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Topic: Scalar field

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	Scalar field - Wikipedia, the free encyclopedia
		Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure.
		In scalar theories of gravitation scalar fields are used to describe the gravitational field.
		Scalar fields are supposed to cause the accelerated expansion of the universe (inflation
	en.wikipedia.org /wiki/Scalar_field (546 words)

	Vector field - Wikipedia, the free encyclopedia
		Vector fields are often used in physics to model for example the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.
		In particular a vector field is not a bunch of scalar fields.
		Suppose we have a scalar field which is given by the constant function 1, and a vector field which attaches a vector in the r-direction with length 1 to each point.
	en.wikipedia.org /wiki/Vector_field (1398 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		The Laplacian of a scalar fieldscalar field is the divergence of the field's gradient.
		The gradient of a scalar fieldscalar field is a fieldvector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.
		In field theoryquantum field theory, a tachyon is a quantum of a fieldusually a scalar fieldscalar fieldwhose squared mass is negative.
	www.worldhistory.com /wiki/S/Scalar-field.htm (1210 words)

	The Tom Bearden Website (Site not responding. Last check: 2007-10-21)
		Scalar field: in vector analysis, each point in space is assigned a magnitude; the set of spatial points and their assigned magnitudes is called a scalar field.
		In the new approach, an observable scalar value is assigned to every point in n-dimensional space, where n is 4 or greater, and the set of n-dimensional points and their assigned observable magnitudes is called a scalar field.
		Also, the scalar field is considered to be composed of two time fields: one in positive time and one in negative time that is the phase conjugate replica of the first.
	www.cheniere.org /books/excalibur/glossary/178.htm (201 words)

	Scalar field (Site not responding. Last check: 2007-10-21)
		Scalar fields are often used in physics, for instance toindicate the temperature distribution throughout space, or the air pressure.
		In quantum field theory a scalar field is caused by theexchange of spin 0 particles.
		In generalrelativity, gravity is associated with a tensor field.
	www.therfcc.org /scalar-field-37879.html (187 words)

	PlanetPhysics: Electric Field
		In physics, an electric field or E-field is an effect produced by an Electric Charge that exerts a force on charged objects in its vicinity.
		Electric fields are composed of photons and contain electrical energy with energy density proportional to the square of the field intensity.
		The electric field is a vector quantity, and the electric field strength is the magnitude of this vector.
	planetphysics.org /encyclopedia/ElectricField.html (562 words)

	Scalar field (Site not responding. Last check: 2007-10-21)
		Scalar fields like the Higgs field can be found within scalar-tensor theories, using as scalar field the Higgs field of the Standard Model (4), (5).
		Scalar fields are found within superstring theories as dilaton fields, breaking the conformal lsymmetry of the string, though balancing the quantum anomalies of this tensor (7).
		Scalar fields are supposed to cause the accelerated expansion of the universe (inflation (8)), helping to solve the horizon problem and giving an hypothetical reason for the non-vanishing cosmological constant of cosmology.
	www.tocatch.info /en/Scalar_field.htm (518 words)

	RMCybernetics - More Electromagnetism - Scalar Waves
		Scalar electromagnetics (also known as scalar energy) is the background quantum mechanical fluctuations and associated zero-point energies (incontrast to "vector energies" which sums to zero).
		Scalar waves are hypothetical waves, which differ from the conventional electromagnetic transverse waves by one oscillation level parallel to the direction of propagation, they thus have characteristics of longitudinal waves.
		A "scalar field" is a set of assigned observable magnitudes at every point in n-dimensional space (compare this with the current academic definition; n is also 4 or greater).
	rmcybernetics.com /science/physics/electromagnetism2_scalar_waves.htm (1447 words)

	Scalar Field Methods - Research - Scientific Computing and Imaging Institute
		A scalar field is an arrangement of scalar values distributed in a space.
		Typically, scalar field data being visualized is not continuous (as the original scalar field is), but is composed of a set of discrete sampled values.
		For example, if a scalar field of atmospheric temperature values is used for aviation flight planning, the range of values is bounded to the values possible in the atmosphere.
	www.sci.utah.edu /research/scalar-field-meth.html (290 words)

	Scalar potential: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-21)
		In vector calculus a solenoidal vector field is a vector field v with divergence zero:...
		In vector calculus, a laplacian vector field is a vector field which is both irrotational and incompressible fluidincompressible....
		In fluid mechanics, an irrotational vector field is a vector field whose curl is zero....
	www.absoluteastronomy.com /encyclopedia/s/sc/scalar_potential.htm (1553 words)

	CLIMBING UP THE GRADIENT (Site not responding. Last check: 2007-10-21)
		The beauty of this representation is that the first vector is a function of the scalar field and the second vector is a function of the direction in which the directional derivative is to be obtained.
		It must be noted that the gradient of a scalar field is a vector and the directional derivative is a scalar even though it is associated with a direction.
		The directional derivative of the scalar field at a point on the level surface along the tangential direction is also the dot product of the gradient vector at that point and the unit vector along the tangent.
	www.freehomepages.com /gradient/gradient.html (1127 words)

	Healing America
		The term scalar was used by Nikola Tesla at the end of the last century as a part of powerful non-Hertzian energy (without frequencies) which he referred to as standing energy or cosmic waves.
		Scalar Fields and Scalar Waves, as explained by Dr. Joseph Mercola: The American physicist Thomas E. Bearden popularized the concept of "scalar waves".
		A survey of the literature suggests that 'scalar' energy is the most appropriate description of healing energy up-to-date, as it allows for the fact that healing energy has been shown to be not part of the electromagnetic spectrum as we understand it.
	www.networkingtheinternet.com /healing-america (2488 words)

	8 Scalar Field Dataset
		The scalar field dataset is a 3-dimensional grid that contains a single scalar value at each grid point.
		Another interpretation is to draw each grid-point with its scalar value represented as a point of varying thickness, or to blend the grid points as a texture (as exploited in medical resonance imaging, also called volume rendering).
		Probably the three most common uses for scalar fields in structural biology are electron density from x-ray data, 3D reconstructions from electron microscopy and electrostatic potential maps from theoretical calculations.
	www.dino3d.org /man/manual-8.html (855 words)

	Unification and distance scales
		The physical scalar fields that oscillate as normal modes about the potential minimum are the massless angular mode and the massive radial mode.
		The oscillations of the scalar field around the flat angular direction of the scalar potential turn into longitudinal oscillations of the physical gauge field.
		The value of the scalar field at the potential minimum determines the mass of the gauge boson, and hence the range of the force carried by the gauge boson.
	www.superstringtheory.com /experm/exper3a.html (684 words)

	Scalar field (Site not responding. Last check: 2007-10-21)
		Scalar are often used in physics for instance to indicate the temperature distribution throughout space or the air pressure.
		The scalar field can be visualized as n-dimensional space with a real or complex attached to each point in the space.
		In general relativity gravity is associated with a tensor In particular with the riemann curvature tensor.
	www.freeglossary.com /Scalar_field (345 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A scalar is supposedly a 'field' that accompanies a magnetic field (or electrostatic field) but is "over-written" so to speak by either the magnetic or electrostatic field's presence.
		The 'scalar' generated this way is a 'residue' of the application and cancellation of two opposite electromagnets' fields.
		The article author and interviewees did say that if scalar fields were generated by opposing coils, driven by a composite of frequencies starting down in the ELF range and including components into the less-than-1-megahertz RF range, much stronger biological effects could be generated than when using non-cancelling magnetic fields.
	www.raven1.net /scalar.htm (928 words)

	Scalar field (Site not responding. Last check: 2007-10-21)
		Some examples of vector field s include the electromagnetic field or the newtonian gravitational field.
		In Kaluza-Klein_theory spacetime is extended to five dimensions and its riemann curvature tensor can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the " dilaton ".
		In the movie Field of Dreams, a mystical voice reassures Kevin Costner's character that, "If you build it, he will come." Sure enough, a few cornfield subplots and a new baseball field later, he does come --...
	www.serebella.com /encyclopedia/article-Scalar_field.html (1107 words)

	Structure formation with a self-tuning scalar field (Site not responding. Last check: 2007-10-21)
		A scalar field with an exponential potential has the particular property that it is attracted into a solution in which its energy scales as the dominant component (radiation or matter) of the Universe, contributing a fixed fraction of the total energy density.
		We study the growth of perturbations in a flat CDM dominated universe with this extra field, with an initial flat spectrum of adiabatic fluctuations.
		The observational constraints from structure formation are satisfied as well, or better, than in other models, with approximately 10% of the energy density in the scalar field, which is small enough to be consistent with entry into the attractor prior to nucleosynthesis.
	www.maths.tcd.ie /report_series/abstracts/tcdm9710.html (108 words)

	ZPEnergy.com - Longitudinal waves
		Of course the electric field is pointed in the direction of the wire (it is the gradient of the electric potential at the endpoints of the wire).
		According to my theory there is no magnetic field, but instead there is a scalar field that alternates with the longitudinal electric field, such that the powerflow is always in one direction.
		Usually the Coulomb field is a near field (falls of as 1/r²) but in combination with the scalar field it might fall of as 1/r.
	www.zpenergy.com /modules.php?name=News&file=print&sid=304 (724 words)

	The revealed secrets of classical electrodynamics
		The scalar field is introduced in the spirit of Oliver Heaviside, who stressed the importance of fields, and of James Clerc Maxwell, who predicted vacuum waves by adding a new displacement current term to the Ampère law.
		The generalised field equations are gauge variant, since it is assumed that field S is not zero in general and related to physical effects.
		The presented scalar field S is defined in the context of a classical theory, which is appropriate since the Maxwell/Lorentz theory is classical.
	home.wanadoo.nl /raccoon (6697 words)

	Scalar Field (Site not responding. Last check: 2007-10-21)
		A scalar field is a map over some space of scalar values.
		A simple example of a scalar field is a map of the temperature distribution in a room.
		Below are a few examples of graphical representations of one particular scalar field.
	cnx.org /content/m12854/latest (105 words)

	On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space (Site not responding. Last check: 2007-10-21)
		In this case the scalar field is regular on and outside the event horizon, with a pole inside the event horizon.
		Therefore the scalar field is unable to have a maximum, which is necessary if it is to tend to zero at infinity.
		In this paper we have concentrated on a conformally coupled scalar field because it is the most physically relevant coupling and also the conformal transformation has its simplest form for this coupling.
	www.shef.ac.uk /~ap1ew/bekenstein/conformal.html (7237 words)

	Re: Unifying gravity and electromagnetism
		One reason I have hope is that Newton's scalar theory predicts half the bending of light by the Sun.
		That is created by a scalar field and a scalar field equation that has static solutions.
		My proposal involves a scalar field and a quaternion field equation that has a dynamic solution.
	www.lns.cornell.edu /spr/1999-12/msg0019738.html (385 words)

	A unified scalar field
		An ambitious goal for this class of models is to unify all the forces and particles in nature using a single scalar field and a simple rule for describing the evolution of that field.
		The quantum wave function and the electromagnetic field are identical in this model as they are in the Klein Gordon equation for a single photon and the classical electromagnetic field equation.
		It is this surrounding field that embodies the gravitational field.
	www.mtnmath.com /book/node78.html (648 words)

	Science & Technology at Scientific American.com: Scaled-Up Darkness -- Could a single dark matter particle be ... (Site not responding. Last check: 2007-10-21)
		If a scalar field changes slowly, it resembles a constant, both in its fixed magnitude and in its lack of directionality; relativity theory predicts it will produce a gravitational repulsion.
		Physicists posited bodies composed of scalar particles as long ago as the 1960s, and the idea was revived in the late 1980s, but it only really started to take hold four years ago.
		That inflation, dark energy and dark matter can all be laid at the doorstep of scalar fields suggests that they might be connected.
	www.sciam.com /article.cfm?articleID=00084A33-908A-111B-87CB83414B7F0000 (781 words)

	Non-minimally coupled scalar field hair for black holes (Site not responding. Last check: 2007-10-21)
		We discuss the possibilities of dressing a four-dimensional fl hole with classical scalar field hair which is non-minimally coupled to the space-time curvature.
		and the scalar field is assumed to depend only on the radial co-ordinate r.
		The field equations for the transformed system can be integrated numerically in this case to give non-trivial solutions for the minimally coupled scalar field Φ.
	www.shef.ac.uk /~ap1ew/conformalposter_files/slide0001.htm (764 words)

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