www-math.mit.edu /~djk/18_022/chapter08/section02.html (157 words)

	The vector field analyzer
		The vector field analyzer is a basic fully interactive tool that is used throughout the new approach to vector calculus by the second author.
		With its built-in features to interactively visualize nonlinear and linearized flows, the vector field analyzer compellingly connects vector calculus and differential equations, while linear algebra (up to orthogonal eigenspaces for self-adjoint operators) is visible in many places.
		This is the beginning of a new century where a visual language may replace much of the traditionally almost exclusively algebraic and symbolic language, thereby facilitating access to higher math for a broad population.
	math.la.asu.edu /~kawski/conferences/99plymouth/proceedings/sld001.htm (429 words)

	Electrochemical Driving Force - Corrosionsource Discussion Boards
		The field E is irrotational at a certain point if the curl of the vector field (curl E) is zero at that point.
		So, if the we move a charge around a closed loop in an irrotational field, the total energy gained or lost, which is equal to the loop integral of (F dl), is seen to be the integral of [q (E dl)] which in turn is equal to zero as per the definition of irrotationality.
		Because of this, it is generally recognised in classical electrical theory that irrotational fields are incapable of sustaining stationary electrical currents because energy is continuously depleted in the form of ohmic heat during current flow.
	www.corrosionsource.com /discuss2/ubb/Forum19/HTML/000008.html (1345 words)

	Laplacian vector field (Site not responding. Last check: 2007-10-28)
		In vector calculus a Laplacian vector field is a vector field which is both irrotational and incompressible.
		Since the curl of v is zero it follows that v can be expressed as the gradient a scalar potential (see irrotational field) φ :
		Therefore the potential of a Laplacian field Laplace's equation.
	www.freeglossary.com /Laplacian_field (434 words)

	[No title]
		When we are asked to “sketch” a vector field, in 2 dimensions, we draw the plane, indicate the domain region R, and overlay R with “representative,” or sample vectors from the field.
		DIVERGENCE OF A VECTOR FIELD This is a numerical description of a vector field.
		If your vector field is a velocity field of a flow of some fluid, then the value of the divergence at a point is essentially the net rate at which the fluid mass is flowing away from (or diverging from) the point.
	frcc.cc.co.us /docs/pages/10082/NOTES_FOR_14.1.doc (940 words)

	AMS Glossary
		Two equivalent properties of an irrotational field are that there is no circulation about any reducible curve within the fluid, and that a potential exists.
		An autobarotropic fluid is irrotational for all time if it is irrotational at any time.
		Meteorological motions of the smaller scales, for example, gravity waves, may be treated as irrotational, but when the scale is large enough to take the rotation of the earth into account, only rotational motions are of interest.
	amsglossary.allenpress.com /glossary/search?id=irrotational1 (116 words)

	Vector Calculus Chapter 17 -- True or False (Site not responding. Last check: 2007-10-28)
		A gradient field turns a scalar t field into a vector field, but we have no way to turn a vector field into a scalar field.
		Divergence of a vector field can be found only when the vector field
		curl F is irrotational if it is zero at the origin.
	cwx.prenhall.com /bookbind/pubbooks/colley/chapter17/truefalse1/deluxe-content.html (100 words)

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