Advanced Z-transform - Revision history

177.18.63.133: /* Example */

2014-05-13T15:09:11Z

Example

← Older revision		Revision as of 17:09, 13 May 2014
Line 1:		Line 1:
	~~{{Technical\|date=September 2010}}~~		Got nothing to tell about me really.<br>Hurrey Im here and a member of this community.<br>I really wish I am useful at all<br><br>my page; [http://janyaa.org/content/how-use-your-psychic-powers-sell-more-products electronic dog training collar]
	~~<!-- {{Standard model of particle physics}} Here it would be essentially inadequate to introduced this well-known graphics! -->~~
	~~In particle theory, the '''skyrmion''' is a hypothetical particle related originally<ref>At later stages the model was also related~~ to ~~[[meson]]s~~.<~~/ref~~> ~~to [[baryon]]s. It was described by [[Tony Skyrme]]~~ and ~~consists of~~ a ~~[[quantum superposition]]~~ of ~~baryons and resonance states~~.<~~ref~~>~~{{cite arXiv\|first=Stephen\|last=Wong\|date=\|title=What exactly is a Skyrmion?\|class=hep/ph\|eprint=hep-ph/0202250\|year=2002}}</ref>~~

	Skyrmions as topological objects are also important in [[solid state physics]], especially in the emerging technology of [[spintronics]]. A two-dimensional skyrmion, as a topological object, is formed, e.g., from a 3d effective-spin "hedgehog" (in the field of [[micromagnetics]]: out of a so-called "[[Bloch sphere\|Bloch point]]" singularity of homotopy degree +1) by a [[stereographic projection]], whereby the positive northpole spin is mapped onto a far-off edge circle of a 2d-disk, while the negative southpole spin is mapped onto the center of the disk.

	~~==Mathematical definition==~~
	In field theory, skyrmions are [[homotopy\|homotopically]] non-trivial classical solutions of a [[nonlinear sigma model]] with a non-trivial [[target manifold]] topology – hence, they are [[topological soliton]]s. An example occurs in [[chiral model]]s <ref>Chiral models stress the difference between "left-handedness" and "right-handedness".</ref> of mesons, where the target manifold is a [[homogeneous space]] of the [[structure group]]

	~~<math>\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\right)</math>~~

	~~where ''SU''(''N'')<sub>''L''</sub> and ''SU''(''N'')<sub>''R''</sub> are the left and right parts of the ''SU''(''N'') matrix, and ''SU''(''N'')<sub>diag</sub> is the [[diagonal subgroup]].~~

	If [[spacetime]] has the topology S<sup>3</sup>×'''R''', then classical configurations can be classified by an integral [[winding number]]<ref>The same classification applies to the mentioned effective-spin "hedgehog" singularity": spin upwards at ~~the northpole, but downward at the southpole.~~<br>See also {{Cite journal\|doi=10.1063/1.1656144\|title=Point Singularities in Micromagnetism\|year=1968\|last1=Döring\|first1=W.\|journal=Journal of Applied Physics\|volume=39\|issue=2\|pages=1006 }}</ref> because the third [[homotopy group]]

	<~~math~~>~~\pi_3\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\cong SU(N)\right)</math>~~

	~~is equivalent to the ring of integers, with the congruence sign referring to [[homeomorphism]].~~

	~~A topological term can be added to the chiral Lagrangian, whose integral depends only upon the [[homotopy class]]~~; ~~this results in~~ [[superselection sector]]s in the quantised model[[Skyrim\|.]] A skyrmion can be approximated by a [[soliton]] of the [[Sine-Gordon equation]]; after quantisation by the [[Bethe ansatz]] or otherwise, it turns into a [[fermion]] interacting according to the massive [[Thirring model]].

	Skyrmions have been reported, but not conclusively proven, to be in [[Bose–Einstein condensate\|Bose-Einstein condensates]],<ref>{{cite journal\|year=2001\|title=Skyrmions in a ferromagnetic Bose–Einstein condensate\|journal=[[Nature (journal)\|Nature]]\|pmid=11418849\|volume= 411\|issue= 6840\|pages=918–20\|doi=10.1038/35082010\|bibcode = 2001Natur.411..918A\|last1=Al Khawaja\|first1=Usama\|last2=Stoof\|first2=Henk}}</ref> [[superconductors]],<ref>{{Cite arXiv\|last=Baskaran\|first=G.\|eprint=1108.3562\|title=Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K$_2$Fe$_4$Se$_5$\|class=cond-mat.supr-con\|year=2011}}</ref> thin magnetic films<ref>{{cite journal\|title=Chiral skyrmions in thin magnetic films: ~~New objects for magnetic storage technologies?\|doi=10.1088/0022-3727/44~~/39/~~392001\|year=2011\|journal=Journal of Physics D: Applied Physics\|volume=44\|issue=39\|page=392001\|arxiv=1102~~.~~2726\|bibcode=2011JPhD...44M2001K\|last1=Kiselev\|first1=N. S.\|last2=Bogdanov\|first2=A. N.\|last3=Schäfer\|first3=R.\|last4=Rößler\|first4=U. K.}}<~~/~~ref> and also chiral nematic [[liquid crystals]].<ref>{{cite journal\|title=Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal\|doi=10.1038~~/~~ncomms1250\|year=2011\|journal=Nature Communications\|volume=2\|page=246\|last1=Fukuda\|first1=J.~~-~~I.\|last2=Žumer\|first2=S.\|pmid=21427717\|bibcode = 2011NatCo...2E.246F }}</ref>~~

	~~==Skyrmions in an emerging technology==~~
	~~One particular form of the skyrmions is found in magnetic materials that break the inversion symmetry and where the Dzyaloshinskii~~-~~Moriya interaction plays an important role. They form "domains" as small as a 1 nm (e.g. in Fe on Ir(111)<ref>{{Cite journal\|doi=10.1038/NPHYS2045\|title=Spontaneous atomic~~-scale magnetic skyrmion lattice in two dimensions\|year=2011\|last1=Heinze\|first1=Stefan\|last2= Von Bergmann\|journal=Nature Physics\|volume=7\|pages=713–718\|layurl=http://www.nature.com/nphys/journal/v7/n9/full/nphys2045.html\|laydate=Jul. 31, 2011\|first2=Kirsten\|last3=Menzel\|first3=Matthias\|last4=Brede\|first4=Jens\|last5=Kubetzka\|first5=André\|last6=Wiesendanger\|first6=Roland\|last7=Bihlmayer\|first7=Gustav\|last8=Blügel\|first8=Stefan\|issue=9}}</ref>). The small size of magnetic skyrmions makes them a good candidate for future data storage solutions. Physicists at the University of Hamburg have managed to read and write skyrmions using scanning tunneling microscopy.<ref>{{Cite journal\|doi=10.1126/science.1240573\|title=Writing and Deleting Single Magnetic Skyrmions\|year=2013\|last1=Romming\|first1=N.\|last2=Hanneken\|first2=C.\|last3=Menzel\|first3=M.\|last4=Bickel\|first4=J. E.\|last5=Wolter\|first5=B.\|last6=Von Bergmann\|first6=K.\|last7=Kubetzka\|first7=A.\|last8=Wiesendanger\|first8=R.\|journal=Science\|volume=341\|issue=6146\|pages=636–9\|pmid=23929977\|layurl=http://phys.org/news/2013-08-~~skyrmions~~-~~electronics.html~~
	~~\| laysource = phys.org \| laydate = Aug 08, 2013 }}</ref> The topological charge, representing the existence and non~~-~~existence of skyrmions, can represent the bit states "1" and "0".~~

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

	~~{{Particles}}~~

	~~[[Category:Particle physics]]~~
	~~[[Category:Quantum chromodynamics]~~]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q1970283

2013-04-15T07:50:53Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q1970283

← Older revision		Revision as of 09:50, 15 April 2013
Line 1:		Line 1:
	~~I woke up yesterday~~ ~~and realised~~ - ~~Today I have been single for~~ a ~~little~~ while ~~and following much intimidation from buddies I today find myself registered for internet dating~~. ~~They guaranteed me that there~~ are a ~~lot~~ of ~~enjoyable~~, ~~sweet~~ and ~~standard people to [http:~~//~~www~~.~~netpaw.org luke bryan sold out~~] ~~meet~~, ~~therefore luke bryan concert videos (~~[~~http~~:~~//www~~.~~ladyhawkshockey~~.~~org www~~.~~ladyhawkshockey~~.~~org~~]) ~~the pitch is gone by here!~~<br>~~My fam and pals are awesome and hanging out~~ with ~~them at bar gigs~~ or ~~dishes is obviously~~ a ~~must~~. ~~As I see you could never own~~ a ~~good dialog with the~~ [~~http:~~//~~Answers~~.~~Yahoo~~.~~com~~/~~search/search_result~~?p=~~noise+I&submit~~-go=~~Search+Y!+Answers noise I~~] ~~have never been into dance clubs~~. I ~~likewise got two undoubtedly cheeky and quite adorable canines who are consistently excited to meet new folks~~.<br>~~I attempt to stay~~ as ~~toned~~ as ~~possible coming to the gymnasium several~~-~~times per week~~. ~~I love my sports and try to play or see because many~~ a ~~possible~~. ~~I am going to often~~ at ~~Hawthorn suits being wintertime. Notice: I've observed~~ the ~~carnage~~ of ~~fumbling matches at stocktake sales, If you would considered purchasing a sport I do not brain~~.<br>~~<br>Here is my page - luke bryan concerts; [~~http://~~lukebryantickets~~.~~sgs~~-~~suparco~~.org ~~click through~~ the ~~up coming page~~],		{{Technical\|date=September 2010}}
			<!-- {{Standard model of particle physics}} Here it would be essentially inadequate to introduced this well-known graphics! -->
			In particle theory, the '''skyrmion''' is a hypothetical particle related originally<ref>At later stages the model was also related to [[meson]]s.</ref> to [[baryon]]s. It was described by [[Tony Skyrme]] and consists of a [[quantum superposition]] of baryons and resonance states.<ref>{{cite arXiv\|first=Stephen\|last=Wong\|date=\|title=What exactly is a Skyrmion?\|class=hep/ph\|eprint=hep-ph/0202250\|year=2002}}</ref>

			Skyrmions as topological objects are also important in [[solid state physics]], especially in the emerging technology of [[spintronics]]. A two-dimensional skyrmion, as a topological object, is formed, e.g., from a 3d effective-spin "hedgehog" (in the field of [[micromagnetics]]: out of a so-called "[[Bloch sphere\|Bloch point]]" singularity of homotopy degree +1) by a [[stereographic projection]], whereby the positive northpole spin is mapped onto a far-off edge circle of a 2d-disk, while the negative southpole spin is mapped onto the center of the disk.

			==Mathematical definition==
			In field theory, skyrmions are [[homotopy\|homotopically]] non-trivial classical solutions of a [[nonlinear sigma model]] with a non-trivial [[target manifold]] topology – hence, they are [[topological soliton]]s. An example occurs in [[chiral model]]s <ref>Chiral models stress the difference between "left-handedness" and "right-handedness".</ref> of mesons, where the target manifold is a [[homogeneous space]] of the [[structure group]]

			<math>\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\right)</math>

			where ''SU''(''N'')<sub>''L''</sub> and ''SU''(''N'')<sub>''R''</sub> are the left and right parts of the ''SU''(''N'') matrix, and ''SU''(''N'')<sub>diag</sub> is the [[diagonal subgroup]].

			If [[spacetime]] has the topology S<sup>3</sup>×'''R''', then classical configurations can be classified by an integral [[winding number]]<ref>The same classification applies to the mentioned effective-spin "hedgehog" singularity": spin upwards at the northpole, but downward at the southpole.<br>See also {{Cite journal\|doi=10.1063/1.1656144\|title=Point Singularities in Micromagnetism\|year=1968\|last1=Döring\|first1=W.\|journal=Journal of Applied Physics\|volume=39\|issue=2\|pages=1006 }}</ref> because the third [[homotopy group]]

			<math>\pi_3\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\cong SU(N)\right)</math>

			is equivalent to the ring of integers, with the congruence sign referring to [[homeomorphism]].

			A topological term can be added to the chiral Lagrangian, whose integral depends only upon the [[homotopy class]]; this results in [[superselection sector]]s in the quantised model[[Skyrim\|.]] A skyrmion can be approximated by a [[soliton]] of the [[Sine-Gordon equation]]; after quantisation by the [[Bethe ansatz]] or otherwise, it turns into a [[fermion]] interacting according to the massive [[Thirring model]].

			Skyrmions have been reported, but not conclusively proven, to be in [[Bose–Einstein condensate\|Bose-Einstein condensates]],<ref>{{cite journal\|year=2001\|title=Skyrmions in a ferromagnetic Bose–Einstein condensate\|journal=[[Nature (journal)\|Nature]]\|pmid=11418849\|volume= 411\|issue= 6840\|pages=918–20\|doi=10.1038/35082010\|bibcode = 2001Natur.411..918A\|last1=Al Khawaja\|first1=Usama\|last2=Stoof\|first2=Henk}}</ref> [[superconductors]],<ref>{{Cite arXiv\|last=Baskaran\|first=G.\|eprint=1108.3562\|title=Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K$_2$Fe$_4$Se$_5$\|class=cond-mat.supr-con\|year=2011}}</ref> thin magnetic films<ref>{{cite journal\|title=Chiral skyrmions in thin magnetic films: New objects for magnetic storage technologies?\|doi=10.1088/0022-3727/44/39/392001\|year=2011\|journal=Journal of Physics D: Applied Physics\|volume=44\|issue=39\|page=392001\|arxiv=1102.2726\|bibcode=2011JPhD...44M2001K\|last1=Kiselev\|first1=N. S.\|last2=Bogdanov\|first2=A. N.\|last3=Schäfer\|first3=R.\|last4=Rößler\|first4=U. K.}}</ref> and also chiral nematic [[liquid crystals]].<ref>{{cite journal\|title=Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal\|doi=10.1038/ncomms1250\|year=2011\|journal=Nature Communications\|volume=2\|page=246\|last1=Fukuda\|first1=J.-I.\|last2=Žumer\|first2=S.\|pmid=21427717\|bibcode = 2011NatCo...2E.246F }}</ref>

			==Skyrmions in an emerging technology==
			One particular form of the skyrmions is found in magnetic materials that break the inversion symmetry and where the Dzyaloshinskii-Moriya interaction plays an important role. They form "domains" as small as a 1 nm (e.g. in Fe on Ir(111)<ref>{{Cite journal\|doi=10.1038/NPHYS2045\|title=Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions\|year=2011\|last1=Heinze\|first1=Stefan\|last2= Von Bergmann\|journal=Nature Physics\|volume=7\|pages=713–718\|layurl=http://www.nature.com/nphys/journal/v7/n9/full/nphys2045.html\|laydate=Jul. 31, 2011\|first2=Kirsten\|last3=Menzel\|first3=Matthias\|last4=Brede\|first4=Jens\|last5=Kubetzka\|first5=André\|last6=Wiesendanger\|first6=Roland\|last7=Bihlmayer\|first7=Gustav\|last8=Blügel\|first8=Stefan\|issue=9}}</ref>). The small size of magnetic skyrmions makes them a good candidate for future data storage solutions. Physicists at the University of Hamburg have managed to read and write skyrmions using scanning tunneling microscopy.<ref>{{Cite journal\|doi=10.1126/science.1240573\|title=Writing and Deleting Single Magnetic Skyrmions\|year=2013\|last1=Romming\|first1=N.\|last2=Hanneken\|first2=C.\|last3=Menzel\|first3=M.\|last4=Bickel\|first4=J. E.\|last5=Wolter\|first5=B.\|last6=Von Bergmann\|first6=K.\|last7=Kubetzka\|first7=A.\|last8=Wiesendanger\|first8=R.\|journal=Science\|volume=341\|issue=6146\|pages=636–9\|pmid=23929977\|layurl=http://phys.org/news/2013-08-skyrmions-electronics.html
			\| laysource = phys.org \| laydate = Aug 08, 2013 }}</ref> The topological charge, representing the existence and non-existence of skyrmions, can represent the bit states "1" and "0".

			==References==
			{{reflist}}

			{{Particles}}

			[[Category:Particle physics]]
			[[Category:Quantum chromodynamics]]

en>Lux2545 at 12:48, 5 November 2011

2011-11-05T12:48:31Z

New page

I woke up yesterday and realised - Today I have been single for a little while and following much intimidation from buddies I today find myself registered for internet dating. They guaranteed me that there are a lot of enjoyable, sweet and standard people to [http://www.netpaw.org luke bryan sold out] meet, therefore luke bryan concert videos ([http://www.ladyhawkshockey.org www.ladyhawkshockey.org]) the pitch is gone by here!<br>My fam and pals are awesome and hanging out with them at bar gigs or dishes is obviously a must. As I see you could never own a good dialog with the [http://Answers.Yahoo.com/search/search_result?p=noise+I&submit-go=Search+Y!+Answers noise I] have never been into dance clubs. I likewise got two undoubtedly cheeky and quite adorable canines who are consistently excited to meet new folks.<br>I attempt to stay as toned as possible coming to the gymnasium several-times per week. I love my sports and try to play or see because many a possible. I am going to often at Hawthorn suits being wintertime. Notice: I've observed the carnage of fumbling matches at stocktake sales, If you would considered purchasing a sport I do not brain.<br><br>Here is my page - luke bryan concerts; [http://lukebryantickets.sgs-suparco.org click through the up coming page],