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Topic: Topological defects

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	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory that can be proven to exist because the boundary conditions entail the existence of homotopically distinct solutions.
		Topological defects are not only stable against small perturbations, but cannot decay or be undone or be de-tangled, precisely because there is no continuous transformation that will map them (homotopically) to a uniform or "trivial" solution.
		Topological defects are extremely high-energy phenomena and are likely impossible to produce in artificial Earth-bound physics experiments, but topological defects that formed during the universe's formation could theoretically be observed.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Soliton_(topological) (636 words)

	Topological defect - Wikipedia, the free encyclopedia
		In cosmology, a topological defect is a (often) stable configuration of matter predicted by some theories to form at phase transitions in the very early universe.
		Various different types of topological defects are possible with the type of defect formed being determined by the symmetry properties of the matter and the nature of the phase transition.
		Topological defects are extremely high-energy phenomena and are likely impossible to produce in artificial Earth-bound physics experiments, but topological defects that formed during the universe's formation could theoretically be observed.
	en.wikipedia.org /wiki/Topological_defect (367 words)

	Topological defect information - Search.com
		In cosmology, a topological defect is an (often) stable configuration of matter predicted by some theories to form at phase transitions in the very early universe.
		Various different types of topological defects are possible with the type of defect formed being determined by the symmetry properties of the matter and the nature of the phase transition.
		No topological defects of any type have yet been observed by astronomers, however, and certain types are not compatible with current observations; in particular, if domain walls and monopoles were present in the observable universe they would result in significant deviations from what astronomers can see.
	www.search.com /reference/Topological_defect (545 words)

	3 New predictions for topological defects
		The formation of topological defects is a generic property of symmetry breaking in unified field theories, and formation of such defects is expected to occur during phase transitions in the early Universe.
		Depending on the properties of the field involved, the topological defects are strings, monopoles, walls and textures.
		However, recent work[35] which uses an analytic expression for the evolution of local strings from the radiation to matter dominated era as well as including a non-zero cosmological constant, shows that it is possible to produce results that contain a broad peak in the angular power spectrum of the CMB (Figure 5).
	relativity.livingreviews.org /Articles/lrr-1998-11/node3.html (652 words)

	Matthew Davis: Research
		Topological defects are structures formed in quantum fields that undergo `imperfect' symmetry-breaking phase transitions.
		One example of a topological defect is a vortex in a superfluid, where the phase of the superfluid component varies continuously through two pi about a point where the fluid density is zero.
		it is suggested that the formation of topological defects in such a transition in the early universe seeded the density fluctuations that have since evolved into galaxies.
	www.physics.uq.edu.au /people/mdavis/defects.html (860 words)

	Georg Foltin (Site not responding. Last check: 2007-10-26)
		Topological defects play an important role in two-dimensional physics and are observed in liquid crystal films, two-dimensional crystals, superconducting films and films of Helium.
		A crucial feature of the defects is a topological constraint on the total charge (valid for a closed surface), which relates the overall charge to the genus of the surface.
		As an application we derive the density of defects for arbitrary curved surfaces, two-point functions in the planar case and prove the validity of two sum rules, resulting from the topological constraint and from screening.
	www-public.rz.uni-duesseldorf.de /~folting/habilabstr.html (419 words)

	Cosmic Strings
		Topological defects are stable configurations of matter in the original, symmetric or old phase which persist after a phase transition to the asymmetric or new phase.
		The type of defect formed is determined by the symmetry properties of the matter and the nature of the phase transition.
		Textures are delocalized topological defects which are unstable to collapse.
	www.aldebaran.cz /texty/Cosmic_strings.html (534 words)

	RMK articles : Topological Defects, Coherent Structures and Turbulence ... (Site not responding. Last check: 2007-10-26)
		"Topological Defects, Coherent Structures and Turbulence in Terms of Cartan's Theory of Differential Topology" in "Developments in Theoretical and Applied Mechanics" Proceedings of the SECTAM XVI conference, B. Antar, R. Engels, A.A. Prinaris and T. Moulden, Editors, The University of Tennessee Space Institute, Tullahoma, TN 37388 USA.
		Relative to the induced Cartan topology, it is argued that a chaotic or turbulent evolutionary process is to be associated with a disconnected topology of Pfaff dimension 3 or 4, while a potential or laminar flow is to be associated with a connected topology of Pfaff dimension 1 or 2.
		Coherent structures are signatures of the disconnected topology, and topological defects can be associated with the discontinuities separating the disconnected domains.
	www22.pair.com /csdc/pd2/pd2fre14.htm (201 words)

	ITFA - Topological interactions in gauge theories
		Much of the relevant physics described by gauge theories is non-perturbative in nature; for example the spectrum, the study of confinement and the study of topological defects and their physical properties.
		These feature topological (magnetic flux) sectors which are characterized by certain non-abelian quantum numbers (conjugacy classes to be specific), whereas the allowed dyonic sectors carry electric charges falling into representations of the stabilizer group of the conjugacy class.
		Defects in phases with non-abelian residual symmetries, often exhibit nontrivial topological interactions with the other (fundamental and/or topological) degrees of freedom in the theory.
	www.science.uva.nl /research/itf/topological.php (1240 words)

	[No title]
		Scalar defects do not present a developed spiral wave around them in the dynamical situation just described, although it may appear in the charged component when initial conditions producing well-separated scalar defects are used.
		They immediately push the scalar defects out of the limits of their large domains, so that a large number of scalar defects are compressed in a limited region of space.
		Note, however, that in the scalar case very special initial conditions are needed to obtain the lattice of defects whereas here the vectorial defect creates a large exclusion island which compresses the scalar defects and leads to the spontaneous condensation, in rather general conditions, of a highly dense cristal.
	www.imedea.uib.es /physdept/publications/downfile.php?fid=2332 (2674 words)

	No Title
		This mechanism of defect formation is very dynamical and crucially depends on the energetics of the OP field.This is unlike the Kibble mechanism which depends only on the topology of the vacuum manifold and the dimension of space.
		We have shown that this mechanism is quite general and is applicable for the formation of topological defects such as monopoles and textures.
		In the latter case, defects are produced due to non-thermal symmetry restoration and its subsequent breaking.
	www.phys.ualberta.ca /~sengupta/research.html (1958 words)

	ScienceDaily -- Browse Topics: Science/Physics/Relativity/Topological_Defects (Site not responding. Last check: 2007-10-26)
		Topological Defects in Cosmology - A review by Ajit M. Srivastava of various topological defects in particle theoryu models of the early universe (in PDF format).
		Topological Defects - This is an introductory set of lecture notes on topological defects, given to an audience with interests ranging from astronomy to particle physics.
		Topological Defects and Cosmology - A review of the effects of defects in cosmology, by Robert H. Brandenberger.
	www.sciencedaily.com /directory/Science/Physics/Relativity/Topological_Defects (709 words)

	Topological Defects
		Topological defects are stable configurations of matter formed at phase transitions in the very early universe.
		Due to their extremely high energies, cosmological defects have not yet been detected, and it is virtually impossible to produce them, even in the most powerful particle accelerators.
		Topological defects are precisely the `boundaries' between these regions with different choices of minima, and their formation is therefore an inevitable consequence of the fact that differentregions cannot agree on their choices.
	www.damtp.cam.ac.uk /user/gr/public/cs_top.html (1046 words)

	Orange Quark: Topological Defects
		The main idea of Bucher and Spergel is that, under certain circumstances, topological defects may lead to an accelerated expansion.
		Topological defects are extended solutions to field theories that can arise when the vacuum structure of the field theory is topologically nontrivial.
		It is a small region of space, in which the field configuration is out of the vacuum manifold, but which remains metastably in that configuration because the topological properties of the vacua chosen by the field at infinity are nontrivial.
	orangequark.blogspot.com /2005/03/topological-defects.html (616 words)

	Topological Defects
		That is, a defect is labeled by two integers (m,n), where m represents the number of extra rows of atoms on the right-hand part of the loop, and n represents the number of extra columns of atoms on the bottom.
		Since this is a point defect in three dimensions, we have to surround it with a sphere.
		It represents the fact that we are surrounding the defect with a 2-D spherical surface, rather than the 1-D curve we used in the crystal.
	www.lassp.cornell.edu /sethna/OrderParameters/TopologicalDefects.html (2660 words)

	Quantum Magnetism in Low-Dimensional Systems (Site not responding. Last check: 2007-10-26)
		The stability of the spiral state against the formation of topological defects is investigated with the use of the replica trick.
		We propose that the dissipative dynamics of topological defects in a spiral state is responsible for the transport properties in the spin glass phase of cuprates.
		Using the collective coordinate method, we show that the topological defects are coupled to a bath of magnetic excitations.
	www.unifr.ch /phystheo/spiral.html (524 words)

	Signatures From Topological Defects (Site not responding. Last check: 2007-10-26)
		Notice the step-like discontinuities in the string model - generally the fluctuations produced by topological defects are non-Gaussian, unlike the Gaussian noise predicted by inflationary models.
		At low multipoles the curves are quite similar - topological defect models predict a nearly scale invariant fluctuation spectrum as expected in the simplest models of inflation.
		It is therefore, not yet possible to compute the accuracies of cosmological parameters expected in defect theories, though we expect that comparable accuracies to those presented in the previous section are probably achievable.
	tonno.tesre.bo.cnr.it /Report/145.htm (551 words)

	INI Programme TOP
		Topological defects appear in a vast array of physical situations, ranging from unified theories of elementary particles at the very highest energy scales to low temperature laboratory phenomena near absolute zero.
		These defects exhibit remarkably similar behaviour, whether it be the reconnection of cosmic strings or of superfluid vortices, or the evolution of a defect network in a liquid crystal or in an expanding universe.
		Indeed, it is not difficult to cite examples of closely related advances which were arrived at independently, a notable example being the simultaneous recognition of the relevance of homotopy theory for classifying topological defects.
	www.newton.cam.ac.uk /programmes/TOP (435 words)

	Energetics of Topological Defects in Carbon Fullerenes, Nanocones and Nanotubes (Site not responding. Last check: 2007-10-26)
		Topological defects such as pentagons and heptagons have to be incorporated into hexgonal network in order to form certain carbon nanostructures including fullerenes, nanocones and nanotubes.
		We compare the energetics and geometries of three types of defect pairs (pentagon-pentagon, pentagon-heptagon and heptagon-heptagon) for three cases: (1,0), (1,1) and (2,0) in which hexgonal coordinate (a,b) represents the position of the second defect with relative to the first at (0,0).
		Thus the (1,0) represents a fused defect pair and the (2,0) defect pair is separated by a hexagon.
	flux.aps.org /meetings/YR97/BAPSPC97/abs/S1700006.html (277 words)

	Materials Research Lab - "Topological Defects, Interactions, and Chaining in Nematic Emulsions"
		Broken symmetry with its accompanying rigidities, low-energy modes, and topological defects is a unifying concept in physics.
		A new class of liquid-crystal emulsions, in which surfactant coated water droplets are dispersed in an anisotropic nematic liquid crystalline host, will serve as the basis for the discussion of topological defects in general and disclination and hedghog defects in nematic liquid crystals in particular.
		Properties of these emulsions, such as chaining of water droplets and long term stability, will be explained by hedgehog configurations around water droplets and companion hedghog defects pulled out of the nematic to preserve overall hedghog charge neutrality.
	www.mrl.ucsb.edu /mrl/events/seminars/show_seminar.php?key=0983404800Lubensky (178 words)

	Topological defects
		These are the models of topological defects, which are produced between regions which ``freeze out'' with different phases during symmetry breaking.
		Another signature of defects which is not apparent in the power spectrum is non-Gaussianity.
		Inflation predicts a Gaussian random field due to the superposition of a near infinite number of differently stretched quantum fluctuation modes, but defects cause isolated sharp features where their gravitational influences are strongest.
	www.iac.es /galeria/raw/cosmosom/node7.html (297 words)

	Superconducting Cosmic Strings (Site not responding. Last check: 2007-10-26)
		These irregular margins are an example of what physicists call "topological defects"-defects because they are places where the crystal structure of the ice is disrupted, and topological because an accurate description of them involves ideas of symmetry embodied in topology, the branch of mathematics that focuses on the study of continuous surfaces.
		Cosmic topological defects lie at the intersection of particle physics, cosmology and condensed-matter physics.
		Although topological defects may be able to produce structure in the universe, it is not obvious that they can generate the right kind of structure.
	www.iafe.uba.ar /relatividad/gangui/SCS.html (6427 words)

	Definition of the topological defect (Site not responding. Last check: 2007-10-26)
		The subject of the present work is to classify and give examples of topological defects in chosen systems.
		The defect in continuum is defined as a space region containing the discontinuity of the order parameter (line defect in 3D, point defect in 2D).
		The topological defect is the singularity in the continuum that cannot be removed by continuous deformation of the local region in the vicinity of the singularity.
	www-rcp.ijs.si /~dean/tdefect_revtex/node1.html (171 words)

	Topological defect -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-26)
		(Click link for more info and facts about Monopole) Monopoles, point-like defects that form when a spherical symmetry is broken.
		They are predicted to have magnetic charge, either north or south, and so are commonly called (A hypothetical particle with a single magnetic pole instead of the usual two) magnetic monopoles.
		On the other hand, cosmic strings have been suggested as providing the initial 'seed' gravity around which the (Click link for more info and facts about large-scale structure of the cosmos) large-scale structure of the cosmos matter has condensed.
	www.absoluteastronomy.com /encyclopedia/t/to/topological_defect.htm (403 words)

	Topological Defects and the Optimum Size of DNA Condensates -- Park et al. 75 (2): 714 -- Biophysical Journal
		Topological Defects and the Optimum Size of DNA Condensates -- Park et al.
		The defect cohesion energy is the loss of cohesion due to the presence of defects.
		Finally, the defect entropy is approximated by counting the number of ways of arranging the defects within the torus.
	www.biophysj.org /cgi/content/full/75/2/714 (3699 words)

	ESF - Topological Defects: Non-Equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology
		Topological Defects: Non-Equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology
		Examples include the vortices produced during the superfluid or superconducting phase transitions and also cosmic strings in the early universe.
		Such regions are called topological defects and give us an experimental handle on the non-equilibrium dynamics of the transition.
	www.esf.org /esf_article.php?section=2&domain=1&activity=2&language=0&article=141 (114 words)

	Amazon.ca: Books: Cosmic Strings and Other Topological Defects (Site not responding. Last check: 2007-10-26)
		This book is a comprehensive and coherent introduction to the role of cosmic strings and other topological defects in the universe.
		After an introduction to standard cosmological theory and the theory of phase transitions in the early universe, the book then describes, in turn, the properties, formation, and cosmological implications of cosmic strings, monopoles, domain walls and textures.
		It concludes with a chapter considering the role of topological defects in inflationary universe models....
	www.amazon.ca /exec/obidos/ASIN/0521391539 (297 words)

	Citations: Topological defects and interactions in nematic emultions - Lubensky, Pettey, Currier (ResearchIndex)
		....topological mismatch between the local director on the particle surface and the uniform director at large distances, a drop with homeotropic boundary conditions will create a hedgehog director configuration in its immediate vicinity.
		A quadrupolar structure with a ring defect (Fig.
		A dipolar structure with a satellite defect (Fig.
	citeseer.ist.psu.edu /context/1692954/177115 (157 words)

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