Discrepancy of hypergraphs - Revision history

en>Magioladitis: clean up using AWB (10476)

2014-10-06T07:20:46Z

clean up using AWB (10476)

← Older revision		Revision as of 09:20, 6 October 2014
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	~~The writer~~ is ~~called Araceli Gulledge~~. I am a ~~production and distribution officer~~. ~~What she loves performing is taking part in croquet and she~~ is ~~attempting~~ to ~~make it a profession. Delaware is the location I adore most~~ but I ~~need to move for my family members~~.<br><br>Also visit my ~~web page~~ ... ~~car warranty~~ ([http://~~roki~~-~~Gaming~~.~~de/index~~.~~php?mod=users&action=view&id=371 Click At this website~~])		Andrew Berryhill is what his wife enjoys to contact him and he completely digs that name. My wife and I live in Kentucky. She functions as a journey agent but soon she'll be on her own. It's not a typical thing but what I like doing is to climb but I don't have the time lately.<br><br>Also visit my weblog ... email [http://www.taehyuna.net/xe/?document_srl=78721 love psychic readings] [http://black7.mireene.com/aqw/5741 free tarot readings] ([http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ http://www.familysurvivalgroup.com])

en>David Eppstein: /* Theorems */ link Beck–Fiala theorem, remove editorialization

2014-02-27T02:10:39Z

Theorems: link Beck–Fiala theorem, remove editorialization

← Older revision		Revision as of 04:10, 27 February 2014
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	The ~~'''Navarro–Frenk–White profile''' or '''NFW profile'''~~ is a ~~spatial mass~~ distribution ~~of [[dark matter]] fitted to dark matter haloes identified in [[N-body]] simulations by [[Julio Navarro (astrophysicist)\|Julio Navarro]], [[Carlos Frenk]] and [[Simon White]]~~.<ref name="NAVARROETAL1996">{{cite journal\|author=Navarro, Julio F.; Frenk, Carlos S.; White, Simon D. M.\|title=The Structure of Cold Dark Matter Halos\|journal=The Astrophysical Journal\|volume=463\|pages=563\|date=May 10, 1996\|bibcode=1996ApJ...462..563N\|doi=10.1086/177173\|arxiv=astro-ph/9508025}}</ref> The NFW profile is one of the most commonly used model profiles for dark matter halos.<ref name="BERTONE2005">{{Cite book\|last=Bertone\|first=Gianfranco\|title=[[Particle Dark Matter\|Particle Dark Matter: Observations, Models and ~~Searches]]\|publisher=Cambridge University Press\|year=2010\|pages=762\|isbn=978-0-521-76368-4}}</ref>~~		The writer is called Araceli Gulledge. I am a production and distribution officer. What she loves performing is taking part in croquet and she is attempting to make it a profession. Delaware is the location I adore most but I need to move for my family members.<br><br>Also visit my web page ... car warranty ([http://roki-Gaming.de/index.php?mod=users&action=view&id=371 Click At this website])

	~~==Density distribution==~~
	~~<!-- Deleted image removed: [[File:rho nfw.svg\|thumb\|right\|The NFW density profile on a log radius versus density plot.]] -->~~

	~~In the NFW profile, the density of dark matter as a function of radius~~ is ~~given by:~~

	~~<math>~~
	~~\rho (r)=\frac{\rho_0}{\frac{r}{R_s}\left(1~+~\frac{r}{R_s}\right)^2}~~
	~~</math>~~

	~~where ρ<sub>0</sub> and the "scale radius", ''R<sub>s</sub>'', are parameters which vary from halo~~ to ~~halo.~~

	~~The integrated mass inside of some radius ''R<sub>max</sub>'' is~~

	~~<math>~~
	~~M=\int_0^{R_{max}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[~~
	~~\ln\left(\frac{R_s+R_{max}}{R_s}\right)-\frac{R_{max}}{R_s+R_{max}}\right]~~
	~~</math>~~

	~~The total mass is divergent, but~~ it ~~is often useful to take the edge of the halo to~~
	~~be the virial radius, ''R<sub>vir</sub> '',~~
	~~which is related to the "concentration parameter", ''c'', and scale radius via~~

	~~<math>~~
	~~R_{vir}=cR_s~~
	~~</math>~~

	~~The virial radius is often referred to as <math> R_{200} </math>, and is defined as the radius at which the average density within this radius is 200 times the critical density~~. ~~In this case, the total mass in the halo~~ is

	~~<math>~~
	~~M=\int_0^{R_{vir}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[\ln(1+c) - \frac{c}{1+c}\right]~~
	~~</math>~~

	~~The value of ''c'' is roughly 10 or 15 for~~ the ~~Milky Way, and may range from 4~~ to 40
	for ~~halos of various sizes~~.

	~~The integral of the ''squared density'' is~~

	~~<math>~~
	~~\int_0^{R_{max}} 4\pi r^2 \rho (r)^2 dr=\frac{4\pi}{3} R_s^3 \rho_0^2~~
	~~\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right]~~
	~~</math>~~

	~~so that the mean squared density inside of ''R<sub>max</sub>'' is~~

	~~<math>~~
	~~\langle \rho^2 \rangle_{R_{max}}=\frac{R_s^3\rho_0^2}{R_{max}^3}~~
	~~\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right]~~
	~~</math>~~

	~~which for the virial radius simplifies to~~

	~~<math>~~
	~~\langle \rho^2 \rangle_{R_{vir}}=\frac{\rho_0^2}{c^3}~~
	~~\left[1-\frac{1}{(1+c)^3}\right]~~
	~~\approx \frac{\rho_0^2}{c^3}~~
	~~</math>~~

	~~and the mean squared density inside the scale radius is simply~~

	<~~math~~>
	~~\langle \rho^2 \rangle_{R_s}=\frac{7}{8}\rho_0^2~~
	<~~/math~~>

	~~==Dark matter simulations==~~
	The NFW profile is an approximation to the [[Thermodynamic equilibrium\|equilibrium]] configuration of dark matter produced in simulations of [[collision]]less dark matter particles by numerous groups of scientists.~~<ref>{{cite journal\|author=Y~~. P. Jing\|title=The Density Profile of Equilibrium and Nonequilibrium Dark Matter Halos\|journal=The Astrophysical Journal\|date=20 May 2000\|volume=535\|issue=1\|pages=30–36\|bibcode=2000ApJ...535...30J\|doi=10.1086/308809\|arxiv=astro-ph/9901340}}</ref> Before the dark matter [~~[virial theorem\|virializes]], the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse of the halos.~~

	Alternative models, in particular the [[Einasto profile]], have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile.<ref>{{cite journal\|author=[[David Merritt\|Merritt, David]]; Graham, Alister; Moore, Benjamin; Diemand, Jurg; Terzić, Balsa\|title=Empirical Models for Dark Matter Halos\|journal=The Astronomical Journal\|date=20 December 2006\|volume=132\|issue=6\|pages=2685–2700\|bibcode=2006AJ....132.2685M\|doi=10.1086/508988\|arxiv=astro-ph/0509417\|url=http://~~adsabs.harvard~~.~~edu/abs~~/~~2006AJ....132.2685M}}</ref><ref>{{cite journal\|last1=Merritt\|first1=David\|authorlink1=David Merritt\|last2=et al~~.~~\|title=A Universal Density Profile for Dark and Luminous Matter~~?~~\|journal~~=~~The Astrophysical Journal\|date~~=~~May 2005\|volume~~=624\|issue=2\|pages=L85–L88\|bibcode=2005ApJ...624L..85M\|doi=10.1086/430636\|arxiv=astro-ph/0502515\|url=http://adsabs.harvard.edu/abs/2005ApJ...624L..85M}}</ref> The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) ~~central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.~~

	~~==Observations of halos==~~
	The observations of both the [[Milky Way]] and [[Andromeda Galaxy\|M31]] may be compatible with the NFW profile for the dark matter halo.<ref name="KLYPIN2002">{{cite journal\|author=Klypin, Anatoly; Zhao, HongSheng; Somerville, Rachel S.\|title=ΛCDM-based Models for the Milky Way and M31. I. Dynamical Models\|date=10 July 2002\|journal=The Astrophysical Journal\|volume=573\|issue=2\|pages=597–613\|bibcode=2002ApJ...573..597K\|doi=10.1086/340656\|arxiv=astro-ph/0110390}}</ref> The dark matter profile of smaller galaxies tend to have flatter distributions of dark matter in the central region, known as the [[Cuspy halo problem]].

	~~==References==~~
	~~{{reflist}}~~

	~~{{Dark matter}}~~

	~~{{DEFAULTSORT:Navarro-Frenk-White profile}}~~
	~~[[Category:Dark matter]]~~

en>Ott2: copy-edit punctuation

2013-10-15T16:00:19Z

copy-edit punctuation

← Older revision		Revision as of 18:00, 15 October 2013
Line 1:		Line 1:
	The ~~author~~'~~s name~~ is ~~Andera~~ and ~~she thinks it seems fairly great~~. ~~One~~ of the ~~things she enjoys~~ most is ~~canoeing~~ and ~~she~~'s ~~been performing~~ it for ~~quite a while~~. I'~~ve always loved living~~ in ~~Mississippi~~. ~~Invoicing~~ is ~~my profession~~.<br><br>~~Here is my page~~ - ~~real psychic readings ([~~http://~~cartoonkorea~~.~~com~~/~~ce002~~/~~1093612 you could try this out~~])		The '''Navarro–Frenk–White profile''' or '''NFW profile''' is a spatial mass distribution of [[dark matter]] fitted to dark matter haloes identified in [[N-body]] simulations by [[Julio Navarro (astrophysicist)\|Julio Navarro]], [[Carlos Frenk]] and [[Simon White]].<ref name="NAVARROETAL1996">{{cite journal\|author=Navarro, Julio F.; Frenk, Carlos S.; White, Simon D. M.\|title=The Structure of Cold Dark Matter Halos\|journal=The Astrophysical Journal\|volume=463\|pages=563\|date=May 10, 1996\|bibcode=1996ApJ...462..563N\|doi=10.1086/177173\|arxiv=astro-ph/9508025}}</ref> The NFW profile is one of the most commonly used model profiles for dark matter halos.<ref name="BERTONE2005">{{Cite book\|last=Bertone\|first=Gianfranco\|title=[[Particle Dark Matter\|Particle Dark Matter: Observations, Models and Searches]]\|publisher=Cambridge University Press\|year=2010\|pages=762\|isbn=978-0-521-76368-4}}</ref>

			==Density distribution==
			<!-- Deleted image removed: [[File:rho nfw.svg\|thumb\|right\|The NFW density profile on a log radius versus density plot.]] -->

			In the NFW profile, the density of dark matter as a function of radius is given by:

			<math>
			\rho (r)=\frac{\rho_0}{\frac{r}{R_s}\left(1~+~\frac{r}{R_s}\right)^2}
			</math>

			where ρ<sub>0</sub> and the "scale radius", ''R<sub>s</sub>'', are parameters which vary from halo to halo.

			The integrated mass inside of some radius ''R<sub>max</sub>'' is

			<math>
			M=\int_0^{R_{max}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[
			\ln\left(\frac{R_s+R_{max}}{R_s}\right)-\frac{R_{max}}{R_s+R_{max}}\right]
			</math>

			The total mass is divergent, but it is often useful to take the edge of the halo to
			be the virial radius, ''R<sub>vir</sub> '',
			which is related to the "concentration parameter", ''c'', and scale radius via

			<math>
			R_{vir}=cR_s
			</math>

			The virial radius is often referred to as <math> R_{200} </math>, and is defined as the radius at which the average density within this radius is 200 times the critical density. In this case, the total mass in the halo is

			<math>
			M=\int_0^{R_{vir}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[\ln(1+c) - \frac{c}{1+c}\right]
			</math>

			The value of ''c'' is roughly 10 or 15 for the Milky Way, and may range from 4 to 40
			for halos of various sizes.

			The integral of the ''squared density'' is

			<math>
			\int_0^{R_{max}} 4\pi r^2 \rho (r)^2 dr=\frac{4\pi}{3} R_s^3 \rho_0^2
			\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right]
			</math>

			so that the mean squared density inside of ''R<sub>max</sub>'' is

			<math>
			\langle \rho^2 \rangle_{R_{max}}=\frac{R_s^3\rho_0^2}{R_{max}^3}
			\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right]
			</math>

			which for the virial radius simplifies to

			<math>
			\langle \rho^2 \rangle_{R_{vir}}=\frac{\rho_0^2}{c^3}
			\left[1-\frac{1}{(1+c)^3}\right]
			\approx \frac{\rho_0^2}{c^3}
			</math>

			and the mean squared density inside the scale radius is simply

			<math>
			\langle \rho^2 \rangle_{R_s}=\frac{7}{8}\rho_0^2
			</math>

			==Dark matter simulations==
			The NFW profile is an approximation to the [[Thermodynamic equilibrium\|equilibrium]] configuration of dark matter produced in simulations of [[collision]]less dark matter particles by numerous groups of scientists.<ref>{{cite journal\|author=Y. P. Jing\|title=The Density Profile of Equilibrium and Nonequilibrium Dark Matter Halos\|journal=The Astrophysical Journal\|date=20 May 2000\|volume=535\|issue=1\|pages=30–36\|bibcode=2000ApJ...535...30J\|doi=10.1086/308809\|arxiv=astro-ph/9901340}}</ref> Before the dark matter [[virial theorem\|virializes]], the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse of the halos.

			Alternative models, in particular the [[Einasto profile]], have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile.<ref>{{cite journal\|author=[[David Merritt\|Merritt, David]]; Graham, Alister; Moore, Benjamin; Diemand, Jurg; Terzić, Balsa\|title=Empirical Models for Dark Matter Halos\|journal=The Astronomical Journal\|date=20 December 2006\|volume=132\|issue=6\|pages=2685–2700\|bibcode=2006AJ....132.2685M\|doi=10.1086/508988\|arxiv=astro-ph/0509417\|url=http://adsabs.harvard.edu/abs/2006AJ....132.2685M}}</ref><ref>{{cite journal\|last1=Merritt\|first1=David\|authorlink1=David Merritt\|last2=et al.\|title=A Universal Density Profile for Dark and Luminous Matter?\|journal=The Astrophysical Journal\|date=May 2005\|volume=624\|issue=2\|pages=L85–L88\|bibcode=2005ApJ...624L..85M\|doi=10.1086/430636\|arxiv=astro-ph/0502515\|url=http://adsabs.harvard.edu/abs/2005ApJ...624L..85M}}</ref> The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.

			==Observations of halos==
			The observations of both the [[Milky Way]] and [[Andromeda Galaxy\|M31]] may be compatible with the NFW profile for the dark matter halo.<ref name="KLYPIN2002">{{cite journal\|author=Klypin, Anatoly; Zhao, HongSheng; Somerville, Rachel S.\|title=ΛCDM-based Models for the Milky Way and M31. I. Dynamical Models\|date=10 July 2002\|journal=The Astrophysical Journal\|volume=573\|issue=2\|pages=597–613\|bibcode=2002ApJ...573..597K\|doi=10.1086/340656\|arxiv=astro-ph/0110390}}</ref> The dark matter profile of smaller galaxies tend to have flatter distributions of dark matter in the central region, known as the [[Cuspy halo problem]].

			==References==
			{{reflist}}

			{{Dark matter}}

			{{DEFAULTSORT:Navarro-Frenk-White profile}}
			[[Category:Dark matter]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-08T06:17:27Z

ISBNs (Build KE)

New page

The author's name is Andera and she thinks it seems fairly great. One of the things she enjoys most is canoeing and she's been performing it for quite a while. I've always loved living in Mississippi. Invoicing is my profession.<br><br>Here is my page - real psychic readings ([http://cartoonkorea.com/ce002/1093612 you could try this out])