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Topic: Helmholtz equation

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	NationMaster - Encyclopedia: Helmholtz Equation (Site not responding. Last check: 2007-10-20)
		Due to its relationship to the wave equation, the Helmholtz equation arises in problems in such areas of physics as the study of electromagnetic radiation, seismology, and acoustics.
		The modern variants of BIE for the Helmholtz equation are based on the complex-valued fundamental solutions (Green's functions) in the two-dimensional (2D) and three-dimensional (3D) cases.
		The equation is valid in the domain D with boundary S. We consider the linear boundary-valued problems with the linear boundary conditions of the irst, second or third kind.
	www.nationmaster.com /encyclopedia/Helmholtz-Equation (1145 words)

	Pioneers of Psychology [2001 Tour] - School of Education & Psychology
		In Helmholtz's theory three sets of fibers in the retina are said to give rise respectively to sensations of red, green, and violet.44 There are supposed to be three kinds of photo-chemically decomposible substances in the end organs, each with different degrees of sensitiveness to different parts of the visible spectrum.
		Helmholtz stressed the importance of the process of unconscious inference in space perception 49 Perception of space, he said, is not inherent; instead we "infer" space from past experience, but without awareness that this process of inference is going on.
		Helmholtz marshalled evidence that a portion of the inner ear responded to an auditory wave stimulus by resonance, vibrating in tune with the frequency of the sound wave.
	educ.southern.edu /tour/who/pioneers/helmholtz.html (6109 words)

	BEM for the Helmholtz equation (Site not responding. Last check: 2007-10-20)
		It is a variant of the direct integral equation formulation based on the real-valued fundamental solutions and the application of the conjugate gradient methods for a resulting linear system.
		The system of N linear algebraic equations with the full matrix was solved by the different methods that described in the next section.
		It is connected with the properties of the solutions of the Helmholtz equation and it signify that size mesh is not enough.
	web.alkar.net /yasko/Helm.htm (2309 words)

	Second law Analysis of Gas Turbines...simple, combined, heat, exchange, recuperated, fuel, cell, solid, oxide, engine, ...
		Helmholtz himself suggested that this be divided up (Bailyn 1994) between free energy, which today is more specifically renamed helmholtz energy, and bound energy.
		The helmholtz energy A is the part of caloric energy Q that could be converted into external energy X in a future process.
		Equation (18, 37) adjust for this and are plotted in Fig 7.
	www.benwiens.com /energy2.html (5528 words)

	Preconditioning the Helmholtz Equation for a 2-D Duct
		A preconditioning technique has been developed for numerical solution of the Helmholtz equation as applied to the steady-state propagation of sound in a semi-infinite, two-dimensional (2-D) rigid duct.
		The Helmholtz equation is preconditioned by expressing the transient potential in the form
		(x,y), causing the left side of this equation to vanish and thus causing reversion to the classical Helmholtz equation.
	www.nasatech.com /Briefs/Mar00/LEW16692.html (681 words)

	PlanetMath: Helmholtz equation (Site not responding. Last check: 2007-10-20)
		The Helmholtz equation is a partial differential equation which, in scalar form is
		Cross-references: coordinates, separation of variables, satisfies, harmonic, interest, wave equation, represent, equation, solutions, Laplacian, vector, scalar, partial differential equation
		This is version 7 of Helmholtz equation, born on 2002-11-13, modified 2006-10-21.
	www.planetmath.org /encyclopedia/HelmholtzDifferentialEquation.html (111 words)

	Pulse Propagation Analysis and the Helmholtz Equation
		It should be pointed out that although the Helmholtz equation (4) is simpler to solve than the full wave equation, this simplification is achieved at the cost of having to evaluate the inverse Fourier transform, Eq.
		Thus, the Helmholtz equation has formed the theoretical basis for the most important numerical methods, including the Ray, Wavenumber Integration (WI), PE, and NM approaches.
		Although all these methods have the Helmholtz equation as the starting point, they differ in the degree to which analytical and numerical components are utilized in the solution scheme.
	www.ucs.louisiana.edu /~nxs7560/pulse.html (641 words)

	Gibbs-Helmholtz equation: Definition and Links by Encyclopedian.com
		...Gibbs-Helmholtz equation Gibbs-Helmholtz equation The Gibbs-Helmholtz equation..., G is the Gibbs free energy and H is the heat content of the system.
		The Gibbs-Helmholtz equation is a thermodynamic relationship useful for calculating changes in the energy or enthalpy (heat content) of a system.
		Two useful general forms of this equation are:
	www.encyclopedian.com /gi/Gibbs-Helmholtz-equation.html (232 words)

	Derivation of Helmholtz Equation from the Wave Equation
		Derivation of Helmholtz Equation from the Wave Equation
		It is a typical hyperbolic equation, and is sometimes written as
		In the literature, derivations of the Helmholtz equation consider the wave equation in cases where all data are simple-harmonic (or zero) :
	www-math.cudenver.edu /~lfranca/research/students/tim/presentation/derive (76 words)

	The Helmholtz equation (Site not responding. Last check: 2007-10-20)
		The solutions of the Helmholtz equation represent (the spatial part of) solutions of the wave equation.
		Physically we expect waves to propagate away from the disturbance generating them and not towards it.
		we recover the Green's function for the Poisson equation.
	www.soton.ac.uk /~jhr/MA361/node50.html (326 words)

	NSDL Metadata Record -- Lattice sums and the two-dimensional, periodic Green?s function for the Helmholtz equation
		Lattice sums and the two-dimensional, periodic Green?s function for the Helmholtz equation
		Many algorithms that are currently used for the solution of the Helmholtz equation in periodic domains require the evaluation of the Green?s function, G(x;x0).
		The fact that the natural representation of G via the method of images gives rise to a conditionally convergent series whose direct evaluation is prohibitive has inspired the search for more efficient procedures for evaluating this Green?s function.
	www.nsdl.org /mr/435970 (159 words)

	High Frequency Wave Propagation 2005: Castella Abstract
		High-frequency Behaviour of the Helmholtz Equation: Radiation Condition at Infinity, Bounds, and a Counter-example
		Abstract: We consider the high-frequency Helmholtz equation in the whole space, with a variable index of refraction.
		The analysis relies on carefully following the dispersive properties of the Helmholtz equation, for small, moderate, and large values of the space variable.
	www.cscamm.umd.edu /programs/hfw05/castella_hfw05.htm (178 words)

	Moon Illusion Explained: Appendix2
		An additional equation is needed to relate the perceived angular size, V' deg, to the physical angle, V deg, and that relationship must involve the retinal image size, R mm.
		All modern researchers agree that we do not perceive or "sense" the retinal image (a proximal stimulus) or its properties, as such: Instead, perception is "distally focused." That is, we have (we create) visual images only of external objects and their properties.
		So, according to the conventional logic, the direct perceptual correlate of R mm is the ratio of the perceived linear size to the perceived distance, multiplied by the nodal distance, n.
	facstaff.uww.edu /mccreadd/appendix2.htm (6187 words)

	Helmholtz equation
		The basic equations we consider are of Helmholtz type.
		In addition these equations have to be completed by boundary conditions on the ``interior'' boundary
		In the subsequent sections only Equation (6.2) is considered.
	www.zib.de /nano-optics/HelmPoleMan/node23.html (75 words)

	SCIENTIFIC REFERENCES
		Helmholtz, Hermann L. F., On the Sensations of Tone, Fourth (and last) German edition (1877) translated by Alexander J. Ellis as the second English edition (1885), revised, corrected annotated and with additiona appendix by the translator, Dover Publications (1954).
		Putnam, C. "The Quantum Mechanical Equations of Motion and Commutation Relations", Phys.
		Tenenbaum, Morris; Pollard, Harry, Ordinary Differential Equations Harper (1963).
	graham.main.nc.us /~bhammel/FCCR/refs.html (2896 words)

	Helmholtz Equation: Steady-Periodic
		Consider the Fourier transform of the above temperature equations:
		For a derivation of this equation see Beck et al.
		Next the steady-periodic Green's functions are given for 1-D bodies for cases XIJ.
	www.engr.unl.edu /~glibrary/glibcontent/stharm/stharm.html (231 words)

	Gibbs Free Energies (Site not responding. Last check: 2007-10-20)
		One has to be given the Delta H for the reaction as well as the Delta S and the Temperature, or one have to be able to calculate Delta Hrx and Delta Srx using the previous methods.
		The question is how large must that term be in order for it to exceed the negative Delta H term and cause the reaction to have a non-spontaneous positive Delta G. Under those conditions any temperature BELOW the equilibrium temperature would make such a reaction spontaneous.
		Since Delta H is negative and Delta S is also negative then it does not matter what temperature is placed in the Gibbs Helmholtz equation it will always result in a negative Delta G. Therefore this reaction will be spontaneous at any temperature.
	members.aol.com /profchm/gibbs.html (2761 words)

	Horizon Technologies...Software Products
		The GASPAK property estimation algorithm uses a highly accurate variable-term Helmholtz equation.
		He) from fundamental state equations, valid from 0.8 Kelvin or the melting line to 1,500 Kelvin, including the superfluid range, the lambda line, and liquid vapor mixtures.
		As a function of pressure, calculations are valid up to 1,000 bars, except between 80 and 300 Kelvin where they are valid to 20,000 bars.
	www.htess.com /software.htm (466 words)

	6.3 Helmholtz equation
		Several new concepts are introduced here, namely the use of a parameter in the equation, the radiation boundary condition, and calculation of a vector-valued function (the gradient) in the second problem
		Fastflo realises that this problem has two degrees of freedom, each with quadratic interpolation.
		This problem calculates the gradient of the solution of the Helmholtz problem.
	www.ualberta.ca /AICT/RESEARCH/NAG/FastfloDoc/Tutorial/html/node63.html (241 words)

	math lessons - Helmholtz equation
		Applying the technique of separation of variables (
		The solution in time will be a linear combination of sine and cosine functions, while the form of the solution in space will depend on the boundary conditions.
		algebra arithmetic calculus equations geometry differential equations trigonometry number theory probability theory applied mathematics mathematical games mathematicians
	www.mathdaily.com /lessons/Helmholtz_equation (197 words)

	Numerical PDE's and Helmholtz equation (Site not responding. Last check: 2007-10-20)
		We have focused on high order methods for the Helmholtz equation.
		Improved Accuracy for the Helmholtz Equation in Unbounded Domains
		Analytical and Numerical Studies of a Finite Element PML for the Helmholtz Equation
	www.math.tau.ac.il /~turkel/helm.html (187 words)

	Re: matlab code for 2D wave equation(Helmholtz equation)
		Re: matlab code for 2D wave equation(Helmholtz equation)
		Programming Forum and web based access to our favorite programming groups.
		Normally I would not respond to the write my thesis posts - but I am doing something similar - and found the Student Version lacking - you need to buy the Partial Differential Equation toolbox.
	www.codecomments.com /Matlab/message814611.html (104 words)

	Magnet Formulas
		Off-axis fields due to round, finite, air core solenoids
		On-axis field due to two coaxial current loops with Helmholtz spacing
		On-axis field due to two round, coaxial, finite solenoids with arbitrary or Helmholtz spacing
	www.netdenizen.com /emagnet (234 words)

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