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Topic: Convective derivative

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Derivative

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	Read about Derivative at WorldVillage Encyclopedia. Research Derivative and learn about Derivative here! (Site not responding. Last check: 2007-10-18)
		The derivative of a function f at x is geometrically the slope of the tangent line to the graph of f at x.
		In this case, the Second Derivative Test can still be used to characterize critical points, by considering the eigenvalues of the Hessian matrix of second partial derivatives of the function at the critical point.
		The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
	encyclopedia.worldvillage.com /s/b/Derivative (2031 words)

	Derivative (Site not responding. Last check: 2007-10-18)
		Derivatives are defined by taking the limit of the slope of secant lines as they approach a tangent line.
		If the second derivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
		Perhaps the most natural situation is that of functions between differentiable manifolds; the derivative at a certain point then becomes a linear transformation between the corresponding tangent spaces and the derivative function becomes a map between the tangent bundles.
	hallencyclopedia.com /Derivative (2293 words)

	2003 Formal Publications (Site not responding. Last check: 2007-10-18)
		Downshear-tilted updrafts imply that convection at the northern ends of the cores may weaken with time relative to the frontal segments at the southern ends, since inflow air would be affected by passage through the heavy rain region before ascent.
		Spatial derivatives subsequently are derived by applying a finite differencing scheme to the field of gridded observations.
		Thus, the joint action of the upper-level anomaly, as a spin-up agent, and the latent-heat flux, as a sustainer of convection, emerges as the primary factor for the genesis and evolution of the small quasi-tropical cyclone.
	www.nssl.noaa.gov /papers/formal/2003formal.html (7913 words)

	Convective overturn (Site not responding. Last check: 2007-10-18)
		The convective overturn model of supernovae was proposed by Bethe and Wilson in 1985, and received a dramatic test with SN 1987A, and the detection of neutrinos from the explosion.
		In the convective overturn model, the core collapses faster and faster, exceding the speed of sound in the inside the star, and producing a supersonic shock wave.
		All of these models exhibit convective overturn in that they rely on a convection mechanism to re-energize the stalled shock wave and complete the supernova explosion.
	www.kiwipedia.com /en/convective-overturn.html (454 words)

	Convective derivative -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-18)
		The convective derivative, also known as the Lagrangian derivative, is a ((linguistics) a word that is derived from another word) derivative taken with a respect to a (A system that uses coordinates to establish position) coordinate system moving with velocity u, and is often used in (Study of the mechanics of fluids) fluid mechanics.
		where is the gradient operator (additional info and facts about del) del and denotes the (The derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant) partial derivative with respect to t.
		Proof is via the (additional info and facts about chain rule) chain rule for partial derivatives.
	www.absoluteastronomy.com /encyclopedia/c/co/convective_derivative.htm (181 words)

	Derivative -- from MathWorld
		A three-dimensional generalization of the derivative to an arbitrary direction is known as the
		In general, derivatives are mathematical objects which exist between smooth functions on manifolds.
		There are a number of important rules for computing derivatives of certain combinations of functions.
	www.comp.nus.edu.sg /~malin/materials/maths/Derivatives.html (350 words)

	Convective derivative - Wikipedia, the free encyclopedia
		The convective derivative, also known as the Lagrangian derivative, total time derivative, and by several other names, is a derivative taken with a respect to a coordinate system moving with velocity u, and is often used in fluid mechanics and classical mechanics.
		In tensor notation (with the Einstein summation convention), the derivation may be written:
		This page was last modified 22:25, 9 November 2005.
	en.wikipedia.org /wiki/Convective_derivative (122 words)

	Derivative Quotient Rule (Site not responding. Last check: 2007-10-18)
		In calculus, the quotient rule is a method of finding the derivative of a function which is the quotient of two other functions for which derivatives exist.
		derivative derivative Qualitatively the derivative is a of the change of a function in a small around a specified point.
		Quotient Rule In Words: The derivative of a quotient is the derivative of the top times the bottom, minus the top times the derivative of the bottom, all over the...
	riskmgmt.biz /mysite/economics%20TE2.2/derivative-quotient-rule.html (1348 words)

	Derivative Find (Site not responding. Last check: 2007-10-18)
		On the definition of the derivative is a dynamical diagram displaying the derivative as the slope of the...
		Derivative -- from MathWorld Derivative -- from MathWorld The derivative of a function represents an infinitesimal change in the function with respect to whatever parameters it may have.
		A "derivative work," that is, a work that is based on (or de- rived from) one or more already existing works, is copyright-...
	riskmgmt.biz /mysite/economics%20TE2.2/derivative-find.html (1235 words)

	Formulas for Physics (Site not responding. Last check: 2007-10-18)
		The left side of Euler's equation is the full derivative of the velocity, comprised of the "convective derivative" (the spatial component) and the partial derivative of the velocity field with respect to time.
		The continuity equation relates the partial derivative of the density with respect to time to the gradient of the momentum density.
		For simple flows through a pipe of length L, the derivative may be replaced by the ratio of the pressure difference from one end of the pipe to the other - the "head" - divided by the length L. Return to fluid list.
	muweb.millersville.edu /~jdooley/formulas/FLUIDS/VECTOR/vector.htm (358 words)

	Oct5.html (Site not responding. Last check: 2007-10-18)
		The convective derivative of T (with respect to the flow generated by v) is defined to be the derivative of g(t) = T(x(t),y(t),t) where x(t) and y(t) are taken from the trajectory R. It is denoted by
		Physically this is the rate of change of the temperature with respect to time as one moves along a flow line.
		If all the tees are suppressed and the derivatives are written in differential notation we get the expression for the convective derivative that you find in the text.
	aero.calpoly.edu /rcumming/MATH501/Oct5/Oct58.html (255 words)

	Lynne's Place: Solar Modelling
		Because no theory of convection exists, the problem of convective versus radiative transport of energy is treated very simply.
		The Schwarzschild condition is used to determine whether the radiative or convective transport derivative is used for each calculation.
		The amount of overshooting past the edge of any convective zone is handled simply: a percentage of the mass of the convective zone.
	www.maths.qmw.ac.uk /~lms/research/model.html (1414 words)

	Lie derivative
		There are derivatives of V in the formula for Lie derivative of vector potential.
		Lie derivative is introduced in Bishop and Goldberg "Tensor Analysis on Manifolds" on p.
		The idea that Cartan's formula for the Lie derivative acting on forms yields the functional format for the Lorentz force as a component of the Lie derivative is mathematically correct.
	quantumfuture.net /quantum_future/lie.htm (8445 words)

	Liouville's theorem (Hamiltonian) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-18)
		Time derivatives are denoted by dots, and are evaluated according to Hamilton's equations for the system.
		The Liouville equation is integral to the proof of the fluctuation theorem from which the second law of thermodynamics can be derived.
		It is also the key component of the derivation of Green-Kubo relations for linear transport coefficients such as shear viscosity, thermal conductivity or electrical conductivity.
	67.15.54.21 /wiki/Liouville_equation (778 words)

	Derivative (Site not responding. Last check: 2007-10-18)
		Function represents an infinitesimal change in the function with respect to whatever parameters it may have.
		Discontinuous functions can be integrated, in a sense there are ``more'' functions which can be integrated than differentiated.
		A 3-D generalization of the derivative to an arbitrary direction is known as the
	www.math.sdu.edu.cn /mathency/math/d/d129.htm (163 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		Also, the norms in Section~\ref{sec5} involve the convective derivative instead of the partial with respect to time, and as Douglas and Russell pointed out in~\cite{Dou2}, for advection dominated problems the convective derivative will typically be much smoother, and therefore easier to approximate well.
		While symmetric error estimates for parabolic equations have a certain attractiveness in the simplicity of the statement that they make, it is sometimes hard to see the precise meaning of the result because the norms involved are made up of several parts.
		Symmetric error analysis and 1-d applications are derived in a manner that parallels the earlier analysis.
	people.cs.uchicago.edu /~dupont/stuff/movmix/sec1.tex (913 words)

	Derivative--from Eric Weisstein's World of Mathematics (Site not responding. Last check: 2007-10-18)
		The derivative of a function represents an infinitesimal change in the function with respect to whatever parameters it may have.
		A 3-D generalization of the derivative to an arbitrary direction is known as the directional derivative.
		Other important rules for computing derivatives include the chain rule and power rule.
	ciencias.unizar.es /~mdg/2003/10eduunivesq/laboratorio99/tercera%20parte/eric/Derivative.html (304 words)

	[No title]
		We based our derivation in part on the idea that since vorticity ( EMBED Equation.3 ) represents a particular type of spatial variation in the velocity field (characterized by “swirl” in the fluid), then changes in vorticity should occur when changes (of the right sense) occur in the spatial distribution of velocity.
		Changes (of the right sense) in the spatial distribution of velocity would necessarily require either (1) spatial variations (of the right sense) in forces acting on the fluid, or (2) patterns of motion that cause the velocity field to rearrange itself to produce changes in vorticity.
		In the second step we (1) reversed the order of the partial derivatives in the first term, and (2) rewrote the second term (the convective derivative of vorticity) in terms of the curl of the convective derivative of velocity plus two other terms that arise from taking the curl the non-linear convective derivative of velocity.
	squall.sfsu.edu /courses/metr502/problems/prob.3.doc (943 words)

	[No title]
		In order to derive their properties, consider a one-dimensional disturbance of small amplitude in an infinite fluid which is otherwise uniform and at rest.
		Most commonly, the derivative in (3.2.8) is evaluated at constant entropy, because the fluid motions in sound waves are usually nearly adiabatic.
		In each case the fluid equations are derived from kinetic equations ({\bf 2.1}) by assuming that the particle distribution functions are very close to those of thermodynamic equilibrium.
	www.physics.wustl.edu /~katz/chap3.tex (12303 words)

	Quiz Prospectus for METR 402: Intro to Atmospheric Dynamics (Site not responding. Last check: 2007-10-18)
		Mathematical relation between (1) total derivative and (2) local derivative, gradient, and velocity of hypothetical measuring instrument; interpretation of terms in the relation.
		Lagrangian (or parcel) derivative and local derivative as special cases of total derivative.
		The vector velocity tendency equation as a combination of the momentum conservation equation and the mathematical relations between Lagrangian (parcel) derivative and partial temporal and spatial derivatives.
	www.geosci.sfsu.edu /courses/metr402/S98/handouts/Quiz_3.prosp.html (521 words)

	The continuity equation
		we count both convection and molecular diffusion (which is a mass-bound flux contribution).
		In the study of the transfer of heat or momentum there are more contributions to the total flux than just the convective term.
		In the derivation of relation 2.13 we have used conservation relation 2.12 for
	www.met.wau.nl /projects/jep/report/ecromp/node9.html (441 words)

	UCSC General Catalog Updates 2005-06 - Programs and Courses
		Partial differentiation, the chain rule, multiple integrals, Jacobians, surface integrals and the divergence, line integrals and the curl, Stokes theorem, gradients and directional derivatives.
		Fundamentals of heat transfer and fluid flow: thermal convection, gravity waves, boundary layers, vortex dynamics, instabilities and turbulence.
		Develop a computer program for simulating thermal convection and gravity waves (required only for graduate students).
	reg.ucsc.edu /catalog/html/programs_courses/physCourses.htm (3074 words)

	Math 252 Lecture 31 (Site not responding. Last check: 2007-10-18)
		A second form of the Reynold's Transport Theorem was also given, making use of an expression for the convective derivative.
		(The convective derivative is the time rate of change of a scalar field due to two processes: an intrinsic time-dependence of the scalar field, and the velocity of the time-dependent region which is under consideration.)
		A "proof" of the flux transport theorem was discussed [Transparancies 5, 6, and 7].
	www.math.sfu.ca /~hebron/archive/1999-1/math252/lec_notes/lec31 (318 words)

	Order of Accuracy of QUICK and Related Convection-Diffusion Schemes
		The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the "curvature" term) is indeed a third-order representation of the finite-volume formulation of the convection operator average across the control volume, written naturally in flux-difference form.
		For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux-difference form; for third-order accuracy, this requires a curvature factor of 5/24.
		For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite-volume formulation as it is in single-point.
	gltrs.grc.nasa.gov /cgi-bin/GLTRS/browse.pl?1993/E-8236.html (354 words)

	Nat' Academies Press, Twenty-Third Symposium on Naval Hydrodynamics (2001)
		Positive streamwise vorticity is given by the solid contours whereas the negative values are plotted as dashed lines.
		On the mid-plane, a circumferential cluster of streamwise structures is clearly evident that was vertically convected approximately one rib height since their origin along the previous rib crest.
		Unlike their lower counterpart, these latter structures only fluctuate in position while being convected downstream by the dominant streamwise velocity component.
	www.nap.edu /books/NI000359/html/171.html (2628 words)

	Fluid equations
		The convective derivative, of course, measures time variation in the local rest frame of the species-
		subscript with each convective derivative, since this operator is clearly different for different plasma species.
		There is one additional refinement to our fluid equations which is worth carrying out.
	farside.ph.utexas.edu /teaching/plasma/lectures/node32.html (222 words)

	Citations: An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms ... (Site not responding. Last check: 2007-10-18)
		Citations: An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms - McKee, Wall, Wilson (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath
		McKee, D.P. Wall, and S.K. Wilson, An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms, Journal of Computational Physics 126 (1996), 64-76.
		However, in the most general case a correlation is present and hence the two factor equation must be solved with a mixed derivative term present.
	smealsearch.psu.edu /context/11681/0 (212 words)

	convective derivative - OneLook Dictionary Search (Site not responding. Last check: 2007-10-18)
		We found one dictionary with English definitions that includes the word convective derivative:
		Tip: Click on the first link on a line below to go directly to a page where "convective derivative" is defined.
		Convective Derivative : Eric Weisstein's World of Mathematics [home, info]
	public.onelook.com /?w=convective+derivative (72 words)

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