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Topic: Deformation theory

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	Rigidity of K-Theory under Deformation Quantization, by Jonathan Rosenberg (Site not responding. Last check: 2007-10-23)
		Rigidity of K-Theory under Deformation Quantization, by Jonathan Rosenberg
		In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains "rigid" under this process.
		From this we derive that the algebraic K-theory with finite coefficients of a deformation quantization of the functions on a compact symplectic manifold, forgetting the topology, recovers the topological K-theory of the manifold.
	www.math.uiuc.edu /K-theory/0136 (114 words)

	Deformation theory - Wikipedia, the free encyclopedia
		In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions P
		One expects, intuitively, that deformation theory, of the first order, should equate to the Zariski tangent space to a moduli space.
		The so-called Deligne conjecture arising in the context of algebras (and Hochschild cohomology) stimulated much interest in deformation theory in relation to string theory (roughly speaking, to formalise the idea that a string theory can be regarded as a deformation of a point-particle theory).
	en.wikipedia.org /wiki/Deformation_theory (556 words)

	Donald C. Spencer - Wikipedia, the free encyclopedia
		There he was involved in a major series of collaborative works with Kunihiko Kodaira on the deformation of complex structures, which had a profound influence on the theory of complex manifolds and algebraic geometry, and the conception of moduli spaces.
		He also was led to formulate the d-bar Neumann problem in PDE theory, to extend Hodge theory and the n-dimensional Cauchy Riemann equations to the non-compact case.
		He later worked on pseudogroups and their deformation theory, based on a fresh approach to overdetermined systems of PDEs (bypassing the Cartan-Kähler ideas based on differential forms by making an intensive use of jets).
	en.wikipedia.org /wiki/Donald_C._Spencer (301 words)

	Method and apparatus for nondestructive testing of the mechanical behavior of objects under loading utilizing wave ...
		Capability to analyze the dynamics of plastic deformation is extremely important for many application problems, especially for nondestructive testing of mechanical behaviors of objects under loading since a failure is always preceded by a localized plastic deformation.
		According to this theory, plastic deformation and a resulting failure can be described by change in the field of the rate of deformation and rotational displacement of the plastic deformation.
		Rates of plastic deformations in the weld zone 20deformation does not propagate into the weld area, and the deformation concentrates in thermal influence zones.
	www.freepatentsonline.com /5508801.html (5678 words)

	[No title]
		In particular, the infinitesimal deformations of this de Rham sheaf are th* *e elements of H1(X;) where is the sheaf of germs of holomorphic tangent vectors.
		It is not difficult to show that the ob* struction to an infinitesimal deformation* of the de Rham sheaf is representable by an element o* f H2(X;) and is identical to the obstruction when viewed in the analytic deformation* the* *ory.
		In fact, the deformation theories of the de Rham sheaf of X and of the analytic structur* *es of X are formally the same.
	hopf.math.purdue.edu /Gerstenhaber-Wilkerson/dga-deform.txt (5926 words)

	Deformation Quantization Homepage: Selected
		Deformation quantization was born as an attempt to interpret the quantization of a classical system as an associative deformation (i.e.
		Flato, Lichnerowicz, and Sternheimer [flato.lichnerowicz.sternheimer:1974a, 1975a, 1976a] introduced and studied 1-differentiable deformations of the Poisson bracket (formal Poisson brackets) on a symplectic manifold and then proposed the current interpretation of quantization as a deformation of the classical theory.
		Deformation quantization was comprehensively presented in the twin papers [bayen.et.al:1978a].
	idefix.physik.uni-freiburg.de /~star/en/selected.html (1772 words)

	Analytical Surface Deformation Theory: for Detection of the Earth's Crust Movements - From Monitor-Data.com Store
		If the results of a deformation analysis are to be useful as initial data based on physical or dynamic models, which generally can be assumed, they have to refer to the physical surface of the Earth (topography).
		This requires a representation of the Earth's surface as a generally curved surface that is embedded in three-dimensional Euclidian space.
		This book presents an analytical surface deformation theory to describe movement of the Earth's crust with application to the velocities derived on the basis of GPS observations in the area of the Adriatic Sea and illustrates some local connections between deformations and stresses.
	www.monitor-data.com /books/3540658203.html (176 words)

	se21b in wp02
		We consider a shear deformation of one-dimensional layer composed of a Maxwell viscoelastic material under a constant velocity and temperature at the outer boundaries.
		Theory for a half-space is usually expressed in analytical form (Okada, 1985; Okubo, 1991) and is easily applied to study or inverse seismic faults due to mathematical simplicity.
		This theory is derived in an analytical form employing the reciprocity theorem (Okubo, 1993) and the asymptotic solutions of an elastic earth to tidal, press and shear forces (Okubo, 1988).
	www.agu.org /cgi-bin/SFgate/SFgate?&listenv=table&multiple=1&range=1&directget=1&application=wp02&database=/data/epubs/wais/indexes/wp02/wp02&maxhits=200&="SE21B" (1645 words)

	Untitled Document
		The theory and one of its variants are variationally consistent, whereas the second variants is variationally inconsistent and uses the relationships between moments, shear forces, and loading.
		The novel feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relationships, satisfying the shear-stress-free boundary conditions at top and bottom of the beam and satisfying continuity of shear stress at the interface.
		The most important feature of the theory is that the transverse shear stress can be obtained directly from the use of constitutive relations, satisfying the stress-free boundary conditions at top and bottom of the beam and satisfying continuity at the interface.
	www.aero.iitb.ac.in /~rpshimpi/PaperInfo.html (1325 words)

	ipedia.com: Several complex variables Article (Site not responding. Last check: 2007-10-23)
		The theory of functionss of several complex variables is the branch of mathematics dealing with functions f on the space C n of n -tuples of complex numbers.
		From this point onwards there was a foundational theory, which could be applied to analytic geometry (a name adopted, confusingly, for the geometry of zeroes of analytic functions — this is not the analytic geometry learned at school), automorphic forms of several variables, and PDEs.
		The deformation theory of complex structures and complex manifolds was described in general terms by Kunihiko Kodaira and D.C. Spencer.
	www.ipedia.com /several_complex_variables.html (739 words)

	Deformation theory (Site not responding. Last check: 2007-10-23)
		In mathematics, deformation theory is the study ofinfinitesimal conditions associated with varying a solution P of a problem to slightly different solutionsP
		The most salient deformation theory in mathematics has been that of complex manifolds and algebraicvarieties.
		The so-called Deligne conjecture arising in the context ofalgebras (and Hochschild cohomology) stimulated much interest in deformation theory in relation to string theory (roughly speaking, to formalise the idea that a string theory canbe regarded as a deformation of a point-particle theory).
	www.therfcc.org /deformation-theory-338046.html (574 words)

	3B(1) Two-dimensional Deformation Theory
		When a wide strip is rolled between two rolls, it is possible to neglect the deformation in the width direction and treat it merely as two-dimensional deformation in the thickness and length directions, except at the edges of the strip.
		P is a stress caused by the compressive load from the rolls, while Q is a stress generated when the deformation in the rolling direction is restrained by the portions of the strip before and after the strip in contact with the roll.
		Heat is generated by the deformation of the material and the friction between the material and the rolls, consequently, the temperature of the rolls and of the material rises, and roll wear also occurs.
	www.jfe-21st-cf.or.jp /chapter_3/3b_1.html (552 words)

	Jahrbuch-CD der MPG 2003 - A Finite Deformation Theory of
		Plastic deformation exhibits strong size dependence at the micron scale, as observed in microtorsion, bending, and indentation experiments.
		In this paper, we propose a finite deformation theory of strain gradient plasticity.
		The finite deformation strain gradient theory is used to model micro-indentation with results agreeing very well with the experimental data.
	www.mpg.de /forschungsergebnisse/wissVeroeffentlichungen/archivListenJahrbuch/2002/31/publZIM236.html (172 words)

	Sub-Yield Behavior of Solid Polymers: Efficient Determination of Material Parameters
		The concepts from incompressible finite deformation theory of elastic bodies that allow the use of tests in a single deformation geometry for the prediction of behavior in other test geometries are extended to viscoelastic materials, including polymer melts and solutions as well as glassy polymers.
		The BKZ theory is then used to calculate the constant rate of deformation response of the PVC in three different deformation geometries: uniaxial extension, equibiaxial extension, and pure shear.
		Such results suggest that the major effect on the behavior of polymer glasses in the deformation range studied arises from similar considerations as those that lead to the ideas in rubber elasticity that 'a stretch is a stretch' and which lead to the so-called Flory-Rehner hypothesis.
	www.msel.nist.gov /structure/polymers/techactv95/subeffvslas.html (809 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		In the deformation theory solution, loading and unloading of the material occurs tangent to the stress-strain curve with both the plastic and creep strain components being zero.
		It has been shown that the deformation theory of plasticity is quite adequate for cases involving "almost" proportional loading or loading with relatively small "curvature" in the stress space.
		Flow theory is presumably a better model of material behavior than deformation theory since certain conditions required by thermodynamic principles are accounted for and path-dependent behavior is predicted.
	www.nttc.edu /cosmic/abstracts/dod-00097.html (482 words)

	MFO (Site not responding. Last check: 2007-10-23)
		Ground breaking work in deformation theory of higher dimensional complex manifolds was done by Kodaira and Spencer in the late 50s of the last century.
		In its beginnings, this theory was basically concerned with variations of complex structures on a given complex manifold, and the theory of elliptic differential operators played a central role.
		Using ideas of Grothendieck, modern deformation theory was soon formalized, and, as a consequence, gained a much wider range of application, e.g., on singularities, vector bundles, and modules.
	www.mfo.de /programme/schedule/2005/41B/programme0541B.html (302 words)

	André de Carvalho (Site not responding. Last check: 2007-10-23)
		We will also present deformation theories for both kinds of dynamical systems which correspond under the the relation we define.
		In the 2 dimensional case, the deformation theory is called pruning theory.
		In dimension 1, the deformation theory is a generalized kneading theory for graph endomorphisms.
	www.utm.edu /staff/jschomme/topology/c/a/a/m/28.htm (120 words)

	q-Quantum Gravity Abstract
		Not only are general relativity and quantum theory are not understood as coming from one theory, but the core principles of the two theories clash.
		The connection between the classical theory of gravity presented in Chapter 2 and spin networks is discussed in Chapter 4.
		This same deformation plays a role in a gauge invariant description of this physical system and is described in Chapter 7.
	academics.hamilton.edu /physics/smajor/Papers/d_abs.html (556 words)

	Engineering Mechanics Courses
		Physical basis of plastic deformation; mathematical theory of incremental plasticity; total theories; numerical implementation; slip and physical theories of plastic deformation; rate dependent (viscoplastic) models; applications to several engineering problems.
		Foundations of the general nonlinear theories of continuum mechanics; general treatment of motion and deformation of continua, balance laws, constitutive theory; particular application to elastic solids and simple materials.
		An introduction to modern concepts in functional analysis and linear operator theory, with emphasis on their application to problems in theoretical mechanics; topological and metric spaces, norm linear spaces, theory of linear operators on Hilbert spaces, applications to boundary value problems in elasticity and dynamical systems.
	www.utexas.edu /student/registrar/catalogs/gradcat/ch4/eng/em.crs.html (939 words)

	Rate-and-State Theory of Plastic Deformation Near a Circular Hole (Site not responding. Last check: 2007-10-23)
		We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate.
		In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters.
		The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics.
	segovia.mit.edu /~leapfrog/hole.abs.html (106 words)

	Mechanical and Microstructural Analysis on the High Temperature Deformation of Gamma TiAl Alloy - Storming Media
		Abstract: It is aimed in this study to investigate the high temperature deformation mechanisms of two-phase gamma titanium-aluminum alloy in view of the inelastic deformation theory and to quantify the relative contribution of each mechanism to the overall deformation.
		However, when the amount of deformation is large (exceeding 80%), flow curves change its shape indicating that other deformation mechanism operate at this stage.
		With the increase in the volume fraction of a sub 2-phase, the flow stress for grain matrix deformation increase because a sub 2-phase is considered as hard phase which acts as barrier for dislocation movement.
	www.stormingmedia.us /89/8926/A892683.html (269 words)

	Deformation of Metals - CTCMS
		Developing new models based upon the underlying deformation physics requires a new statistical-physics based theory of deformation, extensive computer simulations of deformation microstructural changes, and input from recently developed experimental techniques using NIST's materials science X-ray synchrotron beam lines at Brookhaven and Argonne.
		We showed that a deforming metal is a self-organizing critical system, and have related the mechanical characteristics to internal parameters of the system.
		Developed a general theory for Bragg scattering by dislocations in crystals and applied this theory to the specific case of screw dislocations.
	www.ctcms.nist.gov /lel (403 words)

	Amazon.com: Books: Analytical Surface Deformation Theory : for Detection of the Earth's Crust Movements (Site not responding. Last check: 2007-10-23)
		If the results of a deformation analysis are to be useful as initial data based on physical or dynamic models, which generally can be assumed, they have to refer to the physical surface of the Earth (topography).
		This book presents an analytical surface deformation theory to describe movement of the Earth's crust with application to the velocities derived on the basis of GPS observations in the area of the Adriatic Sea and illustrates some local connections between deformations and stresses.
		Presents an analytical surface deformation theory to describe movement of the Earth's crust with applications to the velocities derived on the basis of GPS observations in the area of the Adriatic Sea.
	www.spinics.net /am/3540658203 (454 words)

	An Orthogonal Cutting: Part I (Site not responding. Last check: 2007-10-23)
		ABSTRACT: Based on the finite deformation theory of continuum mechanics, the velocity, Eulerian strain, Eulerian strain rate, and deformation rate distributions along a family of assumed streamlines are analytically obtained for an orthogonal cutting operation.
		The rotation effect of streamlines on the strain and strain rate calculations is automatically considered using the finite deformation theory of continuum mechanics.
		In Part I of this paper, the theoretical underpinning for the orthogonal cutting model is established The verification of the model, including determination of the material constitutive equation using the Hopkinson bar technique, is presented in Part II of this paper.
	www.mfg.mtu.edu /docs/B038.htm (182 words)

	Tom Weston
		Research interests: arithmetic geometry, special values of L-functions, Iwasawa theory, deformation theory of Galois representations.
		I am a regular participant in the Five College Number Theory Seminar and the Valley Geometry Seminar.
		Local torsion on elliptic curves and the deformation theory of Galois representations (with Chantal David) (abstract
	www.math.umass.edu /~weston (282 words)

	A Refined Shear Deformation Theory for the Analysis of Laminated Plates - Storming Media
		Abstract: A refined, third-order plate theory that accounts for the transverse shear deformation is presented, the Navier solutions are derived, and its finite element models are developed.
		The theory does not require the shear correction factors of the first-order shear deformation theory because the transverse shear stresses are represented parabolically in the present theory.
		A comparison of the results obtained using the finite element models of the present theory with the experimental and the three-dimensional elasticity theory shows that the present theory is more accurate than the first-order shear deformation plate theory.
	www.stormingmedia.us /99/9971/A997103.html (222 words)

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