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Topic: Critical density

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	Some Measurements of the Universe (Site not responding. Last check: 2007-10-09)
		This is about one tenth of the critical density of 47 x 10^-28 kg/m^3 or 2.6 GeV/m^3 which is obtained by using a Hubble parameter of 50 km/s/Mpc.
		Since the observed expansion rate suggests that the universe is close to critical density, there must be a large amount of unseen matter, generally lumped under the term "dark matter".
		The density of luminous matter seen in the sky seems to be only about one-tenth the critical density required to "close" the universe.
	hyperphysics.phy-astr.gsu.edu /hbase/astro/umeas.html (256 words)

	Electromagnetic electron wave - Wikipedia, the free encyclopedia
		As the density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the phase velocity is equal to the plasma frequency.
		This density is known as the critical density for the angular frequency ω of that wave and is given by
		As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency ω
	en.wikipedia.org /wiki/Critical_plasma_density (364 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The density is still rather uniform, thus the three balls are well separated, and the ball with density closest to critical floats in the center.
		The density of the liquid state has increased, and the three balls are floating on the surface of the liquid.
		Since the critical density of carbon dioxide is about half that of water, a density increase of 10% will alrady be present in a column of gas only an inch (2.5 cm) high, simply because of the weight of the gas.
	www.chem1.com /chemed/critical.html (567 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The first improvement is to distinguish between a critical density that may best be characterized as an “unstable” environment, and a critical density that is characterized as leading to a “runaway” environment.
		Therefore, the critical density corresponding to a runaway environment is given by RSi = 1/((f V N0 () (4) Notice that although this expression is similar to Equation 1, some of the terms are defined differently.
		The critical density lines in Kessler (1991) therefore represents the spatial density where the equilibrium catalogued population would have a fragment population that is one-half the total catalogue.
	webpages.charter.net /dkessler/files/CriticalDensityofSpacecraftinLow.doc (17089 words)

	Ecology: Detection of critical densities associated with pinon-juniper woodland ecotones (Site not responding. Last check: 2007-10-09)
		This implies that the small convolutions of the edge are controlled by critical densities at fine scales while large convolutions are controlled by broad scale variation in density, i.e., by definition there must be an unbroken field at [p.sub.c] across the map through which the edge meanders.
		Specifically, we assumed that the critical density is constant over a range of scales and that tree cover, and presumably the ecological factors that control it, vary among arbitrarily sized subregions of the map.
		Rather, the general goal of the analysis is to assess the density of occupied cells at a variety of scales and determine which density (measured at many scales) has the highest association with the edge of large clusters.
	www.findarticles.com /p/articles/mi_m2120/is_n3_v77/ai_18262567/pg_4 (1452 words)

	WMAP Cosmology 101: Shape of the Universe
		If the density of the universe is less than the "critical density" which is proportional to the square of the Hubble constant, then the universe will expand forever.
		However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant.
		The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper.
	map.gsfc.nasa.gov /m_uni/uni_101shape.html (532 words)

	IHS ESDU: Data Item 93029
		ESDU 93029 tabulates density and molar volume for 30 compounds in units of kg/cu m and cu cm/mol respectively from near the melting point to the critical point (although for some compounds the tables are terminated at about 0.8 of critical temperature).
		The critical density was calculated using the Rackett and Riedel equations and values of critical pressure and temperature adjusted until the predictions of critical density from the two equations were in good agreement.
		Experimental data for density for each compound were taken from a wide range of sources in the literature and fitted by an equation for log reduced density as a polynomial function of reduced temperature.
	www.esdu.com /graphics/dataitem/93029.htm (222 words)

	critical density
		The average density of matter in the universe today that would be needed exactly to halt, at some point in the future, the cosmic expansion.
		If the density of the universe is greater than the critical density, then not only will the expansion be stopped but there will be a collapse of the universe in the distant future.
		If the density is less than the critical density, an open universe scenario plays out in which the cosmic expansion will continue forever.
	daviddarling.info /encyclopedia/C/critical_density.html (265 words)

	American Superconductor products: htsWire
		In this case, the critical current is defined as the current where the voltage drop across the wire becomes greater than a specific electric field, usually 1 microvolt/cm.
		The critical current retention is the relative ratio of the critical currents before and after a specific process or test.
		In the case of critical current measurements, the self field is the magnetic field that is induced in a straight piece of wire that is being measured.
	www.amsuper.com /products/htsWire/Glossary1.cfm (1481 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		From the fact that after more than ten billion years of expansion the universe has an actual density that is fairly close to the critical density, cosmologists conclude that at the time of the big bang the difference between the actual density and the critical density was amazingly small.
		Cosmologists know of no reason why the actual density could not have been many times smaller or greater than the critical density at the beginning of the big bang, so there is a need to explain why the difference between them at this time was so amazingly small.
		It is generally recognized that there is no reason why the actual density could not have initially differed from the critical density by a factor of more than a million times, so it is hard to believe that such a close correspondence between the actual density and the critical density was due to mere chance.
	www.ling.rochester.edu /~braun/Teaching/101/paper.htm (1128 words)

	Highlights of the Zeno Results from the USMP-2 Mission
		Because critical fluctuations become macroscopic in size and involve enormous numbers of molecules, many features of critical-point behavior are controlled by the statistical behavior of the fluctuations, so that many types of systems exhibit the same behavior near the critical point.
		This was caused by the slowly-forming density gradient in the highly compressible sample: as the gradient became more severe, the amount of fluid near enough to its critical density to show increasing turbidity decreased, and the net effect was a decrease in the turbidity signal.
		As in all the correlograms, the upper curve with the slower decay is the forward-scattering correlogram.
	www.zeno.umd.edu /report/report.html (6203 words)

	Critical Fluid Light Scattering Experiment (Zeno)
		The differences between liquid and vapor density decrease as pressure and temperature increase until -at the "critical point"- there is no difference in the density of the fluid in the liquid and vapor states.
		Most of the sample cannot be maintained at the critical point because the fluid's own weight compresses part of the sample to a density greater than the critical density.
		A sample cell containing a tiny amount of ultrapure xenon held near its critical density is housed inside a high-precision thermostat that controls the sample temperature within a millionth of a degree.
	liftoff.msfc.nasa.gov /shuttle/sts-75/usmp-3/exp/Zeno.html (539 words)

	How was the critical density of the universe calculated?
		The critical density of the universe is actually not 'calculated' in the normal sense of the word.
		When we compare the true density of the universe to the 'critical density', we determine whether we live in a 'closed,' 'flat,' or 'open' universe.
		If the density of the universe is equal to the critical density, then we live in a 'flat' universe.
	www.physlink.com /Education/AskExperts/ae252.cfm (329 words)

	Cosmology
		The density = (mass in the region)/(volume of the region).
		It is the ratio of the current density to the ``critical density'' described in the next paragraph.
		The boundary density between the case where the universe has enough mass/volume to close universe and too little mass/volume to stop the expansion is called the critical density.
	www.astronomynotes.com /cosmolgy/s9.htm (534 words)

	851 - Critical Properties of Pure Compounds - DIPPR - AIChE
		Critical properties are exceedingly important; they are used to estimate such properties as departure functions, liquid density, viscosity, heat capacity, heat of vaporization, thermal conductivity, diffusion coefficients, and surface tension.
		Critical properties are also essential for correlation of vapor pressure and liquid density over the entire saturated liquid range.
		Thus, to measure critical properties of an unstable compound, a small sample in a rapid heating device, with fast temperature and pressure sensors, is needed.
	www.aiche.org /dippr/projects/851.htm (692 words)

	Density of the Universe
		The density of the universe means the amount of matter there is per unit volume, averaged for the entire universe.
		One way to find the average density would be to add up all the matter in the universe and then divide by the number of cubic meters in the universe.
		When the universe is at the critical density, it means that the universe will expand at precisely the right rate to avoid recollapse thus forming a "flat universe."Since the exact density of the universe is not known yet, different sources gave different results.
	hypertextbook.com /facts/2000/ChristinaCheng.shtml (630 words)

	152-154
		The "classical theory" of the critical point makes the strong assumption that the free energy of the fluid is an analytic function of the density and tempera-ture at the critical point.
		The units to use are appropriate combinations of the critical temperature, critical density, and critical pressure for a fluid and the analogous variables for magnetic systems.
		The chemical potential is seen from the data to reflect the symmetry properties of the critical point better than does the pressure, so the equation of state is described in terms of the chemical potential as the density derivative of the free energy per unit volume.
	nvl.nist.gov /pub/nistpubs/sp958-lide/html/152-154.html (1640 words)

	Archive of Astronomy Questions and Answers
		For a 'Hubble constant' of 50 km/sec/megaparsecs, the critical density in equivalent grams per cubic centimeter is 5 x 10^-30 grams per cubic centimeter; about equal to one hydrogen atom in a container 130 centimeters on a side averaged over the entire visible universe.
		The calculation of the Critical Density assumes a globally flat, Euclidean space-time which is infinite and requires the universe to expand indefinitely.
		If you believe that the universe ought to be open, infinite and 'critical' then the various contributions to the observed density of the universe fall short of the Critical Density by factors from 2 to 5.
	www.astronomycafe.net /qadir/q288.html (759 words)

	Friedmann Equation
		Besides the density and gravitation constant G, the equation contains the Hubble parameter H, a scaling parameter R, and a factor k which is called the curvature parameter.
		This k=0 condition can be used to express the critical density in terms of the present value of the Hubble parameter.
		Under this condition, the Friedmann equation can be used to express the critical density of matter in the universe in terms of the current value of the Hubble parameter.
	hyperphysics.phy-astr.gsu.edu /hbase/astro/fried.html (556 words)

	Re: What is the energy/mass balance of the universe?
		The easiest way to answer this question is to consider the density of the various components, i.e., matter and energy, relative to the so-called "critical density" of the universe (which is the density it has to have if the space-time geometry is flat).
		The critical density is the density at which the Universe is balanced between these two possibilities.] Current measurements suggest that the density of ordinary matter (electrons, protons and neutrons essentially) only contributes a few percent of the critical density.
		By contrast the density of radiation (which is the main energy component) is about 1000 times less, at the present epoch, although in the early universe it actually dominated the matter density.
	www.madsci.org /posts/archives/jun2001/992690030.As.r.html (382 words)

	Low Density Universes and Inflation
		Establishing initial conditions so that the mean density remains close to the critical density for more than a fleeting moment is much like trying to balance a pencil on its point.
		For the special case of an expanding universe, idealized as filled with a uniform density of matter, a good approximation on large scales, General Relativity establishes an intimate connection between the density of the universe in comparison with the critical density and its geometry.
		In ordinary inflation, a critical universe could in principle be avoided by shortening the amount of inflation, but in that case the smoothness on large scales remains a mystery, causing inflation to lose most of its appeal.
	www.damtp.cam.ac.uk /user/gr/public/inf_lowden.html (2586 words)

	Curious About Astronomy: If the universe is "bounded" today, could it one day become "unbounded"?
		I mean, as the universe expands its mass is spread more thinly decreasing density until ultimately the average density would be less than the critical density needed to maintain expansion...
		If the density of the universe is greater than that critical density, then it will eventually recollapse.
		The actual density of the universe is something that has been changing over the course of the universe's history.
	curious.astro.cornell.edu /question.php?number=506 (442 words)

	THE DENSITY DEPENDENCE OF THE VISCOSITY UP TO THE CRITICAL DENSITY (Site not responding. Last check: 2007-10-09)
		The critical molar volume is thus nearly equal to five times the molar volume of close packing and the mean distance between the molecules about 0.7 times the diameter of the molecules at the critical density.
		Therefore, at densities higher than the critical the molecules are within the effective range of the intermolecular potential, the attractive forces compensate each other so that the molecules behave nearly as hard spheres and the viscosity can be described by a hard-sphere Enskog theory.
		For densities lower than the critical this mean distance becomes larger than this effective range and we get clusters of molecules hold together by the intermolecular forces, interspaced with empty cracks: mesoscopically the gas is homogeneous, but microscopically it is a mixture of clusters and voids.
	www.zae-bayern.de /ectp/abstracts/gulik1.html (461 words)

	What is dark matter and how do we know it exists?
		The critical density is calculated to be about five millionths of a trillionth of a trillionth (1.9 ´ 10-29) of a gram of matter per cubic centimeter of space, or about one hydrogen atom in every cubic metre.
		Although this is an average figure, in theory, if we know the critical density, we can count up all the mass in the universe and compare it to the critical density.
		W is a Greek letter and it is now used to denote the ratio of the actual density of mass in the universe to the critical density.
	www.coursework.info /i/18562.html (1199 words)

	Density Determination (Site not responding. Last check: 2007-10-09)
		This density has the same dependence on the Hubble constant as the critical density, so we determine the ratio of the density to the critical density, Omega, directly.
		Thus the mass-to-luminosity ratio appears to vary with the size of the region measured, from 3 in the solar neighborhood to 30 in galaxies to 300 in clusters of galaxies.
		Thus the observed gas density profile generates a gravity field under MOND that is not consistent with the observed gas temperature and density profile.
	www.astro.ucla.edu /~wright/density.html (1243 words)

	ASTRONOMY 102- LECTURE 38 (Site not responding. Last check: 2007-10-09)
		If the average density of the universe is less than the critical density of the universe, the universe will expand forever.
		Since the observed average density of the universe is 50x too small to stop the expansion, we could have 50 or 100 x as much dark matter as visible matter.
		The greater the density of the universe, the more deceleration, and thus in the closed universe, distant galaxies seem to be moving much more rapidly than if there density were lower.
	www.gettysburg.edu /academics/physics/clea/A102ol38.html (1135 words)

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