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Topic: Laplacian field

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	Irrotational vector field - Encyclopedia, History, Geography and Biography
		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.
	www.arikah.net /encyclopedia/Irrotational_vector_field (254 words)

	Incompressible fluid - Wikipedia, the free encyclopedia
		In fluid mechanics, an incompressible fluid is a fluid whose density (often represented by the Greek letter ρ) is constant: it is the same throughout the field and it does not change through time.
		An incompressible fluid is described by a velocity field which is solenoidal.
		But a solenoidal field, besides having a zero divergence, also has the additional connotation of having non-zero curl (i.e.
	www.wikipedia.org /wiki/Ideal_fluid (223 words)

	High electrical field degradation in polymeric dielectrics: Electrical tree formation and growth in polyethylene.
		An approach of refining the conduction model at high fields is discussed.
		Using these measured PD inception voltages and the known geometry for which they were measured, we have modeled the discharge process based on the energy available from the electrostatic field during tree channel formation.
		We have demonstrated a self-consistent mechanism for channel formation, in that the energy available from the electrostatic field is sufficient to form the channel size observed.
	digitalcommons.uconn.edu /dissertations/AAI9959396 (275 words)

	Quantum Field Theory
		The dynamic of the field is determined by the field equation.
		The field equations are derived by minimizing the "Action'', which is related to the Lagrangian density.
		The asymmetric forms for the fermion fields in Eq.(42f) is a way to portrait the chiral nature of the objects in weak interaction - the left-handed version is different from the right-handed one.
	www.zamandayolculuk.com /cetinbal/quantumfieldtheory.htm (3167 words)

	E-Field By CSM with Complx Charges
		In the case of capacitive field distribution, the instantaneous field is independent of waveform of applied voltage.
		Firstly, the capacitances between the dielectric interface and electrode are dependent upon the field distribution and hence, are not identical in capacitive and capacitive-resistive fields.
		Their method based on CSM and employing complex fictitious charges is generally extended so that any capacitive-resistive field including volume resistance or surface resistance can be calculated, when the field distribution is Laplacian in the region except on the boundaries.
	www.dlnet.vt.edu /repository/previewRepository/EE000000/EE006000/EE006002/DISK1/DLNET-02-14-2003-0309/resources/EFC.htm (726 words)

	Laplacian vector field -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		In (Click link for more info and facts about vector calculus) vector calculus, a Laplacian vector field is a (Click link for more info and facts about vector field) vector field which is both (Click link for more info and facts about irrotational) irrotational and (Click link for more info and facts about incompressible) incompressible.
		If the field is denoted as v, then it is described by the following (An equation containing differentials of a function) differential equations:
		Therefore, the potential of a Laplacian field satisfies (Click link for more info and facts about Laplace's equation) Laplace's equation.
	www.absoluteastronomy.com /encyclopedia/l/la/laplacian_vector_field.htm (155 words)

	[No title]
		The physical systems analyzed are generalizations, on the one hand, of such EQS situations as Example 5.6.2, where sinusoidal surface charge densities produced a Laplacian field decaying away from the surface charge source.
		Consider the field response to a surface charge density that is in the sinusoidal steady state and represented by
		One is to illustrate the TE fields, while the other is to provide further insights into the nature of electrodynamic fields that are periodic in time and in one space dimension.
	web.mit.edu /6.013_book/www/chapter12/12.6.html (2461 words)

	Research at Rehovot (Site not responding. Last check: 2007-10-21)
		Laplacian Growth Patterns are obtained when the boundary G of a 2-dimensional domain is grown at a rate proportional to the gradient of a Laplacian field P. Outside the domain
		Of course, the ultraviolet regularizations in the two processes were taken different; in studying Laplacian Growth one usually solves the problem with the boundary condition P=sk where s is the surface tension and k the local curvature of G. Without this (or some other) ultraviolet regularization Laplacian Growth reaches a singularity (cusps) in finite time.
		The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome.
	www.agnld.uni-potsdam.de /~gamez/ResearchRehovot.html (896 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Also, you may neglect the falloff of the fields at the ends of the solenoid.
		Never mind about heating effects (which can also be important!) \problem{magnetization of cube} A cube of edge $a$ has one corner at the origin and edges along the positive $x, y, z$ axes.
		\problem{Bending of field lines} The magnetic induction $B$ emerges from a flat surface at an angle $\alpha$ to the normal.
	jfi.uchicago.edu /~tten/rainbow/Physics.227/materials/Prob.set.2.tex (439 words)

	CPC Licence Alert (Site not responding. Last check: 2007-10-21)
		These are to be computed from evenly spaced observations of magnetic field made on the boundary of a hypothetical rectangular box surrounding the volume being considered.
		The magnetic field component in vacuum is fully determined by its boundary values, by Maxwell's equations.
		If it is modelled by a function which itself has a zero laplacian then the errors of representation are largest at the absolute value on the boundary.
	www.cpc.cs.qub.ac.uk /summaries/ABCM.html (243 words)

	Morphology of Laplacian Growth: Theory (Site not responding. Last check: 2007-10-21)
		A theory is formulated for interfacial growth in a Laplacian field.
		Surface effects are introduced as a term in the Hamiltonian that gives rise either to repulsion between the particles and the interface or to a field that enables creation and annihilation of particles.
		The dynamical equations of the particles are analysed and a statistical-mechanical study of the limit distribution of the particles is outlined.
	flux.aps.org /meetings/BAPSMAR95/abs/SK2012.html (121 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Functions of position are called fields, and mathematical techniques for the analysis of fields have proven useful in many branches of physics.
		In addition to permitting the application of vector analysis methods to atomic quantities, the introduction of fields is a valuable visualization aid, because information defined on a coarse regular grid can be added to a picture of a molecular system without overloading it.
		The field values are obtained by averaging the atomic quantities over all atoms in a cube of edge length grid_size surrounding each grid point.
	keres.colorado.edu /mmtk/MMTK_19.html (526 words)

	Module Document - Field_Math
		The module does some field mathematics -- I am intended to talk about it at the AVS94.
		AVSSPL admits two types of variables -simple variables with values being single float numbers; field variables with values being float arrays of dimensions determined by the output field.
		Convolution functions take two field variables as arguments and return convolution or local (masked) minima or maxima.
	www.iavsc.org /repository/avs5/pages/filters/Field_Math/Field_Math.shtml (405 words)

	ONERA - DMPH, Lightning strike to aircraft, simulation (Site not responding. Last check: 2007-10-21)
		Modelling of discharge propagation is performed from fluid equations describing the conservation of mass, momentum and energy for the different particle species (electrons, ions and neutrals).
		The corresponding equations are simplified according to the dominant processes involved in the different discharge regions ; these equations are coupled to a 3D code for calculation of electric field, taking into account the distortion of Laplacian field by the discharge itself.
		At the advancing limit of the corona head, high local electric field enables ionisation and electronic avalanches processes which provide the current sustaining the propagation.
	www.onera.fr /dmph-en/foudre/simulation.html (315 words)

	Session AP - CFD I.
		The possibility of developing stochastic kinetic theories, which are consistent in accordance with [1], i.e., satisfy all fluid equations, including the heat equation in the case of thermofluids, for arbitrary initial conditions for the kinetic distribution function, is discussed.
		Laplace's equation is used for the electric field and Stokes' equation for the fluid motion.
		The idea is based on a kinematic scheme that states the nullity of the velocity field Laplacian, imposing simultaneously conditions of incompressibility and constant curl for velocity.
	flux.aps.org /meetings/YR01/DFD01/abs/S140.html (1231 words)

	Abstract for LMS Durham Symposium on Computational methods for wave propagation in direct scattering (Site not responding. Last check: 2007-10-21)
		At very low frequencies, the electromagnetic field behaves like a Laplacian field which is very smooth and non-oscillatory.
		At higher frequencies, the electromagnetic field behaves like a Helmholtz field which is oscillatory.
		It can be shown that Laplacian fields cannot convey information long distance, whereas Helmholtz fields can carry information through galaxies.
	www.maths.strath.ac.uk /durham02/abs_chew.html (174 words)

	Repeated use of the Del. The Laplacian.
		The Del of the field of position vectors.
		It can be applied on both vector and scalar fields.
		In the case of a scalar field it can be calculated as a repeated use of the Del. We get,
	www.torget.se /users/m/mauritz/math/field/rep.htm (153 words)

	LORETA - discussion forum: Re: Use of Laplacian Montage with LORETA, roberto at 11/30/2004 09:59 (Site not responding. Last check: 2007-10-21)
		As an answer to: Use of Laplacian Montage with LORETA written by Robert Couture at 27 Oct 2004 17:20:24:
		The loreta lead field needs no further clarification, the codes for it have been freely available for years in the downloadable “ethical”-loreta package, and the associated literature is the paper:
		A bipolar lead field can only be used very specifically with its corresponding bipolar recordings.
	www.f27.parsimony.net /forum66500/messages/261.htm (251 words)

	Laplacian vector field - Wikipedia, the free encyclopedia
		Since the curl of v is zero, it follows that v can be expressed as the gradient of a scalar potential (see irrotational field) φ :
		Therefore, the potential of a Laplacian field satisfies Laplace's equation.
		This page was last modified 17:09, 20 September 2005.
	www.wikipedia.org /wiki/Laplacian_field (117 words)

	Solenoidal vector field -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		In (Click link for more info and facts about vector calculus) vector calculus a solenoidal vector field is a (Click link for more info and facts about vector field) vector field v with (An infinite series that has no limit) divergence zero:
		This condition is clearly satisfied whenever v has a (Click link for more info and facts about vector potential) vector potential,
		the velocity field of an (Click link for more info and facts about incompressible fluid flow) incompressible fluid flow is solenoidal.
	www.absoluteastronomy.com /encyclopedia/S/So/Solenoidal_vector_field.htm (151 words)

	Objective Type Questions
		Field calculation by CSM under transient voltage with volume resistance with the help of time-step discretization is carried out employing
		Field calculation by CSM under transient voltage with volume resistance with the help of Fourier Series expansion is carried out employing
		Field calculation by CSM under transient voltage with surface resistance with the help of time-step discretization is carried out employing
	www.dlnet.vt.edu /repository/previewRepository/EE000000/EE006000/EE006002/DISK1/DLNET-02-14-2003-0309/resources/Questions.htm (424 words)

	LMS Durham Symposium on Computational methods for wave propagation in direct scattering (Site not responding. Last check: 2007-10-21)
		It can be shown that Laplacian field cannot convey information long distance, whereas Helmholtz field can carry information through galaxies.
		The information content of the field affects the nature of the fast algorithm designed to solve Maxwell's equations.
		At extremely high frequencies, electromagnetic wave behaves like particles or rays, and yet, a different strategy is needed to design fast algorithms at the high frequency end.
	www.ma.hw.ac.uk /~dugald/durham/abs_chew.html (167 words)

	Odd W. Andersen
		"Laplacian Electrostatic Field Calculations by Finite Elements with Automatic Grid Generation", IEEE Trans.
		Gave courses on numerical field calculations (finite elements) and generalized theory of rotating electrical machines.
		Gave course on numerical field calculations (finite elements) and did consulting work for synchronous machine manufacturers in the area (Onan Corporation and Electric Machinery).
	home.c2i.net /owand (835 words)

	Eeg Cortical Imaging: A Vector Field Approach For Laplacian (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Abstract: The surface Laplacian is known to be a theoretical reliable approximation of the cortical activity.
		Unfortunately, because of its high pass character and the relative low density of the EEG caps, the estimation of the Laplacian itself tends to be very sensitive to noise.
		10 Electric Fields of the Brain: The Neurophysics of EEG (context) - Nunez - 1981
	citeseer.ist.psu.edu /676247.html (232 words)

	IngentaConnect Non-Laplacian ion trajectories in mutually interacting corona dis... (Site not responding. Last check: 2007-10-21)
		However, the shapes of the profiles of current density and electric field for small wire displacements give poor simulations because of the effect of the proximity of the interacting coronas.
		This confirms the failure of the Kaptsov approximation of the field at the corona conductor.
		This trajectory is non-Laplacian in shape and the results indicate that, along this path, a position of minimum field is encountered rather than the monotonic field found at.
	api.ingentaconnect.com /content/iop/jphysd/1997/00000030/00000013/art00013 (399 words)

	Quad-Morphing: Advancing Front Quad Meshing Using Triangle Tranformations
		For nodes not located on the current front, a simple Laplacian smooth (Field,1988) is adequate, or alternatively, a modified length weighted Laplacian smooth as suggested by Blacker (1991).
		Since it is at the front where the new quadrilateral elements are formed, it is more critical at these nodes that the smoothing produce well proportioned quadrilaterals.
		In situations where Laplacian smoothing produces poor results, an optimization based smoothing (Canann,1998) operation may be performed.
	www.andrew.cmu.edu /user/sowen/qm/rt98quad.htm (5391 words)

	ipedia.com: Potential flow Article (Site not responding. Last check: 2007-10-21)
		In fluid dynamics, potential flow, also know as irrotational flow is steady flow defined by the equations Equivalently, where: v is the vector fluid velocity Φ is the fluid flow potential, scalar...
		works which give detailed account, in alphabetical order, of whole field of human knowledge, or of some particular section in it.
		In fluid dynamics, potential flow, also know as irrotational flow (of incompressible fluids) is steady flow defined by the equations
	www.ipedia.com /potential_flow.html (779 words)

	Campo del vector de Laplacian (Site not responding. Last check: 2007-10-21)
		En cálculo del vector, un campo del vector de Laplacian es un campo del vector que es irrotational e incompresible.
		Por lo tanto, el potencial de un campo de Laplacian satisface la ecuación de Laplace.
		English version: Laplacian vector field Next: Residual Up
	www.yotor.net /wiki/es/ca/Campo%20del%20vector%20de%20Laplacian.htm (119 words)

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