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Topic: Isotropy

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	ISOTROPY
		ISOTROPY is a software package which applies group theoretical methods to the analysis of phase transitions in crystalline solids.
		Also fixed a major bug affecting the calculation of isotropy subgroups for coupled irreps where the second (or third or fourth, etc.) irrep belongs to a non k point of symmetry (non special k point).
		Also improved routine for generating isotropy subgroups at non k points of symmetry.
	stokes.byu.edu /isotropy.html (599 words)

	Light Isotropy- Theory and Experiment
		Therefore, our ability to measure the isotropy of light (when it travels through outer space from stars to the earth) depends entirely on the accuracy with which we can measure the direction our telescopes are pointed in.
		The best way to measure the isotropy of light through empty space when it travels here on earth would be to send it through a chamber which is completely evacuated of molecules.
		A somewhat primitive method used to measure the isotropy (or speed) of light on earth was by sending the light through a toothed wheel and/or rotating mirror apparatus.
	www.wbabin.net /physics/alf3.htm (4067 words)

	Where are the real definitions of homogeneity and isotropy?
		If isotropy and homogeneity apply to, eh, every 'point' or 'observer', I think homogeneity implies isotropy, though I don't really know what either of them are or what they apply to or how.
		Isotropy of space (from which the conservation of angular momentum may be derived) states that the properties of a closed system are unaffected by a rotation of the system in space.
		That definition is addressing the homogeneity and isotropy of the laws of physics, something which is necessary for the homogeneity and isotropy of the universe, but not sufficient.
	www.physicsforums.com /showthread.php?t=91401 (3178 words)

	Household Science for Kids: Iso/Thixotropy
		Isotropy is the property of a fluid to become firm when agitated.
		Thixotropy is the opposite of isotropy in that the fluid mixture becomes more fluid (less firm) as it is agitated.
		An example of this is where you strike the end of a ketchup bottle to get ketchup to come out of the bottle.
	www.fatlion.com /science/isotropy.html (436 words)

	Isotropy - Wikipedia, the free encyclopedia
		Isotropy (the opposite of anisotropy) is the property of being independent of direction.
		Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.
		Optics: Optical isotropy means having the same optical properties in all directions.
	en.wikipedia.org /wiki/Isotropic (337 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		Isotropy means that the properties of the Universe are the same in all directions (rotation invariance).
		Is the observed isotropy a consequence of a special position of the Earth in the Universe like that of an observer located at the center of an explosion?
		While that could be the case, cosmologists usually assumes the so called Cosmological principle (or Copernican principle) which states that our position is not special in any way and that the observed isotropy has to be interpreted as isotropy about all points.
	www.amherst.edu /~gsgreenstein/progs/cosmology/expans.html (288 words)

	Isotropy (Site not responding. Last check: 2007-10-29)
		To investigate the isotropy of the model a bubble of fluid with
		This was done on a 64 by 64 grid and the radius of the circle was 13 lu.
		There is no evidence of a departure from isotropy or of the underlying hexagonal grid.
	une.edu.au /Physics/Staff/Buick/Publications/PDF/Thesis/node101.html (193 words)

	TxSpace at Texas A&M University Libraries: Item 1969.1/1158
		While the assumption of isotropy is often made for this structure, it is not always appropriate.
		A conventional practice to check for isotropy is to informally assess plots of direction-specific sample second-order properties, e.g., sample variogram or sample second-order intensity function.
		In this dissertation, we propose a formal approach testing for isotropy that is both objective and appropriate for a wide class of models.
	txspace.tamu.edu /handle/1969.1/1158 (273 words)

	On the ultimate convergence rates for isotropic algorithms and the best choices among various forms of isotropy
		We then recall that isotropy does not uniquely determine the distribution of a sample on the sphere and show that the convergence rate in isotropic algorithms is improved by using stratified or antithetic isotropy instead of naive isotropy.
		We have postulated isotropy : this means that the probability of having one point in each given infinitesimal spherical cap is the same in any direction.
		But isotropy does not mean that all the offspring must be independent and identically distributed.
	www.lri.fr /~teytaud/lbedalong (3220 words)

	IngentaConnect The local isotropy hypothesis and the turbulent kinetic energy di... (Site not responding. Last check: 2007-10-29)
		IngentaConnect The local isotropy hypothesis and the turbulent kinetic energy di...
		We test the applicability of the local isotropy hypothesis to surface-layer turbulent flow; turbulent velocities measured with a three-dimensional sonic anemometer are used for this purpose, and the predictions of local isotropy for the spectra, second- and third-order structure functions are assessed against measured data.
		In general, second-order structure functions display a narrower inertial range than the corresponding spectra; both the known effects of path-averaging and the predictions of the spectral models show that the sonic anemometer is unable to resolve the whole inertial range, even at a measurement frequency of 60 Hz.
	dx.doi.org /10.1256/qj.03.155 (290 words)

	The Implications of Homogeneity and Isotropy
		Yes, a rod could return to it's point of origin with it's length dialated, however it would have to be travelling at a different speed than it was when it was originally at it's point of origin as length dialation is dependent on velocity.
		My question is about geometry and the implications of homogeneity and isotropy.
		It is often said that the Lorentz transformation can be derived from the homogeneity and isotropy of space alone.
	www.physicsforums.com /showthread.php?t=4564 (498 words)

	Brainstorms: Rich Halvorson: Questioning Cosmological Superstition - Separating science from ...
		In examining the origins of the two principles, we note that isotropy was an ingenious insight that managed to connect a few disparate data points into a helpful and accurate theory.
		Homogeneity, on the other hand, was considered a necessary correlate to isotropy not for any scientific reason, but because it seemed necessary to make isotropy compatible with a secular view of the universe.
		This research suggests that the Copernican principle could be true (that all observers in the universe would see the same degree of isotropy), without homogeneity being true (the universe remains “lumpy”).
	www.iscid.org /boards/ubb-get_topic-f-6-t-000539.html (1375 words)

	Isotropy Codes of The On-line Exact Solutions Database at UERJ (Site not responding. Last check: 2007-10-29)
		These characters represent the isotropy group of the Riemann tensor and its derivatives to zeroth, first, second and third order respectively.
		At a particular stage, if it is known that the isotropy group will not reduce when higher derivatives are calculated, the subsequent redundant calculations are not carried out and the field for the isotropy group filled with a -.
		The table below indicates the isotropy group associated with the other characters which appear in the output.
	www.astro.queensu.ca /~jimsk/codes.html (189 words)

	Isotropy AINiCo alloy,anisotropy AINiCo alloy,isotropy AINiCo bonded magnet manufacturer and Isotropy AINiCo ...
		As a professional Isotropy AINiCo alloys, anisotropy AINiCo alloys, isotropy AINiCo bonded magnets manufacturer, exporter, supplier and factory in China.--Ningbo Ketian Magnet Co,.Ltd. is shared by Ningbo Jintian Copper Group Co,.Ltd, and Ningbo Jintian Copper Group Co,.Ltd is one of the 500 top town enterprises in China, and the largest non-ferrous metallugy group in Zhejiang.
		It is mainly engaged in the research, development, produce and sales of NdFeB materials, Isotropy AINiCo alloy, anisotropy AINiCo alloy, isotropy AINiCo bonded magnet.
		Isotropy AINiCo alloy, anisotropy AINiCo alloy, isotropy AINiCo bonded magnet
	www.kt-magnet.com /n_Isotropy_AINiCo_alloy.htm (304 words)

	Isotropy
		Isotropy : The condition in which the hydraulic or other properties of an aquifer are the same in all directions.
		Effects of mean flow direction on energy, isotropy, and coherence of
		Surface orientation from texture: isotropy or homogeneity (or both)?
	www.mongabay.com /reference/environment/Isotropy.html (223 words)

	Far ultraviolet remote sensing of the isotropy boundary and magnetotail stretching
		Several studies have attempted to identify the isotropy boundary (IB) defining the limit between the adiabatic and nonadiabatic trajectories of the trapped protons along closed magnetic field lines.
		The relation between the position of the maximum proton precipitation as well as the intensity of this maximum and the magnetic field distortion is determined by comparison with GOES 8 data.
		We suggest that SI12 images can be used as a tool to globally determine the isotropy boundary and to monitor the level of stretching in the magnetotail.
	www.agu.org /pubs/crossref/2005/2005JA011103.shtml (362 words)

	Correlation Length, Isotropy, and Meta-stable States (ResearchIndex) (Site not responding. Last check: 2007-10-29)
		The "correlation length conjecture" allows to estimate the number of meta-stable states from the correlation length, provided the landscape is "typical".
		Isotropy, originally introduced as a geometrical condition on the covariance matrix of a random field, can be re-interpreted as maximum...
		36.1%: Isotropy and Metastable States - The Landscape of the XY..
	citeseer.ist.psu.edu /112777.html (829 words)

	Isotropy or weak vertical transverse isotropy in D″ beneath the Atlantic Ocean
		Isotropy or weak vertical transverse isotropy in D″ beneath the Atlantic Ocean
		Assuming an anisotropy geometry involving vertical transverse isotropy (VTI), as preferred in most regions of D″ that have been studied to date, <0.5% anisotropy strength within a 100 km thick layer, or <0.25% anisotropy within a 300 km thick layer are compatible with the data.
		These values are low in comparison to those found in high-velocity regions beneath the circum-Pacific Ocean or in the low-velocity region beneath the central Pacific, and many observations are, in fact, consistent with isotropic structure.
	www.agu.org /pubs/crossref/2004/2004JB003004.shtml (500 words)

	Optical isotropy - Wikipedia, the free encyclopedia
		It has been suggested that this article or section be merged into isotropy.
		In the literature, optical isotropy is usually seen as equivalent to the fact that the dielectric tensor function is a scalar function or is reduced to a scalar function in case of polydomain materials.
		The latter is not correct, however, if the domains can not be considered as small compared to the wavelength.
	en.wikipedia.org /wiki/Optical_isotropy (234 words)

	Cycles
		, we showed a robust saddle connection between equilibria of the same isotropy type.
		Another possibility is that we may have robust saddle connections between equilibria of different isotropy type.
		Thus, even though isotropy is constant along integral curves, it is possible in principle for symmetry to increase at limit points of a trajectory.
	www.math.uh.edu /~mike/ima/node6.html (714 words)

	9.3.4 Transverse isotropy
		The presence of gravity provides a symmetry breaking from three-dimensional isotropy down to transverse isotropy about the local vertical direction
		It is important that the stress tensor also respect this symmetry, which in turn provides constraints on the form of the viscosity tensor.
		In order to understand what transverse, or axial, isotropy imposes on the viscosity tensor, it is necessary to recall that a fourth order tensor transforms under a change of coordinates in the following manner
	www.gfdl.noaa.gov /~smg/MOM/web/guide_parent/s2node100.html (230 words)

	Isotropy -- from Eric Weisstein's World of Astronomy
		Isotropy -- from Eric Weisstein's World of Astronomy
		The premise that there is no preferred direction singled out in space (space looks the same in all directions about a point).
		Isotropy may be tested for by searching for anisotropy in the 2.7 K background radiation.
	scienceworld.wolfram.com /astronomy/Isotropy.html (45 words)

	Isotropy
		Because only one or two terms in the dissipation tensor are usually measured, the assumption has gone unchecked.
		by assuming isotropy could be as large as a factor of two.
		This result should be considered with caution until further investigations in high Reynolds number geophysical flows are made, but it casts some doubt on the assurances of Yamazaki and Osborn [1990].
	www.agu.org /revgeophys/caldwe01/node9.html (397 words)

	Optical element employing liquid crystal having optical isotropy patent invention
		An optical element is provided, which can realize high speed response equivalent or more than that of conventional elements without depending on incident polarization.
		However, no example of the construction of a switching element has been disclosed heretofore, which uses optical isotropy and does not depend on incident polarization state.
		Thank you for viewing the Optical element employing liquid crystal having optical isotropy patent info.
	www.freshpatents.com /Optical-element-employing-liquid-crystal-having-optical-isotropy-dt20061012ptan20060227283.php (1283 words)

	Isotropy and Metastable States (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath
		The number of local optima is an important characteristic of a landscape.
		It appears to depend on the pair-correlation of the landscape as well as on its deviations from statistical isotropy.
		We use Tanaka and Edward's XY Hamiltonian as an example for an investigation of the relationships between ruggedness, metastable states, and isotropy.
	smealsearch.psu.edu /9941.html (920 words)

	Astronomy 104 Discussion #2: Homogeneity and Isotropy
		The point of this exercise is to get some familiarity with the meanings of the concepts of homogeneity and isotropy (and their opposites, inhomogeneity and anisotropy.) To do that, we'll make our first use of virtual reality software to explore the spatial distributions of astronomical objects.
		Now it is time to look at some real three-dimensional worlds, based on astronomical data.
		For now, don't worry too much about which data was used to generate each world; we just want to use them to explore the concepts of isotropy and homogeneity.
	physics.syr.edu /courses/AST104/labs/disc0299.htm (694 words)

	Local & global aspects of symmetric dynamics
		We quantify this idea of symmetry of a point by defining the isotropy group of the action at a point of V.
		Using equivariance, together with the smooth dependence of integral curves on initial conditions, it is easy to see that isotropy groups are constant along maximal integral curves of (
		This apparently innocuous observation about isotropy along integral curves has the significant and surprising consequence that V contains subsets which are flow-invariant for all equivariant vector fields.
	www.math.uh.edu /~mike/ima/node2.html (369 words)

	Home Page of Amir Hajian (Site not responding. Last check: 2007-10-29)
		Measuring Statistical Isotropy of CMB; Amir Hajian, Tarun Souradeep; Astrophys.J. Statistical Isotropy of Cosmic Microwave Background Radiation Anisotropy; Tarun Souradeep, Amir Hajian; Pramana, vol.
		Statistical Isotropy of CMB and Cosmic Topology; Amir Hajian, Tarun Souradeep, (astro-ph/0301590), to be submitted to PRL.
		Statistical Isotropy of WMAP: With Tarun Souradeep and Neil Cornish.
	meghnad.iucaa.ernet.in /~amir (360 words)

	A convenient approximation of transverse isotropy for higher-order moveout, prestack time migration, and depth ... (Site not responding. Last check: 2007-10-29)
		Our parameterization of this normal moveout should be consistent with the model of anisotropy used in full prestack time imaging.
		It is recognized that the kinematics of surface reflection seismic data are insensitive to component of transverse isotropy that is essential for an accurate conversion of time to depth.
		A single convenient analytic approximation of transverse isotropy will allow us to generalize prestack moveout, time imaging, and depth conversion.
	billharlan.com /pub/papers/aniso (1672 words)

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